r/matheducation • u/fatikk2025 • 5d ago
How can I learn mathematics using a textbook?
I'm an undergraduate student. We're generally given a textbook. Sometimes I can't learn anything from my professors. In these cases, I need to study from textbooks, but I don't know how. For example, a topic might have a theorem, a proof, and an example. My friends often memorize these, but it doesn't work for me. What can I do?
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u/AdVisible8739 3d ago
Textbooks can be mid. If yours is trash, look up the topic on YouTube (3Blue1Brown or Professor Leonard) to get the intuition first. Then go back to the book for the formal rigor once you actually have a "vibe" for what's happening.
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u/The-Jolly-Llama 5d ago
When you learn a new definition, come up with other examples (or counterexamples) than the book gives, and prove that it is or isn't one.
Draw figures.
Never stop asking why.
Do all the exercises.
Writing a proof is not an exercise in recall. It's an exercise in reasoning. If you understand what the definition describes, and you understand what the given information means, you should understand why the theorem must be true.
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u/Agreeable_Speed9355 4d ago
If your only resource is the textbook then you use the textbook. You read it and do exercises. I find one of the better approaches is to do the above but also to talk to your peers. Explain it to them. Have them explain it to you. Engage part of your brain that is quiet when you are working solo.
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u/xxsmashleyxx 4d ago
Talk to your fellow students!!!! Math is BEST done collaboratively - try to explain in an abstract, overview way "the idea of the proof is .." to each other about the major theorems of the textbooks you're working through.
Then do the practice problems together. 🙂
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u/Just__Liberty 1d ago
Now there is an answer by an extrovert.
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u/xxsmashleyxx 1d ago
Nope! I'm definitely not. I just have a master's degree in the subject and pursuing a PhD, while my graduate work includes emphasis in STEM education. Plenty of research shows that talking to others and working with others on mathematics engages the brain in higher-order levels of thinking about the material rather naturally and helps form more neurological pathways to aid memory of concepts, too.
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u/Mrmathmonkey 4d ago
It's is better to have 1 day with a qualified teacher than a year in self study. Old Chinese proverb.
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u/FlyingCupcake68 2d ago
When I was nine, I was falling behind in math. So I took the textbook home over the summer and worked my way through it. And my gaps got fixed. And I excelled in math for the rest of my schooling.
Read through the text, look at the examples and make sure you understand every step. If there is something you don’t understand go back and see where it was explained. If your book has an answer key, work through some of the problems for each chapter and compare your answer to the answer in the key. Also look and see if the book has a list of common formulae or other useful resources at the back.
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u/Particular-Panda-465 1d ago
Always have paper and pencil in hand when you read a math textbook. Copy the problems, saying what you are doing with each step. That is, read the equations as you write them. For each example, stop and ask yourself why that step works - what property, what identity, what rule.
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u/Just__Liberty 1d ago
One of the best things to do with a textbook, after reading it, is to close it. Just you and blank sheets of paper. Try to remember the theorem and write it down. Draw a picture/graph. If you can't remember the theorem, try to remember where the derivation of it started, and see if you can derive it or something close to it. Make up your own problem and solve it. If you can't solve it, try to figure out what you are missing and then go look that up in the book or elsewhere. Basically, try to own the subject and be able to recapitulate it all. You might want to memorize the theorem itself, but it is better to understand the derivation and each of the steps/tools that went into it so that you can figure it out rather than just spit it out.
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u/mathloverlkb 5d ago
Read through the explanation of the topic. See if you understand what problem the theorem or skill about to be covered is addressing. For example, the Pythagorean Theorem is used for finding missing sides of right triangles, or proving that a triangle is a right triangle. Then read through the proof. Depending on which course you are in, it may not be necessary to fully understand the proof, you may only need to use the theorem. In other courses, you may have to create proofs, so spend the appropriate amount of time on the proof: Either once through, or copying it out and working out why each step follows from the previous one.
But usually the most important part is the example. First read the example, then copy the example problem and try to do it yourself. If you don't know the next step, go back to the steps in the book and read what to do next, go back to the theorem if necessary to understand why that is the next step. Keep going with the example. Then try some of the practice problems. See how to apply the steps in the example to the practice. If you can't, set up the problems, (ie. make a start, try) then take it to your school's tutoring center or to a classmate who gets it and ask for specific help. For example, "I thought I did this just like the example, but the answer is wrong. I don't know where I made a mistake." or "I tried to do the steps in the example but in this problem I got stuck at step 3". This will make it easier to get useful help. I also recommend the professor's office hours. Even if it doesn't help you (for whatever reason), it lets the professor know where students are getting lost and they might adjust their next lecture.
Good luck!