Wednesday, February 16, 2011

The "Three 'R's"

"I am my thoughts. If they exist in her, Buffy contains everything that is me and she becomes me. I cease to exist. Huh." -Oz, Buffy The Vampire Slayer

The Three 'R's represent an old idea on the fundamentals of education are, Reading, wRiting, and aRithmetic. While meandering through East Lansing, I fell to pondering why I still consider mathematics education relevant in a world where computers are increasingly able to perform the calculations that students are called upon to make. While answering this question, I also hit upon why I consider my dual background in math and philosophy a natural pairing, and an overall theory of education that can be explained by the Three 'R's.

To me, the natural product of education is not knowledge, but rather thought. In a society shaken to its foundations by the advent of the Internet, knowledge has become an increasingly available resource. On the other hand, thought, along with love, remain the cornerstones of that which is best in humanity. Thought can be further broken down into a three step process in which we must repeatedly engage to truly fulfill our calling as thinking beings. First, we obtain new knowledge, which I symbolize by Reading. Next, we synthesize the new knowledge with our existing knowledge and thought structure, aRithmatic. Finally, to complete the cycle we must make our new thoughts socially available so others to may obtain and respond to them, which is wRiting.

We can certainly specialize in one of these categories. Authors, advertisers, and my beloved educators focus on the presentation and sharing of information, all of which would fall into the wRiting category. Scientists and historians, for example, attempt to better acquire knowledge, and as such are Readers. Finally, people, such as mathematicians and philosophers, who seek to find structures in the raw data of life are practicing aRithmatic.

Although we may specialize, to fulfill our yearnings toward humanity we must complete the full cycle, although not necessarily completely alone. Thus, the mathematician need both examine previous works for background and present her or his own conclusions with at least a modicum of communicative savoir faire. Similarly, scientists need to synthesize their data, or find a mathematician to do so, then present their findings and educators must first educate themselves, then make their own separate peace with their subject material, before finally preparing it for classroom consumption.

To focus in on the middle step, the importance of aRithmatic lies in this. Somewhere between gaining knowledge and presenting our conclusions, we must add our own immeasurably valuable contribution and think for ourselves! Ideally this is the task for which we are made ready by our mathematics education. The true task of the mathematician is, once very basic ground rules are asserted, to go forth and discern what else must necessarily follow and why. Although this path has been blazed by mathematicians long dead, there is no reason that a student cannot walk it anew as they too are exposed to the shinning structure of mathematical knowledge. All too often mathematics serves the opposite purpose, and students are led to blindly memorize unmotivated methods, encouraging an arcane practice of "mathematics" which greatly resembles the showmanship of a magician, wherein things appear and disappear in somewhat predictable patterns but without respect for an underlying sense or reason.

My word choice here is not mere hyperbole, I often say to my students verbatim, "math is not magic," to emphasize that they ought know why the processes in which they are participating work. If one simply considers math to be the manipulation of numbers and symbols via memorized methods with the desire to produce some correct end value, then the questions, "why do I need to learn this?" and, "why can't I just use my calculator?" make perfect sense, furthermore, they have no good refutations. However, if one takes math to be a process by which one understands a set of rules and manipulates them to obtain logical, but not at all obvious, conclusions, then these questions make no sense, as well they shouldn't. The best computers we have are merely calculators, not true understanders.

This is why math, and more so philosophy, are so important to me. They are, perhaps even more than dancing, an essential expression of who I am and what it is to be human. Pure, magnificent, creation of new thoughts, MY thoughts, out of the read works of those who precede me, which I then write and send forth into the world that I may be known, and through being known create the possibility of fellowship and love. Thus, I implore educators to teach a comprehension, rather than calculation, based math. The math itself isn't important, it could be replaced by philosophy, law, debate, or any other subject based in the recombination of information. What is important is that we claim our birthright, the ability to create thought, without which not only may we never be human, we may never be loved.

1 comment:

Karen said...

This post reminded me of a few experiences that I have had in education.

As I think I have mentioned before, the current high school education paradigm is that teachers need to make everything that they teach "relevant" to students. It is obviously pretty cool when you can do this, and it is very motivating for students if they can see how it applies to their lives immediately. However, as this was stressed to me, I became extremely frustrated because, quite frankly, I can't think of a way to teach that "x^7/x^4 = x^3" (when x!=0) in a way that seems relevant to students. However, I can think of ways to teach it that involve the students "discovering" it for themselves and making conjectures and... thinking.

A few years after taking the "YOU MUST MAKE THINGS RELEVANT!!" classes, I am now realizing that part of what bothers me about that mindset is that it undermines the marvelous value of plain and simple thought and logic. I agree that the way many teach, thought and logic aren't necessarily demanded from the student. What a shame! However, when students are asked to think and reason, I personally believe that we have done our job. Even if the student can't see the value at the time. It is not the teacher's fault that our society has taught people that thought is not valuable, and I believe that we do a disservice to our students if we pretend like anything that is not immediately made relevant holds no place in their lives.

My second thought is how I deal with this when I teach these days. Last term, my students were becoming incredibly sluggish and frustrated in their learning. I got up in front of every recitation one week and explained to them that learning is frustrating and that it downright should be. I also told them that I was well aware that some of them would never use calculus, but that wasn't the point. The point was, mathematics is valuable to anybody because it forces you to think which is a skill that is valuable in any field, even though we don't seem to value it in society.

I might have to create a post on math education as well... I'm feeling the PASSION!