I found this video entitled Math Education: An Inconvenient Truth, which quickly and accurately demonstrates the popular misconceptions of math held my many in our culture. In the clip, a meteorologist, a scientist that must use math on a daily basis and ought to know better, launches a public campaign against a series of grade school math texts being used in local curricula. She is essentially complaining about new-fangled ideas that are different from the ones she learned when she was a kid, and blames the crazy liberal hippies that wrote the books for dumbing-down our kids by not drilling the standard algorithms into students' heads. She is particularly married to that word, and seems to think that her ability to define algorithm gives her the right to shepherd her viewing flock away from these radical ideas.
And would you like to know what these wacky ideas are? They are this: math is not about algorithms. Nor is it about numbers, though they are often used. Math is about patterns. It is critical thinking at its finest. As many times as the author utters the word, one would think that she truly understands what an algorithm is. She does not. It is a tool. You can't hold it in your hand, but it is a tool nonetheless. The standard algorithms that she demonstrates are the ones whose combination of speed, efficiency, practicality, accuracy, and fashion have allowed them to survive natural selection. It is this combination of factors, but no one alone. For example, only when paper technology became affordable were these methods even possible, and even then, skilled abacus operators could beat them for speed. But once paper was readily accessible, written methods won the day. Well guess what, the digital age has brought us a new tool. Its affordable, lightning fast, and never gets bored- the calculator.
I'm not suggesting that we discontinue learning arithmetic. What I am suggesting is that this woman has overlooked the intentions of the textbooks she is critiquing. These books are teaching how to think mathematically. In order to solve the examples she gives, students must master concepts like the distributive and associative properties. They must understand place value. They must think for themselves. Yes, I believe the standard algorithms should be taught, but as a companion to these other ideas. There is no need to memorize times tables or perform speed tests. Proficiency will come with time, but not unless it is accompanied by reason, rationality, and not a small amount of enthusiasm.
I would much rather students understand why they are doing something, to appreciate what the question is really asking, and to think mathematically. This woman clearly misses the point.