Oct 19 Inquiry Project start up

1. Define your question 

Search Topic: The Usage of Proofs in Math to Aid Student Learning 

2. Analyze your topic into concepts 

Concept A: The importance and value of having proofs 

Concept B: In which areas should proofs be implemented and how much rigor is necessary? 

Concept C: Different forms of proofs and their convincingness to students across stages 

When discussing the usage of proofs integrated in math, I want to draw upon existing educational theories, practices, and expert opinions. The role of proofs in math education stems from different philosophies on the purpose of education in mathematical understanding and the skills students need to succeed in the modern world. Including proofs can enhance students' logical reasoning skills and deepen their comprehension of mathematical concepts, while a lack of them might make the content more friendly/accessible but less water-tight/convincing. I happened to be exposed to multiple forms of proof in post-secondary. These may be utilized in teachings to allow students to not only get the right answer from a formula but also understand the inherent logic/structure that governs the notion. Without certain forms of proof, harder topics may be less intuitive. Allowing students to see different ways certain concepts came to be and how they are derived resonates with students in varying ways. The efficacy of a particular method often depends on the specific concept being addressed and the individual student's learning style. I was interested in proofs in latter years of high school. A lot of the equations are derivable based on previous knowledge students have encountered. This allows a build up of past ideas (or use them as a scaffold) into new ones. Certain definitions and evaluations were plopped onto the formula sheet, making it tedious for students to use them as they just take them for granted. Other students may feel indifferent but they lose out on some richness and value in linking information. Finding the sweet spot is hard and to balance how much time is spent on proofs in the classroom is something I have yet to experience.