One of the most common questions asked by Mathnasium students is how to study and prepare for upcoming math tests. These “Mathletes” more often than not also suffer from test anxiety, which leads them to believe that no matter how much they study, they won’t do well on the test. Here, we'll explore some common myths about studying and a very effective way to study for math tests:
Myth #1: Math is just memorizing formulas
While there are definite formulas all math students need to know (e.g. area of a rectangle, triangle, circle, etc.), math is really a matter of problem solving. Those students who are most challenged by math have not developed the reasoning, logic, or understanding they need to find the solution path. Every math student should ask these questions when reading a problem:
- What information is given in the problem?
- What do I need to find?
- How do I break this into parts?
- What should I do first, second, etc.?
Myth # 2: Reviewing a few problems in the chapter is all I have to do to study for a test
While re-doing some homework problems in the chapter helps to review the section covered, it is not the most effective way to study. Top math students will work out every single problem in each section, focusing on understanding the problem solving steps more than getting correct answers! Additionally, they seek help from their teacher or tutor for any problem they cannot solve.
Myth # 3: Even though I did not fully understand the previous chapter or section, if I can correctly solve the problems in the next section, I don’t need to worry
This common belief among students is what causes them to “crash and burn” when they take their tests. Unlike other subjects, math knowledge is cumulative. Sections which are missed (due to absences from class) or not understood create “gaps” in the student’s math level. These “holes” may not manifest themselves until later, when another concept is introduced which builds on the previously introduced math concept. Such gaps lead to confusion and more problems keeping up in class.
Myth # 4: There is only one way to solve a math problem
A student who only knows one way to come up with a solution will run into trouble when the teacher changes the parameters or “reverses” the problem to be solved. Reversing a problem requires an experience-base that includes practice in reverse-thinking. For example, most of us can answer the question, “What is half of 12?” A reverse question would be “Half of what number is 6?” The concept also applies to a student memorizing a formula in algebra. Fully understanding how and mastering when to use a mathematical formula require a lot of practice with similar problems, which in turn results in arithmetic fluency. This fluency is similar to that referred to when learning a language where a student learns to speak beyond phrases and begins to implement his/her own sentences.
Myth # 5: I don’t need to check my results
Many students’ mistakes are caused by human error rather than lack of understanding. It is important to work each problem carefully to minimize the errors, and it never hurts to recheck calculations. Careless mistakes often occur when the calculations become so mechanical that the student’s mind begins to wander and lose concentration. Sometimes a simple arithmetic operation or sign error will lead to an incorrect answer. Organizing the work on paper in a step-by-step sequence helps a student trace back to find any possible mistakes.
The above test preparation strategies, in addition to the following five daily study/homework success steps, are highly recommended for students who wish to excel in math:
- attend class regularly
- take detailed notes from the teacher’s explanation
- do all assigned homework everyday
- ask for help if needed
- review previous math concepts regularly (i.e., several times a week).
In conclusion, preparing for tests and quizzes requires a systematic method for reviewing the concepts, solving all the homework problems, memorizing key concepts and formulas, and taking practice tests (normally at the end of the chapters) in the textbook.