Rethinking math education

The traditional approach to teaching math comes from a time before cheap and ubiquitous calculators. True, there was the abacus and later the slide rule, but those required a firm understanding of math to use. For the vast majority of people, math is merely the tool they use to keep track of money, stuff, and time. In this way, math is more akin to measurement or accounting rather than a method of problem-solving.

Then there is the question of motivation. It seems, at least in the US, that math education has turned into a kind of contest for prestige. Classes like calculus are seen as luxury goods which give students bragging rights. Very little of the math I learned in engineering school came up on the job. I don't regret learning it, but there was a definite mismatch between what I was taught and what I was paid to do.  

In his writings about math education, Paul Lockhart notes that real mathematicians treat their work as more of a form of play or art and often have little interest in practical applications. Deeper mathematical understanding comes from curiosity and creativity rather than just being presented with a variety of problems and solutions. Many mathematical ideas were explored in depth centuries before there were any practical applications for them.  

Given the number of people who are unable to do algebra word problems, there is something very wrong with how math is being taught. Teachers rarely present math as anything but a set of instructions which must be followed in various situations. Many math students who do well in high school and college are tricked into thinking they are good at math when actually they are just good at following instructions. 

Yes, algorithms are useful, but the true learning comes from knowing why an algorithm works and trying to make your own. In my own time as a math teacher, I found it better to explore a smaller number of ideas and questions in depth than to bombard my students with many easy exercises as most other teachers do. That so-called drill-and-kill method was the way I was taught. It was tedious and taught me little. 

So to wrap up this bit of rambling, I propose the following:

1. present the students a wide variety of problems from different topics 

2. choose questions that require some patience and creativity to solve and explain.

3. recognize differences in mathematical ability - don't dumb-down the class

It is enough to open minds; there is no need to overload them.