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

Write a mathematical autobiography. Submit via Gradescope.

You should write ~500 words (unless you would like to write your autobiography in the form of a poem, in which case fewer words are okay!). You can take your autobiography in many different directions, but here are some possibilities for reflection:

• What kind of a mindset do you have towards math? In what ways is it a “fixed mindset” and in what ways is it a “growth mindset”? What experiences in your mathematical history might have contributed to this mindset?

  In case you haven’t heard the terms “fixed mindset” or “growth mindset” before, here’s a quick summary. A person has fixed mindset in an area if they believe their intelligence or abilities in that area are fixed traits that cannot change. Characteristics of having a fixed mindset include: avoiding challenges, giving up easily, ignoring useful criticism, feeling threatened by others, etc. In contrast, a growth mindset is the belief that your intelligence and abilities in that area can grow with time, effort, and persistence. Characteristics of a having a growth mindset include: embracing challenges, persisting through obstacles, learning from feedback, feeling inspired by others’ successes, etc.

• If you feel that you tend towards having a fixed mindset in math, what is another area in which you feel that you have a growth mindset? How do the feelings you associate with engaging in that activity differ from the feelings you associate with engaging with math? What experiences do you think led you to have a growth mindset in that other area? How do you think you might work on transferring that growth mindset to math?

• How does math as a whole, or this math class in particular, fit into your life? How does it contribute towards your goals, towards making you who you want to be? Even if you don’t intend to pursue math as career, in what ways do you expect to grow as a person by studying math broadly, or by studying the content of this course more specifically?

• Who in your life has contributed to your mathematical development, and what role did they play? If relevant, think beyond just teachers (parents, siblings, friends, classmates, etc).

• What’s an example of an experience in your life where you really enjoyed doing math? What made it so enjoyable? Were friends involved? What aspects of those circumstances do you think are within your control to recreate?

• What role do you think diversity plays in mathematics? Can you think of any personal mathematical experiences that were enriched by diverse perspectives?

• “I hate math.” You’ve almost certainly heard someone in your life utter these words (or something very similar), and perhaps you’ve even uttered them yourself at some point! Do you think there’s a difference between how people react to this versus how they might react if someone said something like, “I hate music”? If so, why do you think that is? What might be the social ramifications of how common it is for people to report “hating math”? Do you think it might be valuable to change this culture, and if so, how might we go about that?

• What do you think mathematics is? How would you define it for an alien who is trying to understand what kinds of things human beings think about and how mathematics fits into the landscape of human inquiry? If this line of thought mires you in philosophical quandaries, don’t worry; you’re in good company! In that case, maybe just propose some possible definitions and then discuss what’s problematic about each of them.

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 11:59pm PT on Thursday of week \(n\).

Final Reflection

Write up responses to all of the following (~250 words each). Submit via Gradescope.

1. Cool Idea. Give an example of an idea from this class that you found creative, beautiful, useful, 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/useful/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 use this as an opportunity to reflect on how mathematical creativity/beauty/coolness/etc 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 quarter that you struggled to understand and solve, and explain how the struggle itself was valuable. It can be any problem you encountered this quarter. Describe the problem and your struggle with it. If you overcame it, describe how. Did you have a “Eureka!” moment, and if so, what seemed to bring it about? Do you feel that this struggle built 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?