How to Read a Math Textbook

Many students pay a lot of money for a textbook but don't bother to read it! Before you attempt homework problems, it is important that you carefully read the relevant sections of your math textbook. Study the examples. Note the definitions, properties, and formulas. Study the examples. Note the hints from the author. Study the examples! 

  1. Look at the title of the section and the learning objectives stated at the beginning of the section. 
  2. Skim the section to be read. 
  3. Have a highlighter and pencil handy to mark questions and work out missing steps from examples. 
  4. Put all your concentration into reading. 
    • Read in an environment with few distrations.
    • Highlight important material.
    • Pay close attention to material that the textbook author has highlighted with colors or boxes.
    • Remember: reading a math textbook is not like reading a novel, you need to go slowly and often re-read material to understand the ideas being presented. 
  5. When you get to the examples, go through and understand each step. 
    • Often the author does not show every single step in order to save space. If there are missing steps, fill them in yourself.
    • Study the examples carefully, as they will serve as models for homework exercises and test questions. 
  6. Mark the concepts and words that you do not know. 
    • Make a list of these areas of confusion.
    • Look up unknown words in a math dictionary.
    • Ask your instructor or a tutor about unclear concepts. 
  7. Make lists of important ideas. 
    • On separate sheets of paper, keep lists of
      • definitions
      • theorems
      • formulas 
    • Each time you read a section in the math textbook, add something to these lists.
    • Have the lists in front of you as you do your homework.
    • Review these lists daily. 
  8. If you do not understand the reading material, follow these points until understanding arises: 
    • Go back to the previous page and re-read the information to get into the flow of the author's presentation.
    • Read ahead to the next page to see to where the author is leading.
    • Study all graphs, diagrams, charts and examples used to illustrate the concepts.
    • Read misunderstood paragraphs aloud to engage your other sensory organs.
    • Refer to your notes from class on the same material.
    • Refer to another math textbook. You might find explanations and/or examples that make more sense to you.
    • Use videotapes, CDs and website resourses to help with your understanding.
    • Define exactly what you do not understand and ask your instructor, a tutor or a classmate. 
  9. Reflect on what you have read. Relate this reading to the course objectives.

 (The above material is adapted from Math Study Skills Workbook by Paul Nolting)

The KWL Strategy

K: What we Know already.
W: What we Want to find out.
L: What we Learned from the reading. 

Before Reading

  • Identify what the specific topic is that you are going to read about. In a math textbook, the objectives are usually stated at the beginning of each section.
  • Write down 5 to 9 things that you already know about those specific topics.
  • Write down 5 to 9 questions about what you want to know about those specific topics from the section you are about to read.
After Reading
  • Write down 5 to 9 ideas that you learned from reading the section.
    • In your own words, describe what you learned.
    • Make reference lists to use when doing homework exercises and to study for exams. You can clarify your lists with examples.
      • Make a list of definitions.
      • Make a list of properties.
      • Make a list of formulas.
      • Make a list of theorems.
  • Compare and contrast what you learned to what you knew and what you wanted to learn.

(The above material is adapted from Mission Reading instructor Aaron Malchow)

Review more Math study tips.