In college in the 1960's I discovered that I have a knack for helping people understand technical ideas, and I have used this talent ever since in many contexts, from modeling biological systems using mathematics, to doing research and development in the telecommunications software industry, to tutoring kids and adults in math, to teaching math part-time at several high schools.
I've noticed that emphasis in schools seems to be put on training kids to perform mechanical operations, and despite this focus, a surprising number of kids have no idea why or when to use the procedures they are taught. I don't say this to be critical of the truly remarkable people I have met who teach, and I don't think it's a question of bad teaching. I think it's a question of how people learn and what schools are asked to accomplish.
To learn anything, a person has to interact in a consciously involved way with what is being learned. A student has to mull over the subject matter, examine it from a number of points of view, think about it in a lot of different ways, gradually piecing together connections that make sense out of the new material in terms of what is already known.
The PowerPoint lessons I've posted on this website do not drill students on performing mechanical operations. They provide opportunities to interact with mathematical ideas and are intended to give students a better understanding of when and why to perform the procedures they are taught in school. The focus here is on what math is, what it does, and why it works.
These lessons animate the core concepts in high school math, literally, allowing students to watch ideas unfold. And they are interactive, so students can step back and forth across the points in a train of thought as it develops, thinking things though at one's own pace and putting new ideas together in ways that satisfy and mean something to oneself.
High school math provides an essential foundation upon which further technical study depends. Fluency not only with mechanical operations, but even more importantly with mathematics as a way to model both concrete and abstract relationships, is a prerequisite for contributing something to science, making intelligent management decisions, and developing new technologies.
Math is also fun, because everyone has a brain, and like every other part of the body, it feels good when you use it.
Phi Beta Kappa
B.A. Biology, Clark University, 1967
M.S. Physiology, UCLA, 1969
Course work in Computer Science, CSUS, 1980-1983
Course work in Education, Sonoma State, 2003-2005
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