Mathematics Education: Taking a Clue
From the Recent Technological Revolution
Influence of the Prevailing Culture
The evolutionary zoologist Richard Dawkins wrote in his bestseller, The Selfish Gene:
Most of what is unusual about man can be summed up in one word: 'culture'.
Here's a dictionary definition:
cul·ture n. 1.a. The totality of socially transmitted behavior patterns, arts, beliefs, institutions, and all other products of human work and thought.
Hawkins writes further:
Cultural transmission is analogous to genetic transmission in that ... it can give rise to a form of evolution.
Dawkins named the constituent behavior patterns, beliefs - ideas, in general - memes (rhymes with genes.) Like genes, memes are a form of replicators. Memes replicate by imitation. Some are better replicators than others. A relevant example of a meme is the proverbial "I hate math", which is a very good replicator. Another meme, "The study of mathematics develops orderly thinking habits", is a very poor replicator.
Like genes, memes may compete between themselves for a place in their habitat. In one of his MAA Online columns, Keith Devlin suggested spreading a meme "Mathematics makes the invisible visible" to challenge the obnoxious "I hate math" for a slot in our minds. I joined in with the "Cut the knot!" meme. What is this meme about? It refers to the story of Alexander The Great who applied a radical solution to a seemingly unsolvable problem.
The "Cut the Knot!" meme carries a personal undertone. I have a severe hearing impairment. Which makes it difficult for me to mix with other people. I grew naturally shy about taking part in a live conversation. This abnormality is my personal knot that was needing a drastic solution. I owe much to the current technology that enabled me to go public with whatever I wished to say about mathematics and mathematics education and reach thousands of people.
On a deeper level, the prevailing attitude of disgust and fear of mathematics is most everyone's knot and a personal responsibility. In this context, "Cut the Knot!" is similar to the ideas annunciated by Roger von Oech in his A Whack on the Side of the Head and A Kick In The Seat Of The Pants.
I think that the educational community might have unwittingly helped spreading a few harmful but agile memes by insisting that importance of mathematics lies in its utility. How do you explain what the factorials are good for? - a question I received from a math teacher. Another math teacher posted a question on the k12.ed.math newsgroup asking for examples of where factoring of quadratic polynomials is used in real life. The post had a subject matter "The why's of algebra."
Whether by cutting or otherwise, educators should untie the knot they got themselves into. It appears to me that the action required got to be quite drastic.
I want to tell you of my own experience. Programming is often compared to mathematics. B.J.MacLennan from the Computer Science Department, Naval Postgraduate School wrote in 1982 (SIGPLAN Notices 17):
- Programming is object-oriented mathematics.
- Mathematics is value-oriented programming.
These two principles show the unity between the two fields and isolate their differences.
A couple of years back, I happened to work in an organization of about 500 programmers. The ones I worked with had always struck me as highly intelligent, able to learn new concepts and techniques on the fly. In fact, the company had a broad offering of courses and encouraged its employees to enhance their education. People I worked with were switching between Unix and Windows environments, picking up C++, HTML, Java, Motif, Rete++ (an expert system shell) effortlessly and with a high degree of enthusiasm. Yet, without exception, they were carriers of a milder strain of the "I hate math" meme: "Math? Who cares!?"
If the programmers do not need mathematics, who does? The fact is that those whose chosen occupation requires mathematics have enough motivation to study it. These are few. Motivation for the rest should come from elsewhere. I can't think of a better reason to study mathematics than to study it for its own sake.
Richard Feynman once wrote
You cannot understand science and its relation to anything else unless you understand and appreciate the great adventure of our time.
Modern mathematics is a part of this adventure. Do we need a better reason to study it?
- The American Heritage Dictionary
- R.Dawkins, The Selfish Gene, Oxford University Press, 1989 (first printed 1976)
- D.C.Dennett, Consciousness Explained, Penguin Books, 1993
- R.P.Feynman, The Meaning of It All. Thoughts of a Citizen Scientist, Addison-Wesley, 1998
- R. von Oech, A Whack on the Side of the Head, Perennial Library, 1986
- R. von Oech, A Kick In The Seat Of The Pants, Warner Books, 1990