Reading Mathematics
From Burger and Starbird - The Heart of Mathematics
Reading mathematics is much different from reading about many other subjects. Here's how we read mathematics. We read a sentence or two, stop reading, think about what we've read, and then realize we're completely and utterly confused. Usually we discover that we didn't really understand that previous paragraph. But, we don't get frustrated...it's the nature of the beast. Instead, we either reread some previous sections or just reread the previous sentence. The fuzziness slowly begins to fade ever so slightly, and the concept begins to come into focus. Then we attempt to think about the issue and work with it on our own or with friends. It is at this point that we begin to appreciate and understand the ideas presented. One of the great features of mathematics is that once we do understand an idea our grasp of it is completely solid. There is no vagueness or uncertainty. So, adopt high standards for what you view as 'understanding'. Be actively engaged as you read. Draw pictures, explain ideas to friends. Put yourself in the position of discoverer of each idea. Ask questions, search for answers, and let those answers guide you to still more questions.