In order to understand what Common Core is not, I’m going to begin by providing some educational terminology.

**Standard:** A statement that describes what a student should be able to do at a certain point in his/her educational career.

**Task analysis:** Breaking an activity down into all the components, steps, and/or skills needed to complete the activity.

**Methodology:** The process by which students are taught to arrive at an answer or new understanding of material.

**Curriculum:** The scope and sequence of skills that are to be learned in a particular subject at a particular grade or level.

Have all your Facebook friends been posting this dreadful example of something that has absolutely nothing to do with Common Core while talking about just how horrible Common Core is, based on this single image of how to solve 32-12?

Using the terminology above, what does this image tell us and what does it imply?

The “old fashion” way (which of course should be ‘old-fashioned’, thus rendering this image useless before reaching the mathematical interpretation) shows us nothing. It’s a problem with an answer, missing all of the steps to solving the problem. It does not show how the problem is taught or worked through. None of the aforementioned terms apply.

The “old fashion” way = a problem + an answer. *Not Common Core.*

The “new” way shows a problem with several steps below the problem. Someone has performed a *task analysis *of the steps that can be used to solve the problem and created a *methodology* for solving the problem based on the analysis.

The “new” way = task analysis + methodology. *Not Common Core.*

This “new” way (which is not actually new; the SRA curriculum company has been teaching using this *methodology* – since the 1990s) is probably part of a pre-packaged *curriculum*. Remember, *curriculum* is the scope and sequence of skills that are to be learned in a particular subject at a particular grade or level. Every few years, a school district adopts a new *curriculum* to teach a particular subject area. A team of skilled teachers evaluates multiple published curricula and votes to select the *curriculum* they believe will best meet the needs of the students in that school district. Teachers then must instruct using this pre-packaged *curriculum*.

Classrooms are an ever-changing learning environment. The classroom dynamics we grew up with are incredibly different than today’s classrooms.

- When we were children, the state of Florida did not have a class-size amendment (this passed in 2002). This limits the number of children allowed in a class at each grade level.
- The inclusion of children with moderate to severe disabilities was quite rare until the 1997 update to the Individuals with Disabilities Education Act, giving children with disabilities the right to a free, appropriate education in the least restrictive environment (which is often the general education classroom).
- We also have a growing population of English language learners in our classrooms.

To reach a larger variety of learners, we need to present children with a variety of methods to solve the same problem. What you’re not seeing when you look at something as simple as this above example (that is NOT Common Core) is that children were probably working at their seat with number lines, manipulatives like Unifix cubes, using their fingers, etc. to arrive at the “new” way. This is a multi-faceted approach to looking at numbers. Here are several other examples of multiple ways to solve math problems.

**Common Core is a set of standards.** That’s it. Remember, a standard is a statement that describes what a student should be able to do at a certain point in his/her educational career. I just looked at the first grade math Common Core standards, and I found the following standards regarding subtraction:

*Operations and Algebraic Thinking*

- Represent and solve problems involving addition and subtraction.
- Understand and apply properties of operations and the relationship between addition and subtraction.
- Add and subtract within 20.
- Work with addition and subtraction equations.

*Number and Operations in Base Ten*

- Extend the counting sequence.
- Understand place value.
- Use place value understanding and properties of operations to add and subtract.

When a teacher creates a lesson, she begins with the district’s adopted curriculum, identifies which standards correlate with the day’s lesson (only role Common Core plays in lesson planning), determines what methodology will be used to teach this (may use multiple methods, most likely provided in the curriculum), and instructs her students. A well-composed lesson consists of the teacher’s presentation where methodology is modeled, an opportunity for guided practice is provided, an opportunity for independent practice is provided, and then the teacher evaluates the student’s learning.

With the technology available to even the youngest of children today, teaching a child to “just subtract” is futile. That’s what cell phones and iPods and iPads and laptops can already do for them. We have to actually teach children to think! Let’s provide them with a methodology they can actually use in their heads to quickly perform operations without using a pencil and paper. With that in mind, I have amended the ridiculous image above by performing a task analysis of the “old fashion” way (which I have termed Methodology #1) along with the task analysis of the “new” way (which I have termed Methodology #2). When we perform subtraction problems using the traditional method, we are generally teaching children to solve problems through rote memory. By providing a step-by-step task analysis, you can teach children the *WHY?* behind that process. Click here for a visual representation of Methodology #1. Here’s my revised version, comparing “old” and “new” that shows all the steps we are really performing. And as you can see, it’s actually the same exact number of steps.

**Please understand that this image above still has nothing to do with Common Core. I am only correcting the original image.*

“And something else that matters more – We’ve taught you how to think.”

– Dr. Seuss, *Hooray for Diffendoofer Day*

I’m going to side-step for a moment to complete this post. Forgive my tangental behavior. I graduated high school in 1997. At that time, in my school district, the grading scale was as follows:

- 94 – 100 = A
- 85 – 93 = B
- 75 – 84 = C
- 65 – 74 = D
- below 65 = F

Why is this relevant? Well, if everyone who was educated in Broward County Public Schools attended college in Broward County, this would not be an issue. That is not what happens. Future college attendees applied to colleges across the state, maybe even across the nation. But here’s the problem… all of the 90 – 93% ‘B’ grades I earned were A’s in other states (perhaps other school districts in Florida). This meant my GPA may have been significantly lower than others applying to college with the same earned percentages in equivalent courses. I was being compared to others whose grades did not reflect the degree to which I learned the same material.

By standardizing expectations nationally, a child should be graduating from high school with the same opportunities regardless of where they are educated, so that when they apply to colleges, they are equally as likely to have mastered the same material. At least if the standards were the same from state-to-state, colleges can better gauge what an incoming freshman’s prior knowledge should be across multiple academic disciplines.

I welcome questions and comments on this post!

* FOLLOW-UP: *After reading all of the wonderful comments, concerns, and suggestions below, I have written an additional post –

*with ideas about how you can address your concerns at multiple levels to truly support your child’s learning.*

**Parent Advocacy in the Public School System**–* FOLLOW-UP*,

*the sequel*: I continue to see “Common Core Math” examples floating around social media. I gathered several of these examples to create an additional post,

**.**

*Common Core Math Standards in Action*
Kasandra says

You got methodology #1 all wrong. Here’s the REAL steps for methodology #1

32. 2-2=0

-12. 3-1=2

——

20

Starting from the right, subtract the bottom number from the top then go left and repeat.

2 step problem…. Not 5

Carrie Wells, Ed.D. says

Here’s the thing that you are not grasping about math. You are NOT subtracting 3 – 1. You are subtracting 3 TENS – 1 TEN. Children need to understand that concept to move toward borrowing/regrouping. Otherwise they are just subtracting single digits endlessly rather than understanding place value and base 10.

We can only get by teaching through rote memory and not teaching higher-order thinking skills to a point in math before really losing students.

Darla says

Yes! I had to look at it a minute too, but those five steps are what we do (whether we realize it or not). This awareness is what I WANT for my kids.

Leslie says

In Kindergarten? Because if your child learns basic subtraction first & THEN the why behind it, they are well rounded. Teach the WHY first & the child is only confused.

Shannon says

Have you taught math to a group of students before to know this is fact?

Susan says

Kindergartners well understand subtraction! “I had two cars and my little brother lost one and now I only have one car” No, they may not be able to write an equation for that, but they DO understand the concept!!! And yes, I have actually TAUGHT this to children! I have seen kinders do multiplication and division and understand WHY. No, they cannot write an equation for it, but they understand the math.

Naomi says

Actually, there have been studies done that show that if you teach the “how” before the “why”, students lose motivation to understand the “why” and are not likely to pay attention to it. (Why would you need the “why” if you already have the “how”?) If students get the “why” and have to use it to figure out the “how” (or many “how”s as the case may be) for themselves, then they value the “why” — because they’re using it. In this way why-then-how leads to a deeper understanding of mathematical concepts than how-then-why.

Scott Karsk says

Well said!

S. Carloti says

My post above refers to this particular quote.

=========================================

” Here’s the thing that you are not grasping about math. You are NOT subtracting 3 – 1. You are subtracting 3 TENS – 1 TEN. Children need to understand that concept ………..”

=========================================

For some reason it didn’t make it in the post !

Dawn says

Why not teach children about the “ones” place, the “tens” place, the “hundreds” place, etc., just like has been done for hundreds of years. Children who learned it that way–without the aid of calculators or computers, by the way–managed to put men on the moon and bring them back safely. To force a child to go through all that extraneous “task analysis” is nothing more than a waste of time, and probably quite confusing to children who haven’t already grasped the basic concepts they OBVIOUSLY need to be taught before taking on something as mind bogglingly STUPID as this alleged “higher-order thinking skills”. This isn’t a “thinking skill”–this is a manner to justify moronic double speak, which seems to be all they’re teaching any more!

(BTW, I come from a whole family of teachers–REAL ones, who actually TAUGHT and had students who excelled in life and were capable of ACTUAL higher order thinking skills.

Brenda Payne says

Amen. That is all

Chrissy says

Amen! I could not agree with you more!

Cathy Johnson says

I agree with Dawn. I have no idea what all that extra stuff is for on that paper. Ones, tens, hundreds, thousands……THAT’S math. The task analysis (or whatever you call it) is unnecessary. 32-12=20….plain and simple. You don’t need a half page explanation. Get back to the basics, put away the calculators and computers, and teach what these children need to know…the basics for being able to make it in the real world.

Steve Carloti says

It would be wonderful if we were to keep in mind just two (2) things.

He/She who takes something complicated and simplifies it = Genius.

He/She who takes something simple and complicates it = Idiot

The rest, as far as the educational process goes, is finding out what exactly, of the above two, you are doing.

Michael Occhino says

Your post illustrates why we need to be teaching using task analysis. Your clearly not an educator despite coming from a family of “real” ones… There is no doubt that a few students will understand mathematics from explicit instruction. There are too many people who experience math as mystifying. Understanding and doing mathematics is so much more than algorithms. You don’t know that because of how we were taught so many years ago! Also, I’m curious to know how you know mathematics was taught hundreds of years ago?

Danno says

You are clearly NOT an educator either. When expressing “you are” as a contraction, it is YOU’RE …. NOT YOUR which is clearly possessive. But, we all learn in different ways. Perhaps that is the New English way. PHLTT!

SJMiller says

You’re an IDIOT! Children do not learn this way. My children come home crying because they do not understand this crap. Why make things harder than they have to be.

gene carpinski says

dont be picky . the way of teaching a child math is different then higher ed math.. kids learn different. simple is better .do not make thing complcated so only a few learn n the rest zare left behind but in the end that xhat all this new cirn stuff does is fustrate kids more . let them master the math by memorizing it .to read by learning sihht word n then sounding them out . teach them new words to look them up in the dictionary n know the meaning n how to spell . then inhigher ed you can teach them this if they dont already know n understand it n will teach you. teach our child kindness n loving each other as they love themselves .. do not cause more fustration n anger in our children .. you are an adult teavhing our children child like thing age appropriated. is better then this fustrating thing .. our child are children learning. age things .

lmgnpb says

NICE. Thank you. I’ve been reading these comments and really started wondering from what universe of utopia she taught.

Kaybee says

Because the place of the digit is different then it’s value. That’s the struggle why kids lose sense of math and can’t pass algebra in later years.

Tera says

Well said, Dawn. I couldn’t agree with you more and I’m a “real” teacher with a degree and everything.

Charley says

what you fail to grasp is the concept that math is a simple way to introduce the concept of critical thinking. Once you teach a young child the basics of the concept you can then expound on it and transfer it to other things. And I’ll take a critical thinker over a parrot any day.

I have a nine year old son with Autism. He can do math in his head that amazes people and he’s mostly self taught. He taught himself multiplication and division in Kindergarten and was multiplying by powers at the beginning of second grade. He is now in third grade and is teaching himself how to solve algebraic equations. When I ask him to explain his process to me his process is identical to method two as described in this post. That says a lot to me. His child brain naturally realized this was the easier way to think of this problem. He still understands everything about place settings and number value and all the things that schools have been teaching for “hundreds of years” but his brain also says “wait a minute…this makes more sense”

It sounds to me as if you are simply criticizing a new method of doing something simply because its a new method and not what you were taught, without taking the time to truly evaluate the usefulness of the new method.

Alicia says

THANK YOU!!!!!!!! It’s as if past generations cannot come to grasp with the reality that they didn’t come up with the end all be all answer to everything! Or that they didn’t come up with new ways to do things from the generations before them! It’s called PROGRESS and EVOLUTION, but yea let’s stay stagnant for you arrogant and ignorant fucks.

Jeffery Hall says

I can tell you the usefulness of these new methods. Both of my kids did excellent in school even with all this new crap I couldn’t help them with in elementary school. And both struggled mightily once they got to Algebra because they didn’t know how to do the calculations using the “old” FASTER and EASIER method by heart. So they would get how to do the Algebra part, but because tests “are timed” they either wouldn’t finish on time or get the problem wrong because of the simple arithmetic involved. I am an engineer and I have three Master’s degrees so believe me I have done my fair share of math that no one ever wants to deal with and I am telling you, these methods are stupid to be teaching kids. If you are getting a degree in math or engineering then you can learn all the “whys”. Other than that the only thing people NEED to know is the how!

SJMiller says

Alicia you have just shown your ignorance with your language, i hope and pray you are not a teacher, because I sure wouldn’t want someone with your foul mouth teaching my kids

Russ says

@ Charley – “Once you teach a young child the basics of the concept you can then expound on it and transfer it to other things.” That is what I believe as well.

However, every developmental psych class that I have taken has taught me that children before the age of ~12 think differently– (Mainly Concrete/Sequential) and then after they have the whats and hows down (After age ~12) they learn in the Abstract/Random (Whys). Therefore conceptual thought should be left more to middle/high school.

I have been given a lot of lateral movement in my curriculum. I teach math/science through the learning of practical living skills. This has been a real eye opener to many. It really engages the mind with practical hands on activities that have lasting consequences and accomplishments. The learning that is created through building, repair, cooking, and animal husbandry is invaluable in that they actually get to learn by doing. Manipulatives are ok… They are better than nothing. But they are still somewhat abstract in that you don’t use or see these things in everyday life. The things you can learn in just designing and building a book case for the classroom are amazing. Measuring, accounting, fractions, geometry, physics, chemistry, communication, vocabulary, the list goes on.

If only we could get back to learning skills and teaching academics through the skills.

Katherine says

To Jeffery Hall… It’s unfortunate that even with a degree in engineering you are not able to understand these concepts even at a grade school level. If anything this is proof that there is a problem with the way math was taught with rote memorization, not proof that the old way is better.

M Franken says

Teaching is about more than throwing information at a kid, it’s about teaching them how to think critically and helping them realize their strengths and weaknesses. Teaching is not reading a cook book to them, which is what you just described; “Do subtraction” is the same thing as saying “bake me a cake.” Also there are two very different concepts being illustrated here, yes it is simple to do

12

+ 29

= 41

on paper, it is a whole different thing to do it in your head. The concept of

“12-1 & 29+1 = 11+30” is an approach for thinking without paper. Let me ask you, how often do you do simple addition and subtraction using paper anymore? you don’t, it’s great for practice and developing the skills but later in life you’re using your head. That is what this methodology teaches us. I first saw this example and said that doesn’t make sense. This was because the example was flawed, it was a drastically exaggerated and convoluted reinvention of a technique to prove a point. What the real methodology is, to me at least, simplifying the numbers by using basic, in this case X*10^0, or 1’s place arithmetic, to make higher order arithmetic easier. It is much easier to add 11+30 than it is to add 12+29, especially in your head. This technique is actually something I was never taught but developed on my own through out my many years of learning and considering I have a BA in Engineering and a minor in mathematics I think I can say with a good deal of confidence that I have done a lot of math in my life time.

So the TL;DR version, teaching is about teaching a child to learn on their own, not shotgunning information at them and hoping it can stick. If you’re simply doing problems in the book and not explaining why or how you’re no better to that child than a library.

I think Will said it best (from Good Will Hunting):

“See, the sad thing about a guy like you is, in 50 years you’re gonna start doin’ some thinkin’ on your own and you’re going to come up with the fact that there are two certainties in life: one, don’t do that, and two, you dropped 150 grand on a fuckin’ education you could have got for a dollar fifty in late charges at the public library!”

Sarah says

I read all of this so far not sure where I stood, not having a higher education. I failed Algebra 2 which was traumatizing when I had A’s in almost every other class in highschool. I have been confused by my daughter’s homework lately, but how you just explained it clicked with me. While it is a “new” concept, I would rather my children be able to approach a problem and understand all the steps so they perhaps will excel when it comes to more complex math like Algebra. I may be comfortable with my “old way”, but my children don’t have to remain on my level, I hope they will far exceed it. All arguments aside, we want what is best for our kids right?!

Sara Webb says

I really wish there was a like button for blog comments! Yes! The focus should be on doing what is best for kids!

Heather Adams says

You may come from a family of teachers, but unless you’ve been in the classroom with children you’re opinion is irrelevant. Children think and solve problems in different ways. When we show them only one way to solve a problem, without explaining the thinking behind it, we are crippling them. The “new” math allows children to explore and manipulate numbers. They are learning that there are several ways to solve problems. They are thinking about numbers and it is incredible what they can do. I see in in MY classroom everyday.

Frederick Dietrich says

It’s obvious you did not excel in English. “you’re opinion”???? It should be “YOUR opinion”

Johnnie McHan says

I AGREE TOTALLY DAWN…THIS IS JUST HOW I LEARNED. I AM 71 NOW AND CAN DO PROBLEMS IN MY HEAD MY GRANDS CANNOT.

Fred Kelly Grant says

At 78, I agree with you Johnnie. Sure “progress” is good, but only where it improves on what is in place. In the name of “progress” many cultural, social, political, and historic principles are lost; hope it is not so with math. Someone asked how a commenter knew how math was taught hundreds of years ago—I would imagine the answer is “by reading the history of math”

Ashley says

So what about that child that does not understand the “old way”? Adding is easy but have you tried to teach a second grader how to subtract? If they don’t understand borrowing they will never get it! To borrow they must know that 3 is actually a 30…….on a side note….I actually get to teach up and down or the “old way” this year. We are adopting a curriculum. All 4 Common Core curriculums have the “old way”!!!! I get to teach up and down or the “old way” with common core. There are lessons that cover it!! I mean whole units in my COMMON CORE book! Don’t believe me research new common core curriculums.

Melissa Stager (@melissalstager) says

Dawn,

The people who put the men on the moon went to school during a time when “standards” were not standard at all. Kids were tracked based on their race, socioeconomic status, and behavior. Kids who were learning disabled were put in the basement with a set of low expectations at were not allowed with the other kids. A small portion of the population went to college because most people could get jobs in manufacturing even if they didn’t understand the ones place, the tens place, etc. Teachers knew more than students, even if they were not as smart as their students, because students didn’t have access to information like today. Whether you like the old way or not is irrelevant, that society no longer exists. So we can continue doing what we did before, or recognize that society has changed and teaching is playing catch up.

If you still think the old ways are good enough I will gladly send you an abacus to help you before you do your on-line banking.

Sara Webb says

Thank you!!! Speaking of abacus, you should see the Chinese children who start out counting and learning conceptually using an abacus. They can do crazy hard mental math super fast.

Jeffery Hall says

This is the dumbest reasoning I have heard so far. And then the next comments says “Thank you”, but then says how great kids are that start by using an abacus. Can’t even keep your own arguments straight.

Judy says

Amen Dawn! Teach the basics… they never change. Love your statement about how we put people on the moon and back… I have been to fast food places too many times to not be convinced that too many kids can’t even give change… it’s sad.

Sally says

I have not read all of this but I am an assistant teacher in first grade. We ARE teaching place value. For the first time in 6 years our kids get it. Why you have to take one of the 10s and bring it to the ones side, using longs and cubes. EVERY student in class can regroup. 24-8= only because we teach where you take one ten and make the 8 an 18. It is amazing to see all 23 get it.

Amy says

You know Sally, I was taught that as well–thirty years ago. We used logs and bricks and legos and learned place values. My son recently brought home a math assignment that used a place value chart as an equivalency chart without identifying it as such. Then it further confused by asking him to complete an equation that wasn’t an equation but rather an equivalency number sentence. Common Core was stamped right on the bottom. The materials I’m seeing are terrible and designed to confuse and muddy thinking.

Kim says

Our children are NOT cookie cutter children- they all learn differently. As a mom of twin boys I see the difference every day. One twin “gets” math the “old-fashioned” way and excels. The other twin does math his own way- still gets the correct answers but was ridiculed by his teacher and called stupid. So does that make the teacher “right” saying he was stupid? Twin B adds a 6 or a nine to every equation to get his answers. It is his way of critical thinking. Doesn’t make sense to me but I go with it as he gets the same answers I do just a different way. We should all be encouraging our kids through their schools but no way should we be saying that any one way of teaching is the end all be all. Every child is different and will learn their own ways. We are not supposed to be creating classrooms of exact same “robots”. Let the kids learn. Let the teachers themselves DECIDE how they want or need to teach to a certain group/child. Keep the government out of our schools. Parents and the teachers know what the kids need more than some suit in DC getting lobby money under the table.

Bobbee says

Amen ! Some things are what they are. Lets dont try to re-package and sell as something new and wonderful. It wastes sooo much time! Once you know it..you know it!!!! Why analyze same process EVERY time ? If we did this with every simple task performed in a day’s time how would we get anything done?

Jane says

I agree we don’t always need to know why

S. Carloti says

@ Dawn

Dawn did you say…. “waste of time”, ……. “quite confusing”,… “justify moronic double speak”, etc. etc. etc. ?

But,… Dawn,…. you see …I don’t think you….. understand !

This IS …. the goal ! 😉

Dumb children down, create confusion, and in the end get them used with tomorrow ‘s ‘work” where they will not have to send rockets to space but serve as slaves for the “upper echelon” and be able to make change, and field low paying jobs in the …service industry.

Not quite sure WHAT you see wrong with this ?

Just between us, your first sentence ( a rhetorical question in fact) contains a “secret”. And…. like any other “secret”, we have to keep this ….A SECRET !

Don’t you understand ?

Children are becoming …to smart ! We HAVE to slow them down somehow.

And THIS….. is a method as good as any !

What’s so difficult to understand ?

Liz says

This is exactly what’s going on! Dumb them down even more. If this curriculum is so great, why did the federal government pay off states with large sums of money to adopt it sight unseen. Now that it is in play, some states are trying to back out. Thank God my state was one of the very few that rejected the monetary offer.

Millie says

Well said! So precise!

Millie says

Dawn, you explained it to the point.

Ginger Carlisle says

AMEN !!!!!!!!!!!!!!!!!

Christabel says

I agree! I am so sick and tired of people wanting to pass ridiculous nonsense and call it education! My child went from an All A student to a A B student using that rubbish teaching!!!!

Aimee says

Latricia says

I really like you post, Dawn!

Michael says

oh god thank you!!! these people are loopy if they think they can double talk common core into existence. these kids are just trying to figure out there colors and how to keep their hands to them selves. common core has no place, however I di agree with amp-ing things up and getting creative AFTER the child learns how to properly learn how to make their beds.. Sincerely, Michael

Jeffery Hall says

100% correct!

paulo guimaraes says

I like your way of thinking. This is how I learned, unfortunately Math was not really my best subject, or most liked. My daughter is having a lot of trouble with this method, even with tutors. Go back to the way it was done!!!

Jennie L says

Hear hear!

Russ says

Thank you… I am a math teacher as well…

Sue says

Finally, someone with some common SENSE!!!

Katherine says

I disagree… People that learned to understand math are the ones that invented the shortcuts, not the other way around!

Aimee says

“We can only get by, teaching through rote memory and not teaching higher-order thinking skills, to a point …”

Absolutely. However, in the CC math standards, higher-order thinking skills are focused on and written into the standards BEFORE rote memory.

Teaching concept before algorithm is problematic, at best.

THIS is the problem with the example you cite in this opinion piece. Parents are seeing work come home requiring abstract thinking BEFORE they are taught how to get 1+1 the “old-fashioned” way. Most parents are unable to articulate why or how this is a problem, yet somehow they still know that this is not developmentally appropriate for their child.

Karen D says

Teaching the algorithm before conceptual understanding is what confuses children. If the columns are not perfectly lined up, huge errors are made that are not caught by the child that has no idea what they are doing. Students need to have a concrete understanding of 3 – 2 = 1 by using manipulatives before moving to the representational (pictorial representations of actual manipulatives) and then they can move to the abstract. The Common Core is confusing for parents because it is not the way we learned. I think, and I could be wrong, that children will have a solid, conceptual understanding of what is behind the abstract numbers if the CC standards are taught by a teacher that understands the benefits and buys into these new standards. Parents and grandparents who try to “help” their children by teaching them the “short cuts” at home are not helping their children who would otherwise benefit from the “new way”.

Regina says

Thank you, Aimee. I am an educator, and on the fence about CC. In first grade, I see that the abstract is way above my students’ heads. They struggle with it, routinely. Perhaps, if there were no struggle- if parents saw a remarkable improvement in their child’s understanding of math, there would be no argument. But, that’s not the case. Most children do poorly, at first. Less success= less motivation to know more, my opinion.

In the first few weeks of school, my students learn 2+3=5, forwards and backwards, and in every possible application. And while I applaud that CC addresses their need to touch and conceptualize 2 items plus 3 items makes 5 items all together (even the inverse that 5-3=2), to take it to the level of looking at a picture and saying “There are 5 red boats and 2 blue boats. How many more red than blue are there?” is going a bit too far. Mind you, I’m talking about children who are barely out of K. CC teaches a fact family in every application imaginable, all at the same time, from the get go.

Another example is making 10 to add or subtract. This is great extension or enrichment, but way above the heads of my students who only barely know that 8+2=10. Some students take the entire semester to get to that point. Then I throw this at them: 8+6= …what do you need to make 10? (2) Take 2 from the 6 and now your problem is 10+4=14, so 8+6=14. (That problem requires solidly knowing 6-2=4, as well.) And the inverse is a nightmare: 14-8= …what do you need to do to get to 10? (take 4 away) 8 is 4 + what? (4) Now, your problem is 10-4=6, so 14-8=6. I think this is a great way to conceptualize math, but just not appropriate in first grade!

While the methods behind CC are good for some, or even for all at a higher grade, it takes the option for some to learn their own way out of the picture. Each child should be exposed to the various methods, but only graded upon whether they can do a problem, regardless of whether or not it is learned by rote. Students who have the aptitude and motivation, should learn the “tricks” (like making 10) GOOD TEACHER HAVE ALWAYS DONE THAT!

I guess my biggest beef is that CC feels, to me, like it has, at its core (no pun intended), a basic mistrust of teachers to do their job. The types of math problems to which I alluded, above, are what we used to refer to as “extension” or “enrichment” and certainly appropriate for some, but not developmentally appropriate for all, at the ages it is being presented.

Regina says

*teachers LOL

Tom Franclemont says

Regina, please re-read this article about what Common Core is and is not. There is not a single place in the standards that says you need to be teaching your K students about 5 red boats and 2 blue boats. You might, however, be using the curriculum modules and they might include examples like these, but they are a separate entity from the standards themselves. It’s very difficult to make parents understand the difference between the standards and the modules when even the teacher lumps the two together.

Nicole says

THIS is what I’ve been wondering about as a parent (now) with an education degree and a few years under my belt. THANK YOU for your post, Regina!

Kristen says

Amen, Aimee

David R says

I respectfully disagree. And maybe I’m splitting hairs or misunderstanding your point, but in my opinion, the greater lesson is that if “3-2=1” then 3 of anything minus 2 of anything equals 1. Whether it is jelly beans, seconds, tens, or even millions, what you are doing is just a variation on the simplest version of the concept, which is that 3-2=1.

Kasey says

But there is nothing simple about algebra two and that is what we are preparing them for. I really wish people would just trust it. We have spent years training to teach this way. It can’t be understood from one article. You need to step in a classroom that does it this way and a class that does it the traditional way. I will bet my life the new way kids are doing mathematics way far more advanced. And the beauty of this new way is if you were there now you could come in to a classroom and do math anyway you wanted to see it. Regardless if the teacher agreed. You would do what made sense to you.

Sara Webb says

Kasey, excellent point! If anyone were to come into my school you would not see kids in tears over math!

Denise Fisher says

You make a valid point Tracy about the complexity of math beyond the moment. I also truly appreciate your education and commitment to our children. However, for those who have not spent years educating ourselves to teach, it is difficult to trust it when our children are seemingly falling beyond. I am a college educated parent, who cannot help my child with her homework, because I do not understand it. My child, is in the gifted and talented program, previously made exceptional grades and loved school. She now dreads these times in school, is struggling academically, and her grades are declining. It is difficult to trust it when it is our children’s education at stake. However, it is very difficult to completely change the way a child has learned a task at a 4th grade and 8th grade point in their school career. I am not opposed to Common Core as much as I am opposed to the moment of implementation. It seems to me that a better point would have been with classes entering kindergarten and taking it through with that class. Transitioning my 8th grader during the “5 years of implementation” is unacceptable. My children have exceptional teachers and I am so thankful. This is the only thing that has created any element of trust that I do have. I will tell you that I have discussed (outside of social media or anything in writing) with many teachers who are opposed to Common Core. So it is not just the parents who do not understand it or appreciate it.

Kristen says

My kid, for one, was one in tears over math, throwing meltdowns at school and home. We are homeschooling now and this crazy math is a big part of the reason why. It’s taken months to undo the damage this math caused. He thought he couldn’t do math because he was stupid. In less than a year, he is now able to add and subtract multiple digits, multiply, beginning work on fractions. He is able to do a lot of it in his head, which is where basic math should eventually liven And, he has transferred some of this knowledge to money and time without direct instruction.

I can clearly see that these examples are trying to teach number sense- backwards. They take an abstract problem, pull it apart into abstract, multiple lines, and often ask for a written paragraph explanation. Grammar school children don’t think this way. Most are concrete thinkers for at least another few years. I have a hard time believing any teachers that says this is working for all 23 kids in a classroom as I talk to the parents who, like me, say it is not working.

If you want to teach number sense and place value, get busy with tangible items that demonstrate the concepts. Use games that develop an understanding of borrowing. Of all the curriculum I’ve studied, Montessori is the best at this. Go from concrete to the abstract. Not abstract to abstract, or abstract to the kids come up with concrete. Then, get “old school” with a curriculum like Saxon, or bridge the gap with one like Math U See.

Permanent memory of any process is not created without tons of practice. In other words, “rote”. I have no idea why people think this is a bad word. Musicians, athletes, and anyone who is highly skilled at anything understands this.

If you are a teacher saying, “I really wish people would just trust it,” I would advise never saying this to a parent. You better be darn ready to prove that your method works. My child’s future depends on it.

And, my child is now home schooled. We’ll see in a couple of years who is better able to handle algebra. If you can’t tell, I’m no longer worried about my son, but I’m very much worried for all the friends we have left behind in public school.

Jane says

Why worry about algebra 2in first grade not all children are going to need such in depth math skills teach basics

Doyle says

I do grasp the concept of math. Bottom line, you are still subtracting 2 from 2 and 1 from 3. You are complicating the process. That is not necessary to know place value. I went to school with the generation that sent man to the moon, developed the semi conductor, computer, calculators, and numerous medical breakthroughs. Now it seems that we learned everything incorrectly.u

Nicole says

Kristen! Thank you! YES!

Math Man says

Really? I seem to remember being taught place value quite clearly in the columns. Of course, we started with single digits and worked our way up to 6 places. Not a problem. Quicker and less confusing because all you have to teach them at the beginning is the basics using digits up to 19. And to work each place column (1’s, 10’s, 100’s, etc) individually. Yep! Rote learning at it’s best. Not to mention that the similar concepts apply in multiplication. And it teaches base 1, base 10, base 100, etc.

Later, when you bring in decimals, the concepts remain the same and all you have to do is move the decimal to the right place. A simple concept to adapt to in itself.

Method 2 is merely adding to base 5, then base 10, then base 10 again and adding the remainder. Then adding the addendum’s to get the answer. It is not even subtraction. But you can check your subtraction with it.

Method 1 is even more confusing and in worse organization. Both include far too many steps than are necessary.

This is something that someone doing a doctorate thesis, had to come up with something original for his/her thesis. Nice. But it’s like going around the world in order to cross the street.

R. Craigen MMath, PhD University of Waterloo; Associate Professor of Mathematics at University of Manitoba says

@Carrie you are conflating execution and interpretation. This is a serious error to inculcate at a low grade level – an error that will follow them for life. To demand that in every step a student produces a full-blown interpretation of meaning is to instill a habit that will cripple their performance as they try to advance in this subject. It is essential that students work with efficient encodings of procedures without the demand to continually resort to first-principles interpretation. Kasandra is exactly right: the student performs only TWO steps here. The efficiency and effectiveness of the method relies upon the students using the highly structured encoding that automatically preserves correct place value. The whole point of the method is to free the child up from having to work from first principles.

When initially learning the child, of course, must be exposed to, and tested on, understanding of the meaning of each step. If place value is properly taught as the algorithm is developed this is a no-brainer — a teacher almost has to literally stand in the way of learning for a child not to understand the meaning of the positional notation around which this algorithm is arranged. But to demand that they interpret the exercise at the atomic level, every time it is performed, is to strip the algorithm of its power.

In over 20 years teaching university students mathematics at all levels, I have seen strong students and weak students. It breaks my heart to see students coming out of the “new math” classrooms these days who feel the necessity to interpret every step from first principles and find that cannot be done by anyone hoping to succeed at this level.

Not only are you confusing execution and interpretation you are also conflating teaching and learning. While, at a certain stage as students are learning these procedures, a good teacher will reinforce meaning and have the student confirm their understanding. But for the student to have “learned” the procedure they must have the procedure automatized, and this will entail demonstrating that they can and do perform it without explicit interpretation in those terms with which it was originally taught. Any teacher who demands this of their students is holding them back and has not understood that their pedagogical process is not a take-home skill for the child; it is scaffolding that is erected for the teaching and taken away as the learning nears completion.

When a child is asked to perform this algorithm, as reinvestment of a learned skill, it is essential that they NOT feel the need to interpret the steps. It is like demanding a reader keep one finger on the line while reading, or a person learning a second language to always interpret things into his/her own language while attempting to converse. It is a great way to chain them to the ground, when you should be teaching them to fly.

Nicole says

Clap! Clap! Clap! Yes! My thoughts, exactly! “… chain them to the ground… teaching them to fly.”

Kevin says

Carrie, ALL math problems are single-calculation operations. That’s why we have the Order Of Operations. I am a college level math tutor, have been for 12 years, and I mainly help the freshmen who need to strengthen their skills to prepare for college algebra, trigonometry, calculus, etc. I also help a few high school students who are learning this “new” way to do math. EVERY time one of my students brings me a common core assignment for help, I end up teaching the “old fashioned” way to do it. It might not be the best thing for my students, trying to learn 2 ways to do it all, but at least the student understands how to come to an answer. The “new” way is just plain confusing. And as for understanding place value and base 10, I was taught that in elementary school many years ago using the “old fashioned” way and I learned it just fine. I don’t think the problem is how we are teaching. I think the problem is in the home.

I tell ALL my students this: “Study 30 minutes a day on your own, every day, and you will start to get it, I promise.” And this works for ANY subject, not just math…

To me, everything I have seen linked to common core (especially math) is a long trip around your elbow to get to your thumb. It really seems like it was created by a chimpanzee flinging poo at an abacus.

Kevin says

This proves my point about how confusing common core math problems can be:

I saw this online, read it, and nearly crapped myself I was so confused.

“In each cube stick, color some cubes blue and the rest of the cubes red. Draw the cubes you colored in the number bond. Show the hidden partners on your fingers to an adult. Color the fingers you showed.”

What the heck does that mean? Is that MATH? I don’t believe it, not for a second.

Check it out for yourself here:

http://huppiemama.com/wp-content/uploads/2014/03/Todays-Math-Instruction.jpg

Alyssha Swanson says

Yes, yes, yes!!!! Thank you so much for saying this! I can’t believe how many parents WANT their kids to learn how to memorize instead of learning how to THINK!!!!

Steve says

I’ve pointed out to many people who say, “why can’t they just teach them that 2+2=4 like they taught me?” that we didn’t learn it that way. I am 53 and know that I didn’t learn it that way. I heard adults complaining about “New Math” in the 60s and 70s. Peple remember the outcome of what they learned, not how they learned it.

Alicia says

Thank you! Hello! haha people are just freaking out because it is different.

S. Carloti says

@ Carrie Wells, Ed. D. March.4.2014 at 9:03 am

=========================================

=========================================

Wow ! Is it possible that perhaps….. we don’t see the forest for the trees ? :-))

Is it possible that somehow that…. Kasandra…. as well as… “the Children”…. understand quite well that 32 is in fact 3×10+ 2 ( thirty two) while 12 is in fact 1×10+2 ( twelve ) ??????

I hope you are not advocating that when a child subtracts 257 minus 159 as in

257-

159

———

=98

he/she will think (imagine) that in fact he is looking at 2, 5, 7 ( as simple numbers or units) and 1,5,9, ( also as simple numbers / units ).!!!!

Of course that would not ever happen since their “well learned teachers” have told them already that 257 is in fact,….. 2×100+5×10+5 ….and ….159 is ….1×100+5×10+9 ….and by now they have learned … “the order of operations” ( multiplication and division ….FIRST… and …. addition and subtraction… SECOND… IN A LINE WHERE WE DEAL WITH ALL 4 BASIC OPERATIONS.)

It seems to me that with this “common core” someone attempts to …. “reinvent the wheel” !

I’d posit that rather what we should stress is arranging the corresponding “groups” (units, tenths, hundreds, thousands, etc. etc. ) of the minuend under the SAME CORRESPONDING GROUPS ….of the “subtrahend”

The sore / sad thing is that very few teachers ( I haven’t meet ANY ) know the 3 words which would explain the operation of subtraction ( minuend, subtrahend and .. the difference), and as such there is no “linguistic” link in the minds of a child as to what it is that he /she is dealing with, as well as some of the properties of subtraction ( you can not change the position of the minuend and subtrahend ).

I am not a teacher yet some 30 years ago I had to become one, when I noticed that my son was treated as an idiot in primary school ….. and beyond

With my younger son which I decided to put in a private school I found out from one of the (so called) teachers – who was going to “imprint” his mind – that “calligraphy” or “cursive writing” can not be thought to a child until he/she is 9 or 10 years old.

Reason ?

They don’t have ….”the motor skills” …..until that age !!!!!

Can anyone imagine a more idiotic “belief” ?

So, Carie perhaps you may question some of the ideas you were “indoctrinated” with, while doing your “Master” or while obtaining your PH.D. and consider even for a moment that the ideas you were exposed to had ….an invisible correlation…… to “aspects of life ” which had nothing to do with….. “educating the children”

You may consider reading “Charlotte Thomson Iserbyt – The deliberate dumbing down of America”. It’s free. ( Google it ) It may be tantamount to a real icy ( very icy !!! ) ….shower.

Having experienced education in 2 different “systems” ( communist and capitalist ) it is obvious to me that what school does in the capitalist system “nowadays” is primarily “indoctrination” not “education”.

Don’t believe me ? Watch these splendid examples of a most exquisite educational system. ( youtube.com/watch?v=S6BjqlLvCVk )

As far as “indoctrination” watch this clip ( youtube.com/watch?v=9UiJHkl9dc0 ).

It’s …. SELF EXPLANATORY !

In the very end I would suggest to discuss certain aspects of the “educational process” with people who have as their only emblematic quality….. some “gray hair”. 🙂

They may not have a…. “Ph.D”., a…. “Master” …or sometimes even an…. “University Education”.

And yet, in many cases, they will posses a “human distinguishing characteristic” which seem to be acutely missing in many people, in this day and age.

It is called…. COMMON SENSE !

Alicia says

Wow, I can’t believe that lady said that to you! (Well actually I can)- Wasn’t the whole point of cursive (which I had mastered by 8) to build said fine motor skills!?!?!

Salty Wench says

You, apparently, went to school after they already started teaching this crap. Your examples of methodology 1 & 2 are the same thing, from different directions. The fact that you believe they are actually two different methods supports the theory that these methods are part of the “dumbing down”, desensitization and, ultimately, programming of our children. When I was in school, we definitely did NOT take 5 steps complete that problem. It’s 2 steps, and only takes a few seconds. Also, I have to agree with Leslie, you are confusing our children. If you don’t think so, you haven’t been paying attention.

DrumGuy says

Only because “ones” digit is the same. 54-26 using your methodology #1 would look like this:

4-6 is a negative

5-1=4

10+4=14

14-6=8

40-20=20

20+8=28.

using methodology #2 would be:

26+4=30

30+20=50

50+4=54

4+4+20=28

method #2 is easier to do in your head because there is no “borrowing” to keep track of.

Jacob Robinson says

Using that problem of for methodology #1 actually looks like this

because 4-6 is a negative you take 1 from the 5 and subrtact 6 from 14

54 14-6=8

-26 4-2=2

—-

28 Solution and much simpler than going through 20 steps

Milo Jury says

There is no ‘5’ in the problem you listed. There is a ’50’ which is represented with the digit ‘5’ in the 10’s place. And why did you take a ‘1’, add it to the ‘4’ (which is a step you did not list but certainly computed) coming up with the sum of ’14’?

Your way will certainly get children to compute sums and differences up until algebra. After that, the logic fails because using variables means students need the concept, not the shortcut.

Sara Webb says

Actually, I disagree. There are so many steps in that method to get lost in! The problem is that students get lost in the procedure and don’t understand it. It is much better if they learn other methods FIRST to have a deep understanding of it. Then, with strong number sense, they will be able to do that in their head. 4th grade is the first year students are expected to USE the standard subtraction method. If students had a strong use of other methods like using a number line, decomposing, finding compatible numbers, etc, then third grade teachers could introduce that as a new strategy. They could master if by 4th grade.

It isn’t simpler to borrow from the tens because children forget to cross out the 5 in the tens place and then they get the answer of 38 instead.

Also, why not add 4 to both numbers so that you have 58 – 30. Then, it is really easy to see that the answer is 28. That method has even fewer steps than your example of the standard “borrowing” method.

Kasey says

And speaking with someone who spoke to the authors of common core. Where in the common core it states standard algorithm it means standard as in direct place value not standard as borrowing and carrying as we would call “standard”

Cathy Johnson says

That is where you teach them how to add their answer to the bottom number to see if they come up with the top number…….SIMPLE math. That is checking their work. Basics, basics, basics. It was good enough for me, and I am quite capable of managing a company budget, plus run the household budget. Keep it as simple as possible and it will be much easier to understand. I am 56 years old, and I would not be able to help my grandchildren if they brought me something like that. Methodology used in this example goes way out on a limb for elementary school children to grasp.

Sara Webb says

Cathy, Actually, I have done that. For years. I have taught 3rd, 4th, and 5th grade students. Students who have natural number sense and are good little robotic students do ok no matter how it’s taught. I was one of those students. I could memorize formulas and procedures, but I never understood math until I became a teacher. Then I spent years teaching in older methods. We started with the abstract typical subtraction and addition. I taught my kids and reviewed it and practiced it and required then to check their work with the opposite operation. Bit they still didn’t know how to think for themselves. So, end of the year comes along and brings a math EOG. And guess what, they failed! They did well all year while the skills were isolated and they knew this week I’m working on subtraction. Once it was mixed up, they didn’t think about the problem but just pulled the numbers out and did something. After all, I taught them procedures. And, no matter how hard I tried to teach them how to think all year, it was almost too late. They wanted to be told procedures because that’s what they had all along. Oh, and, remember all those times I taught and required them to check their answer? Half never did when they were on their own without me to say it, and the other half did but had done the wrong operation so it didn’t matter!

Common core starts with concrete, hands on learning. I can touch it, and feel it, so I can understand it. Then moves into representational. I can show it with a picture. And finall abstract. I can do it with just numbers. Students learn multiple ways to solve problems, and that there is no one right way. They are able to discuss their strategy and how it is correct. Do you want your grandchildren to be robotic procedure doers who don’t understand the basic concepts of math? Or, wouldn’t it be better to have creative thinkers and problem solvers?

James says

With the new system, because I have not seen it fully explained, I do not understand how one is supposed to know when he has gone through all the steps. I do know that even after learning the old system, I can come up with my own methods to do calculations in my head without following the same steps I would use if I were doing it on paper. I have a brother 9 years younger than me, who I taught to add and subtract before he ever started school. I have no idea how he did it, but before he started school, he could add 2-digit numbers in his head. In college, he majored in math. He taught high-school math 2 years, then worked full-time in the National Guard until he retired as a Colonel.

Cathy Johnson says

So, Drum Guy, by the time you do all that I would have the problem already figured out by borrowing. Learn the basics first.

Michael Occhino says

Oh no… you are under the misconception that this is a race… When teaching for understanding comes first, you unlock such potential so that more students can think beyond a budget and think about rates of change and matrices to expand themselves as visionaries and citizens with more competencies than you mention.

RK says

I agree. They need to learn basics, how to subtract and THEN when their little minds are ready help them think it through. Also just a point – the methodologies are also just a rote memorization, I bet most kids just do it that way because that is the way the teacher taught them NOT because they thought it through a different way. If they know the basics of math, orders of operation etc without these methodologies they can still solve the problems correctly and MUCH MORE QUICKLY. In double digit multipication (this is 4th grade) they dont do it the easy quick way – use a 0 to hold your space and in the 2nd row and multiply. They have to do 1 line of multiplying for each number and hopefully they line them up correctly because if they don’t and if just one line is off they will get the wrong answer. The normal way leaves less of a chance of misaligning and a better chance on getting the right answer.

Sara Webb says

It is actually not the way that it works. The beauty of multiple ways is that they get to choose the way that they understand the best. I love using number lines with my students for addition and subtraction because it takes away the crazy borrowing and carrying, and forgetting to cross out the number or whatever else it is in the robotic procedural steps. I also love it because there is so much flexibility! I wish I could post a picture on here of the examples of different ways my kids solved our word problem of the day last week.

Judd says

why are negatives not used?

I would suggest method #3

54-26

50-20 = 30 4-6 = -2

then 30 and -2 = 28

these methods are all algoriths. not new, not old.

the focus should be on the concepts of combing (adding) or comparing (“subtraction”)

CJones says

You are not just subtracting 3-1. You have to consider the place value. It’s 30-10 which equals 20.

I agree it’s only 2 steps. The 2-2 left you with nothing. 30-10 leaves you with 20…final answer!

KHeatherly says

This is the misunderstanding you are teaching with your method. “3-2=1”. This is why children have no numerical sense. By teaching children this, they do not see that the 3 actually represents 30 (it’s in the tens place value position). So. it is actually “30-20=10” and needs to be taught that way to develop numerical sense and understanding.

James says

Yes, we did know the “3” represented “30,” because we knew it was in the “tens” column.

Sara Webb says

You know that as an adult yes. The problem is, it is a consistent mistake. Kids today have a major struggle with number sense.

Salty Wench says

Actually, it was the first thing we were taught when we started double digit math. For the vast majority of us, this was long before adulthood.

S. Carloti says

@ KHeatherly March.6.2014 at 11:45 pm

You said ……

=====================================================

“” This is the misunderstanding you are teaching with your method. “3-2=1″. This is why children have no numerical sense. By teaching children this, they do not see that the 3 actually represents 30 (it’s in the tens place value position). So. it is actually “30-20=10″ and needs to be taught that way to develop numerical sense and understanding.””

======================================================

1. You can not teach a…. “misunderstanding” …. by any method.! :-))

2. Children “develop” numerical sense….. if thought properly.

First children learn to count from one to ten. Right ?

Then they learn to add and subtract within this range. Fingers ( although not encouraged ) may come in handy.

3. Then they move to 1-20. Automatically they will be thought that the first position belongs to the “units” and the second to the “tenths”.

Then they learn to add and subtract withing this range now ( 1-20 )

4. Next step is 1-100 where they ALREADY KNOW THAT 37 is 3 tenths and 7 units.

It seems to be that on this tread many adults have little confidence in children’s ability to learn, remember, and apply what they’ve learned. Of course practice (homework) makes perfect.

“Negative numbers” (-2), aka. “elements of algebra” in my opinion should be introduced much later around grade 4.

5-3 is simply “5 take away 3″….. NOT (+5)+ (-3) This comes much later.

Push at this age “elements” kids may find difficult and you’ve turned them off to math …..for the rest of their life. :-((

You’ll hear them, in the years to come, saying ….”I HATE MATH” !

Show me a child who will say this and….. I’ll show you a poor teacher ! :-))

While I understand what is being “tried” here, I believe this could be thought while the children are in the “1-100” zone.

Apply this to “hundreds and above” and you are complicating needlessly a very simple process.

As far as the “old and PROVEN” method, remember the old adage…. “If it ain’t broken don’t fix it”.

In my opinion Shakespeare dealt already with “common core” 500+ years ago when he wrote… “Much Ado About Nothing ” :-))

Of course, if the intent is to “break the family” and “convince children that their parents are nothing but a bunch of idiots” ….”common core”…. is just the right method. 😉

Make changes in school, unbeknownst to parents, and enjoy the stress you introduce in the family, when the child will say….. “but this is how they teach us in school “.

Perhaps this “common core” would be swallowed much easier if the teacher would call the parents to school in a week-end and….TEACH THEM ( explained to them ) … the method they want to use to teach the children.

This way everybody would be …on the same page.

Which usually gives best results, ….. don’t you think ? :-))

Salty Wench says

Thank You!

Cathy says

What a dumb mess…

KShelton says

No, it isn’t incorrect, you just saw the process differently than the author. What happens when the top digit is smaller than the bottom. YOU understand it because your brain is developmentally ready for the algorithm. A child will build better understanding if they are able to understand our base-ten system and WHY it works the way it does.

Kevin says

Understanding and being developmentally ready for the algorithm came from a non-common core education. Just saying…

Rae Norton says

Wow Kasandra your method is exactly what we are trying to avoid. We want kids today to understand that they are not subtracting 3 – 1 they are actually subtracting 30 -10. and yes it does matter…..

K says

This is clear to me you do not truly understand math because that is NOT what you do to figure out the real answer. You have no understanding of place value at all. Please educate yourself before “correcting” those that actually understand how to teach. That is the problem with our society; everyone thinks they can teach and CLEARLY you are one of those that has NO business! You are the reason why we need to teach students a deeper understanding of math, because you obviously never got it.

Johnnie McHan says

I am 71 years old and so agree with Cassandra. I still can do addition, subtraction, and multiplication in my head faster than my grands can on paper. To me all this gobbledy-gook teaching methods have come about because of quasi-intellectuals who re- wrote “methods” to create havoc and insure jobs for themselves because it is so twisted as to be ridiculous. Anytime it takes a child half a page of paper to complete a simple math problem, which I can do in my head, then you know something is rotten in Denmark. Your blog above tends to prove my point. You took all that space and Cassandra solved it in minimum space. Easy solving of math problems goes to the root of learning multiplication tables. I have a degree in accounting, worked all my life as finance officers for. first the DOL and then private companies. I hired many bookkeepers in my life and most were smart and efficient until latter years when the government took over education. Sorry, to me Common Core is just another wasteful mess perpetrated on America.

Frederick Dietrich says

Could not agree with you more.

daveeckstrom says

Johnnie, when you do your super-duper fast arithmetic in your head, what do you see? Do you see the standard algorithm in your mind?

Kristen says

yes, why is everyone suddenly forgetting that elementary school through the 90s was “SHOW YOUR WORK”….if you just wrote “20” under that problem in ANY of the classrooms I was in then it would be marked WRONG for not showing HOW you got to the answer. I can’t for the life of me figure out why everyone in my generation has got this image in their heads that all we had to do was write the answer….

Katherine says

I agree completely and have been wondering the same thing!

Debby says

Sorry Kasandra, you are wrong and the original poster is correct. What you did was subtract the ones from the ones and the tens from the tens. That is an algorithm to solve the problem, it does not EXPLAIN to a child who doesn’t understand number concepts that the tens place is a completely different value from the ones place. Because technically, in YOUR second step, you are subtracting 1 from 3, but it is actually subtracting 10 from 30. Again, methodology vs. solving the old fashioned way

SJMiller says

32 32=10+10+10+2

-12 12=10+2

——–

20 So if you cancel out out the 10’s in both numbers and the 2’s in both number you get 20, what wrong with teaching it this way. This would be much easier than trying to guess why they used a 15 and 5 in the grouping. Maybe i just don’t get it, but this makes more sense.

Christina Moore says

Prime example of a problem with traditional algorithms and not knowing why in the world they work – you never subtracted 1 from 3. You subtracted 10 from 30.

Lisa says

Call it whatever you want… the way children are being taught math is STUPID and they are not learning! Sometimes you just have to suck it up and memorize your times tables. When you hit algebra or calculus, you won’t have time to “contemplate the threeness of three.” If you still have to draw pictures to figure out 6 times 8, your never going to be able to focus on the more challenging parts of the problem. I don’t want to write an essay… or write out ten different math problems to solve one. I want to do the minimum writing possible to aid my memory. Parents in math-related fields HATE this. And NO child should have to stop at “friendly number” 15 before being able to get from 12 to 20. 12 + 8 = “friendly number” 20. Are these children really so lacking in basic math facts that they don’t know that.

Concerned Mom says

there are glaring issues with methodology 1. first, I never learned to take a number given, in your example 32, and add 2 numbers to get it (how do you decide which two numbers to use to arrive at 32….there are several variations how to get to 32, like 15 and 17, why not use those? How about 28 and 4? You can see how this is an issue right there). Second, this methodology as you explained it will only lead to bigger issues with borrowing, as we learned it (if the numbers were 32 and 17, by your version of methodology 1 that would leave a negative integer in one of your steps…then what is the student to do in their line by line explanation as you describe it?). Really, the old way is quite simple.

32

-12

=20

I don’t see why you have to explain that if you have 3 apples and take away 1 you are left with 2. It’s fact. Period. No need to explain it. You can see it as plain as day.

start with the column on the right and subtract 2 from 2 leaving zero. move to the column on the left and get 2. keep them in line and viola, you get 20! You can see it’s a 2 step process, not 5 as your tried to demonstrate to make common core seem like a good thing. methodology 2 does NOTHING to teach subtraction. Just manipulates the numbers to make it addition. That spells HUGE issues when these kids grow up and actually have to balance a checkbook/bank account and need to know how to actually subtract. And according to your step by step process, methodology 2 should have 2 more steps added to it. Why just to make it simple do you add 4 numbers on one line when you clearly only add two numbers at a time? Please don’t manipulate the numbers to make your point valid and show it’s the same amount of steps. Until this “new” way is as easy as the old one, your point doesn’t make sense. We have learned and succeeded for decades using the old system. Clearly this isn’t the issue.

I only hope this experiment is a big FAIL by the time my kids are in school. This isn’t about teaching a new way or making sure they are at a certain point by a certain age. This is just another big step in the government getting more involved in something they need to stay out of and let the teachers (you know, those hired trained professionals we trust to take care of and teach our children for hours each day) actually do their jobs and teach!

Carrie Wells, Ed.D. says

Here’s the problem. Same as the first person who responded. You are NOT taking 1 away from 3. You are taking 10 away from 30. Children have to understand that to understand regrouping.

Let me post a simple question… if all numbers in each column have the same value, why do we work from right to left, rather than left to right?

Parker says

Why can’t we just teach our kids place values instead of over complicating it though?

When I went to school; I understood 22 was twenty-two. I never got confused and assumed it was “two two” or that is was equal to 4?

They can understand the regrouping by understand with a number like 22, the first 2 is in the TENS place, and the second in the ONES place. And solve it by remembering to ‘drop the zeros’

For instance, when we do decimals; we teach our kids .55 is the hundredths place, just like .50 is the hundredths place, but .5 is the tenths place. .50 and .5 are the same, we just dropped the zero.

It should be the same concept for numbers to the left of the decimal. 1.0 is the ones place, 10.0 is the tenths.

They can understand that you take away 10 from 30 instead of 1 from 3 by knowing PLACE values; they don’t need all these complicated steps!

Kb says

There is a difference between a number being in the tens place and knowing that the number represents a ten it’s a totally different concept

Michelle Reagan says

If you expand the numbers to their place values (30 + 2 subtract 10 + 2), it won’t matter which direction you subtract from. Then you can just regroup from the higher place value to the lower if needed. (for example, 30 + 1 subtract 10 + 2). Like you said, it is imperative that students understand the values of the places. Otherwise there is only rote memorization of the process happening and no understanding of numeration.

jeremy says

BECAUSE IF YOU WOULD GET YOUR HEAD OUT OF YOUR BUTT LONG ENOUGH TO REMEMBER, THE OLD WAY TAUGHT US TO START AT THE LEFT, 1ST COLUMN. IS ONES, 2ND IS TENS,3RD IS HUNDREDS, 4TH IS THOUSANDS,5TH IS TEN THOUSANDS& SO ON.THE OLD WAY MADE ME VERY GOOD AT MATH& FROM A YOUNG AGE WAS ABLE E’ER TO FIGURE PROBLEMS IN MY HEAD.IT SHOULD BE KEPT SIMPLE TO MAKE FOR EASIER LEARNING, I’M ASSUMING YOU LEARNED THE OLD WAY.ARE YOU SAYING IT HINDERED YOU OR MADE YOU STUPID?

Not McCarthy says

Maybe you should yell less if you want people to take you seriously. Oh and remove the tin foil hat too.

Susannah says

You have it backwards. If you “start” from the right, you have the ones column, the tens column, etc. you can’t “start from” the right because of something called infinity.

Sara Webb says

Good point! My nephew has super strong number sense. Even he got lost in the procedure of the standard method. He would start on the left instead of the right, and really, doesn’t that make sense? After all, we do read left to right!

I wish that students learning addition in k-2 would really develop strategies that build number sense and allow them to become more fluent with manipulating the numbers. Then, as third grade teachers we could introduce the standard method, and students in 4th grade are required to use it.

Concerned Mom, the reason you would decompose 32 into 30 +2 is because even tens are way easier to work with. You could also break it into 15 + 17. Then you might say that 15 is 3 more than 12. THen, 3 + 17 = 20.

I prefer the method of making compatible numbers. With the problem 32-12, I would say that you could reduce both numbers by 2, and subtract 30-10. You can do this if you really understand a number line and the fact that the distance between 2 numbers is the same as long as you change them both.

R. Craigen MMath, PhD University of Waterloo; Associate Professor of Mathematics at University of Manitoba says

@Carrie, Your question has a false premise. Nobody here but YOU are talking about numbers in each column representing the same values (not “having”). So why do you pose this as if others are saying so?

The key is that the algorithm FREES the child up from having to think (and talk!) about this. It is a release from tedium. When the child DOES this algorithm, therefore, they are not to be continually thinking about this — it defeats the purpose. They should learn the algorithm with understanding, but in the end execute it without continual reflection on meaning — because it is to be executed in contexts in which that valuable short-term memory is required for more advanced tasks.

THAT is “deep understanding”. First principles is not; it is only a dull exercise in elementary-level interpretation, which should be discarded as soon as it is clear that meaning is in place.

Let’s try it a different way. I’ll assume that, unlike about 50% of the education faculty teaching “Math Education” that I have encountered here, you actually have a significant exposure to mathematics past high school in your educational background — is that a good assumption?

Then let us talk about that first-year calculus course you surely passed. This course is the same all over the world, so we can, at least, talk confidently about what went on in that semester of your life.

As the course unfolded you first encountered the abstract definition of limits (and continuity). Then theory was developed and you were taught how derivatives (slopes of tangent lines) arise from secant lines, through the process of limits.

Stop there a moment: THIS IS AN EXACT ANALOG of place value in early arithmetic. This is what the derivative MEANS. It would be irresponsible to teach calculus without developing the derivative in this way, without passing on its correct meaning.

Now you learn to obtain simple derivatives by applying the theory of limits. As you recall these exercises were called “obtaining derivatives from first principles”. This is the exact analog of demanding that students, EXPLICITLY interpret every digit during the performance of elementary arithmetic.

Students hate that. I have met few calculus students who loved to use first principles. But it is an essential step for “deep learning”. However, a student who stops there has NOT learned calculus. You know what comes next.

The laws of derivatives are developed. The student is unchained from the ground and given efficient, effective tools for problem solving and analyzing complex systems. The resulting algorithms are beautiful, easy to use, elegant and efficient. But they DO NOT involve continual reflection on the first-principles meaning. By adopting tools that allow one to FORGET first principles while solving problems the student is freed up to advance beyond those first steps and “grow up” in their mathematical understanding.

Let me reinforce this. The student who cannot — or is trained by teachers to not — let go of the first principles interpretation, is hampered — not a little but seriously, and fatally, in their learning of calculus. The result is a waste of 3 months of their life, and their parents’ payments for their tuition.

Why on earth would you advocate for the analogous chains to be attached to students in primary grades when learning arithmetic?

Salty Wench says

Are you a politician? You sound like one; you keep repeating an argument that several people have already invalidated. How many times do you have to be told “we know all the numbers don’t have the same value” for you to believe it to be true?

Seriously, the more you repeat this same phrase, the more ignorant and programmed you sound.

Richard says

The logic behind your explanation (“it’s right because it’s true”) is the same logic that allows for governments to blind their citizens. Do we want to teach children HOW to think or WHAT to think? I’m not sure about you, Concerned Mom, but to me teaching them WHAT to think is the path to an Orwellian future. Have fun with that.

Sabrina says

Concerned Mom,

I am curious as to who the “we” is you speak of here: “We have learned and succeeded for decades using the old system. Clearly this isn’t the issue.”

By your definition of “teachers,” forgive me for assuming you will be lucky enough to send your children to schools with trained professionals. This truth is not the reality for copious parents due to their zip code. For these same parents, the “old system” did not work for them either and now they are doing the best they can for their children.

From metropolitan areas to rural towns, schools continue to have high rates of unqualified teachers for various reasons. These schools tend to have America’s most at-risk students, who need more than the “old system.” Teachers who follow the “old system” do not have the patience or perseverance to teach these students the way the need to be taught. (In case you were not aware, growing up in poverty affects child development and how students learn. The “old system” is a nightmare for the majority of these students.) Pay freezes on teacher salary also do not motivate these teachers to want to stay around because it’s too much work.

Shockingly, it is not that simple, but clearly, it is an issue.

justmamakoolaid says

First, I need to assert that luck lies in obtaining competent teachers for one’s offspring not in obtaining “trained professionals” for teachers. There is a radical difference between the two. Many competent teachers at our nations best private schools are not trained to be teachers and would not be considered “trained professionals.” I also feel the need to point out that home educated children score better than both public and private schooled children. These test scores vary little between parents who did not graduate high school and those parents with a Ph.D. Unlike students in what most term “traditional schools,” a parent’s level of education has little affect upon the outcomes for the children when home educated. As such it is not the disadvantaged home that is a predictor of outcome, but rather it is the difference in the schools of the disadvantaged when compared to the schools of the fortunate. As the basis for your argument is that disadvantaged children need this presentation of math facts in order to succeed, your entire argument becomes invalid. The root of the problem is not the instruction used, or even primarily in the teachers but in the fact that the property tax system of funding schools allows some schools to have more than they need to produce quality results while others hold class in condemned unsafe buildings without adequate quantity of materials. No child will learn in a school that is physically unsafe, let alone one with school place violence.

rita says

That’s it! “Qualified” teachers use impoverished schools as a stepping stone into a district. They tough it out for a year, then transfer to a more affluent school.

daveeckstrom says

mamakoolaid, I’m not buying your assertion that home-schooled kids score better than kids who went to school without a link to some data. I don’t believe it’s universally true. There may be some home schooled kids who would compare positively, but there will also be a lot of losers from the home-school crowd.

And the reason teachers at top private schools can get away with not being professionally trained educators is because their students come from the best genetic pool and the most supportive home environments. Those kids will thrive in spite of their pompous, developmentally ignorant lecturers. In the real world of public school, you have to know what you’re doing to succeed as a teacher.

Grace says

Oh my God. Are you actually claiming that wealthier children score better because they are genetically superior? That is insane.

Here’s your data, btw:

http://www.hslda.org/docs/nche/000010/200410250.asp

daveeckstrom says

Yes, Grace. That’s part of what I’m saying. Actually, I mentioned two factors. The other one was supportive home environment, which of course is much bigger factor.

Here’s what the International Center for Home Education Research (headed by a homeschool parent) has to say about the source of data provided by the article in your link,

“We simply can’t draw any conclusions about the academic performance of the “average homeschooler,” because none of the studies so often cited employ random samples representing the full range of homeschoolers.For example, two large U.S. studies (Rudner, 1999; Ray, 2009) are frequently cited as definitive evidence that homeschoolers academically outperform public and private school students. But in both cases, the homeschool participants were volunteers responding to an invitation by the nation’s most prominent advocacy organization to contribute test scores (on tests usually administered by parents in the child’s own home). The demographics of these samples were far whiter, more religious, more married, better educated, and wealthier than national averages. And yet these test score results were compared to average public school scores that included children from all income levels and family backgrounds. Not surprisingly, wealthy homeschoolers from stable two-parent families who take tests administered by their parents in the comfort of their own homes outscore the average public school child by large margins.

The simple fact is that no studies of academic achievement exist that draw from a representative, nationwide sample of homeschoolers and control for background variables like socio-economic or marital status. It is thus impossible to say whether or not homeschooling as such has any impact on the sort of academic achievement measured by standardized tests.Full disclosure. I’m a public school teacher who works with private schools frequently. I’m also a home-school parent.

Sherri Mcbride says

AMEN!!! I could not have said it better.

Carrie Wells, Ed.D. says

Thanks, Sherri!

ricej says

What happens when you subtract 123-45? Oh, it’s a confusing process of borrowing from the next column. There is value to using both methods, but understanding number places is the real goal.

KHeatherly says

Many educators were involved in creating the Common Core standards. They were NOT developed by the government. The government is not telling anyone HOW to teach. They are simply standards. Great article! Fully support CCSS!

September says

It was not developed by the government it was developed by several corporations and non profits that have a special interest in making all schools private in order to make a profit. Bill Gates, Pearsons, and InBloom were a few of the corporations involved in making CCSS. They are also linked to the government and have a special interest in making huge profits off of making test, software and data collection on every single student that attends public school or online school. The government used these corporations to bribe states to implement CCSS.

Stephen says

I understand your frustration; it took me a second and I have a degree in mathematics. Here’s the mechanism: when you’re subtracting one number from another, you’re primarily interested in the “distance” between them. i.e., when we say, “5-3=2,” we’re saying that there’s a number distance (or interval) of 2 between the numbers 5 and 3. Another way to approach that is the start with the subtracted number, 3 in my example, and add some interval to get 5. For this example, that’s easy. For the example above though, it’s a little harder. In all cases, start with the subtracted number; hence, the second method starts with 12. Then, we add an interval to get to 32. However, that’s not so easy, so we do it in steps. 12+3 is easy. 15+5 is easy, as is 20+10 and 30+2. Then, to get the whole interval, we just add the intermediate steps: 3+10+5+7=20. We could just as easily have done 12+8 and 20+12. The amount of steps depends on the student’s level of understanding.

I’m not arguing for or against, just attempting to clarify.

James says

This is the best explanation I have seen here. It actually shows how you select the steps you use.

Grace says

3+10+5+7=25, actually. Thanks, but I’ll pass!

SJMiller says

Concerned mom, I couldn’t agree with you more! The government is trying to make our children dumb so they can control everything.

Felicita says

Oh gosh, I’m in trouble! I was horrible at Math. I’m lost just trying to figure out the 2 examples. I graduated high school in ’03 and I learned the simple way to do math. Now I have to learn a new way to be able to teach my kid. Looks like Common Core will be teaching me the “proper” way to do Math.

Carrie Wells, Ed.D. says

The thing is… when you break learning down into its smallest components, you’re actually making it easier for children to learn. Looking at it on paper, it’s confusing. But if I showed it to you using small manipulatives, I guarantee you’d learn much faster than having it just be a paper and pencil task. Not only that, you will gain independence in using the strategy mentally, not just in writing.

Regardless, the key point is that strategies and methods used to teach have little to do with Common Core.

Elizabeth says

But they don’t get too use manipulatives on “the test.” Paper and pencil only. What about the kids who can ONLY do problems with manipulatives? Math in the college and professional world requires paper and pencil.

Kevin Olson says

Actually, at least when it comes to the Smarter Balanced test, some problems involve digital manipulatives that students are REQUIRED to use in some cases. This assesses whether or not students really get what they’re doing and can demonstrate things like breaking apart a ten into ten ones to borrow. The assessments are by no means perfect, and we have yet to see (In CA at least) how they actually roll out, but I am optimistic they’ll emphasize a solid understanding of processes and not just ability to robotically repeat a series of steps.

tyler says

That is so far from true, i prefer pencil and paper for working out math problems needed for home projects but in the college and professional worlds they are rarely used.

Stackey says

I’m sorry…which professional world are you talking about?

I owned a computer business, I taught, I currently homeschool my kids, many family members in carpentry, doctors, a scientist, several writers, I worked for an engineering company, I currently homeschool…

In school we were allowed either one blank piece of paper that the teacher gave us and a pencil, or there was space to write on the test booklet. I took many many certification tests for Microsoft and several other platforms…we were allow pencil and paper…

The tests my children currently take online have an app that allows them to do paper and pencil type work on a form in their test…granted it’s on the screen, but it is a simple mouse-writing tool.

I don’t think I’ve seen the place where pencil and paper are “rarely” used.

KHeatherly says

They are allowed manipulatives. They are virtual representatives of what they have used in the classroom.

Isabelle says

There are shifts in the educational process in which the students move from manipulatives to pictures to mathematical responses. This is part of the Common Core process. Common Core encourages several different ways to solve problems with the final outcome being the traditional algorithms. This is my first year teaching math with the Common Core standards, and because this is the last year for the old test, I have been currently going over the old standards. I have been totally blown away at how easy the material is for the students because they have been working with the Common Core standards and practices. I am a believer!

justmamakoolaid says

If you can show it using manipulatives in a video on you tube and it makes sense, it would do a lot more for those of us who learn through hands activities than the attempt to explain it above.

Michael H says

It seems funny to me. I graduated high c school in 1994. As I remember it the “old” way had steps also.

32

-12

this was solved right to left. You subtract 2 from 2=0. You then subtract 10 from 30=20. 20-0=20 how shocking!

Seriously when did this ever have to be complicated? Math was a language to me so it was always easy. So much of it I was able to do in my head. This actually made algebra and calculus easier. The later man classes taught me how to compute in steps, I did not need the subtraction steps in early math classes. I see this way as ridiculous as it is extra pressure put on kids and their parents. Don’t pretend that “this” is not part of the problem!

If this is really what public school is offering for math then I would rather home school my son! I can teach “grouping” and “thinking” in a better, more reasonable way.

Tbritt65 says

Yes you can! I am well educated, but I am not an “educator”. I have two children who were part of the public school system and home schooled. One is a college graduate at 19, the other will be entering college this fall as a sophomore. Common Core is the worst curriculum I have ever seen! Not just math, but across the board!! Look at the creators of this system.

Sara Webb says

Have you studied the standards? Which standards do you object to as a problem? Have you examined how they build from foundational skills to higher level skills across grade levels? I am really not trying to sound condescending here, but what makes you qualified to say that it is the worst curriculum? What makes the previous set of standards so much better? What are your specific objections?

The Nationalist says

You fail to grasp common mathematical concepts.

you are doing subtraction with a left vs right method.

Subtraction is far more efficient doing it the normal up/down method.

This is especially important for higher education in algebra.

This is a dumbed down version that MAY make it a bit easier for primary kids who aren’t taught by teachers how to subtract, which is concerning in itself.

This long winded confusing approach will, however, confuse the VAST MAJORITY of kids, and seriously mess up their education for more advanced problems. Imagine if they tried doing long division or complex algebra with this!

Focus on blogging about kids, but don’t try and pretend you are a mathematician

Sincerely, someone doing tertiary grade mathematics at university.

Kevin says

Someone doing tertiary mathematics at university does not necessarily know the best practices in teaching elementary children fundamental concepts, and may not necessarily know how to handle students who, when shown the standard algorithm, simply “don’t get it.” A variety of approaches can be used to solve math problems and can make a major difference in making math accessible to kids who would otherwise struggle. As they progress in efficacy, they will likely discover and appreciate the elegance of the standard algorithm, and will also likely understand the math and thinking behind it much better.

Carrie Wells, Ed.D. says

I completely agree, Kevin. Thank you for your thoughtful feedback.

Elizabeth says

“Confuse the VAST MAJORITY of kids” and higher level math teachers!

erin says

well said. what next? will kids have to learn why mixing red and blue makes purple? is it not true children have enough problems with learning as is?

justmamakoolaid says

My kids didn’t remember what colors were made by mixing 2 colors until I showed them with paint what mixing 2 primary colors created and what mixing secondary colors created using paints. Same with shades and tints.

My problem is children who understand it the traditional way are being forced to learn it a way that is not natural to them. I am for teaching each child in the manner that works for them which is why none of my 3 children have used the same curriculum to learn the same material. They are all on track to graduate no later than 16 (the oldest already has).

My other problem is the assumption the accreditation somehow makes a teacher better. This has been proven to be false.

Stephen says

I hold a physics B.S. with a math minor and am currently a Ph.D. candidate in physics, but I must admit I have never heard the term “tertiary mathematics.” I have no idea what you’re studying, but if you find the second methodology somehow less mathematical than rote subtraction with no consideration of place value….. well, I hope your tuition is cheap.

Holly says

Amen!

The Nationalist says

There are some areas where left/right methods are better, but thats for much higher up learning and not for all things, and is easy to teach with a strong foundation of maths learning. The bulk of alot of primary kids’ problems involve up/down, not left/right

Carrie Wells, Ed.D. says

First off, I am not a math teacher, nor do I claim to be a math teacher, nor is this post about teaching math.

This post is to clarify what is meant by “Common Core”. I posted a horrible example that has confused people regarding what Common Core is and is not with definitions of some simple educational terminology. This post was meant to inform parents, so they will know how to advocate for their children.

A Math Teacher says

To The Nationalist — when you were in elementary school, how well do you think you did in math compared to the other students? bottom 10%? top 50%? top 25%? top 10%? I’m willing to bet you were pretty great at math and learning made sense quickly and easily for you. Congratulations on being so lucky.

However, the direction, of all things, is probably the least meaningful thing in a six or seven year old’s math career.

I know you like it, because you personally understood it, but the standard subtraction algorithm is one of the reasons you found yourself alone at the top of your class! I’m sure it’s quite obvious to you that “32” is a group of three tens and two ones — but for the vast majority of children, it’s a huge sticking point! Just look at the facebook comments on the graphic. (And the comments on this article!)

Using the standard subtraction algorithm (and the multiplication one too) produces errors that are orders of magnitude off — because all too often, the student is focusing on up/down right to left and not thinking about the numbers being ones, tens, hundreds, and thousands, so they will turn in a subtraction problem that started in the thousands with an answer in the tens, or a two digit multiplication problem has an answer in the ten-thousands. The traditional way is only more efficient once kids actually get to the point where they won’t do that.

It’s broken and it needs to be fixed. The only reason it will be confusing is parents are unwilling to sit down and look at the math, or ask their kid how it works.

Carrie Wells, Ed.D. says

Thanks, Math Teacher. I am so glad you share my perspective, as clearly you are in the classroom implementing curriculum to address the Common Core Standards.

chris says

Or maybe teachers this day and age just need to TEACH kids RIGHT from the start then we wouldn’t need thiw stupid waste of time idiodic method. Just a thought.

sue says

my kid is a junior and cannot explain the concepts to me at all. I learned the “old fashioned way” and did quite well, I can balance a check book, know when I have enough money to pay the bill just be looking in my wallet and looking a the bill. He can’t. He has struggled with math his entire school life and I cannot help him because the “old fashioned way” confuses him all the more. Even showing him a visual example just confuses him because he has no concept of ones, tens, hundreds, etc. Put a ten dollar bill in front of him and another pile of ten ones in front of him and he cannot figure out that taking five from each pile equals the same thing, especially when using a five dollar bill in the example. This is really sad, he is barely passing math. He is very frustrated and I really don’t know how this math is going to help him in every day life…It is really sad.

Sara Webb says

Just think though, if your son had gotten a really solid conceptual experience from the start about numbers and what they mean, how much stronger would he be now? He was probably a student who really needed to be taught conceptually with a lot of hands on experience to develop strong number sense. I am sorry for his struggles now.

Km says

Is it broken…? Cause I am more than willing to sit down with my kids and I cannot understand any of it. And I am far from dumb. I think the adults need to ask the kids if it’s broken since it’s the adults who are deciding if it’s broken and the kids have no say and it’s the kids who are frustrated and parents are lashing out because kids are becoming disinterested and frustrated. I have a son who is very good in math and suddenly is very frustrated with this new ” common core” math. Which is very sad cause it is the one class he was actually confident in. I graduated in 1988. Ie saint great in math being more of a reader and history buff myself. But I got by just fine with the ” old fashion” math. Even graduated from college with office management classes and am now a dental assistant. Maybe that’s not a big deal for some. But. I don’t see why things have to be complicated. Everything had to be broken down and work had to be shown when I was a kid and throughout the years for all 6 of my kids. This whole thing is getting out of hand and ridiculous. Why frustrate kids further? Is this really helping? I am about to pull my last 2 out of school because of this nonsense.

Carrie Wells, Ed.D. says

KM – What often happens is that when we learn a method, we’re able to quickly skip steps and still demonstrate mastery. In the traditional subtract down type method, we’re missing the understanding of place value and base 10. We learned a quick way to do it without really understanding more abstract concepts. There’s no “new” way to learn math… Math is math. You still arrive at the same answer. Common Core does not force or even imply a set way to solve a problem. It promotes teaching a variety of ways. This is just one method – counting up – that may be used. N

Michelle says

KM,

As someone who graduated the same year as you and a current 4th grade math teacher, I understand exactly what you’re talking about. What I see is that the way we were taught was to take math procedures and formulas and fill in numbers. We did not think about why the math worked or if it truly made sense. Now we are asking kids to figure out the why of math and not give them the steps. We want them to determine their own solutions. It would be much easier to just teach them “how to do” the math, but students these days need to approach problems from all sides and determine where to begin, what to do next, and how they think they need to solve it. We just give them the tools they need to try to use and guide them along the way. They need to persevere in solving the problems in order to be “college and career ready,” according to the government.

patti says

Carrie, my son, who always naturally excelled in math, had to learn AND be proficient in all of the methods for solving the same problem. The traditional method clicked instantly (and he did understand place value). So, no problem. But all of the tests expected him to be proficient in using ALL of the methods. So… why should a kid who is highly intelligent be punished for not understanding EVERY method. Why can’t he just use the one that works for him? It wasn’t good enough for him to use the methods that worked for him. He had to know how to do the other 5methods as well. This goes against your very premise.

Michael H says

I agree completely Patti! “Standardization” isn’t simplifying math for our kids; it is simplifying our kids to the collegiate system.

Let’s try to remember teaching or kids should be the #1 priority!

Mom of 3 says

Thank you KM for your comments. I’m a mother of 3 and I’m also willing to learn but extremely frustrated with trying to understand. Although I wasn’t a strong math student I could understand the basics. I have been out of school now for 28 yrs and trying to keep up with what my kids are learning. Parents are struggling with this new way of teaching for us and the schools should have some kind of informative website for us to refer to so we can help our kids with their homework. Even my 18 year old that is graduating with a Regents diploma this year was somewhat a little confused with some of my daughters 1st grade homework and how things were worded. After emailing my daughters teacher her answer to me was this new system is confusing but will be working on it and at least she did the addition and subtraction. Well for me this wasn’t helping me to try to explain to my daughter how this is suppose to be done. How can we help our kids understand if we don’t have a clue. Now my daughter is struggling and has been asked to extend her already long day at school for math. The kids have been introduced to this new system but they are moving so quickly and now our kids who are struggling have to attend extra help. I’m happy that our district has the ability to have this extra help after school but there are so many students that attend for this extra help due to this common core math. Frustrated Mom that needs “Common Core math help for Dummies”

Concerned mom of teenagers says

Mom of 3:

I completely agree with your statement. I love math but feel incompetent when my kids bring their math work home and ask for help. If they are unable to finish it at school and have questions about the problems how do teachers expect the work to get done when the parents have no idea how to help them? My kids have dropped their grades because of this and believe me their grades used to be very good.

Karen D says

Mom of 3 (and anyone else who is confused by CC math)

Go to engageny.org to find the entire curriculum including step by step instructions at all grade levels written for teachers. These include examples. There are also some videos there. I teach in Baltimore, Maryland and some of what we use in our daily lessons comes straight from NY. It will take you some time, but if you really want to understand and be able to help your kids understand, it will be worth it.

I had so many parent complaints about not being able to understand the homework, I began inserting pages of instruction for students and parents in the homework packets. It is more work for me, but I’m willing to do it because I know how frustrated parents are. A lot of teachers are still confused about some of what we are supposed to teach. Our district does a pretty good job with professional development to help us brainstorm together to understand the content and the methods for teaching before going back to the classroom each month.

Good luck with this. I hope the website helps!

Tiffany says

News Flash: Schooling and education in this country is broken. There are many mitigating factors related to this issue. Many of the problems stem from social factors that will not change because we create new standards for the children to be evaluated. Testing, testing, testing will not help our country rise in education. Addressing underlying problems that permeate our culture will. All of this is band aids. That being said, I am a reasonably intelligent person with a Masters. The highest level of math I completed was calculus in college. I was on an upper level track starting Algebra in 9th grade and finishing with precal/trig in 12th.That being said, I did everything that has ever been asked of me in math by memorizing how problems work and solving based on that. I have NEVER understood math, bc my brain does not think that way. I got A’s and B’s in a subject that I don’t have a clue how it works. I got an A in Calc bc I came home every night and did calc for 3 hours. Drilling and perseverance got me by. Do I wish I understood why problems worked? Yes, maybe it would have made it more enjoyable. Do I think it would have made it easier? NO, because my mind does not think that way.

It is safe to assume that there are many children out there like me. It makes sense to me to teach math in many different ways, so that all the thinkers can get some understanding of it. The way our school systems work in this country don’t allow for this methodology that would provide the best chance for everyone. It seems more important to stress out children out with obnoxious testing from kindergarden on.

As for the common core example given above: It makes no sense to me and I am reasonably intelligent person who got an A in calc in college.

Carrie Wells, Ed.D. says

Tiffany – Common Core is just a set of standards – like writing an IEP or plan of care for a typically-developing style. It does not dictate or even suggest how the goals will be achieved. That’s up to the implementer (teacher). However, when school districts adopt curriculum that claims to align with these standards, people assume the curriculum IS Common Core when in fact the government has not issued its own curriculum.

As with everything… it is a matter of money. Curriculum development is a huge industry. Every company out there wants to develop their curriculum with methods and strategies that supposedly align with Common Core. We’ve taken a great idea – standardizing what students should learn from state-to-state before graduating from high school – and raped it by creating a business of it.

KH says

“We’ve taken a great idea – standardizing what students should learn from state-to-state before graduating from high school – and raped it by creating a business of it.” … Hit that right on the nose.

Steve says

I’m sorry, you can promote common core all you want, but it is ludacris. I sat in a room with 30 other kids my age and wrote and repeated addition and multiplication tables for hours every day. And I guarantee everyone in my class, and every class like ours, knows 32-10=20 because it does. There is no need to create 2 or 3 or 5 steps to solve a problem that should take a macro second to solve when you see it. As a parent, the biggest problem I face everyday is trying to teach my kids how to solve problems quickly and accurately, after they sat in school all day learning the opposite. I’m all for creative thinking, but there has to be a basic foundation behind it.

Steve says

22

Michael Occhino says

lol…

Kevin Olson says

Some of the logic in these comments and the comments being left on the Facebook thread that lead me here is baffling. How does teaching an abstract, decontextualized algorithm right out of the starting gate promote a “basic foundation” for the math behind it? It does the exact opposite!

There is most definitely a time when students just have to use the standard algorithm, but that should only occur if students already have mastery of key concepts of math – the base-10 system, place value, decomposing and composing tens, hundreds, etc.

You can be an excellent mathematician, you can be a successful professional, you can be someone who was an excellent math student in school; that DOES NOT mean you are an excellent teacher with a strong grasp of the progression of skills students need to master. That DOES NOT mean you know the best ways for kids to learn. Trying to apply your skills and experience as an adult in thinking through the concept mastery and alternate methods for teaching these skills will lead you nowhere.

And really, the fact that so many people on here are so confused by Method 2 (and even the very clear-cut logic behind Method 1) speaks volumes as to the low level of understanding many individuals have regarding WHY the standard algorithm works.

Here’s my attempt at explaining the two methods:

32 – 12 = 20

Method 1:

First, think of 32 as 3 tens and 2 ones (30 + 2)

Next, think of 12 as 1 ten and 2 ones (10 + 2)

From here, use place value understanding to subtract ones from ones and tens from tens (the 2 in 32 is subtracted by the 2 in 12, and then the 30 in 32 is subtracted by the 10 in 12)

The result is the number of ones you have and the number of tens you have (0 ones, 2 tens, which is 20)

Method 2:

For students who may really struggle with the idea of taking away or breaking apart, this strategy uses the relationship between addition and subtraction and skip-counting strategies to count up from 12.

First, the student counts up from 12 to the nearest “benchmark number” (since students in first and second grade are learning skip-counting by 2’s, 5’s, and 10’s, these are numbers that fit nicely into those skip-counting patterns), which is 15. To get from 12 to 15, they needed to add 3.

They keep track of how they’re building up to 32 by recording how they skip count.

From 15, they then skip count by 5’s up to 20, the next benchmark. They track, “I already counted up by 3 to get to 15, then I counted up by 5 to get to 20.”

Next, they skip count by 10’s to get to 30. They track this as well.

Then, they count up from 30 to get to the initial number of 32, tracking that they added another 2 to get there.

The last step is to go back and recall how they built up from 12 – they added 3, then 5, then 10, then 2. The sum of these numbers is distance between 12 and 32.

Carrie Wells, Ed.D. says

Thank you so much for your insightful comments, Kevin! I enjoyed each one.

f.p. says

“but it is ludacris”

Seriously?

“32-10=20 because it does”

Seriously, seriously?

So much for “quickly and accurately”. Quickly, maybe. I normally don’t pick on people for stuff like that, but you’re hurting your case here.

Look Steve, none of that even matters because you are missing the entire point of this article. Follow closely here: Common Core does NOT push using the “new” method. It doesn’t. If your kids are being taught that, they’re getting it from a locally chosen curriculum. Another school can use the “old” way and still be following Common Core.

Roxanne says

I have a quick question about Methodology #2, in the first two steps

12+3=15

15+5=20

Where o Where did the 3 and 5 come from?? I understand the rest of the steps.

Carol says

You are moving up to “friendly numbers” on your way to 32. Numbers ending in 5s and 10s are characterized as “friendly numbers” in my child’s curriculum. This ties in to rounding and estimating answers in upper elementary grades

Sara Webb says

What the illustration was missing is the number line. This makes so much more sense when you see it on a number line. It is so beneficial to have a strong understanding of number lines to aid in developing mental math and number manipulation.

Sara Webb says

(function(d, s, id) { var js, fjs = d.getElementsByTagName(s)[0]; if (d.getElementById(id)) return; js = d.createElement(s); js.id = id; js.src = “//connect.facebook.net/en_US/all.js#xfbml=1”; fjs.parentNode.insertBefore(js, fjs); }(document, ‘script’, ‘facebook-jssdk’));

Post by Support Common Core NC.

I don’t know if this will link correctly, but it is a great illustration of this. If it doesn’t link correctly, you can find the post at http://www.facebook.com/supportcommoncorenc

Mother of Three says

To “A Math Teacher”. Thank you for your courteous and well written comments, and also for your command of English and Spelling.

Brandon, Math PhD says

I wonder if the teachers ever talk about which way is more efficient?

The “old way” is clearly more efficient (and it gives only one possible route to completion).

old ways are best ways says

I agree. No one has addressed the “top” ones number being smaller than the bottom ones. 42-16 for example. Kids likely will get confused and answer 4 and then 3 so 34, not realizing the have to borrow/break a ten for more ones.

Susan says

Actually, we my class does discuss what is the most efficient way to solve a problem! My second graders began the year mostly using manipulative to solve problems. We regularly discuss more efficient strategies to solve problems. Many of my kids now use invented algorithms or standard algorithms to solve problems quite quickly and correctly. They UNDERSTAND why it works. They can also look at a situation, tell you what is happening to the numbers and give you the equation they need to solve the problem. Do you want kids to be able to complete page of equations or to be able to use the math in a real situation?

Carrie Wells, Ed.D. says

Wonderful examples, Susan! I am glad you have found this to be successful in your classroom.

Concerned parent from The Buckeye State says

Thanks Carrie for a well thought out message.

Carrie Wells, Ed.D. says

You are so welcome.

DrumGuy says

I admit I got caught up in this too, but apparently so many people have completely missed the point of this article. It wasn’t written in defense of method #2 vs.method #1 in the image. The purpose of this article is that the debate on what methodology should be used has NOTHING to do with Common Core. Common Core is neither of these methods, nor ANY method; it is just a set of standards. It simply says that someone who has completed 2nd grade should be able to solve this problem, regardless of how they were taught to solve it.

The article talks about college, but the need for national standards can be felt much younger if a student is moved. It’s good to know that if I move to a different state, my 3rd grader will have the same background as everyone else in his class. I would hate for him to get bad grades or even be held back because the new school expected him to know something that he hadn’t been taught yet at his old school.

Sara Webb says

Yes!!! I completely agree!

Elisa says

I am a middle school Math teacher. I also have a BSc in Mathematics. My main obstacle when I first get my students is to try to explain to them that Mathematics is not a set of rules, Math makes sense and there is a reason for every “rule”. There are only so many sets of steps a child can memorize, and by the time they get to middle school, these steps can get all mixed up. Fractions, for example, is a topic that can give students a hard time because it is never properly understood. I get a lot of confused students coming into sixth grade who do not remember exactly when to “flip the second fraction”, or “keep the same denominator and just add the top part”. If it these rules had made sense to them when they were learning them I don’t think they would get them mixed up so easily.

Students need to be taught that Mathematics is not a bunch of procedures.

Sara Webb says

yes!! If we can build a solid foundation and students really understand what it means to be a fraction, and can think and reason about that, they will do so much better! There is so much stigma about fractions and how hard they are!

I can’t tell you how many adults have said to me, “Oh, I just never understood fractions!” Clearly, there was something wrong for them in how they learned!

I do not want robotic procedure doers who do not know when to do the procedure unless I tell them!

Ashley McClure says

I agree with “Concerned Mom”. We need to get them to understand addition to understand subtraction, but we do not need to incorporate addition in the subtraction problem unless it is to teach them to check their work AFTER they have completed the problem. How are we as parents suppose to help our kids do the best they can in school and from that in life, when the teaching methods are beyond the spectrum of our understanding, learning, or comfort levels? I am willing to “learn something new” as it will keep my brain growing, however, it is not easy to “teach and old dog new tricks”. Two of my older kids have already gone through this learning process in the third grade and I have a third one learning it now. I didn’t understand it then with the first 2 and I still don’t understand it now, and I still have one more to go through these “learning” techniques.

Sara Webb says

This is a question that I have been asking. How can we help our parents understand the shift without them feeling like we are alienating them. It is not a matter that is as simple as “the old methods of teaching were wrong and therefore everyone who learned that way is inferior to students today who are getting better instruction.” It is not as easy as “our math teachers clearly didn’t teach us right because it was different.” However, it is different. I remember as a student never fully understanding math because no one ever explained why we did things. You just had to do it. I now look at math very differently. Also, I cannot tell you how many times I have had a parent in a conference say to me, “well, I just wasn’t that good at math when I was in school.”

There are two major things at work here. The first being that we must find a way to help parents understand the benefit to conceptual learning and to know that we will get your students to a place where they will be able to do the “standard” ways that we recognize. The second is trust. You have to trust us to build a strong foundation. The first thing to do is ask the teacher if they can help you understand the different ways students are learning math.

I do not send home homework that will cause these confusions for that very reason. It isn’t fair for the students or parents.

Jason hatch says

Forget the graphic for a moment. Think. You begin your article making the case that the sheer diversity of learners is making it difficult to teach and then you continue to prescribe teaching several methodologies to multiple students in an effort to assist them. Does this not INCREASE and complicate the work load?

Secondly, while you are correct that the Common Core standards do not prescribe the represented methodology they are being presented with shiny (and expensive) new textbooks and those standards were devised by an individual, David Coleman, who has expressed a desire to teach kids using abstract thinking. Mr. Coleman disagrees that each student is unique, preferring instead to separate the “wheat from the chaff” so to speak before they arrive at institutes of higher learning.

Finally, adopting this set of standards creates two streams of students. Pre-Common Core and Common Core. If the new standards are deemed “superior” then we have created an entire class of students who are in the midst of their learning who will be seen as having been given an inferior education. Do you not think that there will be employment repercussions as a result?

Now, back to the graphic above. You are correct that there is no prescription for the methodology displayed in the graphic inherent in the Common Core. It is however an accurate representation of what parents will see be brought home from school. It is representative of the kinds of questions kids will be asking their parents about how they should answer homework assignments. Homework assignments as we all know are one of the tools teachers use to evaluate how students are grasping concepts taught in the classroom. How do you expect a parent to assist when encountering this type of methodology? I’d venture to say that they will be frustrated and confused because conceptual learning was not part of their education at least not presented in this (and several other) dubious methodology.

You want to improve education? Group kids together based on ability and not age. You want to improve education? Increase teacher pay, eliminate tenure, cap administrator compensation to within 10% of the maximum teacher pay, eliminate summer vacations and lengthen the school day. You want to improve education? Start by changing the antiquated and outdated restrictions of the public educations one size fits all approach designed to give factory workers the basic skills to keep blue collar jobs.

The Common Core set of standards are not, by your own admission above, going to create a uniform learning experience. It is merely a fresh coat of paint on a broken down jalopy of a public education system.

The graphic serves the purpose it is intended to serve. To get parents to ask questions and object where they see fit.

Stackey says

Thank you very much.

Sara Webb says

Homework is a major topic. Homework is not an assessment that tells me what a student knows. In fact, it is often misleading. Either it a. doesn’t get completed. b. gets completed with a lot of one on one help, but I as the teacher don’t know that so I might think they know something they don’t. c. Is completed by the teacher. or d. is completed but is done totally incorrect and a student has internalized the wrong way of solving it. I do not believe that we should be sending home any kind of practice that this would be an issue for.

Jason Hatch says

So Sara… the anecdotal evidence expressed here in this thread that such homework is indeed coming home is what?

I also made several other points that went unaddressed.

Here’s what it comes down to…

We do not trust the “professional educators” point blank. We were told if we just have them more money, then better testing and on and on.. that then they could “fix” our rapidly declining educational standing in the world. We gave and we got no result to show for it.

Now here comes this new revelation. It’s “just standards” we have been missing.

I’m sorry but I call bullshit. The total package is dysfunctional. Public education needs a top down makeover. Not bottom up.

This ridiculous set of wholly arbitrary and edu-speak laden “standards” is an excuse to pillage the pockets of tax payers and give ineffective educators another pass. Another way to say that they bear no responsibility for the mess they’ve helped to create.

The graphic in question is doing exactly what it is supposed to do and is a highly effective propaganda piece to engage parents to challenge these “professionals” on their grasp of the standards and what they are supposed to achieve.

And for those who are claiming that they’ve been using this method for years… show me the effects. Not anecdotes. Show me progress in a tangible form.

The fact is that you can’t. Making these changes is not the panacea that you would have us believe and you have a lot of nerve being offended that parents won’t just swallow another “magic pill” prescribed to us by the same set of edu-quacks who’ve promised us solutions before.

How can you proudly proclaim the need for this and yet claim you’ve been doing. such a GREAT job all along?

That hypocrisy is nauseating.

Sara Webb says

I apologize for commenting on only one part of your earlier post. I chose that one part to comment on because I believe that the idea of what homework is and should be is a very important topic of conversation when looking at education today. A LOT of the problems presented by parents concerned with common core come from statements about how they cannot help their child with their homework because they do not understand it.

I have responded to many of the comments on this blog, and others, and I felt that sometimes lengthy responses where I address every point made comes across as arrogant or is ignored because no one really wants to read that much.

I have data to support what I do. Oh yes, that crazy point of data. I have surveys given to students and parents where 84% of my students report that Math is their favorite thing about third grade. I do not use a textbook, and minimal worksheets. My students touch, feel, explore, and problem solve with math every day. I can show you lesson plans, to support that if you would like. I students discuss math, and their thinking daily. They critique each others ideas.

You are correct, I would do these things no matter what the standards are. However, with the previous standard course of study, there were more topics that needed to be taught. There were more parts for the skills that needed to be taught. There was less of a connection between grades, and it was not focused on building foundational skills. I could show you this by comparing the old and new standards side by side.

Of course, there are bigger issues than just the standards. My problem is that EVERY concern gets blamed on common core.

Where in Common Core State Standards does it mandate that students should be assessed with multiple choice tests?

Where in Common Core State Standards does it proscribe homework?

Where in Common Core State Standards does it say that students must use “crazy math strategies” or be able to perform math operations in just one way?

Where in Common Core State Standards does it say that you must use a certain program to teach?

That’s right.. it doesn’t. Those are all issues, but they do not mean that the standards are bad.

I haven’t been teaching this way forever. In fact, in some comment on this page I actually explained that. (I am pretty sure it was this page, but there are so many comments it is hard to remember.) When I started teaching I taught using the traditional methods. I would teach, students would mimic what I did, and I taught a lot of little tricks. Key words in word problems, which is great except that they are only true some of the time. My favorite mnemonic to hate is the old PEMDAS, or Please Excuse My Dear Aunt Sally. What do any of those things mean? And by the way, they are also not accurate. It isn’t always M then D… Sometimes it is D before M.

I hated teaching math. I hated it because it was A. Boring! and B. i felt like I was a robotic teacher trying to make my students into little computer robots who could follow processes.

It was frustrating because I had students who could do skills in isolation really well, but couldn’t apply it when it was time because they didn’t understand the concept well enough. I would watch them FAIL the End of Grade test when their grades all along were much higher. I think the highest percentage of students who passed the math EOG in those first few years was about 60%. It was a problem. Then, as they started discussing the shift to common core before we started to implement it, I realized the problems.

I made the change. Was it easy at first? No! The students had 3-4 years of experience being taught to be robots. They wanted to have it the easy way. Materials that we had in our district led us to rote procedural teaching. I had to make a change. I am so glad that I did! Now, my students pass at a much higher rate. Even this past year, with harder standards, and more challenging test, 80% of my students passed the Math EOG. That is data. It works. They can apply the skills.

It wasn’t a problem of “Just Standards.” It was a problem of the fact the way that we learned and the way that I was taught to be a teacher was focused on procedures and rote memorization without thinking.

You asked about what happens to the people who are “pre-common core”? THey are already at a disservice. Those same people everyone keeps complaining about not having any number sense, not being able to do anything without a calculator, not being able to do basic addition and subtraction. Those are the people who learned to memorize procedures.

I have never said that putting more money into assessments is the right idea! However, I do think that it is important to pay teachers a salary that is liveable! I love what I do, but if it weren’t for the fact that I have an amazing administration team, phenomenal coworkers, and my neice and nephew at the school where I teach, I probably wouldn’t continue to do it because I can’t afford it. That is a problem. Our best teachers are facing this question on a daily basis.

I am not offended that parents aren’t just “accepting it.” However, I see the benefits on a daily basis. I recognize that parents don’t have the same experience as teachers. Often, outsiders only see the end result, and not the journey to get there. The journey is so important.

Since you wanted a comment on all aspects of your posting I would like to add that your idea of ability grouping students rather than age grouping students is not appropriate when put into practice. Do you think that it is ok to have a 7 year old in a classroom with 15 year olds? But maybe they have the same abilities. Or you think so, because the 7 year old is really good at procedures. But they can’t apply formulas to a problem unless they are told to do it. In fact, they used to ability group students. Someone else just posted about that in response to the idea that the people did math “the old way” and put a man on the moon. Yeah, they put the dumb kids in the basement. Well guess what, Einstein was a brilliant mathematician. But, he did not do well in school. Should we let the next Einstein, who does not learn best by being a robotic procedure doer rot away in the basement with the other “dumb” kids?

Jason Hatch says

Sara speaking as on of the “top kids” , who was isolated (literally) from my peer group and forgotten by standards based education through out elementary school I can say that it doesn’t work on that end either. Please don’t force me to point to the endless amount of resources devoted to those on the “bottom end” of this farcical line we have drawn in education.

You miss my point and make it all at the same time. The WAY we educate students is broken.

The students aren’t. The problem isn’t a sudden realization of substandard expectations.. the problem is that generations of educators allowed that to happen. All the while blaming everything except HOW they were doing the job.

Now these same people want us to trust that they have it all figured out this time and I’d we will just give them some more money for new texts and such this time they’ll pick “good” ones.

Why?

Because the CCSS?

Will there be testing required?

Do results matter to school districts on these tests?

Will those districts then not buy texts and teach to those tests as a means of self preservation?

The tests, required by the CCSS will indeed drive curriculum choice. As those tests are required to measure the standards, and those asserting the standards are also choosing the test…

It is a bad idea.

It doesn’t matter how banal you make one aspect of the reality of the adoption of these standards sound. Taken together the CCSS and it’s subsequent consequences are a huge mistake. Much more discussion and many more voices need to be heard from.

I stand by my defense of the photo above if it engages more voices. It’s dismissal as simply “wrong” fails to see the point and I will again return to Einstein to make the point…

“Everything is relative to one’s perspective. ”

How parents are experiencing the effects of the adoption of Common Core is indeed a valid condemnation of its content where it’s content is the cause of dubious actions and choices on the part of those who are tasked with its implementation!

shawna says

I am all for teaching in a variety of methodologies, however, using estimation in a extended amount of steps to teach something as easy as placements is crazy. The standards behind common core (having a set baseline of where someone should be in each subject before passing a certain grade) is great, as long as it doesn’t restrict those that are beyond those baselines. Do I have a problem with the way I learned math, no, can I teach it to someone much younger than me who has lived a unprivileged life, yes, and I have. No, I am not a teacher, but I am a mother. Would I get upset if my daughter was bringing her math home to me and saying she had to do it in the way of methodology 2, possibly but only because it doesn’t make sense to me but it might to someone else, that’s what counts is that it’s a way to do something that makes sense to them that allows them to be able to do it that otherwise could not. By the way, the old method works just fine for my daughter too.

Bobbi Dano says

Thank you Kevin Olson I finally get method two…

And huge thanks to happiness this was exactly what I needed to explain the nonsensical image.

Carrie Wells, Ed.D. says

So glad you found this post helpful!

Grace says

I’m amazed that so many teachers who claimed to have successfully used this method managed to utterly confuse most of the commenters here without once saying, “Imagine that you are using a number line. Starting with the smaller number, round up to easily managed numbers. Round up from 12 to the nearest 5, which will give you 15. You’ve added 3. Now round up to the next 5, which is 20. You’ve added 5. Now round up to the nearest 10, which is 30. You’ve added 10. We are counting to 32, so add the remaining 2. You’ve added 3, 5, 10, and 2. Rearrange the numbers for ease. 2+3+5+10=20.”

This would have made much more sense. A good teacher meets her students at their level. As, clearly, none of us were informed that method 2 is meant to teach counting up as a subtraction strategy, the method seemed random and arbitrary.

Furthermore, I’m tired of hearing the “CCSS is a set of standards, not a curriculum” defense. If that’s the case, then testing needs to be unwound from the curricula that require these methods. Don’t force a kindergartener to take a computerized test that requires that they demonstrate methods not included within CCSS. Don’t claim that new instruction methods are about learning through touch and then test children using 2D images on a computer screen. This is where the backlash comes in. My kids have come home with homework that I could not decipher, whether because of a lack of clear instructions, no instructions, no context, etc., or the completed homework was returned marked incorrect because, although the problems were solved correctly, the overly simplistic (in this case) method required was not used. Again, no instructions or examples were provided.

As parents, we constantly hear from teachers that if our children are to succeed, we must be involved. We HAVE TO be there for our kids to pick up the slack when the schools don’t get through to our kids. We’ve always known this, and clearly you do, too. So you can’t change the system overnight, fail to provide us with the information we need, and then blame us for being closed minded and anti-progress when we object. These methods are confusing. If you maintain that they are not, then our children should be able to explain to us what they’re supposed to do- they can’t. They should be able to complete their homework without our help- they can’t. Their grades should be improving- they’re falling.

Some people are so in love with the idea that they’re experts that they forget their place. WE are the parents. These are OUR children. We have every right to ask questions, object when our children’s educations are suffering, demand change when the latest craze fails- again. The responses to concerned parents are telling. “Yes, your pre-CCSS child is falling between the cracks, but wouldn’t it have been awesome if he had been CCSS educated from the beginning? No solution for you now, though. Such a shame.” Or, my favorite: “Your public school education clearly failed you, as your spelling and grammar are horrific. You have no right to an opinion on the quality of a public school education.” Arrogance and blindness to irony are a favorite combination of mine.

Linda Gojak says

No matter how you are thinking about this…what an incredibly awesome conversation about the thinking behind the procedure. That is what we want to have our kids doing…yes, as early as kindergarten!

Carrie Wells, Ed.D. says

Exactly, Linda!

Drewcifer says

I am the smartest person when it comes to mathematics. (Not literally) . Do they really expect this to be easier for kids to learn than the way we were taught as kids? Really? This is some of the dumbest crap I have ever seen or heard of!

Heike Frijouf says

Method #2 just seems to make a simple problem so complicated .My 6 year old daughter understands Method#1 and 2 but she is really getting bored with having to break it all down and is frustrated because of it. Also, this is just one problem. What is really frustrating to my daughter is having to write explanations of how she solved a problem. Her ability to write and express herself clearly is still limited at her age. I don’t know what the answer is but I am not so sure if the Common Core Standards is the answer.

Chris E says

The old way is obviously the quickest and easiest and every child learns what the ones position, tens position, hundreds, and so forth are early on so they OBVIOUSLY know that the 3 in 32 is a tens position. this new way is incredibly retarded in complicating things for them. Im sorry, but I made straight A’s all the way through College Algebra and Geometry, and would NEVER want my child to have things complicated with having to “imagine” a “friendly” number like a 5 and work that into the equation. 32-12=20. work from right to left, get answer, MOVE ON TO NEXT. 2-2 in the ones position =0, 3-1 in the tens position=2, answer is 20. Im sorry but if someone doesnt know numerican postions they need to go back to lower grade level and start over as they have missed something important there. The entire purpose of the old way is that it teaches you the ability to solve the problem quickly and efficiently, to the point that you are able to do them in your head and master it, not come up with 5 problems in your head, OR have to write out 5 problems on a sheet of paper to answer it. IN ALL HONESTY, if you were given that problem and told to do it in your head, do you REALLY, i mean SERIOUSLY, think of 5 seperate problems in your head to answer it? No, you dont. Didn’t think so. Nor are you going to “imagine friendly numbers like 5” to answer it either. If a teacher wants to give a shot at teaching this common core for extra credit, go for it. But my children should not have to learn this as a standard to over complicate a simple problem that can be worked out in their head and masterd in 2 simple steps.

CommonSince says

Nice work by you “Education Advocates” calling for Common Core. Common Core is the answer to a vastly overpopulated education system where teachers are under-paid and aren’t held accountable enough for their performance. The answer should be to increase teacher to student ratio and spend more time with individual students in tutoring sessions. Instead, you want everyone to assimilate to the same way of thinking. The US has over 300 million people and you want the federal government to mandate a method of learning from each and every one of them.

But, by all means, keep shilling for these “standards” that have no hope of being met. Common Core is the equivalent to taking Tylenol to treat a virus.

Jilynn Parmly says

Common Core does not mandate a “method of learning.” Did you read her blog? It is a set of standards. That’s all. You can easily download the Common Cord app and read the standards. If you do that you will see for yourself. You won’t have to take anyone else’s word for it. Any methods or materials come from individual textbook companies and school districts. I’m a teacher. I’ve found this year that whenever parents, students, or teachers dislike something in the curriculum, evaluation system, district guidelines, etc. they blame it on “Common Core.”

Sara Webb says

And to add to that, it is usually something that is not an accurate complaint either. It reminds me of when I was in high school and the Harry Potter books came out. Becuase some groups said they were bad, and had devil worship and witchcraft, many people were vehemently against the books. WIthout reading the books they would quote what they had heard to be problems. I don’t mind objecting to something, but can we be specific and read it ourselves to make sure that the objection is a:accurate and b: your own opinion?

Lynann says

32-12 two minus 2 = 0, 3 minus 1 = 2 Answer is 20(twenty) not two zero Simplicity people simplicity

Sara Webb says

I think you may have missed the previous messages about this same exact response. It is not “3 minus 1” and it is not so challenging with this exact problem, but the challenge comes when you have a lot of arbitrary things that have nothing to do with the meaning behind the numbers.

By the way, if I were solving this, with strong number sense and the ability to manipulate numbers, I would do none of those ways. I was always told that I did math wrong as a student because I was not a robotic procedure doer. I would have simply reduced both numbers by 2 because 20-10 is way easier to solve than 32-12. The answer is still 20. By really understanding the base 10 number system, and how to make tens and hundreds, along with a strong understanding of the number line, you can do all kinds of math operations even faster.

Research how kids in Singapore use an abacus to solve crazy big math problems way faster than any traditional way here. It is pretty impressive.

Raevyn Morrigan says

As a substitute teacher for 11 years I have seen a dozen or more ways to do/explain mathematical concepts and theories. I have seen teachers use both of these methods and the “old” way. It does not matter HOW you teach a student math, just that the student understands what you are teaching and is able to reproduce the results with thought and reason. A teacher needs to show several ways for the problem to be accomplished. When I teach I often have several ways to do the same problem. I don’t care about Common Core/NCLB or any other government claptrap. I care that at the end of a lesson most or all of my student understand what I am teaching. Most teacher that I know follow this idea. If State Standards are met by the end of the year and your students know how to use logic, reason, and problem solving to do all of the “required” tests. As for being a parent teaching your child. Use what you know to teach your child. Just because the teacher or book uses a particular way does not mean you need to follow. But please don’t be disparaging of the ways you see…it is a terrible thing to hear the disrespect from a student because of the words of a parent.

Don't confuse the students says

A teacher of math should never send math homework to a home that the parents do not understand. A ‘new’ math teacher must know that sending homework to a clueless parent is not acceptable. This is what parent/teacher conferences are all about

Debbie Sutherlin says

I think this all boils down to…we don’t like change! Well wake up! It’s a different world! Maybe if we had been taught the why behind what we were doing… it would have made more of us better with math! Thank you for this post!

Carrie Wells, Ed.D. says

Agreed, Debbie. Thank you for the feedback.

Kevin Olson says

Can anyone tell me how to discontinue e-mail notifications once someone comments on this blog post? I initially wanted to know when new comments were added, but I’m now getting high blood pressure reading some of the ignorance and misinformation spewing from people.

“I was a student, therefore I know all the best ways to teach.”

“I got A’s all throughout school and took quantum mechanics and measure theory in college. Therefore, the way I learned math is the only way everyone should learn math.”

“Any student who doesn’t understand the standard algorithm is obviously deficient and should be sent back a grade.”

“The standard algorithm is obvious to me, therefore the only logical conclusion is that it is obvious to all others.”

“Common Core was designed and created by the Devil to trick all of us into raising a generation of mindless robots who are slaves to the government.”

Please, make it stop!!

Carrie Wells, Ed.D. says

Too funny!

Krista says

Thank you for this post! I’ve been arguing about this graphic with some local people on FB, and you stated my argument much more succinctly than I could!

A couple of points. First, the math curriculum that I taught in 2003-ish taught all types of methods for solving math problems. This isn’t new, people! I was frustrated at first, because my brain just doesn’t do well with mathematical thinking and reasoning. I had an a-ha moment when I was struggling to teach a lesson and one of my brilliant fifth grader students understood it better than I did. I actually had her team teach with me! There were a lot of points during the year that I thought, “Wow, so THAT is why (insert math concept here)…” At that point I was sold, because I was learning the actual concepts right along with my students. It was hard, but we all understood so much better because we weren’t just drilling math algorithms.

My second point is that Method 2 is just like making change. I often hear people talk about our kids not even knowing how to make change ($$) anymore. This is the same concept, friendly numbers and all. Something costs $3.42 and you are given a $5 dollar bill. You wouldn’t take $5.00-$3.42. You would could out 3 pennies to get to $3.45, a nickel to get to $3.50, two quarters to get to $4, and then a dollar to get to $5.

Peter B says

Man.. still going the long way round. For those of us with dyscalculia, the above example are a nightmare.

When we were taught take away in school it was much simpler.

32 –

12

__

2-2 is 0

3-1 is 2

We did it in columns. Ones, tens, one hundreds ect.

answer 20. Much simpler.

Elizabeth Bailey says

Thank you for your excellent explanation.

Carrie Wells, Ed.D. says

You are so welcome, Elizabeth.

Math Teaching and Learning Professional says

There are so many problems in math class as well as our every day lives where the standard US algorithms are not the most efficient. When I see students who have been programmed to use the algorithms instead of to think and make sense of the problem, using what they know about the base ten system, place value, the relationship between operations, and methods that might be most efficient for the problem at hand, they make mistakes and they lack perseverance when they get to a problem that they have never been programmed to do. I once had a new student tell me that she did not want to learn any of the ways that students were coming up with to solve a 2-digit by 2-digit multiplication problem because she just wanted to memorize the times tables. She knew her facts and said she wanted to memorize every multiplication problem that exists and not have to think about any steps (traditional or not).

Here are some examples of problems that are more efficient if you reason through using something other than the traditional US algorithm.

17+6

1000 – 998

1.5 x 20

3 – 1.9

15 x 12

99+17

There are genuinely valid arguments out there about why we should be skeptical about the Common Core. This is not one of them.

Instead look to those of the early childhood experts who have found standards that are not developmentally appropriate according to research, and of those who say that we are rushing into assessing them too quickly for schools to have had time to transition.

Frank says

I simply can’t believe you people. In life, all I want the kid to do is subtract and get the right answer. In business and in life I don’t have the time for him/her to go through a 5 step process. Perhaps that’s what’s wrong with our education system today. Too many masters and Doctorial degrees trying to convince me that I can’t figure out that 32-12=20. NEXT PROBLEM!

Jon says

I really appreciate the time you took and the way you explained it. Thanks.

DMC says

Thank you Jason. I couldn’t have said it better myself.

ADJ says

Thank you, thank you, thank you! So much misinformation it is MADDENING!!

Tim says

Your expansion of ‘methodology #1’ is nonsense. Yes, students need to understand the difference between the tens and ones places, but that doesn’t constitute a *step* that is performed every time they subtract. You’re just adding superfluous filler to make it appear that the two approaches have similar complexity.

Tina says

I am really surprised we are asking a kindergarten student to think abstractly. I teach math and in college, when studying the human mind even middle school age students struggle with the abstract. I’m all for students understanding the why’s in math but I think we need to think about what their brains can handle. And yes, some students will be able to reason abstractly before others, but on average it is usually during the early teen years that students are able to move from a concrete idea to abstract. Just food for thought.

James Hazlerig says

Some years ago, I taught at an alternative high school in which every teacher was basically a roving tutor for any student, so I might be teaching math one minute, science the next, and composition the next.

Most of the students there were struggling with the math that typically falls between long division and algebra: fractions, decimals, and negative numbers.

The reason they were having trouble is that all they’d been told how to do was follow various sets of steps that had no meaning to them, because ultimately they didn’t grasp any of the concepts represented by fractions, decimals, and negative numbers.

So I would take out a handful of change and quickly explain all three concepts in real world terms. Suddenly, the steps were no longer arcane; instead it was easy to make the calculations.

BTW, I have zero training in teaching math. My degrees are in English. But I taught math as something that has meaning, not as an arbitrary series of steps.

That’s what Common Core is about: understanding that there is more than one way to skin a cat.

Parents who can’t open up their minds to consider different algorithms are that way because the education system stunted their imagination by teaching “standard” algorithms as though they had been handed down by God.

Sara Webb says

Yes!!!!

Kimberly says

OMG! People got so caught up in the Math problem that they forgot that the article was about Common Core! Common Core is all subjects, not just Math. That Math problem, at least the way it is solved, is a reflection of CGI: Cognitively Guided Instruction. It allows children a variety of tools to solve math problems their own way… In addition to focusing on other things.

Alisha says

Yikes! I’m so glad my son graduates from high school this year!

just me being me says

Browsed County, home of the hanging chad…say no more!!

Karen L says

Here is the scoop on the common core math. The language in the standards calls for controversial reform math, otherwise known as constructivist math. This is not an assumption or a theory, it is confirmed by Professor Jon Star from Harvard.

Baby Boomers will remember the “New Math” in the late 60s. Back then we “needed” reform math to keep up with Russia over the Sputnik Crisis. Parents raised hell and it was gone in two years from the mainstream of public schools. In 1989 it returned. Now the “crisis” is that we must compete with China.

The reform math standards come from the National Council of Teachers of Mathematics. They are reformers and have tried this at least twice before in 2000 and again in 2006 and it failed miserably. This time, they piggy backed it on to the Common Core Standards to make it more sustainable. Language that calls for students to explain, make an argument for, construct, draw diagrams or pictures, and consider math in an “abstract way” are constructivist/reform math standards. They are presented as word problems that often do not line up with the reading level of the student. The standards created by the NCTM were used by many schools as part of assessment under No Child Left Behind. The math scores did not change and have not improved since 1989 despite their attempts to mainstream these standards.

Common examples include TERC Investigations Math and Everyday Math. The problem is that in grades K-5, most students are concrete thinkers not abstract thinkers. This approach has been PROVEN to be cognitively inappropriate by scores of experts in childhood development. Yet each generation the reformers and corporate profiteers try it again only this time all of the researchers and reformers were paid by Gates (NSF, Harvard etc.).

Professor Jon Star from Harvard studies this now along with Vanderbilt University and the National Science Foundation. So essentially, our public school kids are once again an experiment, and this one has already failed for two generations (24 years).

Magically, without reform math, we still manage to be a force in global trade, a leader in innovation and entrepreneurship and space exploration. Check out the NCTM and see how proud they are of their reform making it into CCSS.

http://www.nctm.org/news/content.aspx?id=39349

Karen says

I learned the old way, my child began learning the old way…at that time he excelled in math..common core was brought about and now he is lost and has given up, even says he is stupid. I am lost as well, and as a working mom who wants to help her child, it is very hard to sit down at night after working til 6, starting laundry, cooking supper, trying to have family time and still do homework. It takes me sitting there wasting time to teach myself the new way before I can help my child when all along we could have done it the old way and saved time and frustration. We older parents don’t stand a chance of helping our children and this leaves them upset and unhappy. I also know that out of 27 kids in my sons 7th grade math class, 19 of them are failing…..either common core should be forgotten or they need a new teacher, because obviously it isn’t working. These kids are being failed by the adults that say this way of teaching is best.

Carrie Wells, Ed.D. says

Thank you for sharing this information. I was not aware of this historical portion of the Common Core math goals.

Linda Gojak says

While I appreciate an informed debate, there has been misrepresentation of NCTM in at least one of the comments. And, as a lifelong NCTM member, an award winning classroom teacher because of the success of my students and a very good undergraduate and graduate education in mathematics education, I must clarify some of the misstated facts from some of the previous posts. NCTM has never advocated for a specific approach to teaching mathematics (not constructivist, not traditional). It has specifically stayed out of that debate. What it has advocated for is that children learn mathematics with conceptual understanding as well as procedural skill. Too many of our students leave school without the basic understanding or skills in mathematics to get a job..a basic entry level job. Even the cash registers at McDonald’s do the math for them! Common Core has embraced the same intent with more specific standards for each grade level than NCTM’s standards. (NCTM’s standards defined a vision for exemplary mathematics education for ALL students.) CCSSM also calls for a balance of conceptual understanding, procedural skill and applications. It does not tell how to teach. You can use constructivism, you can use direct instruction, you can use traditional methods. One other important commonality between NCTM and CCSSM is the focus on problem solving. Conceptual understanding leads to successful problem solving. If I can perform the operations and I have no clue what it means…how do I even know when to use it? Finally, NCTM did not write the Common Core but it has committed to supporting its members and all mathematics teachers with tools for successful implementation.

This is not speculation. It is fact. And, if we are going to move the mathematics education of our students forward then we must truly understand the issue and make our decisions on facts…not speculation.

Linda Gojak

President, NCTM

Carrie Wells, Ed.D. says

Thank you so much for this information, Linda. This is beyond my realm of knowledge, so I truly appreciate the feedback. From the perspective of someone who excelled at math early in her educational career, but started to break down around Algebra 2 and Pre-cal, I wish I had a firmer grasp of how to manipulate numbers and justify my responses earlier on, and perhaps I would have continued to excel. I remember getting to ‘proofs’ in high school, recognizing their significance, but feeling unable to perform the type of task analysis required to really understand what I was doing during each step of the problem-solving process.

While in college, I took a course in elementary math education, and I remember it being incredibly eye-opening because it broke down math. It finally explained the WHY? to me in a way that I could understand well and teach to others. The most important lesson I learned: operating in bases other than 10. We are so used to thinking in base 10, that when given a different base, even something familiar to us like 12 (for inches) or 16 (like ounces), we become so easily confused. My hope is that teaching a variety of approaches to math early on (in part because Common Core is requiring students to learn a variety of methods to solve a problem) will create more proficient problem-solvers and independent thinkers.

Linda Gojak says

At this point I will bow out of what began to be an intelligent conversation and has turned to name calling and, quite frankly, online bullying. I will end by saying we want to do what is best for our kids and their futures. Teaching for understanding — whether it is the traditional way or a way that is based on kids developing strategies that make sense for them, is our goal as classroom teachers. When the conversation turns away from what is best for kids…then I will not continue to be part of it.

Grace says

You really shouldn’t abbreviate to CCSSM or NCTM. Wouldn’t it be better to write those out each time to show that you completely understand what you’re saying? Using the same standards now imposed on beginning math learners, abbreviation is a lazy shortcut. It doesn’t matter that you know what the abbreviation means, and I know what the abbreviation means. No; in order to demonstrate that you are a fully actualized human being who has a thorough mastery of the English language, you must use the most tedious method available.

I’m not trolling. I’m simply applying this nonsensical method everyone seems to love to real life examples outside of the math class. I don’t understand why we should force a new convoluted method onto children who are confused by it under the guise of helping those who can’t learn the traditional way. You’re either forcing an unnatural method (ie. the traditional way) on the few who learn best with the new method, or you’re forcing a different method on the majority who learn best using the standard way.

I think very few people are opposed to introducing new ideas to their children. By all means, teach them to look at the world in new ways. Just don’t force them to demonstrate these methods on their tests. If CCSS are separate from teaching methods and curricula, then the tests should not demand that children demonstrate an understanding of the methods found in the new curricula.

Brandon says

Way to completely misrepresent Common Core. The people pushing this will lie, cheat and steal to get it implemented. It’s all about control and money. Why in the hell would you ever teach a kid to do a SIMPLE subtraction problem like this? I’m a well educated 35 year-old man, and I can’t make heads or tails of methodology #2. If people think kids are undereducated and ill-prepared when they graduate high school now, can you imagine the piss-poor shape they would be in after 13 years of this ass backwards education?

I can hear it now:

“Close out that cash drawer, Emplyee A.” “Okay, but I need a chalk board to diagram all my addition and subtraction.”

“Is that right?”

“Yes.”

“You’re fired.”

Dr. W.R. Gilmore says

I do not know if I like Common Core or not. I do trust local teachers here who are advocates of the standards set forth in CC…However, I was terrible at math in school…But one day a brilliant teacher explained to me that math was truth…2+2 always = 4, always…When I understood that math was simply the truth, the methods were easier for me to understand…It seems reasonable to me to teach students that math is simply finding out the truth about the problem posed to them and let them discover through patient guidance and teaching what the true answer is….Just find out the most effective way to get to the truth that is adequate for the vast majority of students…Math is truth…It’s that simple…The most efficient way of arriving at the truth seems like the best approach to teach young children about math….It seems like the more complicated we make it, the harder it will be to get to what is true….

wwhitlock says

Thank you for this post. I need to follow your blog. I’ve been trying to assure parents that CC is nothing to be afraid of. Educrats that push people around in the name of CC is another thing.

I particularly like your reference to tech. The argument that we learned it without calculators is irrelevant to today.

Calculators and computers are not going away during the lifetime of today’s students. They need to know the why so they can check the computers work.

Computers are the slave. Humans are the master. If the humans don’t have higher order thinking than the computers it turns around to humans being slaves to computer masters.

Stackey says

I disagree with Common Core. I don’t believe that a top down drive of education from one point will better the education of our children. That said, I agree with you that AT THIS MOMENT Common Core is not a curriculum but merely a set of standards. The problem that I see, from all aspects, not just math, is that the implementation of the “Common Core” standards is often BADLY done in the name of “Common Core”. From morality issues that I do NOT want my child to make decisions on without conversation from an adult with her best interests at heart (in English classes) to confusing math techniques where the TECHNIQUE is graded, rather than the correct answer…these implementations are at the very least cumbersome, if not downright damaging to the learning process.

As to the math. I have ZERO problem exploring different ways to understand why 32-20=12. Let’s try it both ways. Let’s pull out the abacus and change and sparkplugs…Let’s get out a grid and add/subtract/multiply/divide that sucker 9 ways to Sunday. And then once they understand WHY…let’s just do it, the fastest, easiest way…and then let’s memorize that…’kay?

I taught Microsoft Certification…strangely enough, the people who failed the more MATH-RELATED tests (Specifically, TCP/IP and the routing area of several others) failed because they didn’t just KNOW IT by rote, but had to figure it all out. I recognize that is a small, insignificant sample, but I also taught a 4 grade math class a few years ago, in it was a big jump into division, the ones who FAILED to understand and succeed making the jump from multiplication to division were the ones who did NOT know their multiplication tables by rote, but instead had to figure them out. Those two tiny samples convinced me that for people to SUCCEED in math, they do need to understand the basics, but then they need to memorize the basics so that the equations can just be DONE.

Our Education system broken because we are so busy adding new line items to what needs to be taught that we are not teaching the basics well. I know that it seems simple…but REALLY teaching Reading, wRiting and aRithmetic and TALKING to our kids and to each other’s kids in society helped bring about some of the great minds. It enabled kids to read and interact with the great minds of the present and past and form opinions because they understood and could communicate. They didn’t need to be taught HOW to think because they were able to be part of the greater human discussion and understand because they’d been taught those 3Rs as fundamental tools, instead of being plunked in front of the electronics all day and virtually ignored. Unless we, as a society, slow down a little, unplug a little and just understand / teach the basics, this pass at making it all better will fail.

Common Core is NOT better. Common Core is merely another list that MOST of us won’t want to or will not be able to check off. What you do not mention here, perhaps because it hasn’t been addressed, is the very real possibility that this is just the beginning. That Common Core WILL be a top down curriculum that will be required in all states in the coming years. The possibility that it will be a measure with which to deny funding, deny certification, deny accreditation, deny employment. I don’t know about you, but it also sounds like a perfect way to destroy diversity, creativity and ultimately genius. The teach-to-the-test mentality has already destroyed countless opportunities for excellent teachers to teach. Why would we add to that legacy.

JeremyK says

It’s amazing how most of the people with issues with new methodologies and standards have the mentality and approach like, “What was good enough for my maw and paw, was good enough for me. And my young’uns ought to do their book larnin’ the same way”. What was wrong with the “old way”, you ask? Kids had trouble understanding it. That’s why the things kids are doing in 3rd grade now, you weren’t able to do until the 6th grade. They aren’t making anything more complicated. More complicated for YOU, sure.. Because you didn’t learn this way. But not for the kids. They’re able to do things in ways THEY can understand it, and it works. However, these are METHODS, not STANDARDS. So when you complain about and express your disdain about these “new ways for math”, and then label it Common Core, you sound totally ignorant of the subject.

Stackey says

One assumption that you are making here is that kids SHOULD be doing things in 3rd grade that prior generations did not do until they were in 6th grade.

Another is that they ARE understanding and growing in 3rd grade at a faster rate due to these methods.

Research and testing shows that by and large they are not learning at a faster rate and that the pressures placed on them at earlier and earlier ages is detrimental to their well being. As a matter of fact, I’ve read several studies that compare the early start kids to kids that waited a bit to learn the same things and they find that those kids that started slower completely catch up within weeks or months. So, all the pressure is completely unnecessary for long term educational health.

At least based on the testing that is being done these days. That IS what all of the stink is about. They aren’t TESTING like they should. No matter WHAT they are capable of doing in third grade.

My answer? Who cares.

I would rather have a kid that is not stressed, learning with a teacher who enjoys his or her subject who has a fairly care free childhood. A child that has time to explore HIS genius, whether that is football, or painting, or music, or computers, or whatever, instead of jumping through some sort of method hoop that he doesn’t need to hit a mark on some test that doesn’t actually mark any more than his ability to take a test.

The question we should be asking is should we be TESTING in 1st, 2nd, 3rd, 4th…and if we should, should we be making it a test that can damage both kids and teachers? If we were ONLY using these tests to help teach each kid better, it would be one thing…but that is NOT what is happening.

Melissa C says

I’m a high school math teacher with a Bachelor’s in Mathematics Education, a Master’s in Secondary Mathematics Education, and a Graduate Certificate in Educational Statistics and Research. My issues, and there are several, is NOT with Common Core. Dr. Wells is RIGHT! Common Core is a new set of standards that aligns the nation in what is to be learned at what times and in which classes. That’s great! My issue (and what I think most of you are struggling with) is that the TESTING systems being used to decide whether the Common Core is fruitful (PARCC is the one I’m dealing with, but I won’t go much into that here) are much higher level “THINKING” questions than our kids – or WE as students – were ever asked to perform. Did I memorize my multiplication facts? Yes. Did I learn the “old way” of subtraction? Yes. And am I able to do those in my head without any issue? Yes. But then I went on to learn the WHY behind it, and it all makes more sense now. You KNOW that when you add two even numbers together, you get an even number. You could even give me examples. But I can show you WHY, in a way that encompasses every possible example. My 9th grade geometry students can PROVE it to you. And they want to know! Kids are naturally intuitive, and they can learn the why. Give your teachers the time to teach it to them. Just because you didn’t do it that way, or just because you don’t understand it doesn’t mean it isn’t correct or a useful method.

Please take a step back and realize that the standards of Common Core are NOT the enemy, if there really even is one. The Common Core standards do NOT tell you how to teach, nor what the end product needs to look like. The assessments do. Have you SEEN the sample assessment questions? They’re not the same as what we did in school. The way of thinking and understanding is evolving, people, and the students need more than just the “how” to be successful at it.

For example: In school, I was asked to take a pattern, say, “there are 15 seats in the front row and you add 2 more into each successive row. How many seats are in the 15th row?” End of question. My students, in 9th grade Algebra 1 NOW are asked the following: “John is bidding on a construction job to renovate a theater. The dimensions of the theater are shown in the diagram below. (picture would be shown with dimensions in feet) The seats John must install in the theater are as given below. (picture of the chair with dimensions in inches) The seats must be 7 feet from the stage, and allow 5 feet in the back for a walkway, with 22 inches between each row. There must be 3 feet on each side of the theater as well. If John wants to install 15 seats in the front row, add 2 seats in each successive row, and have 25 rows in his theater plan, will his plan work? Why or why not?”

I kid you not. These are the “tasks” our kids are asked to perform these days. NOT the “simple” calculations we did as kids, where 10 problems fit on one side of the page. Each problem is a task involving multiple concepts and critical thinking. I guarantee you that what my kids have to do today is more applicable to their lives and actual skill sets than what I did in school. The Common Core State Standards that go with this task deal simply tell what concepts the kids need to know to solve it. They do NOT tell the teacher how to teach it, nor the student how to answer it. They only make sure that I, as the teacher, include the necessary concepts in my teaching curriculum so that my students have the structure to address the more complex tasks.

The world is changing, folks. Demands are being made on our graduates that require more forward thinking than you or I had to do in school. What worked for you in school (or me) will not work for our kids now. So changes are made. We adapt, and we move forward. Common Core is not the enemy. Neither is your kid’s teacher.

Stackey says

Your very well thought out answer makes me sad.

Why do every one of our kids have to be assessed that way? Why would they make them answer this question that involves spatial skills that any full blown engineer would have focused on because that is his bent and would have loved to answer…but will just make the more lingual among our students feel like they can’t possibly understand.

I believe in our teachers and support them in any way that I can…but my question is WHY? Just because we can take up the brain space of their childhood with this stuff, why would we do that?

Thank you for your answer, I understand more, but I like it even less.

Melissa C says

And I’m right there with you. My students have not yet been taught to think in the way that they will be assessed in the years to come. (Heck, I haven’t been taught to think that way, nor to teach that way!) They’ve spent the last 9-10 years of their education learning the “rote memorization” method, which again has worked for most of the nation’s adult population thus far. BUT! The tests are coming, and our kids will be assessed on those tests, and our teachers will be evaluated on the kids’ performance of those tests, so… yeah. As a teacher, I got an advance look at the test questions my kids will be expected to answer in the near future… and I’m scared. That tells me something about the tests, and I worry what it will mean for my students’ esteems and motivation for school.

Sara Webb says

Melissa, The transition time is hard, I totally agree. But if we started new standards with Kindergarten and added on one grade every year, it would take 13 YEARS before the change would be addressed in 12th grade. Talk about leaving behind a generation! Every year since we started implementing, I can see a difference in the students. It is coming. The testing is an issue for a whole separate topic. But, I don’t think that means we should throw away something that really is best practice for the small people because it is hard for the big people.

Carrie Wells, Ed.D. says

Great feedback – Thank you!

Allen says

What the author of the article fails to understand is that the “old way” is depicting, is not just a problem with an answer but rather a point on a number line subtracted by 12 units of measure yielding another point on a number line.

Clayton Bulice says

I believe we need standards across our nation’s educational systems. We need an expectation of what a person should have learned after 13 years of education. However, I do not understand the language of the Common Core Standards. For example, what does it mean to “Represent … problems involving addition and subtraction”? And, “Extend the counting sequence”? And “Add and subtract within 20”? I think I understand “properties of operations,” but please clarify so that I am certain.

Chris says

Carrie,

Your whole reasoning behind teaching regrouping to a bunch of hardheaded elementary school students is invalid. Regrouping should be taught to kids ready enough for pre-algebra. End of story.

I apologize to teachers because I’m pretty sure I’m getting ready to insult about 98% of you out there but, UNLESS YOU HAVE CHILDREN THAT COME HOME CRYING THAT THEY DO NOT UNDERSTAND WHY THEY HAVE TO DO SOMETHING ONE WAY IN SCHOOL THAT THEY DO NOT UNDERSTAND HOW TO DO BUT THEY ALWAYS GET THE RIGHT ANSWER WHEN THEY DO IT MOMMY AND DADDY’S WAY THEN YOU HAVE NO BUSINESS TELL PARENTS HOW THEIR KIDS SHOULD THINK!!!! Quit drinking the Kool Aid your superiors shove down your throat and begin trickling it into my children’s. If you have a student that begins to disrupt because they are showing other students how an easier AND right way of doing math then you simply shove them off to the principal’s office. Parents do not have this luxury.

Just in case you didn’t understand it the first time I said it: REGROUPING SHOULD NOT BE TAUGHT UNTIL THE CHILD IS READY FOR PRE-ALGEBRA

They can now break a quadratic equation down by regrouping and THEN use the REAL “old method” to solve the equation.

This method pushed me passed calculus in high school, stats class, and works in REAL LIFE situations like the board room meetings I have every month where if I had to do quick equations using my cellphone, I’d be FIRED.

Bruce Alan Bradshaw says

My son had difficulty understanding subtraction until I told him there was no such thing, it was just addition in reverse. Take the problem above: 32-12=?, I just asked my son, what do you need to ADD to 12 to get 32? He’s been a math wiz ever since.

Clayton Bulice says

Now that is an alternative teaching method. It is accurate, but not one I would have thought of right quick.

DawnP says

I’ve gotten some great insight into how this is being taught in my second grader’s class because one of her favorite games to play is “school.” She stands up at her white board and writes a math problem, and then says to me, “So, what strategies can we use to solve this problem?” And then she proceeds to show me several different ways to arrive at the same answer. I love the fact that she is truly learning and understanding the underlying concepts rather than just memorizing the fact that 32-12=20 “just because it is.” And the fact that she’s learning several different “strategies” to solve a problem cuts down on frustration because if she can’t figure out the answer to a particular problem using the first method she tries, she knows she has several other tools in her toolchest!

Carrie Wells, Ed.D. says

Thank you for sharing your experiences, Dawn! Sounds like your daughter is doing very well learning a variety of ways to look at the same problem.

Chris says

Now I understand why so many have a hard time finding jobs. They are probably given real world tests at the interview and it takes them 15 mins to do a problem the “old way” would have answered for them instantly. By the way, just how long would it take for someone who’s earning minimum wage what their yearly salary would be? 7.5/hr x 2080hrs. I knew the answer before I finished tying the question. Would your kid?

Meagan says

Yes, because all employers give their possible employees math questions to answer in an interview. Be realistic. People have trouble finding jobs because they are asked real world questions in interviews. You got that part right. The problem is, because they’ve been taught the “old way” they are not prepared to answer these real world questions. Their entire educational career has been made up of memorizing how to do soemthing just because that’s how it is rather than learning how to think for themselves to figure out an answer. Common core is just a set of standards. Teachers are responsible for teaching strategies to children. Students learn in different ways. For some, the old way may work for them. No one ever said teachers cants teach the old way as a strategy too. Wouldn’t you rather your child understand what they are doing rather than just relying on memorization? If they’ve been taught using common core, which isn’t all just about math by the way, they should be able to answer a real world question because they will be used to using their brain and being critical thinkers. It will be natural to them to think about what they are saying. Most parents are just mad because they don’t understand common core. People are passing judgements without being educated. They can’t help their kids as easily because they were not taught to think critically and probably get frustrated because they can’t come up with the answer to a question in a split second when helping with homework. Common core is not about how quickly you get an answer. It’s how did you get the answer. The United States used to be at the top in education. Now, because we have not challenged our students, we aren’t anywhere near the top. Instead of complaining about how horrible it is take the time to understand it.

Jason Hatch says

Testing is required. Tests drive curriculum. Point blank.

Holly says

To the author: in five years please remember how you felt about Common Core today and how you cheered it on. When the results of Common Core start to be seen, remember how great you thought it was and how you influenced parents’ thinking.

youngladH says

You DID NOT graduate high school, smart ass. You graduated FROM high school.

Brenda Payne says

My problem with the Common core is not the core but the ridiculous 10 page INDIVIDUAL lesson with 5 – 8 links that I am expected yo implement in ONE period…oh yeah while teaching one whole group and 3 small groups

Oops I forgot I don’t teach. I just facilitate.

Erin says

Common Core is the devil and my children both think the way I help them is way easier than what they are being taught. If I could homeschool just one subject I would ASAP!

Beth says

As a secondary math teacher, I have taught math skills for years but students always struggled with word problems because they know the “efficient” way or the tricks without really understanding what they are doing. After graduation if students need to solve a math problem, it is not part of a worksheet. It is not a skills based situation but an application problem. The real world problems come in the form of situations where we have to decide which operation is going to work. I never see please specific instructions telling us to perform a multiplication or division problem to figure out the best deal on this product…our culture struggles with math applications because we were not taught to understand math concepts, we were just told the efficient way to complete the worksheet and get past the test.

There is no valid research to support kinders cannot understand the concept of addition and subtraction. The standards will provide a solid foundation for understanding math not just completing worksheets.

karisb says

Carrie, you are failing to acknowledge that prior to working the subtraction problem of 32 minus 12 as written, the children would have ALREADY learned PLACE VALUE. In knowing place value, they realize that the 3 represents 30, and the 1 represents 10. That is why when they arrive at 20 for the answer they READ the problem as thirty two minus twelve and they read their answer as twenty (the term used for two groups of ten). Carrie…ignoring place value is the problem. Showing the math equation without it place in the scope and sequence is a problem. Knowing place value is critical, and knowing how to READ a problem…translating the digits shown to their meaning based on place value is everything in math. Adding the mess you have created for the above Methodology #1 is ridiculous as well. The more steps, the more chance of error, and the longer it takes to arrive at the “answer”. As for me, I appreciate that you caught that the title of the original should have said “old fashioned” rather than fashion. I will also say, that currently or common core…my children do better at home, and have excelled in college, careers, the culture and common sense from their home based education.

Sara Webb says

Reading all of the arguments against common core has been frustrating because of how many of them are not arguing things that are a part of the actual standards. It is related to misconceptions and not understanding the benefits. There are many sites out there that are bashing the common core standards. I see through these comments that there are a lot of people who are in support of common core. We need to make our voice heard so that the only voice out there is not the negative.

https://www.facebook.com/supportcommoncorenc

Carrie Wells, Ed.D. says

Thanks for all of your valuable feedback and for sharing that link, Sara!

Becky says

I am a teacher in a state that has not adopted common core. However, many people commenting are spouting incorrect information. The name is Common Core State Standards, standards, not curriculum. The standards do not dictate HOW a standard is taught, the curriculum or teacher does. My school district supplements our chosen math curriculum with other strategies because there are so many ways to solve problems. We also teach students to be able to identify the most efficient strategy for the problem they are solving. After parents have asked me to help them understand our math curriculum better they are on board with the idea of teaching multiple strategies. So, long story short, stop saying that CCSS is teaching things wrong.

Jason Hatch says

Testing is required and tests drive curriculum. Point blank.

Lisa says

“I’m going to side-step for a moment to complete this post. Forgive my tangental behavior. I graduated high school in 1997. At that time, in my school district, the grading scale was as follows:

94 – 100 = A

85 – 93 = B

75 – 84 = C

65 – 74 = D

below 65 = F

Why is this relevant? Well, if everyone who was educated in Broward County Public Schools attended college in Broward County, this would not be an issue. That is not what happens. Future college attendees applied to colleges across the state, maybe even across the nation. But here’s the problem… all of the 90 – 93% ‘B’ grades I earned were A’s in other states (perhaps other school districts in Florida). This meant my GPA may have been significantly lower than others applying to college with the same earned percentages in equivalent courses. I was being compared to others whose grades did not reflect the degree to which I learned the same material.”

Surely you are aware that college admissions are aware of weighted, non-weighted and different grading scales. You are not the first person that a college has seen that graduated from a high school with a different grading scale. They do take this into consideration when applicants send in their grades. That is just one aspect of the post that I found humorous.

Patsy says

I too have believed that common core is just a list of standards. The elementary standards for the state in which I live and taught (I retired Aug/2013) were almost identical to the new standards based on the common core. However, the more I have read and studied I have begun to realize that the strategies and practices teachers are being required to use in the classroom have made the common core a curriculum. Programs and textbooks adopted by school systems are based on the common core standards. These programs and textbooks change the way standards and objectives are being taught. Teachers in our system did NOT have a choice in how to teach the standards, we were required to teach the adopted text the way it was presented to us. Administrators walked through the classrooms on a regular basis to be sure teachers were “on task.” This new way of teaching emphasizes critical thinking, but does not take into account developmental levels of young children. Frustrations arises when students who are concrete thinkers are expected to think abstracting before they are developmentally ready to do so.

Cindy B says

Patsy, thank you for your honesty. You’ve hit the nail on the head. We are not so naïve as to believe that standards do not drive curriculum. We hear the same talking points over and over regarding Common Core and no one in our schools understands where the standards really came from or who wrote them. Our district adopted CC this year. My 5th grader is doing the same math he did in 3rd and 4th grade, but with different “methodologies”. He hasn’t learned anything new. Why? Because the kids have to do well on the Smarter Balance field assessment test being given this spring. He needs to know how to draw cubes and ten-sticks and shade them in to represent the numbers, What a complete waste of time. All the kids are being forced into the same mold. In our school they do ability group. The slower kids are doing the same work, but at a slower pace. Kids in the younger grades are completely lost and frustrated. They are coming home in tears because their little brains aren’t physically ready for the abstract thinking being forced on them. I’m working hard at the state level to convince our Board of Education and legislature to drop CC. We will be opting our student out of testing beginning next week (due to data privacy issues and changes in FERPA by the Dept. of Education) and then will either homeschool or move to a non-CC state…

Patsy says

Sorry, Frustrations arise when students who are concrete thinkers are expected to think abstractly before they are developmentally able to do so.

Kellie says

It saddens me to read some of these comments. It doesn’t matter how you, a now adult, learned to do math. It doesn’t matter if you graduated with honors, have a PH.D in math, physics, etc. Students who are quick learners do not understand the struggle that most students are experiencing. I have been reading these comments and so many of you are bashing something that you obviously do not understand yourself. You read her blog but it seems to me you didn’t really listen to what she was saying. You heard what you wanted to. How do I know this? I am a first grade teacher in a very high poverty, low-socioeconomical school with a high ELL population. There are over 800 students from k-5. I consider myself highly trained and prepared to give my students what they need. Now, the above math is called CGI. (Cognitively Guided Instruction) It is a component of CCSS that we use to teach students about number sense (math). It starts in kindergarten and we’ve been doing it for several years. It is NOT a method, nor the definition of Common Core. I start with counting collections, then writing numbers, identifying numbers,etc. this moves on to basic number sense using base 10, place value, etc. I do NOT teach my students “methods “, nor do they have to learn all of something or nothing. Students get to manipulate numbers and solve number problems with strategies that they derive from their own basic number sense. Nothing is forced onto them. I guide each student depending on level of understanding and on what strategies they are using. Let me say again, these are NOT strategies I force onto them. The concepts of Base 10, place value, counting, patterns, etc., allow each student to use strategies they understand to solve the problem. Then, students share with one another different strategies they used. This allows me to guide each student to the next level. Some of my students use manipulatives to solve, some draw pictures to solve, some use base 10 knowledge, some use place value, number sentences, etc. please stop saying this is a waste of time! Everyone of my students is progressing using CGI. They are understanding what numbers really are. I have 5 students who are already on the level where they can do these problems in there head because they understand what numbers are. They know that 10 ones make up the number 10, that the number 23 has 2 groups of 10 and 3 ones in it, they know that addition and subtraction can be used interchangeably to solve problems. Please stop saying “new way” and “old way”! It doesn’t matter what way as long as they have the true understNding of what a number is and how to solve problems by coming up with their “own way” to solve them!

Kaybee says

I’m a math facilitator and it saddens me that there is such disagreement with all the math. Funny things is I have been doing CGI for six years now but it’s just been brought to light and blamed on common core. I did this way before common core even existed. Parents werent complaining then. They were ecstatic that their first grader could multiply a three digit number.

Kellie says

Yes, indeed! We are trying to educate the parents about this but it is very difficult. Especially in high risk areas. We need to get them in the classroom and model what it is.

Kaybee says

I’m not sure where your from but in my area I am working with the math specialist at our co-op to get this done. It even takes teachers time to believe. Awareness will be key.

J says

Once upon a time, totally converting to the metric system failed, and so this will, too.

wwhitlock says

Non sequitur, J

Andrea says

As adults, keep doing what you learned to do, no one is saying you did anything wrong or that your math skills are under par because you didn’t understand a task analysis. But as a third grade teacher, I want my students to be successful in math and with our culture and population of students, they need opportunities to try to solve in more than one manner. I didn’t understand it at first, but after watching my students THINK and solve in a variety of ways, I saw that they could and would do it. We all read at different paces and our comprehension skills differ person to person; math is catching up to the concept that reading has used for a while now-learning styles vary so teaching a variety is necessary.

It may not always make sense to me the strategies my students use, but they found the strategy and I didn’t tell them how. And that is the thinking they need.

Heisenberg says

I think all of you are missing a major problem, and it has nothing to do with common core. The issue really is the fact that the classroom, as the author stated, is more diverse. Students that would maybe never be able to grasp more complicated math are lumped together in the same classroom with those who can quickly catch on. Both sets of students are receiving a disservice. Why not ability group these students and let those that excel at a subject do so. They will do spectacular on any standardized test you throw at them. (This is the only thing that matters anyway, right?) Let those that have trouble be in a class that goes slower instead of leaving them behind. I believe our system needs a major change. Instead of grade level, students need to be in a learning level. That means different age students in the same class who are at the same learning level. Teaching students to think on their own is what a teacher wants to do. Give them a chance to do it.

marykistre says

It is really irritating to me that people who, apparently, aren’t licensed teachers think they understand what it means to teach. Teaching students a 5-step process does NOT at ALL mean they will have to use this method for basic math in future situations. Perhaps some teachers, who really shouldn’t be teachers, may teach this way – that is unfortunate. But I wouldn’t call that teaching. True teaching may include a 5-step process, but also includes teaching them how to solve quickly and efficiently, which often includes memorization AFTER they actually understand the mathematical reality that is occurring. I guarantee you that my father, who is a mechanical engineer, doesn’t use 5-step processes to do the calculations for his job. He can do it in his head, but he can also sit down and explain the 5-step process to me because he understands the reality of what he is doing.

If all you want is for you child or student to “get through” school and “just do it”, you really aren’t advocating learning.

Gay Lynn Johnson says

I can’t believe the # of comments!!! I don’t have time to read them all . Method 2 is no more than “counting up”, like making change before we had cash registers that report the exact change. (Have you noticed the # of fast food workers who can’t make change if you provide a penny? They have no number sense or understanding of subtraction.) Method 1 helps kids to understand so they don’t have to wonder about “borrowing a 1”, which I was taught in the early 60’s but didn’t know why,and half the time didn’t know whether to do it or not. The skinny is this: Kids don’t have to know that 32= 3 tens + 2 ones. Yes, they can subtract we way we were taught 50 years ago, by rote. But knowing place value provides a sturdier foundation to help them be better thinkers. The answer is the same; so let kids think about the answer and its meaning. Having taught internationally i know that Asian kids are much ahead of ours in math. Understanding mathematics opens other ways to solve problems. We need to have many and varied ways to think to solve complicated problems. Mental agility is a plus not a burden!

James Ray says

Common Core = Common Chaos

Richard Davis says

The article was a good read. But it’s not the whole story in my opinion. One of the biggest challenges educators will face by implementing these new higher level thinking strategies – is the fact that you are inadvertently leaving behind a critical part of the learning equation – parents. Parents are being alienated by much of this because they simply don’t know how to help their children when they have questions. This article and the responses below it are a tremendous example. Look at the diversity of opinions and ask yourself how that will manifest itself in many homes when children ask parents for help? Great educators will not scoff at the parents confusion – they will take note of the position this has put them in, and realize that if the “old” way isn’t good enough anymore, then you must create an easier way to help parents catch up and be a positive part of the educational process again. Without that – are we really moving “forward?”

J Jones says

And this is why the last five workers I hired for my small business ( two were honors college members) are incapable of counting back change without the register or their smart phone giving them the answer. As I watch a critical skills base trained high school graduate struggle with a simple transaction ( literally being given 3 twenty dollar bills for a fifty-five dollar charge, and not knowing how much they should return in change), I find I cannot embrace this methodology as a superior means of teaching math.

So while I “get” your goal(s) of trying to imbue children with problem solving and thinking skills first, you’ve thrown the baby out with the bath water!

rk says

Great real world example. That is why I have a problem with this type of new math. They need to be able to add and subtract without a calculator.

Sara Webb says

rk, what are you referring to? The “new math” promotes a strong number sense and ability to do much more quick and accurate mental calculations. Where does common core require students to use a calculator for adding and subtracting? This argument makes no sense to me.

In fact, the previous poster, J Jones, actually makes a strong argument for why we NEED this “new math”. Those workers cannot count back change because they lacked the fundamental number sense. They were taught in the robotic procedural way and never developed a strong understanding of our base 10 system. They can’t do mental math, because that requires them to be able to think about the numbers. They were not taught conceptually.

Aimee says

Sara, did you just start teaching yesterday? If not, I would hope that you were well aware that this “new math” is not NEW MATH. This was published in 2007. http://www.csun.edu/~vcmth00m/bshm.html#_ftnref4

This could have been written about the CCSS. Note the 1989 NCTM Standards. CC math standards are nothing more than a regurgitation.

Number sense? Kids do not have number sense because they do not know the basics . . . 1+1=2. Why? Because IT DOES! And if they have no idea that 1+1=2, it does not matter how many concepts you teach, they cannot be confident in their calculations because they have no “sense,” no “material inference” of what the answer should or could be. I have personal experience with this lack of “number sense” by students.

Personal experience on a large scale . . . an ENTIRE school district with 5th grade students, from three different elementary schools that cannot fluently multiply because of the “new math” they have been taught for the past 5 years. These kids were not taught rote memorization and instead to skip count or use some other inefficient method. Please do not say that the problem is the school district or the teachers. Interestingly enough, this is one of the top scoring districts in math in the state . . . unless, your standardized test results mean nothing. In which case, these kids have been failed by their school district. But, I don’t think most school districts, superintendents, or CCSSI proponents would admit that standardized test scores are useless, tell nothing of real value, and are a waste of taxpayers dollars, but most importantly, the loss of valuable teaching/learning time in the classroom. However, in this case, it has to be one or the other.

I will leave you with this food for thought:

“Children need to master bodies of fact, and not merely reason independently, in, for instance, biology and history. Does it follow that in offering these subjects schools are stunting their students’ growth and preventing them from thinking for themselves? There are admittedly reform movements in education that call for de-emphasizing the factual content of subjects like biology and history and instead stressing special kinds of reasoning. But it’s not clear that these trends are defensible. They only seem laudable if we assume that facts don’t contribute to a person’s grasp of the logical space in which reason operates.

The American philosopher Wilfrid Sellars was challenging this assumption when he spoke of “material inferences.” Sellars was interested in inferences that we can only recognize as valid if we possess certain bits of factual knowledge. Consider, for instance, the following stretch of reasoning: “It is raining; if I go outside, I’ll get wet.” It seems reasonable to say not only that this is a valid inference but also that its validity is apparent only to those of us who know that rain gets a person wet. . . .”

http://opinionator.blogs.nytimes.com/2013/06/16/the-faulty-logic-of-the-math-wars/?_php=true&_type=blogs&_php=true&_type=blogs&_r=1

Diane Neustadter says

Thank you for a very cogent explanation. It takes the politics out of the issue!

Carrie Wells, Ed.D. says

You are very welcome!

Michelle decker says

Sounds like “Everyday Math” they tried to teach my son in 3rd grade. I believe that was the name of the curriculum. It was the idea of student’s being able to do the math in their head and understanding the concepts. It took me 3 years of undoing the damage from this to get my child to be successful in math again!! I even sent him to outside tutoring at Kumon! The district dropped the curriculum and it has been so much better. Now it seems that this author is encouraging this way of learning to the masses. Education is not for the masses it is for the individual. You want success? More teachers, smaller class sizes!

rk says

You got it exactly right they are educating for the masses instead of the individual. Standards are made to make everyone the same and fill work slots instead of individuals. If you compare our education system to that of 100 years ago they were more educated then now. Just look at some of the school books of that time.

wwhitlock says

You are correct in stating that is an individual experience. That is exactly why concepts should be taught in more than one way. In my experience, most people need things explained in at least 3 different ways. Some professionals say seven. Suffice it to say that learning a concept in more than one way increases understanding.

RK says

BUT kids need to be taught the quickest, easiest way first so they can actually “do the math problems THEN show them a few different ways to get the same answer.

Sara Webb says

It is not about being the quickest and easiest. If they understand it really well, then they will be ready for the quick and easy.

Sara Webb says

Everyday math was a textbook program. I did not like it as a teacher. There were so many things wrong with it. The worst part was that the program spiraled. Common Core does not spiral. It is based on the idea of laying the foundation. There are skills that build throughout the grades, but it is not matter of getting a little bit here and a little bit there. It is more, a layering effect, like building a house. First, you build the foundation, then you can put up the supports, and then you can lay the brick, and put a roof on. Etc.

I completely agree that more teachers and smaller class sizes is something we need as well. And, teachers need to be paid a salary that is livable. It is not acceptable for teachers (me included) to not be able to go to the grocery store the last week of the month, and hope and pray that I have enough food and gas to make it to the end of the month. Or to have to work a second job. But I digress, the focus of this article is to discuss common core, not teacher salaries.

Aimee says

CCSS DOES spiral! It’s on Achieve Inc.’s website and various other places. Please, educate yourself.

L Weber says

Most people replying to this have missed the whole concept of your post. It is about terminology not curriculum. Common Core is standards not curriculum. As a teacher I love the “new” math. Parents may not understand it but the kids do. (I do have elementary aged children).

We have moved from a state that uses Common Core to a state that does not. My sons in 5 th grade is doing what he learned in 2/3 and my 6 th grader was moved to 7/8 curriculum.

My fear is that if a state hasn’t adopted CC yet the students are going to be so far behind and the process to catch up will be worse then staying with their current curriculum.

My children have lost a great deal moving to a non CC state and I worry about their futures and having to complete to get into colleges and for jobs with the students who were educated with Common Core. States who do not adopt it are at a disadvantage.

Sara Webb says

Yes! My students LOVE math!! They would be happy if they could just do math all day long! It is crazy because when I started teaching, I had a love/hate relationship with math. I liked that it was so much more straightforward than teaching reading. But I hated that it was boring and I was teaching my students to be robots. Monkey see, monkey do. I wanted them to THINK and they wanted me to feed them a formula. Except, sometimes they work and sometimes they don’t! They had no way to apply them!

Then, I discovered that they way I thought about math, and did math in my head was actually not wrong! I didn’t know that I really was good at math! (at least through 5th grade!) Now, I still love reading as much as I did before, and feel like I do a good job of instilling a love of reading in my kids. However, more than ever before, I have taught my kids to LOVE math!! They understand what they are doing, and their ability to discuss strategies and ideas about numbers is amazing. I am so afraid that our students will be at a disadvantage if people don’t give it time to show how awesome it is.

Wendy says

When I taught third grade, I used, “trade first subtraction algorithms.” Is that method no longer used? BTW I love teaching new ways to do problems. My goal is to teach children to love learning. Once that is accomplished, my job is easy.

Carl Peter Klapper says

There are more than one way to solve a problem. We should let our children explore those possibilities instead of forcing them down one path. The point is to have fun with it, to explore the various ins and outs of numbers.

For example, one might consider how the problem looks with prime factorization:

32 -12 = 2^5 – 2^2 * 3

= 2^2 ( 2^3 – 3)

= 4 * (8 – 3)

= 4 * 5

= 20

Or let us try integer division and modulus:

32 – 12 = [(32 \ 12) * 12 + 32 mod 12] – 12

= ([(32 \ 12) – 1] * 12) + 32 mod 12

= ([2 – 1] * 12) + 8

= 12 + 8

= 20

Or remaindering:

32 – 12 = (32 + 8) – (12 + 8)

= 40 – 20

= 20

When a student solves (32 – 12) in the straightforward way, they know only how to subtract one value from another, and that for only simple cases. If they discover themselves, or we encourage them, to explore and play with numbers, then they have a better grasp at more complicated problems like:

4,302 – 197 = (4,302 + 3) – (197 + 3)

= 4305 – 200

= 4105

Carrie Wells, Ed.D. says

Thank you so much for all of the wonderful examples!

Grace says

Are you claiming that these are appropriate examples for early math learners? THAT is the argument here. No one is saying that they want their children to learn only one way. The problem is that schools are now skipping over the foundation to focus on material that is not age appropriate.

My youngest was in first grade last year. Instead of giving him a solid foundation in reading and writing, his teacher was making him work on fractions and grammar! How does it benefit a child to write fractions for shaded boxes when he has not yet mastered one-digit addition and subtraction? How can a child who has not yet learned to read two syllable words be expected to identify common vs proper nouns?

Stop pretending that our arguments are invalid because we’re afraid of ‘newfangled learnin.’ We are watching our children, who are technologically proficient and quite intelligent, struggle with simple concepts because they are being introduced OUT OF ORDER. Also, don’t pretend that you (general you) spent years in college learning HOW to teach. You spent that time learning pedagogy, classroom management, child psychology, etc. Get off your collective high horses, and stop assuming that parents are idiots and treating them as such.

Sara Webb says

Check out this article about the use of a number line! So good!

http://www.uwosh.edu/coehs/cmagproject/concepts/documents/Empty_Number_Line.pdf

Marti Jones says

Very well said. Thank you!!

Amanda says

Why didn’t you just say….ONLY comment if you are a teacher? This is what happens with legislation- people who THINK they understand what we do make assumptions that lead to preposterous decisions. The new methods work. I have students who can explain why on every operation. I also teach on an inclusion model, with several learning disabled kids in my classroom. Every single one has made growth this year.

Grace says

Nice attitude. If you’re a parent, your opinion doesn’t count- shut up and move along. Please quit your job if this is how you treat your students’ parents.

Concerned says

Carrie, you said “that strategies and methods used to teach have little to do with common core”, yet the controversy didn’t start until common core was implemented. Can you explain this?

Carrie Wells, Ed.D. says

Good question. I’m not sure I can answer this accurately – but I can speculate a bit. The biggest problem I see is that every curriculum company jumped on Common Core and realized that the easiest way to make money is to align their curricula with the standards and write the word “Common Core” on the front of the book, on the bottom of each page, etc. It does not mean these curricula even align with Common Core. It just means the publishing company has convinced the schools that it does.

Sara Webb says

Yes, Carrie! This: “It just means the publishing company has convinced the schools that it does.” I don’t want a textbook, but if my district adopts one, I want to make sure it is as aligned as it says!

On that note though…. that is how it has been for as long as I could remember. They would “say” their materials align with NC Standard Course of Study. And, they might even say how their old materials that we still have really do align.

Grace says

If that’s the case, then blame still lies with the schools. Textbooks are produced by corporations. Corporations exist to make profits, not to benefit humanity. We all know this. School administrators should not be so lazy, incompetent, or negligent that they adopt curricula that do not meet standards. They have taken upon themselves responsibility for our children’s educations (while adamantly maintaining that they are better suited to the task than parents) and our tax dollars. If they are not up to the task, they should not be entrusted with it. Don’t shove the blame onto book publishers.If you’re the experts you purport to be, then choosing an appropriate curriculum should be simple.

Carol says

I taught math in one form or another from 7th to 12th grades for 27 years (even computer programming) and I know this – Piaget’s theories must be followed. Children start out being concrete operational and progress to the abstract. Start with the “real”ness and the abstraction is easily taught. Skip the concrete and introduce abstract too soon and you have confused kids who end up disliking math. My personal experience.

Aimee says

Thank you, Carol. Finally! A voice of reason.

Randy says

whats wrong with just subtraction 10 from 32 then subtract another 2. Its a 10’s based system. I’ve fought mental math to my kids over the years this way. good way is watching basket ball or football games. whats score? 45-38, how many more points we need to tie? 38+10 – 48, – 3 = 7. or 38+2 = 40, +5 = 7, etc.

gonna have go teach both ways for awhile because the parents don’t under stand the new method and are the ones having to tutor at home.

Danno says

After reading through all of this….no wonder our younger generations are a mess!!! There’s no right or wrong any more….you messed up the test? That’s okay, “honey”, just study and re-take it …. again … and again…until you get it right. When they grow up and enter the real working world and mess up on the job, the boss is not going to say, “that’s okay, “honey”, just try again, and again, and again…..no sireee! They will say…Hit the road!

Lenora says

I’m so glad I teach Spanish.

Timbo says

My issue is math is not subjective, it’s constant. 2+2 will always equal 4, unless you try to make it about critical thinking, then 2+2 can equal anything depending on how the question is phrased. I have no issue with new methods as long as they can be effectively communicated to the students and the parents so we don’t have 10pm meltdowns while trying to do homework, with the parent solving the problem the right way, and the kid yelling, buts it’s wrong if it don’t show my work this way…..which way?!?!?!…..I DONT KNOW!!!!!! Math is not subjective, don’t try to make it that way. Math is rote, memorization and formula application of constants. Get the Dr. Spock out of your mind and teach math about numbers, not feelings.

Azzy says

One simple statement belies all these new “methodologies”. If these new techniques are so great, why are the kids of today so much more dumb than 20 yrs ago and these kids so much less intelligent, literate and competent than 20 yrs before that? Whatever we are doing it is not working and there is no way the regular classroom setting is the best for many if not all of these kids. Learning disabled by definition means you can’t keep up in a regular classroom, why try to cut the shoe to fit the foot?

shaddicus says

My favorite comments are when someone attacks a previous commentor’s YOUR/YOU’RE usage and totally disregards their actual point.

Donna says

The problem is that the schools aren’t giving information to the parents on How to help their children with this system that most parents weren’t taught. It makes it frustrating for both parent and student when the parent can’t understand new terminology and new ways to solve math problems. Maybe if the schools had training classes for the parents, it could help. I am one of those frustrated parents that can’t help her children properly without studying what the new terminology and methodology is, because I only confuse them when I use the way I was taught! Common core can’t be all that great when teachers and parents have to relearn everything they were taught. There should be another way to bring standards up besides redoing everything.

Sarah says

Amen Donna! I am willing to learn anything to help my children succeed! I get so frustrated not knowing how to help my child with her homework, it nearly omits me from her learning! I will ask my school about math work shops and see how that goes…

Jay says

Teaching them the “WHY?” is great for critical thinking. We all learn critical thinking skills at some point, whether on our own, or as we advance through high school and beyond. My only problem is that some teachers neglect rote in favor of critical thinking, when BOTH are needed to solve problems. It’s no good if they understand a new method to solve 32-12, but need to use their fingers to add 3+5+10+2 to get 20.

Charles Edgar Hampton says

I am a certified math teacher, and I decided to explain the math in the picture on the following youtube video. If the link is stripped the title is “The “Common Core” New and Old Math Photo Explained”

Cheers

http://youtu.be/8eTVkkQYRBs

Carrie Wells, Ed.D. says

I got a chance to watch your video last night – Thanks for sharing, Charles!

Liz Evans says

THANK YOU! like many others, i have puzzled over this problem, and (like you said “at first glance it seemed crazy”) thought there were just too many unnecessary steps. but after reading Dr. Wells breakdown of method #1, which i understood perfectly, i kept thinking that if only someone would explain method #2, i might be able to understand it. thank you again. it really is about how each child learns best. peace to you

R1 English professor says

Please, please consult a dictionary for the definitions of curriculum and standard, then you can engage in a fruitful argument. Almost all of the arguments I see against Core are straw men and red herrings, among other ignorant logical fallacies. I have not seen ONE valid argument against Core in this entire thread. The standards of assessment and the implementation through curriculum are completely different. If you want to complain about the methods to achieve the standards, point your fingers at the state and/or school system who, perhaps, follow an ineffective method.

Linda Gojak says

Well said! Thank you!

Linda

James Little says

Q: How many new math teachers does it take to screw in a lightbulb?

A: Six. One to hold the lightbulb and the other five to turn the house.

In my opinion, the moral of this riddle is: Don’t take a procedure that is simple and workable and turn it into something difficult and time-consuming just to provide an alternate and “modern” way of looking at it. I was taught “new math” in the 1960s, and you know what? Teachers abandoned all the complex ways to doing simple problems when they found out their kids couldn’t understand even the most basic math principles.

Yes, you can take a two-step subtraction problem like 32 – 12 and turn it into a five-step addition problem, but what if you are subtracting 1234 from 5678? Does this become a 100-step problem as students keeping adding up and adding up and adding up until they get writer’s cramp–or just abandon pencil and paper altogether and got get a calculator?

Katherine says

Haha James, I think your little joke sums up this entire conversation that I’ve been reading and studying for the past hour or so…

Grace says

My favorite part of this thread is that teachers are saying that a) children are failing to learn math because the old methods are insufficient and do not meet their needs- new methodology is required, while simultaneously claiming that b) these examples are not new and have been successfully implemented for YEARS.

Which is it? If these methods have replaced traditional algorithms for YEARS, and children are still struggling to learn, then how are the ‘old ways’ in any way responsible for that trend? Children are succeeding/failing because they are being taught new/old techniques. No; choose ONE. You sound like frauds when you argue like this.

Jason hatch says

It’s NEITHER Grace. What this whole thing is about is the abject failure of the public education model and the blame starts with the way we changed teacher education several decades back to, as you pointed out earlier, focus on anything BUT actually teaching (child psychology, syllabi creation, etc), administrators who are no longer gatekeepers of educational standards but bean counters who are primarily obsessed with obtaining the maximum funding, and the popular “cult of the teacher” mentality that vilifies anyone who suggests that teachers might not be infallible “saints” who teach out of a sense of self-sacrifice.

The CCSM is a shell game, intended to divert attention, pour BILLIONS of dollars into the educational marketplace and cause exactly this kind of distraction from the fact that those to whom we have entrusted with the education of our youth have utterly failed them.

daveeckstrom says

I know this looks like an unnecessary complication, but for a little kid, who is developmentally not ready for the abstraction of an algorithm, many approaches, especially concrete, incremental ones are very important.

Nicki Greenwood says

Charles – thank you for the video. It did help me to break that down in a way that made sense. It’s a different method of arriving at the same answer, but it a way that seemed “abstract” to me because I learned a much more linear way of arriving at 20. My first grader has not had trouble with the new curriculum thus far, but I think I’ve been lucky because he’s young, and we haven’t “switched horses mid-stream.”

I am more concerned for the older kids who have had to re-learn how they learn, after receiving a few years already of the old methodology. I do agree heartily with those parents who have stepped up to this challenge and said they’re going to approach their teachers about holding a class for us adults, to help us understand these new methods. I would rather give my son several tools in his proverbial toolbox, so that he can develop the ones that work best for him as he goes, and just like the other parents, I’m willing to put myself through some extra “classwork” to do that.

I think we all want the same thing: a better education for our kids, and better preparation for real-world challenges. In my case, it means I need to have an eagle eye on how well my son is progressing – a time-consuming demand, yes, but our kids are worth it. Education doesn’t stop when you leave the classroom – it needs to be reinforced at home, too. 🙂

EM says

If you believe Common Core is “a set of standards. That’s it.” Then you have NOT done your homework.

daveeckstrom says

By “homework” I assume you mean listening to hyped up conspiracy theories with no basis in fact instead of reading the actual CCSS so you know something.

Jason says

Common Core is going to be responsible for our children’s understanding of Math to plummet even further than it already has. Why does 32-12 even need task analysis. Stop the Madness.

daveeckstrom says

The fact that you can’t understand why 32-12 needs task analysis shows me that you probably are not a teacher. If you are, you are one of those teachers that just gets mad at students and blames them when they aren’t developmentally ready to understand the abstractions and algorithms you take as given since you’re an adult.

Lgojak says

You should be thrilled that good teachers care about their students’ understanding to take the time required for task analysis and analyzing student thinking. If it were a medical situation I would want a doctor that looks at me as an individual and analyzes my case before he determines what do do.

Dreamchaser728 says

I was Catholic educated. We learned the “how” & “why” at the same time. It was not confusing, and when I entered public school in the sixth grade in 1989, I was head and shoulders above my peers. Unfortunately I lost much of the mathematics I was taught in public school. Now algebra is lost on me.

daveeckstrom says

” I lost much of the mathematics I was taught in public school. Now algebra is lost on me.” And that is precisely why new teaching methods are needed. As a HS Chemistry teacher I see 150 examples per year of students who think they understand algebra because they have memorized algorithms by doing hundreds of textbook problems, but don’t have the foggiest clue what it means, so applying something as simple as a linear equation to a real situation is beyond nearly all of them, even the top students.

Grace says

daveeckstrom, is there any research research to support the idea that teaching abstract math concepts starting in pre-K helps improve algebra comprehension in high school? I’ve read that CCSS proponents CLAIM it is researched based, but which research? I’d love to read through that. Also, they don’t stand behind the standards. In this link:

http://www.corestandards.org/public-license/

it is explained that:

“Representations, Warranties and Disclaimer

THE COMMON CORE STATE STANDARDS ARE PROVIDED AS-IS AND WITH ALL FAULTS, AND NGA CENTER/CCSSO MAKE NO REPRESENTATIONS OR WARRANTIES OF ANY KIND, EXPRESS, IMPLIED, STATUTORY OR OTHERWISE, INCLUDING, WITHOUT LIMITATION, WARRANTIES OF TITLE, MERCHANTIBILITY, FITNESS FOR A PARTICULAR PURPOSE, NONINFRINGEMENT, ACCURACY, OR THE PRESENCE OR ABSENCE OF ERRORS, WHETHER OR NOT DISCOVERABLE.

Limitation on Liability

UNDER NO CIRCUMSTANCES SHALL NGA CENTER OR CCSSO, INDIVIDUALLY OR JOINTLY, BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, CONSEQUENTIAL, OR PUNITIVE DAMAGES HOWEVER CAUSED AND ON ANY LEGAL THEORY OF LIABILITY, WHETHER FOR CONTRACT, TORT, STRICT LIABILITY, OR A COMBINATION THEREOF (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THE COMMON CORE STATE STANDARDS, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH RISK AND POTENTIAL DAMAGE. WITHOUT LIMITING THE FOREGOING, LICENSEE WAIVES THE RIGHT TO SEEK LEGAL REDRESS AGAINST, AND RELEASES FROM ALL LIABILITY AND COVENANTS NOT TO SUE, NGA CENTER AND CCSSO.”

daveeckstrom says

Please don’t misunderstand. I support some of the methods used by today’s math teachers precisely because they are NOT abstract.

Math ed. research is outside of my expertise, but this is a start, if you’re really interested.

http://bit.ly/1kEhvhX

They have probably drawn on the expertise of many researchers from international sources. What convinces me is that I actually teach my chemistry students algebra by avoiding the algorithms and formulas until they reach understanding by solving real problems.

I don’t know if you’ve ever read the fine print on any product before, but the disclaimer you quote is pretty unexciting. You haven’t uncovered a flaw or conspiracy here. You’ve just discovered evidence that lawyers were involved.

Tamara says

I love this post so very much! Thank you for being a light in the dark on this issue!

Carrie Wells, Ed.D. says

You are so welcome, Tamara!

macs417 says

I don’t understand your version of methodology #1 in the new graphic and how it relates to the aforementioned old-fashion/old-fashioned way in the original graphic. My understanding of the original graphic is that 2-2=0 and 3-1=2. Two simple steps. Your rendition of m#1 consists of numerous steps I’ve never used, never considered using, nor seen students use since I began educating students 20 years ago in both the regular education classroom and within the special education classroom. What does all of that mean? How does it benefit the student?

Phil says

As a teacher of Mathematics for many years, I implore that the use of Mathematics in our lives needs to be predicated on simplicity. Mathematics, in and of itself, is a mind tool that helps us to simplify life matters such that we can accomplish and achieve at a higher rate. We should all be free to choose what works best for us as we grow and learn. Debating about what is best, or even worse, forcing anyone to abide by a particular methodology is truly foolish and damaging to the human spirit. Present any and every methodology you can think of and then watch as the child will naturally pick what works best.

This is analogous to the incessant push to force either phonics or sight word methodology on children who are learning to read… truly shameful. Parents, yes parents, make or break the learning potential of any child through nature and nurture. Those who “wait for the state” to get the job done will always regret it.

BTW, “Common Core” is written all over everything these days. From textbooks, to educational websites, commercials, etc. The marketing end is blatantly obvious. Everyone must buy the “new” clothes. The old clothes are wearable, but, they don’t have the cool logo on them. The educational industrial complex has arrived.

The “why” vs. the “how” arguments amuse me. I help to build mathematical thinking in my students with the following hierarchy of learning:

Knowledge, Understanding, and Wisdom. (In chronological order)

The last one…. Wisdom… is certainly “What Common Core is NOT”

Show me where the word Wisdom is written in the standards.

Diana Trujillo says

As someone who excels in math, I try to show my children how math is a series of patterns. There are multiple ways to solve equations. Methodology #1 makes perfect sense and solves the problem easily. Methodology #2 is absolutely ridiculous!

Julie says

Dr. James Milgram of Stanford University was on the CC math committee and refused to sign off on the math standards because they were so bad. Look it up.

daveeckstrom says

Great Idea!

I actually did look it up. It appears that Dr. Milgram’s main issues with the CCSS are that it is not rigorous enough and at the same time too difficult for young kids’ developmental levels, which is so contradictory that should raise some questions on its own.

He then justifies his comments by comparing the CCSS to the existing California standards at the time, but he conveniently left out the parts of the CCSS that would have greatly weakened his argument.

His only other complaint was that the CCSS lacks standards for math beyond Algebra II, which completely ignores the stated purpose of the CCSS, which is not to prepare every kid for success in any major at any college, but for minimal college and career readiness.

This guy’s argument is weak at best and dishonest at worst.

Linda Gojak says

Dr. Milgrim is also paid to travel the country and speak against the standards by the very conservative Koch brothers. He has been very vocally opposed to any type of mathematics standards for students since before 2000 which makes me wonder why he agreed to to serve on the validation committee.

daveeckstrom says

I don’t think Dr. Milgrim’s lack of objectivity has to even be a part of any discussion about the validity of his critique of CCSS. His actual arguments themselves are sufficiently lacking in merit that we don’t even need to go into who pays him for what.

Linda says

Agreed as long those who understand the common core math standards well enough to realize that his arguments lack merit. However, there are many who do not have the knowledge or insight to recognize his arguments lack merit — as exemplified in the previous post. Given that is the case, the lack of objectivity and fact that he is making money speaks volumes to his lack of credibility.

Jordan A says

“How-then-Why” Is the frustration I had as a student. I would be taught a new skill, and then in my frustration I was asking “why, why, why!?” and by the time the “why came around I no longer cared.

(Problem) clean dirty dishes (Why?) because if you want the smell to go away and something to eat off of next meal, then they need to be cleaned (How?) I’m glad you asked let’s work through it together!

This is a natural pattern that should be preserved. The key is NOT to get too hung up on the “why”. A fine line between “Because I said so” and information overload. How do me measure whether this is effective? ExitTicket.org has the solution! Designed & Built by Teachers

Jordan A says

http://exitticket.org/

John says

I would bet a dollar that Karl Gauss and Mr. Ramanujan didn’t learn math through any of the nonsense described here. Gauss knew math well enough at 3 to spot an accounting error in the work his father was doing. He didn’t need the idea of place values spoonfed to him. While most aren’t as gifted as Gauss and Ramanujan, they are smart enough not to need the tedious spoonfeeding that’s presented here by a teacher who hasn’t displayed math skills beyond adding and subtracting. Has she done calc 1, 2, 3 differential equations, complex analysis, done enough real analysis to know what “countably infinite” means, and maybe done a course in non-Euclidean geometry? I haven’t done all that, but some of it, and I never had to waste more than a day or so on the mickeymouse subtraction method discussed here. If kids learned basketball the same way, Michael Jordan wouldn’t have played any better than Mr. Roboto. That teaching method kills more math talent than it creates by assuming every kid is as dumb as the teacher.

John says

After reading all these pro common core comments I have one simple question. The way each and everyone one of the adults who posted who are pro common core, the way you were taught in school was wrong and you have become a failure in life and your life would be so much better had YOU learned common core ways right? Teach simplistic one plus one is two not 1+1 equals 10+10=20-18=2.

daveeckstrom says

Here’s a simple answer to your simple question. Research tells us that the average American adult doesn’t like math and isn’t very good at it. Faced with that reality, why would be as a society be happy with just leaving things the way they are?

daveeckstrom says

And find any place where the CCSS mandates that students learn 1 + 1 = 2 through the ridiculous method you suggest. It isn’t there. Nice for making a straw man to knock down, but not very based in reality.

Sam says

so you’re all saying math has been wrong for centuries, and “your kids” need aN “easier way” to understand?!

jessica erdman says

Thank you for this. I have been constantly correcting people on what they think common core is. I am glad you went to the common core website and put the standards in the post as well.

Carrie Wells says

Thank you for the positive feedback, Jessica. We can’t effectively make changes to the educational system or even help our children if we don’t understand how everything works.

Millie says

Despite what the poster says, it IS common core. Common core has not only standards but a curriculum that comes along with it. This so called correction on a pin about common core is only on a technicality and not based on honesty. I will keep posting more on common core.

Millie says

By the way, there is data mining opt out form for parents that do not want their kids tested with common core and protects your privacy from common core data mining. Just check on google and search Common Core Opt Out form in your state. More and more states have made these opt out forms available.

Matt says

Sorry author you are WRONG. It is as simple as understanding 2-2 =0 and 30-10 = 20, while holding the place values, total answer = 20. TWO STEPS, THATS IT. The old way.

Kelly says

Yes that is how I see it. Two steps. As for the second method though: Why are you adding to subtract? Even using a number line you would still subtract to so called friendly numbers until you get your answer.

moff says

A well educated earth friendly mama?

Could you be more specific with your credentials please?

Eric G says

I have children that will be attending school soon so this topic generated much interest. I’m going into Engineering/Science Calculus 2, and this just seems like a lot of wasted paper space. I get having the children understand concepts, but to have to repeat different versions of the answer for each answer is b.s.

If a child writes the answer on a one or two step problem without showing a diagram and blocks and a jumping caterpillar on a number line, is that child going to get it wrong? Even if the answer is correct and the arithmetic is sound? Is the child going to have to show proofs and state the Fundamentals Theorem of Arithmetic and state postulates in order to show that it is correct?

I get the blocks and even lines to show ones and tens, but that should only be done to show another way of seeing a problem, not necessarily part of the answer, and not for every question from there on out. Lets face it, there’s more sub-par teachers out there than decent ones. To make it a requirement for ALL teachers to teach four plus ways of how to do addition, those sub-par teachers are just going to confuse the kids at a faster rate. From what I hear teachers bitching about a lot is that there’s isn’t enough time to teach what they need to. So how is making a simple enough math problem four times as hard, or at the minimal, four times longer, going to help with the lack of proper teaching time?

Good on word problems, but at least get the kids used to multiplication table and adding/subtracting at a high speed.

Also, just because child A does this magical math in their head, doesn’t validate that way of teaching, and restructuring the whole education system. What about the Child B that just sees the answer in their head, would that validate trying to teach kids to just see the answer?

How about less vacation days off for the students, longer class periods (longer school day)? Other countries have more school days throughout the year from what I remember reading, it doesn’t seem illogical that more time in the classroom, more time reviewing material, less stagnant time off would produce better results.

My wife and I have decided to not only help our children with this common core, but to also teach them the older way of just doing math. This way our children wont get lost or caught up in trying to draw a correct picture for a problem but rather just doing the math problem.

David Hicks says

I think that I am seeing the second coming of the “new math” of the 1960s. With what I have seen of common core I am afraid that, sometime in the future, someone is going to have to make a calculation, there smartphone calculator will not work, and they are going to have to get a sheet of paper and work through the common core method of subtraction. Remember the Army uses GPS but they still teach map and compass.

David Hicks says

Just a note to the “grammar police”. I used the there instead of their. I do have trouble typing on an iPad keyboard.

Jocelyn says

No matter how you justify the “new” way, it still doesn’t make any sense.

Are you seriously suggesting that all of us who learned math the “old” way can’t perform analyses in problem solving??? Of course America wants to fix a system that isn’t broken instead of fixing the actual problems.

FYI i am a pre-school teacher, no kid is going to understand any of this.

Mugsy Malone says

Idk what retard school this bitch went to in the 90’s but when I was in school in the 90s if you wanted to subtract 12 from 32 you would count from 12 to 32 and the amount from 12 to 32 is your answer, ie, 20. Of course by the time you are learning basic subtraction you should know how to count by tens and thus coming to the answer in seconds. Rather than taking minutes to do useless math that adds unneeded complications. That is the methodology. We don’t need common retard core to make one. It already exists and is easier to teach and understand. They should bring back dunce caps. But only liberals who support common core should have to wear them.

Bob Madore says

Your statement about GPA is wrong. It is not based upon letter grades!!!! IT is numerical, which still should be the same relative number in All states!!! So what is your point now?

R. Dodds says

I’m a college math student, and I honestly do not understand method 2 at all. I don’t understand why you’re adding to get 15, adding to get 20, adding to get 30 and adding to get 32 all so you can add 4 more numbers together to get 20. Method one is the way I was taught, the way it is easiest to teach, and can actually be visualized by using objects or pictures. I remember using special blocks in elementary school that represented ones, tens and hundreds for the purpose of adding and subtracting that also taught how to borrow. This “New method” is honestly confusing and mind boggling at how asinine and roundabout it is. When a college student WHO IS MAJORING IN THE FIELD OF MATHEMATICS can’t understand how a problem is being done by looking at it, it’s not exactly a smart way to teach. And what happens when you amplify it to 3 and 4 digit numbers? What then? By using the first method you can properly teach about grouping and borrowing, leading to a better understanding of how to subtract/add numbers larger than 100. And honestly, the first method is easier to eventually develope into mental math, as I can easily do 3-5 digit addition and subtraction in my head using grouping and borrowing.

The problem I have with the so called “common Core” method or method 2 in the corrected image, is that it is so stupidly complex and long that anyone who was taught using method one, doesn’t understand it. I don’t understand method 2 at all, and I’m getting ready to take multivariable calculus.

Mac says

I think something really needs to be pointed out about this article, and it’s author…

“The “old fashion” way (which of course should be ‘old-fashioned’, thus rendering this image useless before reaching the mathematical interpretation) shows us nothing. It’s a problem with an answer, missing all of the steps to solving the problem. It does not show how the problem is taught or worked through. None of the aforementioned terms apply.”

That quote is probably the most blatantly dishonest bit of this article.

The image does not show the process used in the ‘old’ method’ directly, but it is there. The image does show however the expanded explanation of the “new way”, and even with that expanded explanation it is overly complicated and actually does not explain anything.

I highly encourage the author of this article to cease with such blatant intellectual dishonesty. If the system of educating that she’s backing requires lying to support it, then it is worthless, and she should question why she is involved in education in the first place.

S. Carloti says

@ Mac September.8.2014 at 3:03 pm

“” I highly encourage the author of this article to cease with such blatant intellectual dishonesty. If the system of educating that she’s backing requires lying to support it, then it is worthless, and she should question why she is involved in education in the first place.””

AMEN ! 🙂

Caleb says

If you teach them base tens, all you have to do is tell the kids to line up the numbers like #1 and then take the number on top and subtract the one on the bottom. No problem I see with that. No new method needed.

S. Carloti says

@ Caleb September.8.2014 at 7:11 pm

Noooooo ! What are you doing Caleb ? We are not trying to “simplify” things ! We are trying ….”to complicate” them. The reason ? The more complicated they are ….THE MORE MONEY YOU MAKE !

Don’t believe this ? Remember the joke with the old woman going to the dentist ? After diagnosing the problem and administering the local anesthetic the doctor took about 30 seconds to remove the tooth.

When faced with the $ 100 charge, the woman, somewhat perplexed, objected.

” A 100 dollars for a tooth you took out in one minute ?” she angrily asked.

” Oh, madam you should have told me, (the doctor replied ). I could have taken a half hour…. to do the same thing” :-)))

Richard Bragg Ph.D. says

I’m getting really tired of Math Education people. I am getting really tired of people pretending that Ed.D. is a real degree. Try getting a math degree.

Maureen Wellington says

yes

Maureen Wellington says

Same

Maureen Wellington says

This is a joke, right? Your example and the one that you say is Not Core, are the same. Where do you get the 15+5, etc. from – thin air? This would make me think less and Hate math more. I was a straight A math student in school and very proud of my math skills. There is no rhyme nor reason to your attitude. One of the things I enjoyed most about Math is that it WAS constant. 1 always equaled 1, etc.

GabeDC says

The problem as we can see by the heated comments above is not common core, it’s not the kids , it’s not the teachers old or new, it’s just a simple fact that everyone dislikes change, will do anything to avoid it, also nobody wants to feel stupid (though by some of the comments above some of you tried) and that is what this is all about.

I was doing Algebra in Argentina in the 3rd grade, when I came to the states because I was taught to do things differently I was told it was wrong, not the answers they were all correct just the method I used, I was finishing my math work in one third the time but because I did it differently I was told I was not up to standards. Again a teacher who didn’t grasp a different method and was afraid of change to her way of doing things and didn’t want to look or feel incompetent tried to hold me back for two years.

To those speaking of the “old ways” how they were good enough for me and my family and back when….. Let’s face it, it’s a cop out so get over it or next time you get sick instead of going to the doctors office go see a barber and have him apply some leeches for that infection/tumor/diabetes etc … That excuse is only used when it’s convinient to YOU, you’re not going to give the internet, nor get on a horse to go grocery shopping and you sure as heck are not going to learn Morse code anymore than you should expect the children to learn Math the Old way because you did and that’s good enough….. It’s idiotic to think that way.

Next for the New method folks, yes it is difficult for many to grasp so they will fear it and not all will embrace the new methodology because of many reasons so please be patient, like all new things adoption is not always easy and we all know that when it comes to our children we all want what’s best but here’s the thing, if you want to change the way you educate our children you must first start with the parents. Most of the negative and deprecating comments above come from parents who don’t understand the new methods and when their child comes to them for help and the parent doesn’t understand the solution other than the “Old” way they don’t want to look stupid so they tear it down, “if I’m from a family of college educated…. And I don’t get my 2 or 3rd grade child’s math you must be doing something wrong and making my child stupid, your ways are stupid….etc” See the pattern….

Change is part of life, how we educate our children is changing, when I went to school we didn’t have calculators and my first computer program in college was done in punch cards (look it up youngsters), but I use them now and the punch cards went the way of the floppy disk etc…

I don’t want my kids, grand kids, or anyone else’s kids be tied to the old ways because that’s the way we do things and not grow to accept that there is more than one way to learn and teach something. You want your doctors doing the new latest procedures, you don’t want a whole drilled into your skull you want a Tylenol for your headache right ??? You want those Drs and other professionals to keep on learning experimenting asking the hard questions and doing new things to take care of you BUT you’re not willing to give your kids that same opportunity in the fear that they will grow up smarter or make you look dumber and that the new ways will make you obsolete… Sad

S. Carloti says

@ GabeDC September.27.2014 at 8:16 am

My dear Gabe,

I loved your post, “bitching” about how others can not understand the “New Method” because they dislike …”change”. Your advice is, without a doubt, very well…. “intended”. It’s obvious that you know a lot more about “psychology” than the average person, since I’m almost sure you took it as a subject, along with “algebra”, ….in 3-rd grade. Right ? 🙂

Having said that, the question really is …. DO YOU UNDERSTAND WHAT COMMON CORE IS,….. and in particular HOW it is applied to Arithmetic? I’d love to hear your “dissertation ” about this “new method”, AS YOU UNDERSTAND IT of course, and why it is superior to ” the old method”, the one the rest of the parents learned in school.

So let’s put aside the “psychological considerations” for a moment, and discuss simple…. (even by Argentinean standards, I imagine ) … Arithmetic.

“How” and “where” you see “the strengths” of the ..”new method”, as you call it ?

How would you apply it when you deal with “large numbers” ( tenths and hundred of thousands. millions, etc. ) ?

Well….. are you ready to ..”tango” ? :-))

By the way, if you DO decide to dignify my post with a response,…. CAN YOU PLEASE…. make an attempt to avoid run-on sentences, keep your sentences short, mark their end with a “period” (.),…. and…… (C)apitalize the beginning of the sentence. . You’ll make a much better impression with the readers, and ….. make Argentina proud of you :-)). What do you say ? ¿Crees que puedes hacerlo? :-)))

Mike Eubanks says

Oh my God, she’s now teaching English as well. WOW. So rounded!

Mike Eubanks says

I graduated school in 1981 with straight A’s in mathmatical studies. My question to you is, why make anything including math that is relatively simple, so much more difficult by “adding” extra steps in a problem that are completely unnecessary? I for the life of me have NEVER understood why people do this! To me, its like backing out of your circle drive and going around the block to get to your other drive way. RIDICULOUS! ! There are many more things to break down into steps than a 2 step mathmatical problem. If you want kids to THINK, then start teaching them psychology in Kindergarten. If you want them to learn MATH, teach them math for God’s sake. Not a 3 dimensional means of personal interpretation! MATH IS MATH IS MATH.

moff says

Just a heads, you can opt out of the PARCC test in some states. To find the Information, search ” against common core” there are several groups that can point you in that direction. You will be heavily discouraged from doing so.be prepared to fight.

Jason says

The vast majority of children understand place value when taught ones, tenths, hundreds etc. The methods posted here are over simplifying it for the minority of children who do not. A common core “standard” is nothing more than a convoluted word for equality. Let’s hinder the vast majority of children who can easily conceptualize place value by using methods that hold them back, or hold them to a standard all children can meet. That being said, I would use what ever method that would give my child a chance to out compete the other children. I understand that no parent wants to believe their child is having a harder time learning than other children, but life is not fair and equal. Help your child be the best THEYcan be, and don’t implement standards that will inhibit the vast majority of children from being the best they can be.

Phoenix Sparks says

And THIS is why my A student/daughter struggles in math. Its ridiculous. She can do math in her head….I taught her how, its not complicated. But when you take 20+ lines to do one problem, and have points deducted because you missed a step, or you get confused doing these ludicrous steps to reach the answer and the end result comes out wrong because of total frustration….I’ve watched my straight A daughter, now an 8th grader, fail a quiz this year already because no one out of ALL THE STEPS said “two negatives equal a positive number”. No, I am not joking. 1- (-4+3) = 2. Why? If the state of NC would teach children correctly, she’d know this:

1-(-4+3)

1-(-1)

1-(-1)=1+1

1+1=2.

How was she doing this?

1-(-4+3)

1-1=0

I’ve even seen her doing this:

1-(-4+3)

1+4+3

5+3=8

That was after I told her negatives this way become positive. No one taught her to do the work in the parenthese FIRST! She is in 8th Grade!! I was already in advanced Algebra by then! I graduated in 1995. So, please tell me, what on earth are they forced to teach our kids that is so complex even teachers make errors teaching them all while they are doing what to me is 3rd grade math? I do not blame her teachers. This has been ongoing for several years on this one subject. The teachers must follow rules and guidelines that do not even make sense to them. I spend my evenings watching my 4 year old and being a math teacher. That concerns me.

S. Carloti says

@ Phoenix Sparks September.30.2014 at 11:17 pm

Pathetic ! After reading your post I am convinced now that there is a “conspiracy of sorts” to prevent kids from developing to their full potential. Children should be “gradually” thought the 4 operations and the role of “brackets / parentheses” and “parentheses within parentheses”… by the the end of grade ONE. The concept of, and operations with, “negative numbers” should start by the end of grade 4, beginning of grade 5. It’s been done before, and believe me it works like a charm. In so far as placement ( ones/units, tenths, hundreds) I learned that ….in grade ONE !!!,…. as soon as we moved from… “counting to 10″… to …”counting to 20”, and later on, in the grade to…. “counting to 100”. We started multiplication in grade ONE!!!!…. and HAD to learn “by heart” the multiplication table during the summer holiday.

I can not describe you how proud I was when, at the beginning of grade two, when the teacher was explaining again the concept of multiplication ….I ALREADY KNEW THE RESPONSE !

What is being done in today’s schools is nothing less than criminal. I’ve heard of “no child left behind ” program which, if it is “what it sounds like”, would be similar with getting a group of athletes to compete and telling them that “First, Second, and Third Place” …mean absolutely nothing.

What is important is that we all move “in unison”, so other children will not feel bad, or “feel” …left behind.

Would you imagine that happening ? :-))

I’ve seen with my own eyes “competition” working wonders with children. And, in the end, children are not all the same. Putting the brakes on the smarter ones for the sake of equality, is getting some brighter children bored. As such, they may / will disrupt the class, and before you know it you’ve got them diagnosed with ADHD, and put on psychotropic drugs. This…… is really an even worse crime. 🙁

( although it works great for the pharmaceutical industry later on )

If you want to “get change” talk with the other parents, and … make your ideas known going up the ladder, as far as needed, until…. “changes” … ( the ones YOU THE PARENTS REQUIRE) ….. will start trickling down the same way. After all you pay taxes, don’t you ? Keep in mind that,….without your support…”the system would collapse”.

Ask to assist “in class”, as an observer, and convey your observations to the other parents. Ask THEM to do the same. Get involved !

For God’s sake, it’s YOUR child, and ….they don’t …”belong to the community” …as MSNBC, or other media outlets, may try to make you believe.

https://www.youtube.com/watch?v=N3qtpdSQox0

https://www.youtube.com/watch?v=29FhZ5Dseec

Do you love your child ?

Are you interested in their progress ?

Do you want him/her to perform to the best of THEIR ability ?

Do you want them to get in life as far as possible ?

Get together with the other parents, and make “your wishes” known. And don’t let go,…until …. “you get what you want”. What you’ll get is after all….for your child’s benefit. And, I imagine that’s what you want in the end anyway, isn’t it ? 🙂

Don’t criticize “the system” in front of your child… EVER !

THEY DON’T KNOW HOW TO HANDLE THAT !

Yet do what needs done, to get what you want for them.

YOUR CHILD…will thank you some day ! And if he/she won’t, at least you’ll sleep much better at night knowing that you did … what was needed to be done !

And if, as you describe in your post …” The teachers must follow rules and guidelines that do not even make sense to them.”…. get them on your side !

Ask them to help you decide what they want …PRESENTING IT AS ….”WHAT YOU WANT” !!! They don’t have the same clout, and they can’t speak as forcefully as YOU CAN, since they may be afraid of …repercussions of all sorts.

So… SPEAK UP ! :-)))

Politely but…. firmly !

And don’t let OTHERS tell you what.. “you should want”,… for … YOUR CHILDREN !

All that, …. while YOU…. are paying …. THEIR salaries !

mike magnuson says

Stupid. Stupid stupid stupid. This methodology will only turn the students OFF to learning. You need to learn to live in the real world.

Ella says

I understand teaching tenth…hundreth…place and what not but to say 3 is actually 30…Ya…go into a shop with 3 dollars and try to buy a 30 dollar item…after all 3 is really 30 right? New method…all well and good for those that understand but don’t cancel out the option of doing it old school if you understand better that way. Like said…each child learns different so long as they arrive at the correct answer so be it…

Jeffery Hall says

Exactly, kids should use what they want and what they are comfortable doing as long as they get it right. The first thing I had my kids ask the teacher when learning this stuff was “will I HAVE to use a particular method during tests etc, as long as I get the right answer” all the teachers said no you don’t have to use a particular method. So I told my kids who were confused by these new methods to just forget that crap and do it this way (showed them the “old” way). They got it and could do it well. Then the first test comes and sure enough the question says solve this problem using the “lattice” method or what ever other names they have for this stuff. So they would get the question wrong, even when the actual numeric answer was correct. So I just had to stop helping them until they got to higher level math when they didn’t use that stuff any more.

Jeffery Hall says

So here is the main thing most people are missing here. This “new” method of addition or the “lattice” method for multiplication and so on is just fine for 28-12 or 12×23 etc (well not really, but for arguments sake we’ll say it is). Let’s see how long it will take to do 7,876,234-756,432 or 2345×56 using the “new” methods. Once a child really knows how to do the “old” way it doesn’t matter how long the problem is. Show me a child that knows and understand the “new” method perfectly that could use it to do the problem above in a reasonable amount of time (if at all, which I seriously doubt) and I will stop thinking this is a totally rediculous waste of our kids time.

c.j. says

I live in Arkansas and graduated from Bismarck high school, and I can tell you that the educational standards vary greatly from school to school, not just state to state. People from Lake Hamilton school (a school close to but much bigger than bismarck) had classes that weren’t even offered in my school like languages other than Spanish, tennis and swim teams, along with what we would have called advanced courses offered in earlier grades than we were. People would move to bismarck from other schools in the 9th grade and have to retake math courses they took in 7/8 grade at their old school. I completely agree with you, but the change needs to be a bit more locally focused in my opinion.

gene carpinski says

i still like my method better 32-12=20. take 32pennies n take 12pennies away i have 20.. your way will fad out soon .math is exact . n factual .. you dont need to stretch it out like that thevkuds already know how. you got there . thes children are not robots they are smart ..

nicole says

I think its crap just keep it simple and maybe more kids will stay in school the old generation did good in school my generation did OK in school with out all this extra crap to just solve a problem and now to have kids dropping out all the time I say keep it simple

countrysunshine says

I am still confused as to why those particular steps in method 2 are taken. Why are we adding 3 to 12? If we want kids to understand place value, we teach them 32 is 3 tens and 2 ones. 12 is 1 ten and 2 ones. Subtract the tens: 3 tens-1 ten=2 tens. (30-10=20) Subtract the ones: 2 ones-2ones=0 ones. (2-2=0) Add: 20+0=20.

For problems that require “borrowing” the problem can still be broken down to show how the place values relate to one another. The ones borrow tens, the tens borrow hundreds, the hundreds borrow 1000s.

Kevin olson says

That is the stupidest thing I have seen in the education system ever! This is just making shit more complicated! Basic is that, BASIC math!

Carol says

I really like your breakdown in this post. I find it helpful. Thank you.

Zachary Dunn says

This is ridiculous i was taught in kendergarden place vaules as in 0nes tens hundreds and so on then the is taught and repeated in firat grade then you start learning double digit add and subtract if we are taught correctly then there should be no reason why they cant get this. So in my thoughts one day all these samrt people decide “You know what i think i will start calling the sky green cause i have nothing better to do then to change everything so the parents have to pay more for education cause they cant help their children anymore.” I was all ways taught if it aint broke dont fix it.

S. Carloti says

@ Zachary Dunn October.10.2014 at 2:02 pm

Zachary, You are close to what everything is all about, although I doubt that you have already “zeroed in” on what is… “the greater underhand plot” . First off all, CHANGE ….. “IS”… the name of the game.

To better understand why, where, when , and how, read the link below,… regardless of how uncomfortable you may feel reading it.

http://100777.com/nwo/barbarians

Read to “understand” it, as opposed to perusing it, to just have a general idea, and make a perfunctory judgment about it. Whatever happens in education is nothing but one aspect of a greater scheme, destined to re-write in entirety a whole bunch of aspects of how you and I are leaving our lives.

If you are a “me no read” type of person, try this link …….. https://www.youtube.com/watch?v=Gjc4ywQVHEQ

A word of advice ? Empty your bladder before you either read or listen to the recording.:-))) Also,… you’ll experience what’s called “cognitive dissonance” with all its corollaries. ( Amongst them ” a state of shock” is one of them )

If you want to better understand what’s afoot in this world, while a lot of people are spooked by “details” such as this “common core”, research ANYTHING you can get your hands on about Agenda 21, a program leading to a complete, tight, and never heard of before, program to “inventory and control” EVERYTHING on this planet, from natural resources, to trees, animals and ….. human beings alike.

A word of caution ! If you are someone for whom “what restaurant/s you’ll go this weekend, and what time is your favorite show on TV ” is the primary preoccupation, what you’ve read so far will sound like the writings of a mad man, and the whole post will seem like the ranting of a lunatic.

A good place to start as far as Agenda 21 is youtube ( given that we are a ‘primarily visual” society ). Search for “Agenda 21 Explained”

( https://www.youtube.com/watch?v=9GykzQWlXJs )

and also everything you can find which has…. “Agenda 21″…. and two more names in the title …..1. Rosa Koire, and ……2. Deborah Tavares.

Also Google “Agenda 21” and choose “Images” ( top row ) You’ll get several pictures of the US map. Choose the one with the best resolution ( here’s one http://thetruthwins.com/wp-content/uploads/2014/04/Agenda-21-Map.jpg ) and read the legend of the map. Ponder quietly as to what you think it may mean ! :-))

Notice how large ;-)…the “green ” areas ( normal use) are. Now…. THINK AGAIN what that means ! Are you already awake, and “ready to dig deeper” ?

As far as the process this common core is using ( if I understand it correctly ) there is nothing wrong with it, if you use it as a “stepping stone” to help students understand certain aspects of the four operations. My main peeve is that it considers children kind of dumb, it treats them as such, and most likely the final result will be that they will end up ….dumber than you and I. Again there is an explication for as to “WHY” some one would do something like this yet I’m sure that you will be able to put 2 & 2 together and arrive at the correct result.

Hopefully the lines above will prompt you to take a few steps back, and have a look at the “greater picture”. The “common core” and other NEW aspects our children will be thought such as “masturbation”, between ages of 5-8 ( sounds crazy doesn’t it ) warranted by none other than U.N.E.S.C.O., are only a few “ASPECTS” of a much larger PLAN !

Oh ! just in case you are shocked and believe I’m making things up, here are a few supporting links …….which may make you …THINK harder.

And…. maybe…. want to….. WARN OTHERS ! :-)))

http://www.foxnews.com/story/2009/08/26/un-report-advocates-teaching-masturbation-to-5-year-olds/

http://cnsnews.com/news/article/un-agency-calls-teaching-children-5-8-years-age-about-masturbation

http://www.catholicvote.org/las-vegas-school-district-considers-teaching-5-8-year-olds-about-masturbation/comment-page-1/#comments

Here’s the UN document ! Notice the education is…. “mandatory” !

http://www.foxnews.com/projects/pdf/082509_unesco.pdf ……..

Go to….. PAGE 48…. “OF THE DOCUMENT”, ( top left ), although I’d recommend you read the entire report.

Here’s a response behind which ALL OF US should rally

http://www.familywatchinternational.org/fwi/documents/fwipolicybriefunesco_REVISED_after_new_guidelines_000.pdf

And you thought we were having problems with this……. “common core ” ? :-))))

Aly says

I am deeply saddened by the name calling that some commenters posted in response to this article or to some well intentioned commenters. Obviously the people who read this post are educated, but many are so deeply empassioned about their own beliefs that they treat others with disrespect. No matter what your feelings are about CC, I hope people realize that when you start trashing the opinions of others rather than sharing yours and providing evidence to support your claims, no one will ever really listen to what you have to say because people don’t usually respect the ideas of @$$holes.

Aly says

Btw, before someone jumps on me for my typos, yes, I saw them

Tracy says

Thank you for this. If I could reiterate one point I would say that, judging from the comments, people still don’t understand that Common Core STANDARDS are not CURRICULUM. They are two different things people! The Common Core standards have not changed a single thing in my classroom because I always taught these important skills. Panicked districts may have loaded up on bad (and pricey) curricular materials but that mistake shouldn’t be laid at the feed of the standards.

Steve Wright says

Maybe THAT isn’t CC but my children brought home PLENTY of unbelievable garbage that IS CC. For that reason they are now homeschooled. I will not have them dumbed down like the children of NY are. They had a 2 year head start on us in CC and their test scores in math have nosedived. Wait until science is released on the unsuspecting public. Then you’ll really see the indoctrination. Your children will begin learning they descendants of monkeys and are destroying the planet causing “man made climate change” which is just plain stupidity. Then they’ll learn they need to be killed to save the planet. Bill Gates is an evil SOB and he’s coming for our kids. Don’t be stupid. Stop Common Core!

Nancy says

http://www.washingtonpost.com/blogs/answer-sheet/wp/2014/09/17/four-common-core-flimflams/

Nancy says

I don’t have a problem with teachers teaching the process and the “why” part behind equations such as 32-12. But even in breaking apart this equation to show the “why” and the “how”, there may still be kids who don’t understand. They may understand using the manipulatives but why pressure kids to feel that they have to show all the steps. For students who already understand the “why”, just let them answer the equation and for those who struggle, can they not just use the manipulatives without having to write down all the steps. Common core I feel is more than a set of standards. The standards themselves are very specific in how and what they want the students to do. If it weren’t a curriculum, why else would there be such a great change in what students are required to do. Why else would there be such an uproar among parents all over the country.

Candice says

I’m just curious: if the “new way” isn’t Common Core, does anybody know what it is?

Denise Pauley says

I am sorry but the “correcyed methodology ” described in this article is ridiculous. First of all, no one in the real world looks in their wallet & go through all those steps mentally or otherwise to conclude they will have $20 left after giving their child $12 of the $32 they have in cash. Secondly, the education gap across our country is not caused by a difference in standards, you would see that if you actually resesrched pre-common core standards across the country. The educational gap comes from over crowded classrooms, lack of support for teachers, lack of resources, and a very large fluctuation in funding from one district to another.

D.A. Jackson says

Unlike virtually everyone else on this thread, I come here from a position of complete ignorance. I have never been a teacher, nor do I as yet have any children of my own, I am, therefore, largely unaware of the changes that have taken place in the way mathematics is felt should be taught, which seems to have undergone vast changes in the past 25-30 years, and not without its opposition. On the contrary, it is clearly a highly charged and emotional debate, as can be seen from this very thread. And while I certainly cannot offer any expertise on the subject, my lack of a dog in this hunt puts me in the apparently rare position of near complete objectivity. I am speaking, not as a parent, nor as a teacher, student, or administrator, but as a relative outsider, with virtually no emotional tie to the situation. Reading into this thread a good bit, and into the subject in general, I’ve stumbled across a few observations. They’re worth about what you paid for them…

1). I have learned – from life, nowhere else – that mathematics is very much a flick-a-switch, you-get-it-or-you-don’t subject. Mathematics tends to create its own sub-classes of “haves” and “have-nots” – sub-classes that, for many, carry on into adulthood. I know, as we all likely do, quite a few adults who will openly express their fear of maths, despite taking and passing all the necessary maths classes – all taught, by the way, using the traditional model. Mathematics can be an intimidating endeavor for child and adult alike. It would seem obvious, therefore, that new teaching methods are needed. But that is where the next issue begins…

2). One would like to think that most, if not all, of our mathematics teachers have come from the “haves” group, people who tend to pick up the fundamental concepts relatively quickly. Obviously, teachers have to at least be able to complete their own exams. Frankly, I have no doubt that the overwhelming majority of teachers can, for lack of better words, “do this stuff in their sleep.” After all, many of these fine ladies and gentlemen have been educating our kids (…well, YOUR kids…) for years now. Now, these men and women are being forced to learn an entirely new method of teaching. From what I’ve read, they don’t particularly care for it, and I can’t say that I blame them. They have been told, in so many words, that they’ve been doing their job wrong for the last 10,20, however-many years, and they’re not supposed to take that personally? I know I couldn’t do it. So now, you have potentially resentful instructors, having to go back to school to learn how to to teach the same thing they’ve been teaching for years? Most likely, many of them, if not most, felt coerced into learning these new methods, which certainly can have an effect on how much of this new information sunk in. I think it’s safe to say that, to recall an earlier analogy, there are fewer “haves” when it comes to common-core maths teaching than when it was being taught in the traditional manner. It is simple human nature – or canine, perhaps.

Something about old dogs and new tricks…

Keep in mind also: Virtually none of the parents understand these new techniques at all, at least in the beginning (although surely, schools will offer quick-course studies on common-core techniques at PTA gatherings or elsewhere).

There sure seem to be a lot of reasons why common-core techniques should be dropped from school curricula. Teachers don’t like them; parents don’t understand them – everyone seems to have one gripe or another. But none of these arguments change the fact that our current, traditional methods for teaching math are not working for far too many of us. There is no reason why anyone with a high school diploma should need something like a tip calculator. The fact that so many of us cannot grasp a concept such as dividing by ten and doubling it to calculate to get 20%, or that “4+x=5” is simply another way to ask, “What do you need to add to four of something, in order to have five?”, is shameful, and illustrates a breakdown at the institutional level. I don’t know if common-core is the solution (although I will definitely be learning more about it), but what we’re doing now, despite the hard work of earnest, dedicated teachers, is failing far too many kids.

And to our teachers: If a better method, whether open-core or something new yet-to-come, turns out to be a better, more graspable way to teach mathematics, that does not in any way undo all the great work you’ve done. Change and progress can be good things, especially if that progress comes in the form of fewer hours going over material again and again, waiting for those last few light switches to flick on…

Straight A Tutoring says

I would strongly argue against the assertion that math is something “you either get or you don’t get.” I hopelessly didn’t get math – until I got it. When it was actually explained properly to me. Perpetuating the myth that math is some scary thing that only a certain, special subset of students can ever hope to understand is very damaging to the vast majority of students to who go through life thinking they are too stupid or don’t have the proper analytical skills to understand math. Math, fundamentally, is codified logic. Everyone whose IQ is above the legal threshold for medium to severe mental retardation is capable of thinking logically (albeit to varying degrees, but logically nonetheless). If you know to put your foot inside the boot first and zip up the boot, congrats: you’ve just had a logical thought. The more complex the math, the more complex the logical thought required.

I would also strongly argue against the assertion that most math teachers actually “get” math. They don’t. I went to a private college prep high school, and even there, some of our math teachers were coaches with rudimentary understanding of the concepts they taught us. We even had a teacher admit in class that he couldn’t explain the reason behind a particular concept because he didn’t understand it himself!

Straight A Tutoring says

While I think “Common Core” has many flaws, I agree with Dr. Wells and am truly shocked and dismayed at the amount of people who arguing that students don’t need to understand WHY they are doing something, and should be taught to merely do it by rote.

I am very good at math. I pick up mathematical concepts easily and find it easy to manipulate number and equations in my head. I’ve had straight A’s in all my math courses ever since I can remember. I’m one of those unicorns that *get* and like math. However, it wasn’t always this way.

Once upon a time, when I was in 1st grade, I was introduced to vertical addition. And I could not understand for the life of me what the “carry” numbers were and where they were coming from. 97% of my answers were incorrect and the 3% that was correct was purely due to blind guessing. My teachers tried to explain it to me throughout the entire class time, and I still wasn’t any closer to understanding it. They were giving me the formula – the “how.” But because I didn’t understand the “why” behind the formula, I could not properly execute the “how.”

After school that day, my mother spent hours with me trying to explain it to me. I still couldn’t understand where all the carry numbers were coming from. Thankfully, my father is an engineer, and he took it upon himself to explain to me the WHY behind vertical addition. And within half an hour I finally understood it! And the way he explained it was using the ones, the tens, the hundreds, etc. – i.e. basically a variation of this methodology. What took my teachers and my mom literally the entire day to unsuccessfully teach, my father was able to successfully explain to me in about 20-30 minutes. Ever since then, my father tutored me in math by explaining the WHY behind it. And ever since, I’ve always excelled at math and found it easy. I didn’t have to memorize formulas because I understood the concepts.

It is SO important that students understand the WHY behind math and to understand it before they understand the HOW. To see people saying otherwise – and with such passion – is truly very, very disconcerting and dismaying.

Now, I suspect that a lot of these teachers don’t really understand the WHY behind math themselves, which is why sometimes these problems can be so convoluted and confusing. Like Dr. Wells said, the standards behind Common Core are not the same thing as curriculum and methodology. However, relating mathematical concepts to real life is very important and can really help students in understanding math. Math is all around us, EVERYWHERE. We use math everyday. Our lives are affected by math in nearly every way. We wouldn’t be reading this blog or typing these comments without math. Every time we breathe in and out, math is a play. Every time we walk, math is at play. But understanding math is more than that. Learning – truly learning math so you understand it – teaches you how to THINK critically and logically. It’s like going to the gym. It trains your brain to THINK RATIONALLY, which will come in handy in all aspects of one’s life. And THAT is why math is so important and why it is so important to actually understand the concepts instead of memorizing formulas and multiplication tables and mindlessly doing them by rote.

Cassandra says

When I learned how to add and subtract, I learned by using place values.

Michael Toso says

Should have included a standard like addition & show it does not specify methods, except the standard algorithm. Maybe people would connect.