As we’ve already discussed, test prep and math class often do not go hand in hand.
However, it’s important that teachers don’t hide from the reality that students are going to be judged based on their standardized test scores. Here are some suggestions for how to bring classroom math and test prep closer together.
The biggest difference between math in school and math on a standardized test is the multiple choice format.
In school, students show their work and often can earn partial credit for correct intermediate steps, even if the final answer is wrong. Because standardized tests are graded by computer, partial credit is impossible. The upside of multiple choice, however, is that strategic elimination can improve their ability to guess the correct answer. When doing math problems, give students a range of answer choices and ask them to eliminate any unreasonable answers. This is a great opportunity to integrate real learning into test prep—ask them to provide reasons they think the particular choice is unreasonable.
Additionally, working backwards is a viable option for finding the correct answer on a multiple choice test. In some of your problems, make it a point to show students how to plug in answer choices to the problem to see which one works. Another valuable lesson is that there are always multiple mathematical approaches to a problem. If students can learn which approaches come more easily to them, they can save themselves time and stress in a testing situation. To help them recognize their best approaches, use complex problems (mixed figure geometry problems from the SAT are a good bet, since they combine geometry concepts with algebra and arithmetic) and have students map out all of the possible ways to solve. They’ll not only learn that other approaches are valid, but they’ll also likely latch on to the approaches they find easiest as well. You could also set up a contest in which teams have to present the most elegant solution to a given problem.
Another way to strengthen students’ abilities on standardized tests is to have them list out resources available to them: formulas, information given in the problem, information that can be deduced from what is given, and so on. The formulas are especially important. These include geometry formulas, common algebraic patterns, exponent rules, etc. Students should become comfortable using formulas backwards and forwards (for example, finding the area of a circle given the radius, or finding the radius of a circle given the area).
One of the more challenging aspects of math on standardized tests is that concepts are often tested in combination as opposed to isolation, like in the classroom.
In your own quizzes and tests, be sure to test both ways whenever possible. Especially for topics that don’t naturally build on one another, loop them together in surprising ways so that students get used to seeing them in combination. Having students write complex problems that combine mathematical topics can also be helpful. They’ll reinforce what they know about math while gaining perspective on how these topics connect with one another. They’ll also learn to think about how test problems are constructed, which will give them insight into how to approach these difficult problems.
Even though not all of these methods may be helpful (or desired) for classwork, they can impart to students the value of estimating, memorizing common formulas, and seeking creative solutions.