THE MATHEMATICAL UNDERGROUND

Growing Tired of Waiting for the Professionals To Free Us From Math Prison

Michael Round

June 25, 2009

AN INTRODUCTION

For those who don’t enjoy math, why wait for the profession to come up with another way to teach math. Time is too short! For those who do enjoy math – what else is there for us?

When I think of fractals, modeling, simulation, probabilities, chaos theory, etc., I wonder why this is nowhere to found in the curriculum.

What can be done – for both groups of people? What can we do – by ourselves?

A FIRST STEP

The Graphing Calculator, as it is used now, is the enemy. No, this is not an attack on technology. It’s an attack on a tool that has taken the joy out of learning, of programming, of understanding.

If the graphing calculator is the enemy, who can we call “Friend”? The blank spreadsheet in a program most everyone has access to: Excel.

But isn’t Microsoft Excel for keeping your checking accounts and business applications? What good is it for the student? What can possibly be done in Excel?

This series provides an answer to that question.

THE GOAL

The goal of “The Geometric Mind”, Part I, is to whet the appetite of the student, to let them know good things are possible in this environment. It’s a learning environment where the novice can be up-and-running in a short time, not relying on the crude algorithms of the graphing calculator.

Part II of the “The Geometric Mind” series will explore how specifically to do all of this – plus more.

The presentation will be quick, explicit, with plenty of examples. That’s the nature of the game. Get up-and-running quick, and let the joy in learning commence!

Part III: The briefest of examples. By this time, the veil has been lifted, and the reader should be able to grasp possible ways the graphics were done. At this point, a "recipe" or "instruction booklet" is not needed. In fact, it's a hindrance to understanding what's going on. With an idea of "what to do" and "how to do", you're "off and running"!

THE GEOMETRIC MIND

In Search of …

So what exactly am I calling “The Geometric Mind”?

Is it the use of visual logic tools to understand the flow of the argument? Yes.

Is it the use of math in – and out – of these visual logic tools to understand the mathematical flow of the argument? Yes.

Is it the use of ambitious targets to diagram and understand what needs to be done to solve a problem? Yes.

Is it programming, animation, simulation, graphics? Yes.

Is it the use of all of these tools – plus many more – to better understand and solve problems?

Yes!

What’s possible when any one of these intellectual “pistons” is firing? An example is here: