How to Study Math and Prepare for Tests
IMPORTANT INFO ABOUT TESTS for students in my online classes:
Read all the info below, and especially see point 4 below for how to study for each test throughout the semester.
Anything from the entire semester may be on a final exam.
To study for the final, first learn the new material well that you haven't been tested on yet by doing any reviews or practice tests. If tests are online, open previous tests in review mode, and practice taking them again in a timed setting without using notes.
Another excellent way to study for the final is to copy each question from previous tests on a separate index card (or half sheet of paper). You can label each card by test and problem number to refer back to the problem. So for Test 1, problem 3, you could write T1-3. You can also make index cards from problems that are on a video. Copy the instructions and problem on one side, and put the full solution to that problem, showing all the steps for the answer. Mix up all the index cards, pick about 30 cards at random, set a timer for 2 hours, and pretend that is the final. Sit down without interruptions as if you were in a proctored test setting. Do this procedure (practice taking a test of 30 random problems) until you easily do them correctly and feel confident. This is a start to studying, but other types of problems similar to any homework problem or example or video may be on the final, or even one that is a little different where you may have to use critical thinking skills using what you learned to do a new problem. Make sure you study any new material after the last test given in class.
Even though you may not use notes for a test, an excellent way to prepare is to write a page of notes with important information and any formulas. Study notes, and rewrite the notes. When you get your test, take a piece of scratch paper and write all the notes you remember on the scratch paper. This is called a memory dump onto the paper to help you as needed throughout the test.
Learning mathematics is a time-consuming process, and it is not possible to learn all the material in a math course during 60 or so hours of lecture. The teacher can only give an outline of what and how much students need to learn, and then the students must spend a significant amount of time on their own between class meetings to fill in the blanks to learn the concepts. In general, for every two hours of college lecture time (or watching videos to learn), the student should spend 4 hours on their own reviewing notes from class or videos, reworking examples done in class on their own, and doing more examples and problems, including homework, in order to absorb and own the material. If you commit yourself to spending this many hours per week, you will have the best chance of being successful in your math class. Below is a general guide.
How to Study for a Math Class: The main ingredient is TIME: Work on math daily. Commit to spending the time it takes YOU to fully understand the material. There are no short cuts. For each unit, you should spend about 50 hours over the semester. So for a full 16 week semester course that is 4 units, that is 200 hours, or about 12 hours per week. For a 6 week summer school class, that's about 33 hours a week. That time is for studying, doing homework and reviewing.
1. If written material is provided (book, handouts, modules, etc.), always read it. If you are taking a class on campus, do this before coming to class. You should take notes, and copy all definitions and examples. After you copy a definition, write it on an index card stating the section and page in the book where you found it. Keep these. After you copy each example, you should then try to do each example on your own on a separate piece of paper without looking. Then check to see if you did it correctly. If not, copy the example again, and then try it again until it is easy for you to do. Next, get out a large index card. On one side of the card, write the section number and page you found it in the book, and write the directions and problem. On the opposite side, write the full solution with all steps shown and any notes. These index cards will be helpful for studying for a test.
2. If there are any videos, watch each video, writing each problem and the steps on an index card. Then write the problem only on the other side of the index card. That way you can mix up the cards and try any problem again, and look at the back if you need to see the steps or watch the video again. You can put a rubber band around each group of cards and label by topic or section or chapter, etc.
3. When you do written or online homework, first write every problem on an index card as described in point 1 above. Put the section number, problem number, page, directions and problem on one side, and the solution on the other side. You can put more than one problem on one index card if the directions are the same and you have enough room on the back for the solutions. Always check answers (if provided) to make sure you did them correctly. If not, get help by doing parts 1 and 2 above, or going in the MLC, or asking for help.
4. After you’ve done your index cards for all problems on an assignment, then do your work to be turned in or graded. You have done the problems once on the index cards, so it should be easier to do them a second time. Always write the directions and problem and show all steps or pictures or diagrams so if you review it, you can tell how you figured out the answer.
5. You should end up with tons of index cards. You can keep them by section, or chapter, or mix them up. Throughout every week, constantly review problems you’ve done in the past week or two, as well as from sections since the beginning of the semester. It’s easy to forget what you learned if you don’t constantly review and do the same problems several times. You need to get used to randomly picking any problem and being able to do it correctly without help. Quiz yourself often, picking 20 problems and pretend you are being tested to be more prepared for a test.
6. Math has its own language and there are a lot of concepts and ideas in every section. Students need to be able to put the concepts together, and realize problems may be worded differently. If you understand the concepts, you should be able to understand what is being asked.
7. Math is not a spectator sport, and most students need to spend a lot of time reviewing and doing exercises more than once. A common mistake is to think if you do a problem once, you know it. When you can do several HW problems correctly, picked randomly without looking at examples or notes or getting hints, and when you feel confident you can teach someone else how to do the problem, that is when you start to know the material.
8. Ask questions if you ever need help. Use office hours. Get help in the MLC. Use tutoring services if needed. Work with other students. But it’s important before you do any of these things that you first put in a very good effort on your own first, following the points above. It’s sitting down and struggling on your own first that is necessary. That’s how your brain learns to problem solve.
It's a good idea to keep all the HW problems you do in a notebook that you can review.