How to learn

How to study from a textbook on your own

A textbook is one of the most reliable sources for self-study: it has structure, exercises and answers. But reading it like a novel throws away most of the benefit. Here is how to work through a textbook so that it acts as a course.

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In this article

How to choose a textbook#

Look for three things:

  • Exercises with answers or solutions. Without them you cannot check yourself, so the book is only good for reading.
  • A gradual build-up. Every chapter rests on earlier ones, and the start covers what you already know or almost know.
  • The right level. Open the middle of the book: if everything there is incomprehensible, it is too early; if everything is familiar, it is too late.

Reviews from people who worked through the book alone are more useful than ratings: teachers sometimes praise books that are good in class but hard without explanations.

One chapter, several sessions#

A textbook chapter is usually a week of work, not an evening. A convenient split:

  1. First session — skim the chapter, read the theory, write down new terms and rules in your own words.
  2. Second — go through the worked examples: cover the solution, try it yourself, then compare.
  3. Third and onwards — exercises, from easy to hard.
  4. Last — review the chapter from your notes and solve a few problems from earlier chapters.

Exercises are the main part#

Theory without exercises fades quickly. Solve in writing, in full, and only then look at the answer. If the answer does not match, find the mistake yourself before reading the solution: hunting for a mistake teaches more than the right answer.

You do not have to do every exercise. A good rule is every second one, and all of them if you are making many mistakes. Mark the especially hard ones so you can return to them a week later — that is spaced repetition applied to skills.

When you get stuck#

If one spot will not give way for more than half an hour:

  • reread the previous chapter — the gap is often there;
  • find the same explanation in another source — a video, an open course, a reference book;
  • write the question down and ask it on a forum or a friend — the answer often turns up while you are phrasing it;
  • mark the place and move on, coming back in a couple of days.

How to keep notes#

Keep a file or a page per chapter: new terms, rules in your own words, mistakes from the exercises with an explanation. Keep your solutions alongside. When the textbook is finished, you are left with your own short reference on the subject — much faster to reread than the book.

How much time to allow#

An honest estimate for most textbooks is three to eight hours per chapter with exercises. From that the timeline is easy: a twenty-chapter book at five hours a week is half a year. If that does not suit you, choose in advance which chapters you can skip rather than abandoning the book halfway.

Step-by-step plan

  1. Choosing a textbookExercises with answers, a gradual build-up, the right level.
  2. Session 1 — theorySkim the chapter, read it, put the terms into your own words.
  3. Session 2 — examplesSolve the worked examples yourself and compare.
  4. Sessions 3+ — exercisesIn writing, in full; find mistakes yourself before reading the solution.
  5. Closing the chapterReview from your notes and a couple of problems from earlier chapters.

Start learning this in your own space

The plan goes into your repository: tick off stages, keep notes — the change history shows how far you have come.

Start the plan

Sources

  • OpenStaxFree open textbooks in math and the sciences
    free
  • MIT OpenCourseWareCourse materials that work as a second explanation for hard chapters
    free

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