Reading Math Textbooks Efficiently

What You’ll Find Here: 3 Videos • Reading Strategies • Self-Check

On This Page: How Math Textbooks Are Different | What to Read | Turning Examples into Practice | A Better Reading Routine | Self-Check | When You Get Stuck | One Action

Reading a Math Textbook Is Different

If you have ever tried to read a math textbook the same way you would read a novel or history chapter, you may have found yourself reaching the bottom of a page without remembering much of what you just read. That does not mean you are bad at reading math. Math textbooks are designed differently. Important information may appear in definitions, equations, diagrams, tables, examples, notes, or even a single symbol. Understanding the material often requires you to stop, think, write, calculate, and try things yourself as you read. On this page, you will learn:

• How reading mathematics is different from reading other subjects

• Which parts of a math textbook deserve the most attention

• When it is okay to skim and when you should slow down

• How to turn worked examples into useful practice

• How to create a simple reading routine you can use in any math course

You do not need to understand everything the first time you read it. Effective math reading often involves returning to an idea more than once.

Math textbooks contain much more than paragraphs of information. A single page might include vocabulary, notation, formulas, diagrams, explanations, and worked examples - and each piece may be important. Reading mathematics therefore requires a more active approach than simply moving from the top of the page to the bottom.

As You Watch

Think about this question: When you read your math textbook now, what do you pay the most attention to—and what do you tend to skip?

Try It Now

Open your textbook to a section you are currently studying. Before reading the entire page, look for:

1. The section title and learning goal

2. New vocabulary or definitions

3. Formulas, rules, or important notation

4. Diagrams, graphs, or tables

5. Worked examples

6. Notes, warnings, or common mistakes

7. Practice problems

Then ask yourself “What is this page trying to teach me to understand or do?” Knowing the purpose of the section before you begin reading can make the details easier to organize.

Reading efficiently does not mean reading every word at the same speed. Some parts of a math textbook deserve careful attention. Other parts can be skimmed initially and revisited when you need them. A useful goal is not “I need to finish reading these ten pages.” Instead, try “I need to understand the main idea well enough to begin working with it.”

As You Watch

Think about this question: Which parts of a textbook section would you need to understand before you could solve a problem without help?

Try It Now

Choose one short section of your textbook.

Pass 1: Preview

Spend a minute or two looking at:

• Headings

• Bold vocabulary

• Formulas

• Diagrams

• Example titles

• Summary boxes

Do not worry about understanding everything yet. Your goal is to see the structure of the section.

Pass 2: Focus

Now read the portions that explain the main idea. Slow down when you reach:

• A new definition

• A new symbol

• A formula or rule

• An explanation of why something works

• A worked example

Stop periodically and ask “Could I explain what this means without looking at the page?”

Pass 3: Revisit

After you try some problems, return to the textbook. This time, look specifically for information that can help with questions that came up while you were practicing. A textbook can become much more useful when you stop treating reading as something that must be completed before practice begins. Reading and problem solving can work together.

Worked examples are one of the most useful parts of a math textbook - but only if you do more than read them. When you read a completed solution, the steps can feel obvious because someone else has already made all of the decisions. The real test comes when the solution is no longer in front of you.

As You Watch

Think about this question: When you look at a worked example, could you reproduce the solution after closing the book?

Try It Now

Find one worked example from your textbook.

1. Read

Read through the example once. Pay attention not only to what was done, but also to why each step was chosen.

2. Cover

Cover the solution or close the book.

3. Try

Solve the problem yourself. Write down every step you can. If you become stuck, resist the urge to uncover the entire solution immediately. Ask:

• What do I know?

• What am I trying to find?

• What strategy was this section teaching?

• What could my first step be?

4. Check

Compare your work with the textbook. Look for the first place where your solution differs.

5. Explain

Try to explain why the textbook used each step.

6. Change

Create a slightly different version of the problem. Change a number, sign, measurement, equation, or other detail and solve the new problem without looking at the example. That final step helps turn an example you recognize into a skill you can actually use.

You do not need a complicated system to read mathematics effectively. Try this six-step routine.

1. Preview

Before reading carefully, look through the section. Identify the main topic, important vocabulary, formulas, diagrams, and examples.

2. Read One Small Piece

Do not try to absorb an entire chapter at once. Read one definition, idea, or explanation. Then stop.

3. Put It in Your Own Words

Ask yourself:

• What does this mean?

• Why does it matter?

• How would I explain it to someone else?

Write a short note if that helps.

4. Work With the Idea

If the textbook gives an example, cover the solution and try it yourself. If it gives a formula, use the formula. If it gives a graph, explain what the graph shows. If it introduces vocabulary, create your own example.

5. Mark Questions

You do not have to solve every confusion immediately. Write down specific questions such as:

• Why did the exponent change here?

• How did they know which formula to use?

• Why is this value negative?

• What does this symbol mean?

• Why does this method work for this problem?

Specific questions are much easier to investigate or ask someone about than simply writing, “I don't understand.”

6. Revisit

Return to the textbook after you have attempted some problems. You may notice explanations that did not seem important the first time but make much more sense now that you have tried using the idea.

Preview → Read → Explain → Try → Question → Revisit

You can repeat this cycle as many times as you need.

As you work through a textbook section, ask yourself:

• Can I identify the main idea of this section?

• Do I know what the important vocabulary means?

• Do I understand the symbols and notation being used?

• Can I explain the main idea in my own words?

• Have I stopped to work through the examples myself?

• Can I solve a similar problem without looking at the example?

• Have I written down anything that is still confusing?

• Do I know which parts of the section I need to revisit?

You do not need to answer “yes” to everything the first time through. These questions are not a test. They are clues that can help you decide what to do next.

Sometimes you can read a section carefully and still feel confused. That is normal. A textbook is one learning resource, not a test of whether you are capable of learning the material. If something is not making sense, try changing what you are doing. You might:

• Look at another worked example

• Return to an earlier definition

• Draw a picture or diagram

• Substitute simple numbers into a formula

• Try one problem and see where you become stuck

• Compare the textbook explanation with your class notes

• Watch a video explaining the same idea

• Ask a classmate to explain how they interpreted the section

• Bring a specific question to your instructor or tutor

Instead of saying “I don't understand Chapter 4”, try identifying the exact point where you became confused. “I understand how they set up the equation, but I don't understand why they divided both sides by 3 in the next step.” Finding the point where your understanding breaks down can make it much easier to get useful help.

You do not need to completely change the way you read your textbook. Choose one small strategy to try:

• Preview your next textbook section before reading it.

• Stop after one definition and explain it in your own words.

• Cover the solution to one worked example and try it yourself.

• Create a new version of one textbook example.

• Write down one specific question while reading.

• Revisit a textbook section after completing your homework.

• Try the six-step reading routine on one page.

Math textbooks become much more useful when you treat them as something to work with, rather than something you simply have to finish reading.