There is a quote that I love from the article is that "If I'm having to remember...then I'm not working on mathematics."
I totally agree with this statement. I think that's why I picked math as my major in the first place. Solving math problems becomes so much easier if you understand the reasoning behind them. Otherwise, students may find math is very difficult. When I was in university, I always spent more time on the first few questions and trying to understand all the questions' ins and outs compared to my classmates. I think that's just how I learn and my habit of learning in general. Since I have a horrible memory, I can't even remember what I was going to say during a conversation if someone interrupts me mid-way. For me, knowing the "whys" is a much easier and sustainable way to learn.
As a teacher, I love working through math questions with my students step by step. I try to think like my students; I sometimes also purposely solve the questions with common mistakes students would make. By doing that, students would go through the logical process behind the solution, which offers them a deeper understanding of the "why" behind the solutions. Showing the students the "wrong" solutions also offers students an understanding of the "why not" behind the questions. My teaching philosophy is that students should know the "why" instead of "how", because the "how" will naturally come with the "why".
Lovely! A very thoughtful commentary on these ideas with personal connections, as a learner and a teacher.
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