Reflection: Quasi-empirical Reasoning (Lakatos)

“Lakatos claims that mathematical theorems are not irrefutable true statements, but conjectures,” and this got me thinking about how my math knowledge was learned and how math is usually taught as schools. Based on my experiences, math was taught by assuming the theorems are correct, and my math classes focused on how the theorems worked and applied. At the university level, my professors would sometimes proof theorems, but I have never seen anyone in the class question the validity of the proof, or even propose a different way of proofing a theorem. I think this connects to inquiry-based learning where we should promote students to question a theorem on not only how it works, but also why it works. At secondary level, formal mathematical proofs may be too complex and challenging for students to generate themselves. However, I think if we showed the proof and pose good guiding questions while explaining the proof, it will really promote inquiry-based learning, let students have a deeper understanding in a theorem, and have a stronger mathematical way of thinking. Lakatos also said “conjectures can be a starting point of the growth of knowledge.” Relating to that, the IB program has an internal assessment where students investigate on an inquiry math project on a topic they are interested, and I think that is a great example of what the author wanted to portray. In a regular class, My SAs also work very hard in making good real-life projects for students to do, and that is also something I hope to continue when I am teaching in my long practicum.