I learned through this project how the notion of proof is encapsulated in secondary math classrooms. This was my first time doing a research based project in university so the process was a bit difficult. However, navigating through google scholar and reading articles by recommended authors allowed me to see many people's point of views on this topic. There were also some findings that I never came across such as mathematicians' views on proofs, and reasons why teachers won't implement proof in the class. The concept of rigor and formalism isn't necessary for younger secondary students and proof is less deductive as they may see the bigger picture. I would like to touch on using using technology/software to address proof that may also enhance student reasoning. When can Desmos be used to be convincing for students when they don't have the sufficient background knowledge for other forms of proof. How many proving questions should I put on an exam, say an easy question like "show that the sum of two linear functions with no constant is a linear function with no constant?" I definitely should bring some logic into the context of student's work as well and bring in more social perspectives say from teacher's perspective: Although proof promote a deeper understanding of mathematical concepts by requiring students to justify their reasoning, teaching proofs might take longer to students and potentially affect the pace of covering the curriculum. As it isn't mandatory in the curriculum, students aren't expected to learn it in full great detail, nor do problems relate to it. . . besides questions like computations and finding errors in step X. My curiosity leads me to explore how proofs can be introduced effectively in secondary mathematics classrooms while still covering curriculum topics. I'm interested in understanding the challenges students might face when learning to construct proofs and discovering innovative teaching methods that make this abstract concept more accessible and engaging, either more visually, with more technology, or showing that they can come up with it using knowledge the students already possess. I believe this class has led me to further teacher inquiry, to ponder on issues society is facing nowadays and how it affects education. How to bring math into these issues may be a great way to help. It was fun exploring around in the garden too, learning how to make ropes. The first class topic was also memorable as it was on forming good relations with students. The notion of grades, competition, and cooperation was also interesting as I read articles and watched videos (like Kohn) on it to see such a different perspective. Nonetheless it is crucial to hear what they have to say inorder to better understand their viewpoint and why they believe it is so. This course made me delve further into the nature of this profession of being a teacher and how teachers affect students' lives and their own.
