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BCAMT 2024 - Assessing Virtues: Ideas and Examples - Francis Su

Assessing Virtues: Ideas & Examples


  •  There are many ways to be mathematical (visualization vs. defining things vs. etc). 
  • "Problems that give me problems." -- These questions are so interesting that they bring up more questions. 
  • Lecturing -- break up every 10 minutes to engage students in thinking
  • Math is about thinking: The process, not the result
  • Active thinking raises the class performance by at least half a letter grade
  • Mudd Math Goals (Su's school)
  • Coach Collaboration: https://bit.ly/hmc-math-collab
  • Coach Communication: https://math.hmc.edu/su/writing-math-well/

  • Make Assignments More Exploratory
    • Start with a natural question
    • Many entry points
    • Many solution methods
    • Many ways to continue the investigation
    • Goal: at least 1 interesting exploratory problem on each assignment
  • Examples:
    • DULL: Simplify...
      MORE INTERESTING: 
      - Two numbers sum to 10. Find a pair whose product is as large as possible. 
      - Which is larger: 9x11 or 8x12?

    • Jelly beans in jars for estimating volume
    • Math Fun Facts - Francis Su website
  • How do we assess virtues? 
    • Every assessment is subjective
    • Visual Project:
      • Using art, video, webpage, photography, or any other visual medium, showcase the beauty and/or the humanity of mathematics. 




    • Give opportunities for reflection
      • Formative; virtues are just as valuable as skills
      • Get to know students
      • Learn from students new ways to think about your subject
      • Responses will delight and move you
    • Reflection examples:
      • Take one homework problem you have worked on this semester that you struggle to understand and solve, and explain how the struggle itself was valuable. In the context of this question, describe the struggle and how you overcame the struggle. You might also discuss whether struggling built aspects of character in you (e.g. endurance, self-confidence, competence to solve new problems) and how these virtues might benefit you in later ventures. 
      • For any problems you cannot solve on this exam, suggest a strategy you might try to tackle the problem, and show what happened as a result. Describe any strategic gaps you were unable to bridge, and list 3 helpful insights that may help another person trying to tackle the problem. Doing so will earn you up to 1/2 credit on the problem.
      • Consider one mathematical idea from the course that you have found beautiful, and explain why it is beautiful to you. Your answer should: (1) explain the idea in a way that could be understood by a classmate who has taken classes X and Y but has not yet taken this class and (2) address how this beauty is similar to or different from other kinds of beauty that human beings encounter. 
      • What mathematical ideas are you curious to know more about as a result of taking this  class? 
      • Choose one interesting problem from the text of medium difficult that was not assigned. Describe why you find it interesting. Then either solve it, or find a solution online and work through it, using your own understanding to critique that solution and improve it. An alternative to this question might be: Write 10 true/false questions that illustrate a variety of ideas from this course that you might put on this this exam if you were teaching the class. give a key, explain the answers, then explain why you chose these particular questions and what you hope they will assess. 
      • Semester Reflection: Reflect on the following question: What have you learned in this class about the process of doing or creating mathematics? Weave in potential answers to the following:
        • have you experienced: joy, beauty, reward?
        • what have you learned about the value of struggle?
        • what have you learned about the importance of community?
      • Semester Reflection: Reflect on your overall experience in this class by describing an interesting idea that you learned, why it was interesting, and what it tells you abotu doing or creating mathematics.
      • https://www.francissu.com/post/7-exam-questions-for-a-pandemic-or-any-other-time
    • Writing Reflection Questions
      • Decide what virtue you want to focus on. 
      • Be clear about what's expected (e.g. how long, specific components you are looking for, give question ahead of time).
      • Connect the question to what it means to be human.
      • Think of it as low-stakes, meta-cognitive, formative assessment.
      • Announce full/near full credit for any thoughtful answer. 



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