Topics in
High School Mathematics

About this page:

My name is Martin Cohen. I work as a computer programmer. My college education was in mathematics and I have had a lifelong interest in both mathematics and the teaching of it. On this page I present several topics in high school level mathematics.

We are constantly being told about how poorly Americans are doing in science and mathematics. I don't know how much truth there is in all this. I do know that we are living in an age of information and that our schools have not yet adjusted. The ability to reason abstractly is going to be of increasing importance.

When I went to college I did some substitute teaching between the end of the college year and the beginning of the public school summer vacation. Nobody expected me to teach anything so to give the students something to do I presented several problems in recreational mathematics. We all know the type of respect that substitute teachers command. I was therefore quite pleasantly surprised by both the enthusiasm with which the problems were tackled and by the ability of the students to solve them. This was the case for both advanced and less advanced classes. Some of the problems I presented were fairly challenging.

It is clear to that nearly everyone has an intrinsic interest in mathematics; it is simply a matter of being able to tap into it. Everyone should come out of high school being able to perform basic algebra. In the examples I am assuming knowledge of algebra. The topics covered are normally either not presented in high school or are not thoroughly covered. These are all ideas that I either came up with on my own or read about after leaving public school. The topics proceed from concrete examples to abstract principles. I welcome any comments on what I present. I also welcome any ideas on how to teach mathematics in public school. If you provide the latter, please try to be as specific as possible. It amazes me how people can talk endlessly about how to teach mathematics without presenting any actual mathematics. For my part, I have dispensed with any formal discussion of teaching principles. In this regard I will let the examples speak for themselves.



Topics:

Teaching Geometric Series
Mathematical Induction
Use of Slide Rule as a Teaching Tool
The Joy of Counting - Introduction to Combinatorics
Rotations and Revolutions
Pythagorean Triples
Gentle Introduction to Continuity
Some Problems
Modular Arithmetic

Mathematics Education Sites:

Very good introduction to infinity (couldn't have done better myself)
Drexel University Math Forum
Cambridge University's NRICH project
Mathematical Association Of America columns
An argument against placing an emphasis on teaching practical applications of mathematics

Please give me your opinion! Constructive criticism is welcome. In particular, I would like to know if there is anything you had difficulty following. Your feedback would be helpful in guiding me to make improvements.



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