One of the questions I’m asked most often when I present about teaching with clickers is the “coverage” question: How do you cover all the content you need to in a course if you spend class time having students think about, vote on, and discuss clicker questions?  All that active learning during class must mean you can’t cover all the same content, right?

Although I find the term “cover” problematic, I understand these questions.  Particular in courses that are prerequisites for other courses, there’s a need to make sure students learn a certain (usually large) amount of material.  In talking with faculty who teach with clickers, I’ve heard several different kinds of responses to the “coverage” question, ones I detail in my book.  One response is to move some of the learning that would have taken place during class to out-of-class time.  One way to do this is by having our students read their textbooks before class, which I’ve done in my math courses for several years now.  This means that students come to class with some exposure and understanding of the material, which allows class time to be spent helping the students make sense of that material and go deeper via clicker questions and other active learning techniques.

An added benefit to having students complete pre-class reading quizzes is that I can draw on student responses to open-ended quiz questions to create in-class clicker questions.  Here’s an example:

Consider Question 1 on the Introductory Problems handout and Example 1 in Section 1.6.  These two problems involve input-output relationships between different sectors of an economy.  In what ways are these problems essentially different?  Which of the following is the best answer to this question?

1. The output from one sector in the example is entirely used up by the other sectors. In the handout, the output is only partly used and a net excess is provided.
2. Example 1 asks for the total annual outputs of the coal, electric, and steel sectors. Whereas question 1 is looking for the production levels for an outside demand.
3. In the original example, we’re solving the system to meet a single expectation from a foreign country of three demands, whereas the book’s example is looking to maximize the productivity.  This means the book’s example has multiple solutions and we’re looking for the best of them, where as our original only has one.
4. The two problems are different as the first is trying to find the initial inputs to achieve certain outputs while the second problem is about finding the market price.

The exact same question was posed on the pre-class reading quiz the night before as an open-ended question.  The answer choices you see here actual student responses to that open-ended question.  During class, I had my students respond to this clicker question, letting them know that four of them should recognize their own words in the answer choices.

The votes were split 30% / 0% / 43% / 26% among the four answer choices, which is a great distribution for generating discussion about the question.  It helped that the most popular answer (#3) was partially incorrect.  (The book example did not, in fact, deal with maximizing productivity.)  The other two answers selected by the students (#1 and #4) are both correct, although #4 gets at the heart of the difference between the two examples more than #1 does.

Some of the students were bothered by the fact that this question doesn’t have a single correct answer.  However, since I’m trying to help my students improve their ability to communicate mathematical and technical ideas, it’s worth spending time on a question like this one, where the quality of the explanation plays an important factor.

We had a funny moment when the student who supplied the popular but incorrect answer choice (#3) spoke up after we had discussed what that choice was incorrect.  He didn’t directly own up to his answer, but instead said something like, “I think the student who gave that answer probably didn’t catch on to the fact that productivity wasn’t being maximized.  He probably has a much better understanding of the example now.”

It can be challenging to write clicker questions with answer choices that align well with student understandings and misunderstandings of a topic.  Taking the students’ very own responses as answer choices is one way to get around this.  It also communicates to students that the pre-class reading quizzes are an integral part of their learning experience.