President's Message - December 2005

Knowing Mathematics for Teaching Mathematics

KATHY KUBOTA-ZARIVNIJ

kkz@oame.on.ca

How's your school year going so far? What mathematics have you been doing lately? Are you thinking that you were doing mathematics when you were teaching mathematics lessons? When you read mathematics teacher's guides and student textbook pages were you engaging in some mathematical thinking? When you were making sense of student problem solutions, how were you using mathematics to understand student learning? Or, when was the last time you solved mathematics problems yourself, for your teaching, for your learning, or for the simple intrigue and joy of it?

As this is my third president's message, I'd like to spend some time with you, doing and thinking about mathematics within the context of the ideas highlighted in my previous president's messages. In my first president's message, I introduced the five key conditions of a complex learning system (i.e., internal diversity, redundancy, decentralized control, organized randomness, neighbour interactions), in terms of the structure and activities of the OAME community. In my second president's message, I introduced and outlined the purpose, structure, and content of OAME's latest professional development resource, Growing Up Mathematically.

In this president's message, I am inviting you to engage fully in mathematical thinking and doing, as a means of furthering your experiences and insight into the range of K to 12 mathematics. John Mason (2005) explains full mathematical engagement as ''actively doing such things as jotting own ideas, doing tasks and constructing your own examples, trying to make connections, getting involved in detail, standing back to get the big picture, explaining what you are doing or trying to do to someone else; being prepared to struggle; acknowledging feelings'' (p. x). Also, by doing mathematics yourself, rather than reading and hearing about mathematics, you will have the immediate experience upon which to consider your own mathematics content and pedagogical knowledge needed for teaching mathematics to students. So, get some colleagues together from your division or department and let's do math!