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You probably paid quite a bit of money for your textbook in this course. The only way this investment will pay off is if you read it. The textbook should be your primary source of information. It contains a wealth of explanations of concepts and methods, as well as hundreds of step-by-step examples. Also, there is a chapter summary and an exam review section at the end of each chapter.
Sadly, many students don’t read their math books, paying good money simply to have a source for homework exercises. Often, they complain that math texts are hard to understand, but I would contend that it only seems that way because most students don’t know how to read them.
You cannot read a math text the same way you would read a text for, say, history or English. First, make sure you preview each chapter and/or section by reading the introduction. This may seem relatively unimportant, but it provides a rationale for what is to come. Then, be prepared to slow down. Yes, I said s l o w d o w n .
You see, when reading a section of mathematics text, you shouldn’t think that you should be able to simply open the book and start reading. It just doesn’t work that way. Instead, get out a pencil and some paper, preferably your notebook. As you begin to work your way through the text, write down formulas and examples as the author presents them. Read s-l-o-w-l-y, pausing frequently to make sure you understand what has been written. Sometimes, an extremely important fact may be provided in a few short words or symbols.
Speaking of those words and symbols, be sure you know what each one you encounter means before proceeding. Look up words you are not familiar with, either in the text glossary or a good dictionary. Use a separate sheet in your notebook to write out, in words, what various symbols denote, thereby creating your own glossary of these symbols. Most of the words and symbols you will see are used throughout all of mathematics, so you will probably encounter them again.
Also underline, star, or highlight key ideas that are presented. This includes, but is not limited to, important formulas. Paraphrase key ideas in the margins. This helps you synthesize the information. Try very hard to understand how things work and not just memorize.
Ideally, you should do all this before the material is covered in class. You may have difficulty motivating yourself to do this, but coming to class prepared will help you get much more out of our discussion. Often, you won’t understand everything that you have read, but it will be enough to familiarize you with the the terminology and procedures. Besides, if you take some notes on the material before you come to class, you won’t need to write down everything I say and do, and you will have a pretty good feel for what kinds of questions to ask.
Lastly, use the chapter summaries and sample tests (either from the text or ones you create) to review before exams. This implies that you made sure you have the time to review. Don’t get so far behind in your homework that, instead of summarizing before an exam, you’re trying to cram in the last few sections of material.
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