Math Study Tips :: math.ucdavis.edu

How Do I Study Math Effectively?

This document is meant to give you some tips and tricks for how to study math effectively. There will be too many things on here for you to do all of it; we encourage you to try some of these techniques and see what works for you. Everyone’s brain works differently, and so while most of these study techniques have been drawn from psychological research on how to learn and remember things, each of you will find that certain things work better than others.

What Should I Study?

Before we even get to the how part of studying and learning, you first have to decide what to study. The good news: you can use your class structure! Look through class notes, homework problems, and discussion problems. Look at the corresponding textbook chapter(s). While you are doing this, you will find some things that are uncomfortable or make you hope they aren’t on the exam. These topics are a great starting point. Remember: your instructor has made conscious choices about what material to cover in lecture and put on homework, and exams are meant to measure how well you’ve learned the course material.

How to Study.

The following techniques are in no particular order. We tried to include what each technique is, why it works, and how to apply it to math. Note that these techniques come from the book Make It Stick, by Brown, Roediger, and McDaniel. We encourage you to read if you get the chance; doing so will help you become a better, more efficient learner all around.

Retrieval Practice

Interleaved Studying

Space Out Your Practice

Reflect

Elaborate

Study Intentionally

Mindset.

Remember, math is hard! Learning takes effort, and failure/setbacks are a part of the learning process. Neurologically, the process of making new connections in your brain to remember new material takes time, energy, and effort. If you aren’t putting effort into a class and/or you aren’t failing at least some of the time, you aren’t learning the material very well. (And something that often isn’t shared until too late: people who get paid to do math–like your professors–fail A LOT. All it takes is one good idea to write a research paper! No one sees the many ideas that didn’t work.)

As much as you can, focus on learning the material instead of a grade. While you study, remember to pause and celebrate what you have accomplished and reflect on what you have internalized through your hard work.

During an Exam.

You’ve studied (or not) and now it’s time to take the exam. A few parting words for you: take a deep breath. You are a wonderful human, regardless of how any exam goes.

Frame the exam as a way to show what you’ve learned! Most likely, you wouldn’t have been able to understand what the questions were asking before starting this class. Just understanding all the questions proves that you’ve learned something already.

If you’re feeling stuck, write down what you know. You can write down definitions or theorems you remember related to the question. If asked to prove something abstract, find an example. Even showing that what you are asked to prove works for your specific example demonstrates an understanding of the material (and more often than not, you’ll get an idea of how to prove the general case). You can also write down why/where you are stuck. If you can prove the problem assuming some extra little lemma or fact, then do so (but be clear about what else you are assuming).

You got this!

Math Study Tips, by Alexander Simons and Ally Nagasawa-Hinck, UC Davis graduate students, 2023.