Leigh Nataro teaches elementary statistics and business calculus at Moravian University in Bethlehem, PA. Leigh has been an AP Exam Reader and Table Leader and was on the AP Statistics Instructional Design Team, where she helped to tag items for the AP Classroom question bank. In addition to leading AP Statistics workshops, Leigh is also a Desmos Certified Presenter. Leigh can be reached on Twitter at @mathteacher24.
With multiple choice questions weighted as 50% of the AP Statistics exam score, it is important to give students concrete strategies to maximize success on that component of the exam. Although there is no penalty for guessing, we don’t want our students to guess on many questions and when the students do guess, we want their guesses to be educated guesses. In this post, I’ll share three strategies to help your students become educated guessers and more successful with MCQs.
Strategy 1: Annotate the Question
For some students, the reading load of the AP Statistics Exam is quite heavy and this may cause them to see all the words in a question as having equal importance. Annotating the question can help students see the key components needed to successfully answer the question. For example, students may circle or make a note in the margin for the numbers they think are important. What do those numbers represent? Are the numbers in the problem the sample size, population mean, sample standard deviation, or some other value? Underlining the actual question or key words in the question may help students to identify the concept needed to solve the problem.
Let’s consider how a student might use this strategy on the following question.
They might circle 10% and 40 and label those values as p and n. The student could next underline the words “probability that exactly 5”, which may lead them to think we are looking for a specific number of successes. They may look at the formula sheet in the section of probability formulas and recognize that this is a binomial situation. This might lead them to write the word binomial beside the question. Note that the strategy of annotating the question would also work well for free response questions.
Strategy 2: Annotating the Answers (First)
Students often approach a MCQ by reading the question first and then reading the answer choices. For some questions, it might be more helpful to read the answer choices first and annotate the answer choices. Let’s consider that strategy for the following question. The red text are the annotations the student would create when reading the answer choices.
After annotating the answer choices, the student can circle the word proportion in the second sentence. The customer either redeems the K cash or does not redeem the K cash. Since we only have the one variable, it is not a chi-square test of homogeneity. At this point, the student is looking at the prompt for information about the number of samples. Two numbers are given - “two hundred randomly selected customers” and “eighty of them redeemed their K cash”. This is one sample and eighty out of two hundred would be the sample proportion. The correct answer is B - one-sample z-test for a proportion.
Strategy 3: Scratch One, Choose One
On my classroom tests I give both MCQs and FRQs. For MCQs, the directions tell students to scratch a wrong answer and then circle a correct answer. Students get partial credit (1 point out of 4 possible points) for scratching a wrong answer. In class we practice the strategy of eliminating incorrect answers every time we review multiple choice questions. I ask my students which answers they can eliminate and why. Usually 2 or 3 answer choices can be eliminated fairly quickly this way. Noticing how answers are alike and how they are different can be used to help eliminate answers, as seen in the following question.
Since all of the answer choices start with 0.24, students should be encouraged to focus on what makes these answers different. The critical value is either 2.576, 1.96 or 1.645. Since we are creating a 99% confidence interval, the correct critical value is 2.576 and answer choices C and E can be eliminated. At this point students may turn to their formula sheet to see how the standard error is calculated. In the numerator, we have the sample proportion and in the denominator the sample size. This means that the correct answer is A, because 0.24 is the sample proportion and 500 is the sample size.
Combining Multiple Strategies
Here is an example where students can apply multiple strategies. Students would start by annotating the answers. Here we can see key words and numbers that the student might highlight before looking at the computer output. They may also annotate the question, circling the word slope and labeling the variables as x and y.
Since the slope is positive, height increases as femur length increases. This would lead students to eliminate answer choices C and E. Recognizing that the slope on the computer output is 1.654 would lead students to eliminate answer choice A. Since slope is a 1 unit increase in x (femur length) for a slope unit increase in y (height), the correct answer is D.
To help your students be more successful with MCQs, have them practice with MCQs frequently in assignments, quizzes, and tests. Model using these strategies with your students, and remind them that using these strategies will increase the likelihood of getting a question right if they need to make an educated guess.
For practice with these strategies, I recommend the Desmos Activity called “Scratch One Choose One: Multiple Choice Practice” in the Unit 6 Stats Medic/Desmos Collection.
The entire Stats Medic/Desmos Activity collection can be found here.