Experimenting with Math Testing in Groups

A MiddleWeb Blog

A couple of months ago someone posted a comment on my Meaningful Math post, Do My Classroom Rules Help or Hurt Learning? and recommended group tests. He suggested putting students into groups of three and allowing the students to collaborate on a test.

Every student would work the test, but only one test from each group would be graded, therefore all the students in the group had to agree on every answer. (Shout out to Bill Hunt who suggested this; you can see the original comment here.)

I was interested in trying his suggestion as soon I read it. In January we experienced many class interruptions due to weather, assemblies, school trips and a bad flu season. This made my unit on exponential functions pretty choppy.

When it was time for the test, students were really apprehensive so I decided this would be a good opportunity to give a group test. I didn’t tell students until the day of the test. They found out when they came in and saw the desks grouped together in pods (in groups of four). Students came in and sat wherever they chose. I did not assign students to certain groups (as Bill Hunt did), although that is certainly an option.

I had never given a group test before and didn’t know what to expect. I gave the students the following instructions:

  • students are only allowed to confer with the students in your group,
  • every student must work every problem,
  • and everyone in the group must agree on all answers.
  • I will only grade one test from each group so when you staple your papers together, you should staple the one you want graded on top.

I was pretty adamant that if they didn’t follow all the instructions this experiment could be stopped and we could go back to individual testing. I emphasized that if I saw them dividing up problems to work – or if one person was doing all the problems – I would consider that cheating.

My Fears Going Into This

I wasn’t sure what to expect. I was actually pretty nervous. I kept having this nightmare scenario run through my head where I would have to stop the test in the middle of the class and regroup (or de-group!). I think my biggest fear was that one student would do all the work, and the rest of the group members would just watch. I was also afraid the classroom would become loud and chaotic, and it would be hard for students to concentrate. Honestly, I had no idea how the students would respond.

What Actually Happened

From the beginning I was pleasantly surprised. As I walked around the room, I heard students talking in quiet tones. Most, if not all, of the students were working and involved in the process. The chaos that I had feared did not materialize. I have listed below what I consider to be the pros and cons of group testing after this first experiment.

PROS

Students were very careful to make sure their answers matched with everyone else in the group. When answers didn’t match, they had discussions about which answer was correct and why. How awesome is that! Some discussions actually got pretty intense, which from my standpoint is a good thing!

Students received practice defending their answer and explaining their thinking in a civil manner. I enjoyed listening to students patiently explaining to others in their group how they arrived at their conclusion. I also got to witness several a-ha moments when students were shown by classmates where their mistake was.

I think peer pressure was a positive influence in this case. Students wanted to be able to contribute. One student in fact said that he enjoyed the group testing but wished he could “have helped more.”

Several students who suffer from math anxiety and test taking anxiety specifically said that the group testing helped overcome much of their anxiety. In fact, several students thanked me afterward for allowing the group test, citing a reduction of test stress as a major benefit.

CONS

Some students in some groups did more work than others and knew the content better, but they received the same grade as others in their group. It was also possible that a few students copied the work of others. I tried to prevent that from happening by careful monitoring, but that’s not foolproof.

For more introverted students it’s conceivable this testing approach could be uncomfortable. (However, the anonymous written feedback from my students didn’t indicate that this was an issue.)

I was able to get a good picture of the groups’ understanding, but I didn’t get as clear a picture of individual understanding. I did learn a lot by listening to each group’s conversations, but you can only listen to one group at a time.

What did the students think about it?

The day after the group test I gave students a post-it note and asked them to discuss how they felt about group testing. The responses were anonymous and students gave some thoughtful answers. Students were overwhelmingly in favor of group testing. Some of the comments are listed below:

  • “I liked it, it was nice having people to help you through it and we had a good system of everyone helping.”
  • “I think we should take the test in groups again because it helps people understand what they messed up on and go back on those problems.”

I was worried that the stronger students would feel put upon, but that didn’t seem to happen. In fact, in instances where I could discern who wrote what, their feedback suggested that they were some of the strongest advocates for the group testing method.

Final Thoughts

I was skeptical about being able to get all thel students to buy in and participate fully. I thought I might do this one time and might not do it again.

But after witnessing it firsthand, I realized that as a teacher I prefer a scenario where a student is able to work every problem with the help of his group over a student failing the test individually. In fact, many students who usually struggle had much higher grades than they usually have. Full disclosure: the average grades for the group test were about 10 points higher than the average for the last test the students had taken.

On a personal note, I really enjoyed only grading a fraction of the tests. In a class of 28 I only had seven papers to grade. I was actually able to get all the tests graded before class the next day. The group format meant that the students didn’t make as many minor math errors, because they had three other people to check their work with.

I wouldn’t do this for every test. I need to see what concepts students have mastered, and that requires individual assessment. There are many circumstances where group testing is not appropriate.

However, under the right circumstances group testing can be a great tool. I think it’s critical that parameters and expectations are clearly explained and adhered to, and there is room for students to abuse the process. But that can be minimized. The engagement and cooperation I witnessed coupled with the positive effect on student morale made it worth it to me!

Michelle Russell

Michelle Russell (@michel1erussel1) is a math teacher at Florence (AL) High School, where she serves as the Academic Leader of the math department. She began her career as a student teacher in middle school and has taught students from 7th to 12th grade. For the past nine years, she's taught high school math, including Algebra IB, Algebraic Connections, Pre-Calculus, AP Statistics, Algebra with Finance, and Algebra 2 with Trigonometry. She is currently involved in the Laying the Foundations initiative and the Mathematics Design Collaborative. In her free time, she enjoys reading blogs and tweets from other math teachers.

16 Responses

  1. Tiffany Sammons says:

    How would this work with students who have accommodations? Would you put the students who have to go somewhere else to have tests read to them in one group since they are out of the room, or would you consider keeping them in the class to test with the rest of the students and making sure an adult or yourself was available to help with the reading of the test since they are in a group and more than likely someone is reading the questions out loud?

    • That’s a great question! I think both options you mentioned would work. I think in most cases a student with accommodations would probably do well in the group testing situation, but it would ultimately depend on what accommodations the student has.

  2. Pamela says:

    At my school, all the Algebra 2 teachers use group tests and individual tests for most chapters. We put more difficult problems that require more critical thinking on the group tests, giving the students the chance to discuss their approaches. The individual tests have the more straight-forward questions that allow for assessment of their skills.

    One difference for us is we create four different versions of the group test so every student has a different test that gets graded, but all four versions are very similar. That way each student needs to do the work instead of one person carrying the team.

    • What great suggestions! I actually used the same test that I had prepared to give individually and only later did I realize that I should have included more critical thinking questions, so that is a great suggestion! I also like the idea of giving 4 similar versions, that would prevent one person from doing all the work.

  3. Cherri says:

    I also like to do this on occasion. I tried this for a midterm and really liked it. The midterm was multiple choice. I graded their first effort, then grouped like scores together ( in pairs or in threes) and had them work through the test (without their previous answers in front of them) as a group. I let that group score be a second score in my midterm category, effectively averaging the two. If the second score was lower for some reason, I exempted it.

  4. Myra Deister says:

    I have used Group Tests for several years. My process is slightly different. I have the students turn in the Group Quiz and I grade problems from each student in the group so that I have graded every problem only once. The students don’t know which problem I will be grading from their test.

    I also give an individual test. I tell the students if their grade on the individual test is better than the group quiz, I will raise their grade on the group quiz to match the test. The students complete a reflection after the group quiz to help them determine what they need to study for the test.

    They are given the answer key and time to correct their group quiz. I allow them to take it with them to study and then turn it in on the day of the test. If a student is absent, I give them a blank copy and have them write the answers on it. They also have the same study guide.

    • I like your idea of grading problems from each test, I think that would increase accountability for each student. I also like the idea of the reflection after the quiz, so that the student determines what they need to study. Great suggestions!!

  5. Mary Poluse says:

    When I taught Pre-Calculus and Calculus, I occasionally offered partner tests for content that students considered particularly challenging. My approach was similar to Bill Hunt’s approach. I ranked students according to test scores and paired accordingly, top two students were paired, those ranking 3rd and 4th were paired, and so on. If my class had an odd number of students, then the last ranked group had 3 members. Those three students appreciated the support and the other students didn’t seem to mind.

    When I presented the idea of partner tests to the students, I explained that, in my experience, no student scored lower on a partner test than his/her average test score, and that often students score the same or a little higher than his/her average test score. I also explained how I would pair the students and that partners could turn in tests separately if they were not in full agreement on all test responses.

    Students were only permitted to work with the assigned partner and turned tests in at the same time as partner. I asked each partner whether the answers were the same or different. If they replied “same”, then I stapled the tests together and graded the top test; if they replied “different”, then I graded tests separately. Seldom did partners ever say they had different responses.

    When the class met the next day, I asked for anonymous responses regarding the partner test experience. Most students said they were less anxious about the partner test than when taking test on their own, were appreciative that the partner would pick up on arithmetic or algebraic errors, and some said they actually prepared more for the partner test because they did not want to let their partner down.

    • My students felt the same way as yours, they said they were a lot less stressed out taking a group test. I noticed a big reduction in math errors, I think partly because students were less nervous and partly because they had a partner to help catch minor errors. I let my students pick their own groups, which had its own pros and cons. I think in the future I will probably assign students to groups in a way similar to what you mentioned. Thank you for your suggestions!!!

  6. I teach different mathematics courses for undergraduates at Wayne State University (Detroit). I came up with this idea when I taught an Elementary Statistics course. I too, was nervous about some things but my Associate Chair at the time encouraged me to try out different strategies.

    To put it lightly, the students loved it! Not because anything was easier but it was a way to collaborate and to show me what they had learned. I also did careful monitoring of conversations so as to avoid students who might coast. For anyone who wanted to challenge an answer, they could, with written explanation, but if they were wrong, they risked losing points. I think I have had only one student challenge a group’s answer to a question in the 10 times I have done this.

    I have since used group testing in my Discrete Mathematics and Calculus II courses, albeit at a university level. One student commented that it was the most relaxing exam they had ever taken. There are a number of iterations of this format which I appreciate being shared in the comments. Sometimes, we have to think outside of the box and our own comfort zones. Well done!

    • Thank you for your comment, I really appreciate getting the insight from the college level. As a high school teacher I worry that I’m making it too easy for my students. And that was one of my worries about giving a group test, I thought it might not be “rigorous”. But, like you said group testing is not about being easier. I think it’s about giving students an environment where they can do their best and actually show us what they know. A lot of times stress and anxiety interfere with students ability to do well on tests. -Also, absolutely right about having to monitoring conversations. It helps me understand their thinking and keeps the students accountable. Thanks for your comment!

      • Thank you for the article! I worried too, about the rigor and what I found was that the students provided the rigor naturally. I made sure to frame questions in such a way that required them to talk about the material with one another, but not too difficult that it would take them the entire time to finish one problem. Another important point to make here is that with so much anxiety surrounding mathematics as it is, students should not have to compound that fear with testing anxiety. If they can talk about the material in a less stressful setting, then their mastery of the material can be better measured and perhaps more importantly, better demonstrated. Keep up the good work!!

  7. Joe says:

    I think that students working collaboratively to build on each others’ ideas and help support each others’ learning is fantastic. My concern is that the work they do collaboratively is included in their individual grades. If a grade is to accurately reflect a student’s understanding of material, it is difficult, if not impossible, to know from a group grade who contributed what and whether the result accurately reflects each student’s knowledge.

    Plus, group work depends on parity of confidence, language, inter-personal positive relationships, but we know that among students of different genders, races, incomes, English language proficiency, and confidence, that this is unequal within groups, which can warp the amount of participation and learning that happens in group work. This is something that students can get better at with our help, but this is another reason why their grades shouldn’t be dependent on this inequity.

    A solution is that students should do this collaborative work but have their results not included in individual grades. I’ve found that in my own classroom as well as with my work with other teachers, that group work can be framed as a means to an end (learning), not as an end in itself (grade). Students can work in groups and then, after the work is completed, take an individual assessment, and then the results of that assessment can help us know how effective the group was. That’s the only way our grades will be truly accurate.

    • Thank you for your comment! I appreciate your insight and I agree with much of your comment. I certainly don’t disagree that group testing has limitations. I also agree that working in groups has to be a part of the learning process. In fact, I don’t think that my students would have done as well if they were not already accustomed to and comfortable working in groups. It would unfair to tests students in a group test situation if they had not already been learning collaboratively with their peers.

      However, if we as teachers are already using group work and collaboration as a part of the learning process, I think a logical next step would be for it to be part of the assessment process. One of the reasons I feel this way has to do with the specific anxiety that students experience when taking a math test. Students who are normally very nervous and anxious flourished given the opportunity to take their test in a group setting. Some students become so nervous before taking a math test that they never perform up to their ability, so I am never really able to accurately assess that student’s knowledge.

      So, individual testing also has its limitations. However, as you mentioned accurate grading is critical which is part of the reason that I will give many more individual tests than group tests.
      Thank you again!

      • Joe Feldman says:

        Really appreciate the dialogue. I would just argue that the need to reduce students’ test anxiety can be addressed without having to compromise teachers’ ability to judge the accuracy of each individual student’s level of knowledge, and inviting the often-inequitable social dynamics between students (particularly those who have historically been more marginalized) in group work often doesn’t help.

        There are alternatives that don’t make this compromise. For example, we’ve seen through research that when students know that teachers will allow them to retake or redo assessments it reduces stress and students perform better (and often have no need for the retakes because of it). Or we can expand the ways in which we assess students that allow them to demonstrate their knowledge in modalities in which they’re more fluent.

        For what it’s worth, for the past six years I’ve researched this alongside teachers and written about it in a book, Grading for Equity, if you’re interested.

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