Other People’s Thoughts

I’m entering my third year as a math teacher. For a while, I’ve been a math blog/book lurker, keeping my thoughts and reflections to myself. I finally feel a need to write my own thoughts down, to make sense of them and also to share.

Too bad, because my first post here will be a collection of other people’s thoughts. Here’s a bunch of posts, articles, and books that have strongly influenced my thinking on math and teaching:

  • Teaching as Decision Making (educating grace) – Is good teaching a collection of best practices or is it situationally dependent? The answer is unclear – this is education of course! But a nice takeaway is that a teacher move that’s effective in one context may not be effective in another. I can’t watch you do something successfully and be sure that it’ll work as successfully in my own classroom. Good teachers have instructional judgment.
  • Creating Cultures of Thinking (Ron Ritchhart) – Teachers tell students to do their work. Schools adopt a workshop model. The “work” metaphor leads everyone to believe the purpose of school is the completion of work. No, the purpose of school is to think. Is what I’m doing enabling and encouraging my students to think?
  • Math Girls (Hiroshi Yuki) – I really enjoyed this book. Examples are the key to understanding. For some reason, this idea has sparked a new wave of mathematical problem solving insight for me. In the midst of a complex math problem, the examples you create become mini-laboratories for playing with and testing ideas. Examples are a way to push definitions and concepts to their limit, giving way to new understandings and avenues for exploration.
  • The Having of Wonderful Ideas (Eleanor Duckworth) – I’ve never been better at teaching myself math. I’ve tried for many years to extend my content knowledge on my own but I’ve always had a lot of trouble. Recently the difference is that I’ve stopped trying to do every exercise in textbooks according to a subscribed order of learning. I’ve been creating mini-projects for myself based on my own curiosities, based on mini-projects I’ve worked on before. You learn a lot when you work out the answers to your own questions and not just somebody else’s.