Math Is Just Math...Isn't It?
My training as a practitioner and researcher is in literacy, but I had an opportunity in 2007 to work up an argument about mathematics learning that, expanded with the help of two co-authors, has been published in a new book (forgive what is my first ever shameless self-promotion). That work is just a synthesis of theories and studies by others who write about numeracy and learning, but it presents an argument that seems to challenge some things that we take for granted about what math is and how people learn it and use it.More and more people seem to accept that there's not just one right way to go about using language; people who struggle to write essays or take vocabulary tests in school might be skilled users of language outside of school. People can struggle with analogies on a standardized test in school and then go home and read books, follow written instructions, write letters, speak persuasively, compose poems, and surf the Internet. We can do a much better job of connecting those out-of-school practices to how we work with kids in school, and more and more teachers are explicitly interested in doing so. We can also distinguish between being good at school literacy and being good with language more generally (or in other settings), and more and more teachers (and students) do so.
But what about math? There seems to be less of a belief that the math that goes on in school is, say, just a school kind of math, and that people who struggle with school math might be good at various forms of math outside of school. Some would concede that this is technically possible, but it's still much more common to believe that math is a universal set of skills that just exist...if you can't do math in school, chances are you can't do math at home either...math is math.
The problem with this is that education researchers keep proving that students who struggle with math in school can do very impressive and accurate stuff with math outside of school, when math is part of a practice they care about and are comfortable with...selling stuff, comparing sports stats, playing strategy games. Something about these outside-of-school practices makes (some) kids do math better than they do in school. It also turns out that math professionals do math in a way that looks very different from how math works in school...they do it collaboratively, creatively, and they do this math in the process of doing stuff they care about. The kids who do the best with school math tend, really quite often, to be the kids who have home lives peppered with school-math-esque problems and contexts...when home looks and sounds a lot like school, you've got a leg up over people who encounter math in very different settings from school-ish ones. But does that mean you're better at math?
Because we think of math as a set of universal skills--a universal language, as you'll hear said sometimes--we don't consider that there might be a direct link between what math is being used FOR (or in the language of my book chapter, the wider numeracy practice in which you're doing this math stuff) and how successfully it's being done, even though several fields of psychology and even economics show over and over again that our social relationships, self-image, and motivation impact how we do everything.
For as long as we think of math as somehow pure and immune from the context it's in, we'll fail to think about the math that struggling math students are already doing and why learning often works outside of school but not inside. By treating math as "just math," we allow ourselves to make judgments about students' intelligence or effort when they struggle with school math...and when they succeed. We also ignore some critical differences between how math looks in school and how it looks when professionals do math in the "real world." Smart reform of school math might involve us paying more attention to some very important aspects of school that don't (at first) sound very mathematical.
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