When asked what math is, students typically give descriptions that are very different from those given by experts in the field. Mathematicians define their subject as the study of patterns. They say it is an aesthetic, creative, and beautiful subject (for example, Keith Devlin, “Mathematics: The Science of Patterns”; and Steven Strogatz, “The Joy of x”). Knowledge of mathematical patterns has helped people navigate oceans, chart missions to space, develop technology that powers cellphones and social networks, and create new scientific and medical knowledge. But students will typically say that math is a subject of calculations, procedures, and rules. They believe that the best mathematical thinkers are those who calculate the fastest—that you have to be fast at math to be good at math. Yet mathematicians 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.
Jo Boaler, theatlantic.com, Dec 31 2015.
