Math teaches more than we may think
Published 12:00 am Wednesday, December 29, 2004
As the days of the year now quickly form into a new annual set, I reflect on a number of things, which hopefully will make my new year something worthwhile – things like resolutions to be a better person, more diligence in my professional endeavors, more patience with my children, and more stamina to make determined contributions to the world in which I find myself.
One of my annual renewal rites is re-reading some of the classics which have given me a perspective on my relationship to how I approach others I encounter in daily routines.
Of those readings, one of the most mind-clearing masterpieces is Machiavelli’s “The Prince” for its sheer timelessness and understanding of human motivation.
Another is Sun Tzu’s “The Art of War”, which follows closely on the heels of Machiavelli for making strategic moves.
About seven years ago I added Stephen Hawking’s “A Brief History of
Time” to my yearly literary “to do” list.
Hawking really does simplify some of our contemporary considerations of physics, just as Bertrand Russell’s “The ABC’s of Relativity” did several decades ago.
But the real challenge for me has always been trying to understand the importance of applications of mathematics, just as Hawking and Russell did in their works.
And that is where the real fascination of thinking begins to take hold in American education, for little though we recognize or acknowledge it, our basic forms of deductive reasoning are mathematical applications of principles set down a few centuries ago by a Greek mathematician named Euclid.
Now, for most of us, the mere thought of a proof for our sophomore geometry class is enough to send us to the bath for a cold shower and a cup of wake-up coffee after trying to put one postulate together with another to justify why the angle of one part of a figure can make the difference in how we build the next bridge!
And future applications of these principles will tell us just how much and at what rate to put water into a bucket with a hole in it so that we can fill the bucket – and just how long it will take to complete this vital task. (I still think it is ridiculous to use a bucket with a hole in it!)
At any rate, it is these kinds of mathematical gymnastics we are exposed to in our secondary school paths.
And it is these kinds of mathematical “problems” which cause us so much frustration and consternation, and ultimately force us to pose the question,
“Why do we study math?”
In most practical instances, we learn basic math so that we may function in a world, which demands such basic skills.
Someone working in the retail industry certainly needs to understand basic mathematical calculations in order to survive!
Someone who works in a lumber yard had better well know basic measurements and calculations or that venture will dissolve in a morass of under and over cuts resulting in consistent miscalculations.
Now, aside from those very fundamental reasons, there is another more subtle and more profound reason we study mathematics, from Algebra I, to Algebra II and to Geometry.
It is to expose us to the basic principles of deductive reasoning.
Of course, most of us believe that the end-all of this kind of deduction is Pythagoras’ Theorem regarding right triangles – you know, a2+b2=c2.
But more familiarly, we can remember the basic deduction declaring that “if A=B and B=C, then A=C.”
Whether or not we realized it when we first witnessed this magical equation, it was laying the foundation for our ability to think clearly.
It was not until I was in a freshman logic class in college that I came to realize that three years prior to my venture into the world or symbolic logic I was being indoctrinated, albeit on the theoretical level, to the foundational rubric for how we think, how we formulate ideas, and how we reach conclusions – as well as how we come to rationalize that which we wish to promulgate and eventually to pontificate.
Thus, the study of mathematics gives us a real opportunity to study the structural rudiments of our method of argumentation, of discovery, of theorizing, and of constructing our approaches to the universe we try to understand on a moment-by-moment basis.
And at this time of year, I always ponder just why my sophomore geometry teacher never took the time to tell us that she was teaching us how to think, not what to think, but how to organize those random mental images floating in and out of our conscious awareness into a working body of knowledge which indicates a person exposed to an expansive, comprehensive education.