Reflecting on teaching through the lens of history of mathematics 

Some questions that come to mind as I read through the objections and advantages include:

-          What constitutes the history of mathematics and development of mathematical knowledge within the discipline? Are the proponents and opponents conceptualizing ‘history’ the same way? As mentioned, history is not just a list of facts—though it is often presented as such. It is a story of development. If we think of the history of mathematics as the story of how we came to know what we know and what motivated us, it can act as a model for the process of solving a math problem (which necessarily involves changing motives and making mistakes), for students. In this sense, it may act to disrupt the all-to-frequent fear of making mistakes or changing one’s mind in math class.

-          If we think of the supposed ‘final’ products of mathematical research as the refined versions of history, in what way might we be erasing or betraying the messiness or ponderous nature of problem solving? There is certainly a meditative beauty to the process of pondering, refining, revising, and verifying a solution to a particular problem. Even more, there is a sort of storytelling that occurs through history as we explore the multiple different motives for engaging with particular math problems.

As a former math teacher, my favourite solutions were the ones with parts of the solution crossed out and arrows pointing me in the direction of the thinking process of the student. These were much richer sources of information for knowing what students know (assessment) and understanding misconceptions than the elegant step by step refined version of a solution. The article alludes to mathematics as an evolution of ideas by humans, for humans (a human endeavour). I think this can be a parallel to students’ evolution of ideas and the nature of their learning and ideas about mathematics.

A cautionary note that came to mind as I read through the article. We know history is told by those in power at the time the history was recorded and at each time it is recounted. The article mentions this in a different way, indicating that western mathematics dominates classroom content. There are many areas in which the history of marginalized cultures and populations has been silenced or lost and histories in mathematics are no exception. How might we ensure that the multiple narratives of the development of mathematics are presented? How might we ensure that the histories of mathematics are contextualized in the multiple histories of people—not just the dominant narrative of history? Some ideas that come to mind to supplement those on page 214 include: exploring the students’ thinking process through a problem, structuring some assignments around math talks at home then inviting students to share these math talks in class, and—as the article mentioned—presenting multiple approaches to the same solution all the while being mindful of the cultural source and context of the chosen solutions.