The Rote Memorization/Standard Algorithm/Lack Understanding Narrative

This particular rant/polemic is by someone who rests her authority on being good at math, and most likely because she learned it in the way she now says is ineffective. Like many of the defenses of Common Core math, hers rests on a denigration of traditionally taught math.

I’ve written much on Common Core math and I maintain that it contains watchwords (or dog whistles per Tom Loveless of Brookings) of reform math that cause it to be interpreted along those lines. That is, emphasis on alternatives to the standard algorithms prior to teaching the standard algorithms in the belief that teaching the standard algorithms first eclipses the “understanding” of the algorithm. And the “understanding” of the algorithm is believed to be essential for students to solve problems.

I’ve also maintained that Common Core can be taught using traditional methods, and the standard algorithms can be taught first, with alternative approaches later (as it used to be taught).  Jason Zimba has agreed with me on this in articles.

To wit and for example:

The criticism that I referred to earlier comes from math educator Barry Garelick, who has written a series of blog posts that aims to sketch a picture of good, traditional pedagogy consistent with the Common Core. The concrete proposals in his series are a welcome addition to the conversation math educators are having about implementing the standards. Reading these posts led me to consider the following question:

     If the only computation algorithm we teach is the standard algorithm, then      can we still say we are following the standards?

Provided the standards as a whole are being met, I would say that the answer to this question is yes. 

With that, let me turn to the blog piece I had linked to originally. The argument starts out with the usual:

The traditional way involves rote memorization and algorithms performed on paper. They require little to no understanding of why the algorithm works. It simply works.

This statement is so far off, it’s not even wrong. In fact, older textbooks do explain why the algorithms work as they do, and later, after students master the algorithm, alternatives to the standard algorithm are introduced. (See for example, this article.) In many cases, students discover these methods by themselves. And it isn’t as if teachers do not teach the understanding; most do. But as many teachers will tell you, many students do not glom on to the reasons, and instead rely on the procedure.  Understanding is a process that works in tandem with procedural fluency. Many students will understand in time.  And some will never fully understand. There are varying levels of understanding. But being able to solve problems using a procedure or algorithm does not necessarily make the student a “math zombie”.

She goes on:

We forget. All the time. Especially when we don’t understand why the algorithm works or if it has been a long time since we last used it. I can guarantee if I took a survey at Starbucks right now, and asked people how to perform long division, convert a mixed number to a fraction, recite the quadratic formula, factor a binomial, and complete the squaremost would fail. Not because math is too hard or people are bad at it, but because memorization and algorithms are not the best ways to retain information. We remember through contextunderstanding and application.

We also remember through continued application. For example, if I haven’t worked with percent calculations for a while, I have to brush up on it. Same with finding derivatives of certain functions. The survey of people at Starbucks might be different if the majority of customers were practicing engineers. That people forget how how to do something if they haven’t worked with it for years is not evidence that the traditional method of math teaching is ineffective. And like many authors of similar rants and polemics, she also does not provide evidence that her methods are superior to those that she feels do not work.

She then goes into a demonstration of how mental math provides a superior and quicker way of adding two three digit numbers than the standard algorithm and states:

Number sense allows us to have an arsenal of ways to problem solve, including but not limited to the traditional algorithm.

Quite true. And many of us got to that point by discovering these shortcuts ourselves after having been taught the standard algorithm, not to mention that the shortcuts she mentions (and gives a demonstration of) were also included in the old textbooks in the era of traditional math that she and others find so destructive.

She leaves us with:

The Common Core math standards are an attempt to expose your child to this flexible way of thinking. It may not be perfect, but it is in the right direction.”

Yes, and the standards can also be met quite effectively perhaps more so, using traditional methods. The “understanding uber alles” approach to math is likely to result more in “rote understanding” and an inability to solve many simple problems. Interestingly, students in the 80’s and 90’s entering algebra classes in high school knew how to do basic computations with fractions, decimals and percents, whereas now many teachers will attest that this is not the case.  Traditional math is the usual culprit, but such finger pointing fails to acknowledge that the reform methods have been around for almost three decades.

Oh right. It’s because reform math hasn’t been taught correctly. I keep forgetting that.








2 thoughts on “The Rote Memorization/Standard Algorithm/Lack Understanding Narrative

  1. “The traditional way involves rote memorization and algorithms performed on paper. They require little to no understanding of why the algorithm works. It simply works.”

    Rote strawman 1 – stop reading.

    “Why is Common Core Math Hated by Parents?
    Because the Common Core Math standards are trying to teach number sense and mental math techniques through various forms of diagrams and step-wise procedures that are new and look confusing.”

    Rote strawman 2 – Really. Stop reading! I guess I’m not paying attention.

    Forget the fact that CCSS is non-STEM by definition, starts in Kindergarten, and that the highest level expectation is no remediation for community college math. Forget the fact that the College Board knows that this is a problem and has defined Pre-AP in ninth grade as an attempt at crossing the chasm of content and skills between fuzzy K-6 CCSS math and AP Calculus. Never mind that it’s a failure before it’s even started.

    Her advice to parents?

    “Befriend math! Be open to new perspectives and ask questions.”

    In another article, she says:

    “Respect the Teachers
    They are experts on child education. They have the best intentions for the students in mind. This teacher made a decision [5X3 = 5+5+5 marked wrong] based off a lot more information about the student and class setting than we can tell from a photo. We don’t have to agree with it, but we can respect it. If you are confused, ask them why they did something before you discredit a teacher on the Internet.”

    I had to put my hip boots on for that one. They are the experts of their own opinions. They are especially not experts in math. They might not be held to peer review, but mathemeticians are, and the mathemetician of this opinion piece is getting some bad peer reviews.

    I asked a lot of questions about my son’s K-6 math using MathLand and later Everyday Math and was treated like they’re the experts and I only want what I had when I was growing up – rote memorization. Miraculously, the world righted itself and went back to normal for my son’s AP Calculus track in high school where I didn’t have to help at home or ask questions, and where his math teachers were mostly from industry. Unfortunately, it will still take help at home or with tutors to prevent (not cross) the CCSS NO-STEM K-6 chasm. Meanwhile, educators will be thrilled if little Urban Suzie is the first in her family to get into the local community college even though she might have been able to get into MIT.

    What I find most amazing is that these people are not raising the issue of what’s best for those not headed for a STEM career – ignoring the issue of whether they create these kids in the first place. They claim that this approach to math is best for all and that it provides everything that one could want for understanding and number sense. This is an incompetent viewpoint that has no basis in reality along with the idea behind Pre-AP classes.


  2. I never did memorize the quadratic formula. But my math teacher showed us how it’s derived, and I quickly did that before each test in the margin of the test paper.

    Problem solved. (And, as a result, I never forgot about “completing the square”!)


Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s