My student bird procrastinated on this problem for over a week. I always feel a sense of imposter syndrome when it comes to problem-solving questions in Math. I'm confident in my teaching abilities but this doesn't necessarily translate to confidence in my Math abilities. I often humorously undercut my abilities to mask this lack of confidence. For many social/societal/personal reasons, I feel like my Math skills are limited to repeating algorithms. This is obviously a distorted view of my skills since I managed to get a Math degree; however, this view remains pervasive. Thus, my teacher bird concludes that Math trauma and success in Math are not distinct dichotomous paths -- I've had both. Math feelings are varied and complex and knowing this will enhance my empathy for my students.
I would do a similar "aspect" problem based on this picture of my dad in front of the coal-mining truck he drives and trains other people to drive. I could ask many questions about this picture. For example, how high up is the driver's seat? How far does the truck go before the wheels have completed one full revolution?
Madison, thank you for this thoughtful, meaningful personal reflection. I'm so glad that you're thinking about these somewhat contradictory issues about confidence as a teacher and as a math problem-solver at this early point in your career. Your clarity and work on this for yourself will no doubt also help you shine a light on so many people's similar feelings about math. In your case, it's quite clear that you ARE a good mathematician and problem-solver, yet those emotions can persist and make things more difficult. I would be most interested in hearing, from your introspection, what might be the origins of these worries and especially what might help gradually dissolve them. And -- good solution, and excellent extension questions! What an enormous truck that is!
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