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History is a convenient and readily available proxy for shifting content focus away from mathematical facts and toward mathematical processes such as problem-solving, proof-writing, problem-posing, abstraction, theorizing. History's appeal I think lies in the concrete, engaging narratives involving the struggles, dreams, and failures of actual people going through those processes. In my experience, differences in mathematical inclination are correlated with the ability of perceiving the abstract mathematical processes as engaging narratives in and of themselves. Professional mathematicians, as much as I've witnessed such speak to one another, tend to describe, e.g. a sequence of algebraic manipulations to solve a problem, as a journey taken by known facts during which they grow, combine, and ultimately transform into new knowledge. I myself have always considered numbers, variables, etc. abstract concepts, to be my friends, and like with any friends I care about their relationships, their states of being, and so on. This of course all begs the question of what mathematical facts and processes should be part of the curriculum in the first place, i.e. what is it that we would like to teach better using history in the first place? |