Mathematics for HS Teachers

An Advanced Perspective

What is meant by “an advanced perspective”?

• Looks at interconnections among HS math topics and their relationship to college level mathematics.

• Includes a deeper analysis of problems and concepts drawn from HS math to reveal important new mathematical insights and understandings

• Is mindful of the historical and conceptual evolution of mathematical theory and school mathematics

Goal of “Advanced Perspective”

• The goal of this advanced perspective is to encourage you to explore mathematical ideas in depth and to explain mathematical ideas with clarity and precision.

Principal Features

• Concept Analysis• Problem Analysis• Mathematical Connections

Concept Analysis

• “Concept analysis involves tracing the origins and applications of a concept, looking at the different ways in which it appears both within and outside of mathematics and examining the various representations and definitions used to describe it, and their consequences.”

• Usiskin, p.1

Problem Analysis

• “Problem analysis involves more than finding different ways of solving a problem. It includes looking at a problem after it has been solved and examining what has been done.”

• Will the method of solution work for other problems?

• Can we extend the problem?

The average test-grade problem

Jane has an average of 87 after four tests. What score does she need on the fifth test in order to average 90 for all five tests?

Solutions: Algebraic and Arithmetical

Graph of the problem equation