Recall that active practice is required to learn math. In mathematics, the purpose of homework is to practice and prepare to perform well on tests.
- Review textbook material and/or lecture notes relating to the homework. This refreshes your memory on the material, giving you a better idea as to how to complete the homework. It also helps you know where to refer to if you get stuck on a problem. Many students who are stuck simply do not understand the definitions involved in the question.
- Don’t use your textbook/notes as a crutch. On the other hand, don’t rely completely on your textbook or notes to complete problems. They can be used as a first step, but eventually, you will have to solve them without references. Relying totally on resources can give you a false impression you are prepared for the test. If you look at a similar solved problem for guidance, ask “how could I have thought of this next step in the problem?” rather than simply copying down the steps.
- Write down every step or procedure. Some steps will seem trivial or can be done in your head, however, writing them down reinforces your memory. Also, if you make a mistake, it will be easier to retrace your steps to find the error. After you are comfortable and experienced with a procedure, then you can stop writing it down each time.
- Understand the reasons for each problem step. Most math problems require using some mathematical rules, laws, and properties. Understanding these rules will make it easier to apply them to other similar problems on tests. In contrast, simply memorizing the procedure to do a specific problem, will not apply to other problems requiring that property.
- Complete homework neatly. This will make it easier to review later for tests. It also makes it easier to get help from an instructor, as they will be able to read your writing.
- Summarize concepts in your own words. After completing a problem, try to summarize the concepts and steps used in your own words.
- Check your answers, if possible. This lets you confirm if you’re on the right track. First, consider the back of your textbook. If not, there are free websites (and other paid websites) which have textbook solutions. However, this is a double-edged sword, because you absolutely don’t want to use a solutions manual as a substitute for working through the problems. This is a guaranteed way to do poorly on tests (I say this from experience).
- Start on homework as early as possible. This is helpful for multiple reasons. First, spacing out learning is more effective than doing it all at once. Second, it gives you time to think about problems, if you are stuck at first. It is common to be stuck on difficult problems the first time you encounter them. Third, it allows for plenty of time to get help from an instructor, if necessary.
- Complete homework fully. Avoid rushing through homework, just to get it done. This will require that you don’t do homework at the last minute.