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From reviewing before a test to various ways for students to take tests collaboratively, this article looks at ways that groups can be used to evaluate student learning while increasing that learning.
Background and Purpose
As a student, the opportunity to collaborate with other students was instrumental to my success in learning mathematics. As an instructor, I take these approaches one step further. If the structure of a class is largely group-based, why not use group activities during testing as well? Exams then become genuine learning experiences.
I have been teaching at large state universities for five years. I use these approaches in classes ranging from College Algebra to Advanced Calculus. The average class size is about thirty, but the techniques can be used in larger classes as well.
Below is a list of group activities that can be used to assess learning in the mathematics classroom. They are arranged from modest to radical, so if you are just starting group activities, you might find it helpful to move through the list sequentially. I discuss findings and use of findings with each activity, and make brief remarks that apply to all the methods subsequent the Method section.
Method
Group Exam Review
This approach allows you to cover a broad spectrum of problems in a limited amount of time. Hand out a worksheet with all the problems you would like students to review for an upcoming exam. Divide the class into groups, and have each group begin by solving only one problem and putting the solution on the board. Then, instruct groups to work on additional problems throughout the class period, always entering their solution on the board. When it is clear that several groups agree on a solution, mark that problem as "solved." When groups disagree, have the entire class work on the problem until agreement is reached. At the end of the class period, everyone has a completed solution set for the entire worksheet, even though as individuals they only wrestled with a few problems.
Findings. Students really like this approach for review. They spend the class period actively solving problems and feel that their time has been used wisely. They make contacts for forming study groups.
Use of Findings. This approach excites students to begin studying: they've gotten started and have a guide (the remaining problems on the worksheet) for continuing their studies. They have some sense of what they do and do not know, and thus how much studying will be necessary.
Think, Pair, Share
Write a problem on the board and ask students to think about how to solve this problem for a few minutes. Then, have them pair up with a neighbor to share solutions and require each pair to agree on one solution. Next, ask each group to report its result to the class.
Findings. Since some students are more prepared than others, this technique prevents the most prepared students from dominating an open class discussion on a new topic. It forces each student to spend some time thinking alone. They can then refine their ideas and build confidence by pairing before sharing their solutions with the entire class.
Use of Findings. Student confidence increases and they are more willing to participate in the class discussion.
Quiz for Two and Quiz Consulting
In Quiz for Two, students pair up on a quiz. They can catch each other's mistakes. In Quiz Consulting, students are allowed to go out in the hall empty-handed to discuss the quiz, or to talk to each other for one minute during a quiz. By leaving their work at their desks, students are forced to communicate ideas to each other verbally.
Findings. Students learn during the assessment itself. I've been surprised to see that a wide cross section of students (not just the weakest ones) choose to take advantage of opportunities to discuss quizzes with their peers. Performance on these quizzes rises while student anxiety declines
Use of Findings. I have found that I can make the problems a bit more challenging. One must take care, however, not to overdo this, as this may cause the class' anxiety level to rise, defeating the purpose of the technique.
Collaborative Exams
Option 1: I give an extremely challenging multiple choice exam to the class. I allow the class to discuss the exam, but require that they each turn in their own solution at the end of the class period. I've seen this technique used in a sociology course with hundreds of students at the University of Rhode Island. Option 2: Give a shorter exam, but have them work on it twice. For the first half of the testing period, students work alone and turn in their individual answer sheets. Then, allow them to work in small groups and turn in a group answer sheet at the end of the period.
Findings. One danger with collaborative exams is that students frequently defer to the person who is perceived as the "smartest"—they don't want to waste precious time learning the material but rather hope to get the best score possible by relying on the class genius. Option 2 gives students an opportunity to discuss the exam more deeply since they have already spent a good deal of time thinking about the problems. Discussion can deteriorate, however, if the students are more interested in trying to figure out what their grade is going to be than in discussing the problems themselves.
Use of Findings. With Option 2, the final score can be an average of their two scores.
Findings
While group work is a slower mechanism than a lecture for transmitting information, a well designed group activity can lead to deeper learning. Moreover, activities can combine several topics, thereby saving time. My main finding is that student anxiety about testing is reduced. Students think of quizzes as learning exercises instead of regurgitation exercises. Students are thinking more during testing and are learning more as a result.
I use Group Exam Review several times each semester. Think, Pair, Share is most useful when I am introducing a new concept. There is a definite penalty to pay in class time when using this technique, so I try to use it sparingly. I use Quiz Consulting frequently; it is one of my favorite techniques.
Use of Findings
I primarily use these methods as part of students' overall grade for the course. As with all teaching techniques, it is important to vary assessment methods so that any weaknesses are minimized.
Success Factors
I solicit regular feedback from my students and rearrange groups based on this feedback. I ask students individually, for example, how well they felt the group worked together, and whether they would enjoy working with the same group again or would prefer a new arrangement next time. Students who report that they do not want to work in groups at all are grouped together! This way, they can work individually (perhaps checking their answers with each other at the end) and don't spoil the experience for other students who are more invested in this collaborative approach.
A concern with allowing collaboration for assessment is that the strong students will resent "giving" answers away and carrying weaker students, or that weaker students will receive an unfair boost since they "scam" answers from others. This is a real worry, but there are ways to address it. It is helpful to rearrange the groupings frequently. I've found that students who do not contribute adequately feel embarrassed about their performance and consequently work harder to be well-prepared for the next time. If there are enough opportunities for students who are strong to demonstrate their individual understanding, there is not much grumbling.
Although many people use groups of four to five students, I've had more success with groups of three to four. Experiment with different grouping approaches — try putting students with similar scores together or pairing dominant and talkative people. For my initial group arrangements, I have students fill out information cards and then pair them according to similarities — commuters, parents, students who like animals, etc. Some instructors like to assign roles to each group member — one person is the record keeper, one person is the doubter/questioner, one person is the leader. I prefer to allow the leadership to emerge naturally. I am constantly rearranging groups until members unanimously report that they like their group. This can be a lot of work, however I feel it is worth the effort.
It helps to give specific objectives and timelines in order to keep the group on task. Group conversation can wander and it helps to forewarn them that you will be expecting a certain outcome in a certain amount of time.
Give your students guidelines, such as those found in [1]. These guidelines can, for example, encourage students to listen to each other's opinions openly, to support solutions that seem objective and logical, and to avoid conflict-reducing tricks such as majority vote or tossing a coin.
References
[1] Johnson D.W. and Johnson, F.P. Joining Together; Group Theory and Group Skills, 3ed., Prentice Hall, Englewood Cliffs, N.J., 1987
[2] Peters, C.B. (sociology), Datta. D. (mathematics), and LaSeure-Erickson, B. (instructional development), The University of Rhode Island, Kingston RI 02881, private communications.
[3] Roberts, C.A. "How to Get Started with Group Activities," Creative Math Teaching, 1 (1), April 1994.
[4] Toppins, A.D. "Teaching by Testing: A
Group Consensus Approach," College
Teaching, 37 (3), pp. 96-99.
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