After observing hundreds of math students over many years, from peers to students under my own instruction, I have noticed that one of the most difficult things to learn in math is not the content but often how to study the content. Math is unique from some other subjects in that looking through notes and examples, while somewhat beneficial, is often not enough to ensure an understanding of the material. Studying for math requires completing practice problems similar to those that may be included on an assessment independently and checking them for both correctness and completion.
This is one reason that daily homework completion is so important in math. The homework allows the students to complete the types of problems on their own that they will likely see again on quizzes and tests.
As a teacher I always compared this process to practicing for a football or basketball game. While an athletic team is often judged on their record for a season, which is solely dependent on games, the successful team generally spends much more time practicing than it spends playing games. Similarly, a student is often judged more on test and quiz grades than on homework scores, but the successful student generally spends much more time practicing by completing homework and review problems. Working through practice problems, in this analogy, is similar to running the plays that a team might utilize in an athletic game.
In addition to practicing daily by completing homework, it is often necessary to review prior to a quiz or test, again by doing problems. Completing review problems may may mean re-doing old homework assignments, as well as completing review problems provided by a teacher or tutor. If a textbook is available, it is also beneficial to complete problems from the chapter review or test, provided at the end of each chapter.
Here are two additional precautions for completing review problems prior to an assessment:
1. Make sure to complete review problems from different lessons mixed together. Some students struggle on larger assessments, such as unit tests, because, while they may know how to solve each type of problem, they do not know which method to use to solve when all types of problems are mixed together. For example, there are many methods of factoring, and these methods are often taught in separate lessons on separate days. A test over factoring is likely to include problems that require the use of several different methods all mixed together. Therefore, a student must be able to determine which factoring method should be used on each problem, in addition to using it correctly. Consequently, it is important to review problems that require different methods of solving all mixed together.
2. Check answers for correctness. Sadly, I have seen students complete entire homework assignments and entire quizzes using an incorrect method consistently. Not only does that mean that the students’ scores were lower, but they often then have more difficulty learning the correct method because they have practiced a wrong one until it stuck in their heads. If these students had spent a little extra time checking their answers, they would have realized that they were making mistakes. Therefore, it is extremely important to check the answers on problems that are being used as review, either by going over them with a tutor or by using a key provided by the teacher. Most math textbooks also contain the answers to at least some of the exercises in the back of the book or online.
In conclusion, studying for math on a regular basis by completing practice problems is as essential to performance as regular practices are to the success of an athletic team. Additionally, how to study for math is a beneficial skill for students to learn at a young age. In doing so, they will be better prepared to take on more difficult math courses during their high school and college years.
Written by Sara Garrison, Connections Tutoring