Introduction to Reading Mathematics

This introduction is all about what to do if this list is threatening because you “never read a math book in high school” or “can’t do problems”. Here’s the good news: you can do some mathematics or you wouldn’t have gotten into college. Here’s the bad news: what worked before may not work this time. Success may lie in improving or discarding many habits that were good enough once but aren’t now. Let’s see how we’ve gotten to a point at which someone could dare to imply that you have bad habits.

The typical elementary and high school mathematics education in the United States tends to teach students to have ineffective learning habits, and we blush to admit college can be just as bad. A lecture designed to make it unnecessary to read the book, for example, tends to make you not read the book. If lecture and text present you with a list of formulas to memorize and model problems to imitate, you reasonably assume mathematics consists of memorization and imitation. The answers in the back of the book teach you that the answer is the important thing. If the book is written so that there is no place for a reader to participate actively (by asking questions, constructing examples, or solving problems), you are trained to believe that reading mathematics is a passive activity. If you are not given effective tools for word problems (story problems), you use ineffective methods of attack (two popular favorites are frantic but unthoughtful activity and an endeavor to keep the problem at least 10 feet away and poke it with a stick to see if it is safely dead). If the benefits of good notational habits are not shown, you adopt poor notational habits [for example in solving equations I have seen 3x = 9 = x = 3, which is not what is really meant]. If a test consists only of problems exactly like those in the book, you are encouraged to believe that doing mathematics is having success at doing old problems.