In Defense of the New Math (Everyone Seems to Hate)

I’ve seen the posts on my Facebook feed.

“Why can’t they teach math the same way they always have?”

“I can’t even help my second grader with her math homework!”

“Why is math homework so complicated these days?”

And my favorite…”I’m a summa cum laude engineering blahblahblah graduate and I can’t even do this first grade addition problem.” (Whatever.)

I’m going to try to set a few things straight.  Because I teach this apparently odious “new math” to multiple grade levels. And I’m here to say-there really isn’t that much new about it.  But there are a lot of really good things that come from it.

First, let me just get something straight before we go any further.  New math and the common core are two completely different things.  Common core is not making your kid’s math homework problems harder.  In fact, common core requires teachers to teach math the good old fashioned way everyone seems to be bemoaning the loss of.

Here is a third grade common core math goal:

CCSS.MATH.CONTENT.3.NBT.A.2
Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction (Source: http://www.corestandards.org/Math/Content/3/NBT/)

Note the use of the word algorithm.  That’s the plain traditional way of doing addition and subtraction, folks.  You know, where you stack two numbers on top of each other and you start in the ones place and sometimes you trade or borrow or regroup or whatever the term you choose to use for moving between place values.  So.  New math is not, truly, common core.  Today I am talking about new math, not common core.  So spare me that in the comments, huh?

Anyways.  Here’s the thing about new math.  We aren’t really teaching students new ways to do math as much as we are teaching them new ways to think about math.  Because the old school way was to simply teach the algorithms, rules, tips, and tricks for math and then expect students to blindly follow them.  And students blindly followed them and they all got good grades in math!  But…when more complex math came along, things like algebra and calculus that require the rules to bend a little or be applied in new ways, everything fell apart.  I know this was the case for me.  I was a straight A student in math, and then in about 8th grade, everything fell apart.  People laughed at the “smart girl” for suddenly needing math tutoring because I was getting an F.  Not good.

I don’t blame my teachers, because they were teaching the best they knew how, and this was the way they’d been told to teach, the material they’d been given to teach, and the way they learned themselves.  But still, I knew something was not right. Let me illustrate by example.

In first grade, we were learning simple subtraction.  My teacher told us that the largest number must always come first in subtraction.  She told us it was the rules of subtraction and that we were not ever allowed to break the rules.  Besides, it was simply impossible to take away more than you had in the first place, wasn’t it?  That’s how subtraction worked!  And I bought in 100%.

Until later when we learned about negative numbers.  I remember, very clearly, thinking, “Oh my God my teacher LIED to me about subtraction!”  And I started wondering what else I may have been taught that was not true.

My favorite example comes from fifth grade.  We were learning how to divide fractions.  You know how you divide fractions? You flip the second fraction over and you multiply those fractions, that’s how!  So I asked my teacher (I must have been the world’s most irritating student, seriously) WHY we flip the second fraction.  How does that work?  Why does it work?  You can’t just flip subtraction around and call it division or something, so why can you flip a fraction and change division to multiplication?  Do you know what she told me?  “Go sit down.”  Then she repeated it when I persisted, adding “Because those are the rules, Amy.  Go. Sit. Down.”

Do you know when I learned why you flip the second fraction?  When I was a junior in college and I took an education class on how to teach math.  From fifth grade until age 21, I was just blindly flipping fractions.  I’ll bet you did, too.  Maybe you still are.

This is exactly what the new way of teaching math is trying to avoid.  We can’t just keep teaching students to do things this way “because I said so” and expect them to apply the rules differently in the future.  If we do, we’re just continually creating a population of people that doesn’t really “get” math.  And that’s pretty scary.  Now before you go off all, “But I know math AND I understand it!” and quit reading, bear with me for a moment.  I’ll get to that.  Obviously, we don’t have a bunch of people wandering around who can’t add.  Just hang with me for a moment longer.

I want to draw a comparison to reading.  We do not teach children to read by only having them memorize lists of words blindly.  I don’t mean kindergarten sight words, I mean ONLY learning to read by memorizing words.  Of course we don’t! There are millions of words in our language!  What would happen if they were reading a book and came to a word they hadn’t memorized or had forgotten?

Instead, we teach them phonics skills and word attack skills they can use to figure out new words as they come across them.  We teach them some of the rules of language and word building, like the silent e at the end of some words or that blends like sh make a new and different sound.  And-most importantly-we teach them that virtually every one of these rules has exceptions.  To teach reading through 100% pure memorization would be ridiculous.  Yet that’s what we were doing with math.  Here are a bunch of rules, kids.  Memorize them!  They always work! Until they don’t.

Within the new math, we are trying to teach students that there is more than one correct way to think about numbers, operations, and math in general. That there is more than one way to solve a problem, and often many ways.  I, personally, don’t try to teach that one method is better than the others, but I want to give them as many options as I can to attack math in any form they may find it.  Math problems in real life don’t come in neat little isolated rows like they do on math homework sheets.  So the one thing I do make sure I teach is that math is everywhere and there’s no getting away from it, so it’s really valuable to learn.

I want to share some examples from my second grade classroom.

Example one:

“Someone has $2.00.  They spend $1.60.  How much do they have left over?”

Now, traditional math and the algorithm state that you need to whip out a piece of paper and write something like this:

$2.00

-$1.60

$0.40

And then there would be a lot of regrouping or borrowing or whatever.  And some of my students did it that way.  And that’s just fine-they’re learning.  But, as an adult, is that what you did?  Did you seriously go get a piece of paper and write that down?  I doubt it.

I’ll bet you answered it using one of the below methods that some of my students used:

“I counted up by tens four times, which gave me forty until I got to 200.”

“I already know that 6+4=10, so I knew that 60+40=100, so forty must add up to equal the whole dollar.”

Did you use one of those?  Or at least something like them?  Here’s my big question-Where did you learn how to do it that way?

Because that’s totally how I do math.  I wouldn’t use a piece of paper or even a calculator to do that problem.  I’d add up in my head.  Subtraction wouldn’t even come into it, really.  And definitely not borrowing and regrouping.  Yet no teacher taught me that.  I didn’t learn that method in school.  Did you?  If you’re at all like me, at some point you probably just stumbled across doing math this way without even realizing how or why.  Maybe you just noticed that you do math that way when I pointed it out.

But, as a teacher, I’m not happy with just hoping that my students figure it out someday.  That’s how successful, thinking people do math.  They don’t whip out a pen and a pencil for every problem.  I don’t want my students to have to, either.  I want to equip them with real, useful ways to do math.  So yes, I teach them the old fashioned way.  But I also teach them multiple, real, useful ways.  That’s new math.  Except, as you can now see, it isn’t really anything new, it’s just being taught now instead of stumbled upon later (too late, in my case, as I struggled with math all through high school and college until I finally started to teach it and began to realize how this number stuff really works.)

Here’s another example:

“Jenny wants to earn 100 stars in class this year.  So far, she has earned 27.  How many more does she need to earn to reach her goal?”

Yes, you can subtract 100-27, regroup, and get 73.  But I’ll bet you didn’t.

That’s why I ask this question all the time in my math class- “Who solved it another way?  Explain how, please.”

Student: I added.

Me:  Tell me how you did that. (This quote is a key difference.  I know when I was in school, the teacher most likely would have said, “Wrong.  This is a subtraction problem.”)

Student:  Well, I added three, and that took me to 30.  Then I kept the three in my head while I added 30 + 70 to get to 100, and then I added the three back onto the 70 and got 73!”

That’s new math.  It’s not always easy.  Sometimes it’s really, really hard.  It’s definitely not the way we learned it. Sometimes it’s too many steps or it almost seems silly because “I can do it the old way in less time.”  I know!  But we are no longer going for super speedy mathematicians who are driving blind.  We are going for young people who may take math slow, but really get it, and thus open worlds of possibilities and understandings we never even imagined.

Love it or hate it, it’s here to stay.  I really wouldn’t want to have it any other way.

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4 Comments (+add yours?)

  1. PWizzle
    Feb 16, 2015 @ 18:50:13

    I quite enjoyed this, and I understand your position. I never did well in maths, and oddly enough, in your examples, I did subtract. Everyone else always tells me about the “counting up” and the things in the examples that you did, but that doesn’t make sense to me. Perhaps I’m weird or an anomaly. I am neither for nor against the “new math”. If it helps people learn and understand, then I’m all for it.

    Reply

  2. Linda
    Feb 17, 2015 @ 14:51:41

    Excellent article. It’s about developing number sense.

    Reply

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