Spring 2001 Course Announcement

M175: SEMINAR FOR PROSPECTIVE TEACHERS

Unique Number: 55195 Instructor: Smith

Prerequisite: Interest in teaching mathematics, upper division standing, and consent of instructor. (Instructor may be contacted at mks@math.utexas.edu or 471-6142)

Time: T 5:00 — 6:00PM Room: RLM 6.112

Topic: Some "Why’s" of School Mathematics

Course description: What will you do when you are teaching if a student asks questions like:

Why is the Pythagorean Theorem true?

Why is the sum of the first n integers n(n+1)/2?

Is there a formula for the sum of the first n odd integers?

Why does the formula for sin(x+y) work?

Why are the double angel formulas true?

Can you answer these questions? Can you explain them in more than one way? Can you show rather than just tell your students why these things are true?

This course will focus on helping you learn to see and explain why mathematical "facts" such as these are true. We will use the book Proofs without Words: Experiences in Visual Thinking, by Roger B. Nelson. It consists of pictures and diagrams that can help you see why a statement is true. Students will work in pairs building complete explanations around the pictures, then presenting them to the rest of the class.

This course will help you prepare to meet nationwide and state standards for mathematics teaching. In particular, it addresses the Reasoning and Proof Standard of the Principles and Standards for School Mathematics (National Council of Teachers of Mathematics ) and Standard V (Mathematical Processes) of the Texas State Board for Educator Certification.