For Math Teachers

My Pearson Textbooks

Basic Mathematics



My musings about mathematics and the teaching of mathematics.

Here are some of the presentations/handouts I gave at AMATYC, CMC3-North, and CMC3-South.

1. Are We Speaking the Same Language? (Presented at CMC3 and AMATYC)

This discussion is about mathematics dictionaries and their similarities and differences. The most surprising is the differences. It turns out that not all math terms are defined the same. Also, is it too late to invent new terms?

This is a pdf of my PowerPoint presentation at the CMC3-South Spring 2010 Conference.

Are We Speaking the Same Language?

Here is a link to a web page that has, itself, links to many on-line math dictionaries and glossaries.

A list of On-line Mathematical Dictionaries

Here is a link to a web page that shows the earliest known uses of many mathematical terms.

Earliest Known Uses of Mathematical Terms

2. Developing the Quadratic Formula (Presented at AMATYC and CMC3)

Here, I show a variety of ways to develop the formula, including a graphical method I developed. The explanation of the graphical method first develops the graphing of a parabola and its various features.

I challenged myself to "discover" the graphical approach after pondering the question, "Is it possible to develop the formula without ever having to complete the square?" I believe that my graphical approach does exactly that.

Also, two "ancient" methods are shown, the Babylonian method and a geometric method. The Babylonian method actually develops a Quadratic Formula, whereas the geometric method solves a quadratic equation.

A. The Traditional Approach

B. The Babylonian Approach

C. The Geometric Approach

D. The Graphical Approach

3. The Order of Operations (Presented at AMATYC and CMC3, along with Mathematical Tidbits)

I contend that the order of operations used in arithmetic, algebra, etc. is not an arbitrary order to which mathematicians the world over decided to agree. I contend that the order of operations must be the way it is.

Here is my position paper on The Order of Operations: Math or Myth

4. Mathematical Tidbits

Here are some mathematical tidbit that may interest you. I presented these as handouts at the AMATYC Conference in San Diego, November 13, 2005.

A. Math Tidbits Some of these are related to the Order of Operations handout.

B. Dividing Fraction Why we invert and multiply.

C. Divisibility Rules A list of the divisibility rules for 1 through 11.

D. Divisibility Rule for 7 A thorough look a the divisibility rule for 7. In this paper, I prove that the rule works 100% of the time. I also show the divisibility rule for 13 and show how you can develop divisibility rules for 17 and 37, and a new rule for 11!

5. Math to Go: Podcasting Lessons

A. Podcasting Presentation Handout.doc at AMATYC November, 2007

B. Practice Streaming Video-1 (brief clip, 1:00 in length)

C. Practice Streaming Video-2 (brief clip, 1:26 in length)

D. Factoring Trinomials Video (full clip, 28:24 in length)


Contact me at

To top of page