Reading Your Textbook

It is essential in this (and all math courses) to read your textbook. The text contains a wealth of knowledge. It is often a work of a master teacher in the subject, who is not only giving examples of how certain skills are performed, but really trying to teach the subject to the reader: the vocabulary and concepts, why these concepts are important, how certain procedures/skills arise from those previously learned, the thought processes when approaching different types of problems, and what aspects of a problem make it different (so that it requires a different approach) from another. What better than to have two teachers, one with whom you can interact and ask questions, and the other who is a recognized leader in the field and whose “lectures” are with you whenever you are free to open the book?

Reading a math textbook is not, however, like casual reading. You must be inquisitive as you read. Each section you read will contain new concepts, new skills, new vocabulary. You should continually ask “why?”: “What questions can be answered using this new material that could not have been answered before? Are these the types of questions that it would be natural to ask? Had they occurred to me? If not, why would someone want to know their answers?” You should also ask “how?”: “How is the new material related to material I have already learned? How is it different?”

At the same time, you must pick up the vocabulary. In some sense it is like learning a foreign language. How can you expect to accurately convey your ideas if you do not speak the language? But it is not quite as simple as when you learn, say, French. Since people in different cultures generally think and converse about the same things, learning a foreign language is usually a matter of word substitution — saying “pain” (French) instead of “bread” (english), “j'ai faim” instead of “I am hungry”. In math sometimes the vocabulary includes words you already know and use in daily speech. Nevertheless, the word will have a very specific meaning in the mathematical setting, often an idea or concept that you have never formulated or thought about before. Learning math vocabulary entails pinning down just what this concept is, and being able to use the word in sentences where this concept makes sense.

Some specific suggestions (along with those mentioned in the last couple of paragraphs) as you read:

If you are not already accustomed to reading mathematics in the fashion described above, be aware that it will definitely increase the amount of time you devote to reading. Nevertheless, it is time well spent, as it generally prepares you much better for doing homework problems (and the kinds of problems you will find on exams as well) than a more cursory reading of the text would. The amount of time required to complete homework should drop as a result of your efforts.

This page maintained by: Thomas L. Scofield
Department of Mathematics and Statistics, Calvin College

Last Modified: Wednesday, 11-Aug-2004 17:05:07 EDT