Math Study Skills – How to Read a Mathematics Textbook

March 9, 2010 at 6:12 am Leave a comment

This article will provide an overall strategy for reading a mathematics textbook. The article is written for mathematics students. If you are an instructor, feel free to share these tips with your students. If you have an further suggestions, share them in the comments section or send me an email through the contact page on my website – http://georgewoodbury.com.

Survey the Section

You should begin your reading with a quick survey of the section. This will give you a rough idea about the contents of the section, and will improve your concentration when you come back to read the section in earnest.

Begin by reading the title of the section, and try to form some questions in your mind about what you will be learning in this section.

Continue on to read through the list of objectives. This list will give you more specific details on what you will be learning. At this point you will have a great idea of what will follow, and that gives you a better chance of being able to read and understand the material that will be presented.

Skim through the chapter looking for new words or terms that are being defined. You will often find these words in bold print, and occasionally the definition will appear in a box. If you do not immediately understand the word or term from its definition, place a check mark next to that word or term. When you come back to read the section thoroughly, the definition might make more sense when read in context.

You should also look for explanations of new procedures. As you run into such a procedure you should ask yourself “What will this procedure show me how to do?” and “Do I understand these steps at first glance?”

Look quickly through each example to get a rough idea about what is being shown in these examples. At this point you should not focus on understanding each step and detail, you just need an overview.

Once you have surveyed the section, ask yourself some questions to review what you have read as well as to motivate yourself as you come back to read the section thoroughly.

  • What is the main idea being covered in the section?
  • What are the learning objectives for this section?
  • What new terms are being introduced?
  • What new procedures are being introduced?
  • What types of problems will I be solving in this section?

Reading the Section

At this point you are now ready to read the section. As you read through the paragraphs, read slowly and think back to what your instructor said during the lecture. Your textbook should supplement your instructor’s lectures, and help you improve your understanding.

Be sure to have paper and a pencil available as you read. Students that are active readers will be able to understand more of the material they read than passive readers will. You’ll want to create a vocabulary list as you read. You will also want to have paper available as you read through the examples so you can try them for yourself.

As you come to a word that is being defined in bold print, do you understand its definition? If you do understand the definition, add the word a list of vocabulary words for that section. Recall the suggestion for placing a checkmark by words that you did not understand – often these words will make more sense when you read about them in context. If you still do not understand the definition of one of these words, record it in your vocabulary list with a checkmark placed next to it. This will remind you that you need to learn the definition. Look to your class notes for a definition that your instructor may have given for that word. If you cannot find a definition in your notes try asking your instructor or a classmate, or search for definitions online.

If you read a paragraph and do not understand what you have read, be sure to reread the paragraph slowly with your fullest attention. If you still do not understand, reflect back upon the paragraphs that led up to this paragraph. The background material may help you to understand. If that doesn’t help, consider looking ahead to the next example. This may help you to understand by providing an example that illustrates the topic being presented. If you are still struggling, try visiting a tutor or asking a classmate for help. At the very least, ask your instructor for some clarification.

As you read through the examples in the textbook be sure that you ask yourself plenty of questions, such as “What happened in this step?” or “Why is this step the correct step to take?” This will help you to understand the steps we take to solve problems. In each example in this textbook, each step is explained in detail to the right of the problem. Be sure that you understand these explanations. One suggestion while reading through an example would be to rework the problem from the example in your notes. As you write down the next step you can focus on the what (“What happened in this step?”) and the why (“Why is this the correct step?”).

After reading an example, flip back to the homework exercise set at the end of the section. Look through the exercise list for problems that appear to be similar to the example you just read, and write down the example number and page number next to these problems. This will remind you to refer back to this example if you get stuck on one of the problems.

As you come to a new procedure in the textbook, be sure to ask yourself the following questions.

  • What type of problem is this procedure for?
  • Do I understand the steps?
  • Do I know when to use this procedure?
  • Did my instructor cover this procedure in class?
  • Are there any differences between my instructor’s explanation and the textbook’s?

You should also look for warnings about typical mistakes and how to avoid them. When you are sure you understand the procedure, take a quick look through the exercise set and determine which problems you can use this procedure on. Make a note in the exercise set, listing the page number where the procedure can be found.

Conclusion

Give as many of these suggestions as you can a try. If one of my suggestions really helps you, then incorporate it into your study plans. You will find that your textbook can help you to learn, and is not simply a device that carries your homework.

You may also want to check out my other 3 articles related to math textbooks.

How To Use Your Textbook
An activity that reviews the main features of your textbook and how to make the best use of them.

Reading A Math Textbook (Activity)
This is a classroom activity to help students learn how to read a math textbook for content.

Reading Ahead
How to use your math textbook to prepare for class.

-George

I am a math instructor at College of the Sequoias in Visalia, CA. Each Tuesday I post an article related to Math Study Skills on my blog. If there’s a particular study skill you’d like me to address, or if you have a question or a comment, please let me know. You can reach me through the contact page on my website – http://georgewoodbury.com.

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