Thursday, October 20, 2016

Math as seen through a glass, darkly

A professor of education and mathematics education (but not, I notice, of mathematics) announces that "mathematics can be decolonized." Oh joy. She can't see any obvious ways of changing the content, so she looks for the "human aspect:" how do students see themselves.

"what mathematics actually is... Mathematician and academic Jo Boaler points out that mathematics is the only subject where students and mathematicians give very different answers to this question."

Mathematicians view the subject as an exciting, creative endeavour in which problem solving, curiosity, excitement, intuition and perseverance play important roles - albeit in relation to abstract objects of study.

For school and even undergraduate mathematics students, these aspects of mathematics are often not experienced and remain opaque. Students tend to believe that mathematics is a set of procedures to be followed. They think only particularly gifted people can do and understand these procedures.

Not true. IIRC Latin was another subject that the skilled and the students had wildly different opinions about. PE is another: humiliating agony for some of us, fun for others. I saw premeds struggling with physics.

One reason for this is given by a study in the US, which showed that the more a field attributes success to giftedness rather than effort, the fewer female and black academics are in that field. This is because the field perpetuates stereotypes about who belongs in the field. The same study found that mathematics professors hold the most fixed ideas about giftedness.

But this view of giftedness versus effort is not borne out by research. A number of scholars have argued that all people are capable of learning mathematics, to high levels.

Go ahead, follow that link. It's a 2-page PDF book review, and it doesn't say what Prof Brodie says it says. The book discusses human mathematical ability in general, not in degree. Nearly everybody can abstract to 1+2=3. Most of us can master the times tables and get some feel for fractions (not always taught well). Somewhat fewer, but still a lot, can learn algebra and proofs. Fewer of those are skilled at it, but that's not a problem--they've been trained in the rudiments of a new language and way of knowing things. I didn't use high school French much for years afterwards either.

If Prof Brodie actually did a little math, instead of math education, she'd know that accomplishment is about giftedness. I've a BS in math, and my only solo paper is in mathematical physics. John Baez is a mathematical physicist. I'm not in his league. He's not in Erdos' league, and would be the first to say so.

Whether stereotypes have any significant effect is open to question. For this or that individual, perhaps. I've seen nothing convincing that shows any causal link of the right order of magnitude. On the contrary, elementary textbooks (perhaps not in South Africa) are drenched in "diversity." The problem-solving children in the explanations are carefully mixed in race and sex. Side-bars extol the accomplishments of 2nd tier mathematicians in order to achieve the right sex ratio. The way is made as friendly as possible--but it turns out there's no royal road to math after all.

That's not to say that we can't do better in math education. There are plenty of subfields. Some kids do fine in algebra but bomb proof-based geometry; some do the reverse. At least the rudiments of algebra are very widely used, but some aspects of topology or knot theory might be accessible in place of more "advanced" algebra (e.g polynomials) or geometry. I tried to teach some TAG 3rd graders a little bit about abstract groups, and I think some of it stuck for at least a week.

But "decolonization" of something as thoroughly abstract as math? There's no ethnic culture associated with it, no economic culture--there are a few mathematical cultures, if you like, but nothing that screams "dead white men."

No, I'm afraid that her real goal is in the tail:

Everybody deserves access to its beauty and its power - and everybody should be able to push back when the discipline is used to destroy and oppress.

That sounds very much like "if the numbers mean something I don't like, I get to reject them." And reject them in good conscience, because labels like decolonization and liberation automatically put you on the side of the angels. Perhaps she means she doesn't like certain technologies, but she puts the blame squarely on math, and I assume she means what she says.


RichardJohnson said...

She is an Ed School prof. Ask most primary and secondary school teachers about how useful their Ed School courses were in their teaching in real-world classrooms. Most will reply that their Ed School courses were, to put it charitably, less than useful when applied to real-world classrooms. Take an Ed School prof's statements as seriously as you would those of a relative in the latter stages of Alzheimer's.

Assistant Village Idiot said...