Another serious problem we face in math education is that people believe that mathematics is all about calculating and that the best mathematics thinkers are those who calculate the fastest. Some people believe something even worse—that you have to be fast at math to be good at math. There are strong beliefs in society that if you can do a calculation quickly then you are a true math person and that you are “smart.” Yet mathematicians, whom we could think of as the most capable math people, are often slow with math. I work with many mathematicians, and they are simply not fast math thinkers. I don't say this to be disrespectful to mathematicians; they are slow because they think carefully and deeply about mathematics.
Laurent Schwartz won the Fields Medal in mathematics and was one of the greatest mathematicians of his time. But when he was in school, he was one of the slowest math thinkers in his class. In his autobiography, A Mathematician Grappling with His Century (2001), Schwartz reflects on his school days and how he felt “stupid” because his school valued fast thinking, but he thought slowly and deeply:
I was always deeply uncertain about my own intellectual capacity; I thought I was unintelligent. And it is true that I was, and still am, rather slow. I need time to seize things because I always need to understand them fully. Towards the end of the eleventh grade, I secretly thought of myself as stupid. I worried about this for a long time.
I'm still just as slow… At the end of the eleventh grade, I took the measure of the situation, and came to the conclusion that rapidity doesn't have a precise relation to intelligence. What is important is to deeply understand things and their relations to each other. This is where intelligence lies. The fact of being quick or slow isn't really relevant. (Schwartz, 2001)
Schwartz writes, as have many other mathematicians, about the misrepresentation of mathematics in classrooms, and about mathematics being about connections and deep thinking, not fast calculation. There are many students in math classrooms who think slowly and deeply, like Laurent Schwartz, who are made to believe that they cannot be math people. Indeed, the idea that math is about fast calculations puts off large numbers of math students, especially girls. Yet mathematics continues to be presented as a speed race, more than any other subject—timed math tests, flash cards, math apps against the clock. It is no wonder that students who think slowly and deeply are put off mathematics.
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When people are asked about how mathematics is used in the world, they usually think of numbers and calculations—of working out mortgages or sale prices—but mathematical thinking is so much more. Mathematics is at the center of thinking about how to spend the day, how many events and jobs can fit into the day, what size of space can be used to fit equipment or turn a car around, how likely events are to happen, knowing how tweets are amplified and how many people they reach. The world respects people who can calculate quickly, but the fact is, some people can be very fast with numbers and not be able to do great things with them, and others, who are very slow and make many mistakes, go on to do something amazing with mathematics. The powerful thinkers in today's world are not those who can calculate fast, as used to be true; fast calculations are now fully automated, routine, and uninspiring. The powerful thinkers are those who make connections, think logically, and use space, data, and numbers creatively.
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