# How to keep students engaged during a quiz that is not at the end of class?

I'm getting down to details here:

When a quiz or exam is the last thing in the class period, students can leave when they are done. If not, there is necessarily a time when some students are done with the quiz but others are not.

I have tried multiple different approaches to dealing with this and am dissatisfied with all of them so far:

• Have students turn in the quiz at the front so they can do other things.

This is ineffective because the "last person to turn in the quiz" has to do so by walking up to the front of the room after everyone else, which is demoralizing. Also the "first person to turn in the quiz" is equally demoralizing to the class. This "first person" also hopes to impress the instructor by turning in the quiz first instead of checking their answers.

• Have students keep the quiz and all pass it up at the end.

This is ineffective because students have an assessment in front of them, so they are less willing to take a break or read a book even if they are explicitly told it is okay -- they are much more likely to put their head on the desk to rest or stare forward with hostility, poisoning the atmosphere of the class.

• Put a very hard extra credit problem on the quiz that is worth one point.

This is ineffective because it creates unwanted time pressure for B students and takes the focus away from the important concepts being tested.

• Put an unrelated riddle on the board for bored students to solve, to keep their brains turned on.

This is ineffective because I don't have enough interesting riddles to use, and I'm not sure this is a good use of my prep time. I basically have one interesting riddle that I use on a particularly sleepy quiz day.

How do you give a start-of-class quiz without totally losing the class?

• What age group are we talking about here? My college students have no problem writing a quiz at the beginning of class, and then pulling out their phones for five minutes while everyone else finishes. – David Steinberg Apr 8 '14 at 15:23
• Do you have them keep the quiz in front of them? I'm asking a very low-level question about a tiny detail of the mechanical operation of the quiz. How do they show you that they have their phone out but are not working on the quiz anymore, so it is okay? How do you show them that this behavior is acceptable? And I'd prefer an outcome that is better than students surfing the internet, although that at least keeps them awake... – Chris Cunningham Apr 8 '14 at 15:34
• @ChrisCunningham When they finish the quiz, they turn it face down on their desk. Some amount of trust is required, but they also know that I watch them pretty carefully. A break after a quiz can help them focus for after the break, so I don't count it as lost time at all, sort of like taking a moment to catch your breath after running. – David Steinberg Apr 8 '14 at 15:37
• @Jim Belk: I often gave my quizzes at the beginning of the class so that students wouldn't have to spend the prior class time worrying about it. By "quiz", I mean a 5 to 10-minute one page (with 2 or 3 questions) assessment, not an hour test. Also, I almost always included an extra credit problem. One approach I sometimes used was to design the extra credit problem to be a natural lead-in to what was going to be covered after the quiz, an idea that Chris Cunningham might want to try. – Dave L Renfro Apr 8 '14 at 17:40
• I prefer giving quizzes at the beginning of class for the same reason—I don't want the prospect of the quiz to distract them during the lesson. – Adam Bjorndahl Apr 8 '14 at 18:14

## 3 Answers

In a comment you asked for some examples of extra credit questions I've given.

Example 1:

Roxelle Porter-Knight is driving an early 23rd century gravity-pulsed car with $700$-factor inertial dampers along a one mile course laid out in the desert salt flats and manages to average only $28$ $\frac{\text{mi}}{\text{hr}}$ for the first half mile. How fast must she average over the next half mile so that her average speed for the entire one mile trip is $55$ $\frac{\text{mi}}{\text{hr}}?$ Give your answer to the nearest $0.1$ $\frac{\text{mi}}{\text{hr}}.$

I asked variations of this one in classes such as college algebra, precalculus, calculus 1, and occasionally others. I often asked a different version again in the same class, letting students know in advance that I would. I did this because I thought the underlying principle was important enough (average of velocities doesn't have to equal average velocity), especially in calculus 1, and it was an easy way to get most students to master something somewhat relevant to the material without putting in a lot of class time. Usually in college algebra and precalculus classes I would work it on the board for them the first time, and in calculus classes I left it up to them.

Example 2:

$$\lim_{n \rightarrow \infty}\frac{(2n^3 – n^2 + 6)^4(3n-7)^3}{n(1+7n)(2+3n^2)^2(3+4n^3)^3}$$

I often put something like this on a calculus 2 quiz on a day when I wanted to review limits of rational functions (e.g. for ratio test with series convergence), with the review being at a more mathematically mature level than was probably the case when they covered this in precalculus or calculus 1. By "more mathematically mature level", I mean knowing the idea of using dominate terms and being able to quickly find the dominate terms. I'd work the extra credit problem to demonstrate the idea: $$\frac{(2n^3 – n^2 + 6)^4(3n-7)^3}{n(1+7n)(2+3n^2)^2(3+4n^3)^3} \;\; = \;\; \frac{(2^4n^{12} + \cdots)(3^3n^3 + \cdots)}{n(7n + \cdots)(3^2n^4 + \cdots)(4^3n^9 + \cdots)}$$ $$= \;\; \frac{2^43^3n^{15} + \cdots}{3^24^3\cdot7n^{15} + \cdots} \;\; \longrightarrow \;\; \frac{2^43^3}{3^24^3\cdot7} \;\; = \;\; \frac{2^43^3}{2^63^2\cdot7} \;\; = \;\; \frac{3}{2^2\cdot7} \;\; = \;\; \frac{3}{28}$$ This specific example came from a quiz given to a very strong high school class, by the way. Note that it is easy vary the difficulty of something like this.

Example 3:

Evaluate the following, where $a$ is a constant greater than $1.$ Your answer will be an expression involving $a.$ Show appropriate work! (A suitable graph along with some high school geometry area calculations is acceptable.) $$\int_{0}^{a}|ax-a|\,dx$$

Example 4:

Expanding as much as possible using the chain rule, find the 2nd derivative of $f \circ f \circ f.$

Example 5:

$$\int (6x – 1)^2 \sqrt{2x-1}\,dx$$

This is a good type to use near the beginning of covering integration by $u$-substitution. It's a standard type, but students will remember the trick better if they struggle with it a bit on a quiz (or hour test). The idea, of course, is that the square root function is not an additive function, so you want to let $u = 2x-1$ (and not $u = 6x-1).$ Then you have to "force" the substitution by solving for $x$ in terms of $u$ in order to express $(6x – 1)^2$ in terms of $u.$

Example 6:

Find the unique solution to the following ODE that contains the point $\left( 0,\,1\right).$ Express your answer as $y$ solved in terms of $x,$ making use of the error function. The error function is defined as $\text{erf}\,(x) =\frac{2}{\sqrt{\pi}}\int_{0}^{x}e^{-t^{2}}dt.$ [Footnote: Your text discusses the error function on pp. 84-85 and in Section 165 (pp. 511-518).] $$y' - 2xy\;=\;1$$

I put this on a differential equations quiz on a day that I wanted to talk about using unfamiliar functions and indicated integrations to express solutions. I had planned to work this problem as one of my lecture examples, but then decided it would be worth the time to put it as an extra credit problem on that day's quiz. I'm certain the extra time I gave them for the quiz (I probably give them 20 minutes for what was otherwise a 10-minute quiz) was more than made up by their retention of the idea and by their attention to my working it out after the quiz.

• Awesome! Sorry to keep pestering you for more details, but do you put an extra credit question on every quiz, so they were used to it? – Chris Cunningham Apr 9 '14 at 23:45
• @Chris Cunningham: I probably put extra credit questions on about 90% of my quizzes over the years. The exceptions I can think of are when it was a short memorization type quiz (which I often gave in trigonometry courses) or when it was a "small groups" quiz. Speaking of group quizzes (which cmhughes discusses in this thread), I've tried every one of the 8 subsets of {group, open book, open notes}. What worked for me and what didn't depended far more on ability and social aspects of the students, and the level of the course, than the method. So experiment! – Dave L Renfro Apr 10 '14 at 13:37

I have found that group quizzes work remarkably well in all of the (Community College-see below) levels of Mathematics that I have taught. I typically give them at the end of class, but I imagine it would work nearly as well at the beginning. The rules are always the same: no notes, no books, but you can work together, walk around the room, and work at the boards.

I stress to the students that one of the outcomes of this quiz is collaboration, and that I don't want them to leave anyone on their own; I try to encourage folks to touch base with people, and make sure that everyone understands what's going on as much as possible.

This has, generally speaking, helped to form a stronger community in the classroom- when there are points for a grade at stake, people generally seem to work harder. Furthermore, when I set non-graded activities, the students are more likely to work together because of the quiz experience.

I initially worried that, because the students could work together, they would all get perfect scores. This has never been the case--I still receive a wide range of scores and the quality is still varied; the main benefit is that it seems to ease some of the tension and anxiety that students feel when faced with a quiz.

Community College level mathematics covers a fairly wide range of Mathematics, from developmental (pre-GCSE/high school) to first & second year University level. Community College students are typically adults, and vary widely in demographics.

I have a suggestion which is related to my answer to this question regarding time pressure. I typically design 5-10 minute quizzes in such a way so that there's a bit of a time crunch. Of course, this might not be ideal in some cases, depending on how you're using the quizzes. But personally, I tend to put relatively easy questions on the quizzes so that, combined with the time crunch, they function as "do you have this down cold?" wake-up calls (and are worth a correspondingly small fraction of their final mark).

This might help with your problem since it will reduce the number of people who finish early as well as the average extra time they have to twiddle their thumbs. Judging by a visual survey, I'd say typically only 1-3 students finish with more than a minute to spare. I've never actually experienced students "staring forward with hostility"—perhaps because they don't have to wait too long?