Framing and Practicing: Ongoing development beyond the course, CE3 (classes 9-12)
(A CE in which students, building on CEs 1 & 2, formulate specific plans for how to continue your own development as a mathematical thinker and, as a result, be able to foster the same among colleagues or students in your work/life/teaching situation.)

Books such as Julia Cameron's The Artist's Way provide readers with a program for developing one's creativity, but what is the equivalent for developing one's mathematical thinking? In any case, given that a mark of creativity is to develop one's own program, not follow someone else's, what would your program—or framework—for mathematical thinking look like? This said, all invention involves borrowing, so the challenge is really to synthesize elements from sources encountered during and before this course. These syntheses should be selected and organized in a framework so as to inspire and inform your efforts in extending mathematical thinking beyond the course. For a brief introduction to the experience of past students who prepared frameworks (called "manifestos") for critical thinking (i.e., not for mathematical thinking), see section 2 of Taylor (2002). (For the full manifestos from a 1999 critical thinking class, see Readings.) Your frameworks might make up a 3rd section of the book from CE1 and CE2.

Corresponding to your framework, what is your plan for practice to develop your ability to foster the development of others as mathematical thinkers in your work/life/teaching situation? The plan should demonstrate how and when you plan to put into practice the skills and tools from the course - in your work situation or community, and/or how you could adapt and practice using those tools for opportunities in the future. You should include a plan for evaluating the outcome so you learn from experience and practice. (Test score results are not the only measure of improvement in mathematical thinking!) For examples of Plans for Practice from different CCT courses, see Readings. (Steps to undertake and when.)

Steps