Math and the NYS Regents Exams

Math and the NYS Regents Exams

After the big test, students brush up on probability by playing blackjack

One common complaint against math is, "When are we going to use it?" (or what students really mean when they say that—"Is math ever relevant and exciting?") So, let's use math to find the probability of passing the New York Regents exam by guessing. It's relevant because the NY Regents exam is a high-stakes test, both for students and teachers. It's exiting because there is some controversy over the grading curve that they use. Some say that it's too easy to pass. Let's examine this question.

The New York State Algebra 1 Regents exam is required in order to receive a Regents diploma in New York. It consists of 30 multiple-choice questions and 9 open-ended questions. To pass, all you need is a raw score of as low as 30. (For example, check out the scoring chart for the January 2011 exam on this page.) Because the multiple-choice questions are worth 2 points each, all you need are 15 of them to pass. This makes for an interesting test-taking strategy—Is it possible to pass by ignoring the open-ended questions and focusing only on the multiple-choice questions?

To answer this question, we'll need some probability theory. Ironically, the necessary math is covered in the NYS Algebra 2 curriculum. In terms of probability, what we want is the probability of getting at least 15 out of the 30 questions correct by random guessing. This is just a Binomial experiment:

• Each multiple-choice question is an independent event with two outcomes: correct or incorrect
• The probability of answering one question correctly is 1/4, or .25.

Since there are a total of 30 questions and we want to know the probability of getting at least 15 correct, this is a Binomial experiment with 30 trials, r = 15, and p = .25.

Doing the math (which you can do on your Regents-approved TI calculator or Excel), the probability comes out to be very low, as in, about .0008. Putting this number into perspective, if 10,000 students used this strategy, we expect to see about 8 students pass the exam. Most students would fail.

So, blindly guessing all multiple-choice questions is not a viable option.

Obviously.

I mean who in their right mind would do that? Let's try a slightly different (and more realistic) strategy. What if you answer 10 questions using your knowledge of Algebra 1 (and hopefully get them right) and guess at the remaining questions? Answering 10 questions with math knowledge is reasonable, right? What's the probability of passing this way? It's now a Binomial experiment with n = 20 and r = 5. With these values, the probability of passing is now about .38. Putting this number into perspective, if 100 students (about the size of a freshman class) use this strategy, then we expect to see 38 of them pass the Regents. That's a heck of a lot of students who don't really have a grasp of Algebra. The real numbers may be worse because most students will try to answer the open-ended questions, picking up partial credit.

So, what we've shown with math is that there is some truth in what the critics say—the first-year NY Regents math is meaningless when it comes to showing whether or not students understand the material.

Irony of ironies.