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.