Should You Read the Textbook Before or After Class?

Textbooks and lectures serve different purposes:

• Lecture often shows the main ideas, highlights common patterns, and sets expectations for what matters.
• Textbook often fills in details, provides more examples, and gives structured practice problems.

If you use either one passively, it won’t help much. Reading math is not like reading a novel. You can “understand” a paragraph and still be unable to solve a problem.

Also, time is limited. Most first-year students can’t realistically do a full textbook reading before every lecture plus assignments plus other courses. So the best approach is the one you can do consistently.

Mistake 1: Doing a full pre-read and burning out. Some students try to read the entire section carefully before lecture, then they stop after two weeks because it takes too long.

Mistake 2: Reading after class as a comfort activity. It feels productive, but if you don’t attempt problems, you’re not training exam skills.

Mistake 3: Highlighting and rewriting without solving. Copying definitions and theorems can look like studying, but calculus and linear algebra grades come from problem-solving.

Mistake 4: Using the textbook only when you’re desperate. If you only open it when you’re stuck, it becomes a stress trigger instead of a learning tool.

Strong students treat the textbook as a tool for two things:

• previewing structure (what are the key definitions and problem types?)
• building practice (working problems and checking solutions)

They don’t try to read everything perfectly. They use a “light preview” before lecture and a “problem-first review” after lecture.

Here are two approaches that work well. Pick one based on your schedule.

Option A: Light pre-read + problem-based post-work (recommended for most students)

• Before class (10–15 minutes):
• skim the section headings
• read the key definitions (limits, derivative, chain rule, etc.)
• look at one example and identify the method (don’t fully solve)
• After class (30–45 minutes):
• do 3–5 problems related to the lecture
• write down any stuck points
• bring those to office hours, a tutor, or a study group

This approach makes lecture easier to follow and turns the textbook into practice.

Option B: No pre-read + structured post-read (if you’re overloaded)

• Go to lecture.
• Then do a focused read of only the parts that connect to the problems you’re assigned.
• Use a timer (20–30 minutes) so reading doesn’t replace practice.

The key is that reading supports problem-solving, not the other way around.

Suppose the section introduces the chain rule and you see an example like:

Differentiate f(x)=sin(3x^2-1).

Passive reading: you follow the steps and feel like you “get it.”

Active reading: you pause and ask:

• What is the outer function? (sine)
• What is the inner function? (3x^2-1)
• What should I multiply by at the end? (the derivative of the inner)

Then you close the book and try a near-twin problem:

Differentiate g(x)=cos(5x^2+2).

If you can do the near-twin, the reading worked. If you can’t, you need more practice, not more highlighting.

• There isn’t one correct answer; the best reading approach is the one you can do consistently and actively.
• A light pre-read helps lecture make more sense; the real learning happens in post-lecture problem-solving.
• Reading should support problems, not replace them.
• Test your reading by doing a near-twin problem without looking at the book.

If you want structured, concept-focused help, Learn4Less offers tutoring sessions designed specifically for first-year university math.