I posted this on Twitter a few weeks ago:
— davidwees (@davidwees) February 25, 2013
In response, someone asked a very sensible question; how do I do this?
Here are some ideas.
- Find an area of mathematics with which you are not currently very familiar, and start exploring it. This might look like a combination of reading what other people have written about this topic, and experimenting with it yourself (mix and match according to your preference). One excellent starting place here I recommend is Paul Lockhart’s Measurement book. Another area of mathematics (or that uses mathematics) that I recommand all math educators learn at least a little bit about is programming.
Alternative: take an area of interest and see if you can develop your own mathematical framework around it. After all, no mathematical framework existed until someone started exploring patterns and the relationships between objects and then creating a language to describe these relationships.
- Solve the challenging problems from whatever textbook you are using. Don’t rely on the answer key! Ask for help from colleagues if necessary. Getting stuck will help you develop empathy for your students when they get stuck. Try and reflect on how you got "unstuck" and help students learn this process. Another source of challenging problems: past mathematics contests.
- Explicitly look for mathematics. Keep a journal of the mathematical ideas you find. Share what you find with others. Incorporate whatever you can into your classroom. See if you can apply mathematics you know to solving some of the problems you encounter in your daily life.