Seeking guidance on how to assist students who possess a solid grasp of problem-solving concepts, allowing them to intuitively arrive at solutions, yet encounter difficulties when it comes to communicating their understanding through formal proofs and written formats.
These students exhibit a deep comprehension of the underlying principles and can often visualize the solution or approach to a problem. However, they face challenges in articulating their ideas in a structured and rigorous manner. It is crucial to help these students bridge the gap between their intuitive problem-solving abilities and their ability to express their reasoning formally.
I am interested in hearing your suggestions regarding effective strategies or techniques to support these students. How can we help them refine their problem-solving skills by guiding them to articulate their intuitive ideas in a more formal and coherent manner? Are there specific exercises, resources, or approaches that have proven successful in facilitating this transition?
While my primary preference is to focus on undergraduate students, I am also interested in insights and strategies that are applicable to high school-level students. Hearing perspectives from both levels would provide valuable insights for supporting students in their transition towards more formal proof-writing.
Please note that the focus here is not solely on teaching proof-writing techniques but also on empowering students to leverage their existing intuitive understanding to construct sound and logical arguments in written form.