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Pedagogy: Outlook on teaching math (3rd of 3)

January 26, 2007 am31 10:05 am

Dave at Mathnotations wrote this big ideas about teaching math post. It got me thinking.

I maintain a resume. Years ago I added to it an “Outlook on Teaching Mathematics” page. I jammed as much of what I thought was most important as I could into one page (without using small fonts or obnoxiously narrow margins). I started posting it here last weekend. The first part is here. The second part is here. Read on for the last and final piece.

• An effective instructor is also a learner. I continue to take courses in mathematics and to study on my own. I am an avid problem-solver. I have never stopped trying new techniques in the classroom, and modifying, or rejecting them based on actual experience. As a role model it is necessary to share this love of learning with students. I freely admit when I do not know, and gladly share with students how I intend to search for “the answer.”

It is not acceptable to know just a bit more than the students.

(more below the fold) —>
• A teacher of mathematics must be able to distinguish between right and wrong answers. A teacher evaluates alternate approaches, and distinguishes between minor and conceptual errors. The teacher can place a topic into a broader mathematical context, and answer the questions “Where is this topic next applied within mathematics?” and “Where is this topic applied outside of mathematics?” (if there is an answer) Grade level curricula are a subset of mathematics as a whole. It is the teacher’s responsibility to ensure that what is being taught not only leads to a correct answer, but is mathematically valid and will not need to be corrected at subsequent levels. It is not acceptable to know just a bit more than the students. An effective teacher’s knowledge of mathematics must be extensive.

I freely admit when I do not know

[note: I will put the three pieces of this document back together and post them as a subpage to “jd2718 is …” which is accessible from a tab at the top. ]

The whole piece is available here.

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