Learning Through Mistakes
People often say that we should learn from our mistakes—that reflecting on past actions can guide our future decisions. It would be nice though rather than to reflect and learn from past mistakes (when it is often too late) that we learn through our mistakes as they are happening. I came across a tweet recently that made me think of how to foster this in a classroom. A few things jump out at me here: It looks like the question was made by the student and while it is fun, it wouldn’t be considered a real-world application problem. This shows that problems don’t need to be useful to be relevant. This is a non-routine problem that invites mathematical thinking, and for learners to start seeing that as useful is already a win. It likely isn’t a big leap for this student to see how the thinking involved to solve this problem is valuable in many ways. I think we often get too caught up in trying to answer, “when will we ever use this?” by trying to find specific applications for t
