Retrospective: The uncrossable line of math (4.16.2006)

Editorial: This is installment #6 in this week’s retrospective series where I’m reposting some classic articles with updated comments. For me, there’s a deep interplay between pedagogy and culture that we don’t make nearly enough of. I’ve posted many articles trying to make the point that many of the problems in education, particularly math education, that we try to treat with curricula or technology or pedagogy are doomed to fail because they are not problems with teaching — they are problems with the culture. In this article, I make that point and go one step further, bringing in a theme from my Calvinist/Lutheran religious beliefs. 

The uncrossable line of math

Originally posted: April 16, 2006


Darren at Right on the Left Coast has spot-on commentary on a spot-onpiece in the Seattle Times about math instruction. The part I want to highlight for now is this quote from the Times article:

[B]y high school, kids have spent years marinating in a culture that disses math. Few people in this country boast about being illiterate. But it’s long been a laugh line to declare “I’m not a math person.” Not so in countries such as Japan and Singapore, where students are expected to conquer math — and keep trying until they do.

And in America, where are the math bees, the volunteer math tutorial corps, the math-is-fundamental public-service campaigns? As a society, we root for reading. But we expect success in math to just happen … or not.

Ilana Horn, associate professor of mathematics education at the University of Washington, says that makes a big difference. “We have a belief in innate ability. It perpetuates this idea that you either have it or you don’t, instead of that you aren’t trying hard enough.

“It allows teachers to not question student failure in the same way, and it allows parents to excuse the kids’ poor performance, and kids to excuse their own poor performance.” [Emphasis added]

I think that’s right, although I don’t think Prof. Horn goes far enough. “Innate ability” suggests that some people have more to work with than others — that for whatever reason, some people “get” math faster or more deeply than others. Frankly, we don’t believe in that when it comes to math. We believe in a sort of mathematicalpredestination — that there is a select group, a chosen few, who have been endowed by their maker with mathematical skill; and that the rest of humanity does not have that skill and cannot attain it by our own efforts, no matter how hard we may work. We believe in an un-crossable line when it comes to mastery and fluency with mathematics — the chosen ones on one side, the rest of humanity on the other, laughing and cracking jokes about how bad we are at math and how nerdy the people on the other side of the line are.

There may well be differences in innate ability with math. Regular readers will remember this comment thread that features a discussion by virusdoc about possible evolutionary reasons for differing innate math ability. Sure, OK, those may exist. They certainly appear to exist, although by the time I see students when they are 18 years old, the layers of evolutionary or biological causes on the one hand and social and cultural forces on the other are so conflated that you simply can’t tell why one student might be doing well and the next one poorly.

But assuming those differences actually exist, and whatever the causes may be, what do classroom instructors make of them? In other words, what do we do about it? I fear that the majority of instructors, high school and college and elsewhere, assume the existence of the uncrossable line and proceed in their classes to separate the sheep from the goats. We make excuses. Instead of setting clear goals for all students that aim toward mastery of the material, and creating classes that push students toward those goals, we mitigate those goals and let the lower-acheiving students settle for less. Because, after all, they just haven’t got whatever the higher-acheiving students have; they are not chosen.

No more excuses, everybody. All of us — math teachers and students, and the culture as a whole — need to come to terms with the importance and centrality of mathematics throughout all of education, and start expecting more of students and of ourselves. We need to erase that line that we have so conveniently drawn. 

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