Why teach math history? Before reading this chapter by Tzanakis and Arcavi, my views on whether, why, and how math history should be incorporated into my math teaching were largely unformed. I struggle to think of even one time in my high school math classes when math history was mentioned! Certainly it was never the focus of a class. Still, my view was that at least some attempt to incorporate math history should be attempted, primarily as an attempt to "humanize" math, providing connections to people and the world in which they lived. I would have said that providing some idea of when and where mathematical ideas developed would make the material more interesting to the students. But I would have struggled to make any meaningful suggestions regarding how this should be done.
There were a few "stopping points" for me in the chapter -- one of which was at the very beginning of the article. The authors write, "Mathematics is often regarded as a collection of axioms, theorems, and proofs" with the assumption that "the logical clarity of such a presentation may be sufficient for understanding mathematics" (p. 201). But, as they later write, in such a presentation, "questions and problem which constituted basic motivations for the development of an idea, as well as any doubts along the way, remain hidden" (p. 204). I was struck by how rarely I ever paused to consider the development of the math I was learning in high school (and university). This meant I missed out on seeing mathematics as an "evolving human intellectual process" (p. 207). The effect is that I learned to view math as something "outside" of this world, when the opposite is true.
Along these lines, I was struck as well by the authors' comments regarding mathematics as a cultural endeavor that was in many cases "developed for its own sake, motivated by aesthetic criteria, intellectual curiosity, challenge and pleasure" (p. 207). Understanding more about the history of math and the motivations of those who were part of its development would have motived me to care even more about it, and perhaps to ask different questions as a student. Maybe I would have become more curious as to the importance of various math topics in the times in which they were developed.
My views on whether and why to incorporate mathematics in my own teaching are not fundamentally changed after reading this chapter, but they are certainly strengthened and enriched. I am now armed with many more reasons for incorporating math history in my teaching. But what has changed even more is that I am beginning to form some ideas of how to do this. While some of the specific examples the authors mentioned in the second half of the chapter involved unfamiliar mathematical concepts to me, the concrete examples of how math history can be integrated in the classroom have given me a number of new avenues to pursue. I especially appreciated the ideas of historical packages, having students work to solve historical problems, and developing a play to "re-experience the life of mathematicians in the past, as a way to appreciate the human side of mathematical activity" (p. 229).
I found your point about seeing math as something “outside” of this world really interesting. When we only see the finished formulas and proofs, it’s easy to forget that real people developed these ideas through curiosity, questions, and sometimes struggle.
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