Reflection Assignments

Here are some assignments whose goal is to get you to reflect on your mathematical learning and on your attitude towards mathematical learning.

But why?!? You might not have been expecting this kind of writing in a math class. There are two reasons for doing this. First, we would like to learn something about your relationship with math. Second, there’s research in pedagogy suggesting that reflecting on your learning experiences can be very beneficial to learning.

Grading. We want to be able to understand what you’ve written, but we won’t be marking you off for your spelling or grammar or anything of the sort. All we’re looking for is evidence of genuine reflection and visible effort into organizing your thoughts into writing.

Mathematical Autobiography

Overview. Write a mathematical autobiography (around 500 words) and submit via Gradescope. You can take this in many different directions, but here are some possibilities for reflection:

Weekly Reflections

Towards the end of weeks \(n = 2, \dotsc, 9\), you should take a few minutes to fill out the Weekly Reflection Form. Your reflection for week \(n\) is due by 4pm PT on Friday of week \(n\).

Final Reflection

Write up responses for each of the following (around 250 words each). Submit via Gradescope.

  1. Cool Idea. Give an example of an idea from this class that you found creative, beautiful, or just “cool” in some way. Explain the idea briefly as you would explain it to someone who hasn’t taken this class before, and then write about what you find creative/beautiful/cool/etc about it. The idea could be a concept or technique you learned that you found particularly compelling, or an example of creative problem-solving that you encountered in your own work or in someone else’s. You might also reflect on how mathematical creativity/beauty/coolness is similar to (or different from) other kinds of creativity/beauty/coolness/etc that human beings encounter.

  2. Persistence. Write about one specific problem you worked on this semester that you struggled to understand and solve, and explain how the struggle itself was valuable. It could be a quiz problem, or an exercise in the notes, or a problem we worked on in class, or even a problem you voluntarily engaged with in some other way. Describe the problem, your struggle with it, and how you overcame it. Did you have a “eureka!” moment, and if so, what seemed to bring it about? Do you feel that this struggle build aspects of character that might benefit you in future ventures (endurance, self-confidence, growth mindset, etc)?

  3. Meta-learning. Every week this quarter, you spent some time reflecting on your (mathematical) learning habits by filling out the Weekly Reflection Form. You used this to tell me about what you were doing to learn things, what you weren’t doing, what you were hoping to change about your learning habits, etc. Describe one thing you learned about your learning habits this quarter. Did you discover that you weren’t doing something that maybe you should have been doing, or that you were doing something that you shouldn’t have been doing? If you set a goal for yourself to change one of your learning habits and followed through on it, what did you find? Was there a learning habit you acquired this quarter that you hope to carry with you into the future?