1) Before this reading, I had been fortunate to take a History and Philosophy of Mathematics course during my undergraduate studies. That course deeply moved and inspired me to integrate historical perspectives into my own teaching. During my third field experience, teaching Grade 9 mathematics, I began the year by introducing Babylonian mathematics, the sexagesimal number system, Greek mathematics, and Pythagoras. Later, while teaching number sets, I briefly discussed the contributions of Cantor and Zermelo.
By the end of the placement, many of my students- whose cultural backgrounds included Greek, Arabic, Persian, and Chinese- expressed excitement and pride in learning that their cultures had played integral roles in the development of mathematics. However, I couldn’t help but question whether my integration of history had been too superficial or lacking in depth. I continue to reflect on my own perspective and how I interpret student progress. I often wonder: what would truly demonstrate to me that a student has meaningfully engaged with both the history and the subject of mathematics? And is such proof even necessary?
2)
a) I really enjoyed reading about the genetic approach and the concept of the necessity of the subject. From my understanding, this approach is grounded in students' own developmental processes and emphasizes the why behind specific theories, methods, and concepts. This resonated with the idea that mathematical activity is not purely intrinsic but is shaped by cultural and social contexts. It prompted me to consider questions such as: Why were certain formulas created? What problems or needs prompted their development? What were the intentions behind them? As I reflected on these questions, another one naturally emerged: How can I foster an environment where my students are encouraged to ask the same kinds of questions?
This line of thinking reminded me of Francis Su’s (2020) chapter on exploration, in which he emphasizes that exploration is a deep human desire- and that mathematical exploration begins with questions. Tzanakis and Arcavi (2000) similarly note that mathematics is motivated by curiosity, challenge, and pleasure—aligning closely with the desire Su describes. For me, the why questions feel natural; they arise spontaneously, like popcorn, throughout the course of a lesson. Being able to flexibly adapt to these moments of curiosity and make space for them in the classroom feels vital to nurturing genuine mathematical thinking.
b) One point that stood out to me was an objection highlighted on page 203, where some argue that the absence of assessment could lead to a lack of perceived value for students, ultimately resulting in disengagement and reduced motivation to participate. However, the pressure and perceived role of assessment are highly context-dependent. In some cases, assessment may provide structure and motivation; in others, it might hinder curiosity and risk-taking. The tension between assessment and its perceived "necessity" in the classroom is not new, and it continues to raise important questions about how we define learning, success, and student engagement. When, then, is assessment truly necessary—and how can it be designed to support rather than undermine meaningful learning?
3) Some ideas I will continue to reflect on after reading this paper relate to the cultural and societal factors that have shaped the development of certain mathematical domains. In particular, recognizing the dominant Eurocentric narrative that is often implicit in the curriculum and subject material raises important questions: What would decolonizing mathematics look like? How can we broaden the mathematical story to meaningfully include diverse cultural contributions and perspectives? Which students’ experiences and cultures are excluded or marginalized in this history? And how can I bring those voices into the story?
References:
Su, F. (2020). Mathematics for human flourishing. Yale University Press.
Tzanakis, C., & Arcavi, A. (2000). Integrating history of mathematics in the classroom: an analytic survey. In J. Fauvel., & J. van Maanen. (Eds.), History in mathematics education: the ICMI study (pp. 201-240). Dodrecht: Kluwer.
Ann, your post is rich, thoughtful, and deeply reflective. You not only connected the reading to your own prior experiences but also raised meaningful questions about assessment, motivation, and the cultural narratives in mathematics. One of the strongest aspects of your response is the way you weave together personal classroom practice, theoretical ideas (like the genetic approach), and broader philosophical concerns such as decolonizing mathematics.
ReplyDeleteSuggestion: For next steps, you might consider choosing one of your key questions (for example, on assessment or decolonizing the curriculum) and sketching a concrete example of how you could try it in practice. This would move your reflection from questioning toward possible classroom strategies.