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How To Read Math Books
It is just not possible to read a math textbook like you would a read a novel and be able to understand and learn the material.
Have you ever read through a section of a math textbook and at the end you have no idea what you just read? If so, you are not alone. And most teachers don't know these techniques or they learned them by trial and error on their own and expect you to do the same.
[ There could be other reasons you have never been taught to do this. See the study techniques page for more info. ]
Well, what are going to tell you on this page will help you skip the trial and error part and jump right into being able to learn and understand math directly from textbooks. Many schools are implementing a teaching method called flipped teaching and these math classes require you to know how to read math textbooks. Part of the beauty of these techniques is that begin to you learn on your own and become a more independent student. So, if you have a teacher sometime that is not very good, you will still be able to learn.
So, what do you need to do? We have listed below the main techniques that we think will help you.
Before starting, scan the section to see what the important points are. It would be nice if your instructor provided an overview of exactly what you are supposed to do and learn for each section but that usually won't happen. So you need to do it and you will need to learn everything, unless your instructor tells you otherwise. Assume everything is going to be on the exam and assume you will need to know everything for your next class or sometime in the future.
1. Get out a pencil (not a pen), an eraser and a notebook. You will use these to write notes as you go along. These notes don't have to be organized or clean.
2. Slow down and read each word and sentence carefully. This a hard one since we are so used to reading quickly so that we can through with whatever we are doing, so that we can go through the next task as quickly as possible. You need time for your mind to become aware of what the book is saying and process new terms and ideas.
3. When going through examples, carefully process each step until you understand what they are doing. If there are things that are going on that you don't understand or it seems like the book is skipping steps (which all books do), then write out the step in your notebook, filling in the missing steps. Process it by writing it out until you understand the step. Then go to the next step. If you get stuck, write a note to yourself in your notebook and see if subsequent steps help you understand. If not, then get some help from your study group, fellow student, tutor or instructor.
4. Do not skip the proofs. Although most instructors skip the proofs and do not even require you to read them, read them anyway. The proofs give you an idea of when and how to use theorems and push your learning so that you can understand even more of the material. As you go through a proof, write out each step and fill in the gaps, similar to examples. However, with proofs, it helps to rewrite the proof in your own words.
5. Do not skip graphs and pictures. They are excellent ways to help remember concepts. If you understand a graph and how it relates to an equation or concept, you now have two ways to remember the material.
6. Write down important terms in your notebook along with the definition, in your own words. So what are the important terms? When you are first learning, you don't know. So write down the obvious like bold, italicized or highlighted terms and concepts. Include theorems or anything with proofs. Then write down what you THINK are important terms. You will find out later if they are or not. Don't be afraid to write down too much.
7. Read other textbooks and supplemental math books. What?! Read more than just what I am required to read?! Yes, because the point of reading is to understand and there is not any one textbook that will help every student. We have some suggestions in our math bookstore but they are just to get you started. This is important and will help you a lot.
8. Work a few practice problems even if you don't have to. As a student, your time is limited. You have a lot to do and not much time. But if you take the time to do a little bit of work over and above what you are asked to do, you save even more time later since you will not have to relearn the material. You will already know it and have some experience with it.