A Convenient Lack of Meaningful Content Masquerading as Exposé

I just finished watching Al Gore’s An Inconvenient Truth and in the course of cruising around the web for commentary about the movie and the science presented therein, I stumbled across this.

It is a short film about mathematics curriculums titled Math Education: An Inconvenient Truth, put out by a parent advocacy group in Washington called Where’s the Math? In particular, the film is arguing against the use of two particular curriculums, TERC and Everyday Math. Go watch the film (it’s about 15 minutes) and come back.

Ok. In the spirit of the film, in which she likes to lay out her degrees (note that none of them are actually math, education, or math education), here are mine:

Bachelor of Science in Computer Science, Mathematics, and Psychology, with a senior thesis on early algebra education.

Currently pursuing Ph.D. in Cognitive Psychology, with certification in Education Research. My dissertation topic will be geometry education.

Although I am far, far from being any sort of leading expert on math education (for that, go read people like Alan Schoenfeld or Rich Lehrer or Jim Stigler or Liping Ma), I have considerably more expertise in this area than she, or whoever wrote the script she is working from, appears to have.

The argument in the film appears thus:

1. We must teach our children to do math correctly and efficiently!
2. But not by using calculators, because that would be too efficient. Or something.
3. So instead of teaching kids how to use calculators, or to use these newfangled “reform” methods, we should make them memorize this efficient paper-and-pencil algorithm instead.

If you figure how this argument follows, please let me know, because I don’t follow it. The umbrage at calculator usage seems to imply some concern with conceptual understanding of mathematics, but then why trash a couple of alternate algorithms* that, unlike the “standard algorithm,” require actual conceptual understanding to execute on the basis of inefficiency? Especially when said inefficiency is largely due to the roundabout solution path chosen and is not a flaw inherent to the method?

The film also assumes that the so-called “standard algorithms” are even the most efficient. When I was in grade school my parents, who did not receive their primary math education in the US, were horrified at the inefficiency of the very algorithms being lauded in this film. They often referred to the standard algorithms as outrageously stupid and made me learn and use more efficient ones instead. That’s how I became the “math whiz” at school.

And why critique the algorithms on the basis of parents not knowing them, especially since all the alternate algorithms presented are simple mathematical decompositions that any parent with a solid math understanding should be able to pick up quickly? If we follow that line of reasoning to its logical end, then we should never teach anything new because parents might be confused by it.

I’m also not sure how she can draw the conclusion that reform (sometimes called standards-based or constructivist, although the terms aren’t quite interchangeable in my mind) curricula like TERC or Everyday Math are responsible for her college classmates’ math difficulties without collecting data on their math educations. Really, she’s just speculating here without real data to back it up.

It seems like this film is targeted not only at people who are bad at logic, but people who are bad at math. Take her critique of the TERC algorithm for long multiplication, which begins with her writing out this equation:

(26 x 31) = (20 x 31) + (5 x 31) + (1 x 31)

This (like all the long multiplication algorithms presented) is an application of the distributive property, a property that’s critical to understand if you are to master algebra. She doesn’t seem to recognize this, which makes me question her math ability and the method by which she was educated. Don’t see it? Let me replace 31 with x and 20, 5, and 1 with a, b, and c and add/remove parentheses as needed for clarity:

(a + b + c)x = ax + bx + cx

As a point of interest, the About page on the distributive property linked above says:

The Distributive Property helps with mental math and should be taught to children as a method to multiply much quicker in their heads. Children need lots of experience using the Distributive Property. Children make greater ‘connections’ with the ability to use the distributive propertly for mental math.

I further question her math ability when she admits to experiencing confusion in the middle of the partial products calculation. The partial products calculation is mathematically identical to the standard algorithm (look at the pattern of multiplications and the lineup of numbers in the addition if you don’t see it); the only difference is that the notion of place value is made explicit in the partial products calculation while it’s merely implied in the standard algorithm.**

If you don’t see where the math is in these algorithms, or if you believe, as she implies, that these algorithms somehow don’t work every time if applied correctly, then honestly, you’re not very good at math. If the text is written in such a way to highlight to math in these algorithms, and math teachers have sufficient mathematical and pedagogical training and time in the classroom to teach these methods properly, then research suggests that you will wind up with a crop of high-achieving math students. Unfortunately, research also shows that there’s a high probability that none of these are true for an unfortunate number of math classrooms in the US.

There are valid criticisms to be made of these particular curricula and of the reform movement in general, but the film generally doesn’t make them. Everyday Math gets a needed kick in the pants for the lattice method and for devoting space to a full-color atlas, but I still don’t understand exactly what the problem with TERC is, other than it teaches an algorithm that forces kids to understand the distributive property, which…isn’t necessarily bad. And even if the reform movement is completely wrong about everything, teaching the standard algorithms isn’t necessarily the way to go. In the course of my own research, I’ve analyzed reams and reams of paper in which students butcher those standard algorithms in sometimes hilarious and usually cringe-inducing ways, ways that suggest they have no idea where the math is.

Overall, I found the film to be a barely-coherent, transparently ideology/agenda-driven rant that fails to make a meaningful contribution to the math debate. Two thumbs down from me.

—
*The lattice algorithm shown on the film is indeed a Bad Idea. I see how it works, but it suffers from a serious excess of what we researchers call extraneous cognitive load. You’re never going to get a kid to really understand math by teaching that.

**One of my labmates is actually studying the difference between the standard method and the partial products method in large mental multiplications. The partial products method seems to be both more accurate and efficient when doing it in your head.

And if you can do it quickly in your head, then you most assuredly can do it faster than someone who needs to do it on paper. It happens often when I go yarn shopping. I will finish calculating 4 balls of yarn x 132 yards per ball in my head while the saleslady is still fumbling around for a piece of paper and a pen. Or a calculator.

2 x 130 = 260, so 4 x 130 = 2 x 260 = 520, 520 + (2 x 4) = 528

It looks like a mess and takes forever written out, but it only takes a few seconds to do it in your head. And then people look at you like you’re some kind of genius, when really it’s just about turning a hard mental calculation into a string of easy ones.

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Yvonne posted this on June 30th, 2007 @ 9:19pm in Education, Mathematics | Permalink to "A Convenient Lack of Meaningful Content Masquerading as Exposé"