Two "Different" Math Sections?
When the College Board first released the specifications of the revised SAT several years ago, my colleagues and I knew what the test creators were trying to do in distinguishing a "No Calculator" Math section. The idea would be to test what students really understood about algebraic manipulation, mathematical relationships, and data interpretation, all without being able to use the calculator as a crutch. What we didn't know at the time was just how similar the two sections would be, and how important it would become for students to look at just about every problem as something that could show up on the No Calculator section.
To be clear, there are indeed some problems on the Calculator Math section that do necessitate the use of a calculator. The reason though, falls solely under the realm of computation. For example, let's suppose a problem asked students to use a two-way table to determine the percent of tenants in an apartment complex who use air conditioners, and that the answer could be obtained by dividing 155, the total number of air conditioner users, by 196, the total number of tenants in the complex. This is not a reducible fraction, so the Calculator section might provide answers that look like 79.1%, which is the rounded percentage of air conditioner-using tenants. The College Board isn't interested in making students run through laborious long division, so the test creators are fine with having students use a calculator to do the arithmetic for them––it's testing the process that gets students to the result that really matters.
But therein lies the point: the same question could just as easily appear on the No Calculator Math section, but with the answer choices stated as irreducible fractions, like 155/196. Because the essential problem solving process is the same, the identical question with differently stated answer choices can appear on either math section.
You might be thinking that this whole discussion is moot, because the question above is easy. But this is just one example of hundreds of questions that students could be expected to solve with––or without––calculators just the same. For example, take the following, which is similar to a question that showed up on a recent Calculator section.
Given that a student understands that a "solution" in the context of this problem basically means "intersection point of the graphs", this is pretty simple when it appears on the Calculator Math section: the test-taker can simply rearrange both equations to isolate y, hammer them into the calculator, and then use the device's graphing tools to find that the graphs intersect at two points, one of which has a y-coordinate of –5. Here's the rub: questions exactly like this one regularly show up on the No Calculator section. What now? There are many ways to handle this problem without a calculator, but all of them involve algebraic know-how. Only students who have a well-developed understanding of algebra and coordinate geometry will be able to work through to the solution.
All this boils down to a very simple piece of cautionary advice that every student should hear: do not allow your successful solutions on the SAT's Calculator Math section to lull you into a false sense of security. Treat every problem you see, regardless of the math section in which it appears, like one you could see on the No Calculator Math section of the exam. In this way, you'll be prepared for anything, and will have the skills to achieve a significantly higher SAT Math score.