Participation Quizzes

I am going to be doing a lot more intentional group work next year with my classes. I’m definitely envisioning this for my Algebra II classes, and if I can come up with some good materials, for my Calculus classes too.

Today at PCMI, I was introduced to a way to do groupwork well. I am dismayed that I haven’t seen this before, because in some ways, it’s so obvious that I don’t know why it hasn’t made the rounds into my brain. I need to type it out here to codify it in my brain.

It’s called a “Participation Quiz.

What I’m going to do is describe the video we watched of a teacher implementing it.
The teacher has students sitting in groups of 4. She introduces a worksheet she created to help students multiply binomials, but with some positive and some negative constants — because she saw that it was tough for her kids to deal with negative numbers when multiplying binomials. She had everyone’s attention on her, at the front of the room, and she says “today will be a participation quiz.” She then lays out her classroom norms for groupwork, some of which included:

  1. Everyone in the group must participate equally. There isn’t a leader, or the same person leading the show. The voices are shared.
  2. Students should not work too quickly. If they work simply to finish the sheet, without any other consideration, they aren’t doing it right.
  3. No one moves on until everyone understands. This isn’t about everyone having the same thing written down — but everyone has to know why.
  4. Students should think out loud. Students should check in with each other. Students should ask questions of one another.

She then let’s them get started.

As the groups work, she is both circulating, and sometimes at her laptop. When she is at her laptop, she is taking notes on each group — and displaying her notes on her smartboard live. Initially, her smartboard has group names (“purple group” “red group” …) written on there. It also has some specific actions which can be copied/pasted under each group, if they occur. Examples are:

negative actions: too quiet, talking outside group, off task, texting, different problems [students in the group are on different problems, not on the same problem]

good phrases: “I don’t get how you…”, “What did you get for…?”, “Can you also do it this way…?” “How did you…?” “Are we ready to move on…”

good actions: quick start [group started right away], reading directions out loud, same problem [everyone in the group is on the same problem], pointing and explaining, WHY???, BECAUSE!!!, calling group members out, all heads in, checking calculations/work, thinking out loud, equal participation.

Notice that these are specific things the teacher is listening for and looking for. They are actions — body language, speaking, interactions, etc.

The teacher watches and listens as she walks around or is at her computer. If she noticed any of the actions/phrases/comments, she typed them in her computer under the group name. It appears automatically on the SmartBoard for all to see.
At one point, one of the groups wasn’t working together. The teacher sat down and re-explained what the participation quiz to them, and even said “I’d rather you all work together and be stuck on one problem the entire class. This is about working together and coming to a shared understanding.” She then started getting them talking to each other, and then left.

The teacher also didn’t only copy and paste from the pre-written list on the SmartBoard, but also transcribed specific phrases/actions: everyone trying combos,  oh right, you’re multiplying” “would it be -21?” “so you mult… and…” “I got… that’s because…” “what do you think about that?”

At the end, her SmartBoard was full — a bit messy, but full. She did not shy away from writing the negative comments too. One group had “off task” written 3 times! What’s nice is that the teacher had a mathematical learning goal, but the lens through which she viewed the class (and the lens through which she had students view the class) was about classroom participation/engagement/teamwork. The two aren’t divorced.

She recapped the mathematical goal, but then she talked briefly about what she observed. She asked them questions about her SmartBoard. Under one group, her note said “I don’t know what to do after this?” and then she asked the class if that was a good or bad interaction. Most of the class said “bad” but through discussion she got them to realize it was good! That by saying that, someone is going to help that student, and the student may soon understand something. Through this process, she started clarifying the group norms for teamwork.


There are so many amazing things about this. For me, this sort of activity, done a lot at the beginning of the year, is a concrete way to provide meaningful feedback for kids when talking about something as vague and “in the air” as participation. It builds the expectations for the rest of the year. It generates good conversations about what good groupwork is, and why. It provides the teacher a tool to get students to talk mathematically, and provide feedback. (Carol, one of the PCMI organizers, told me she will sometimes told me that sometimes she will do this and tell her kids she will only be looking for students justifying mathematics and those are the only notes she puts on the board.)

I don’t know if the teacher in the video actually assigned grades to each group. I think that’s something we’re going to be discussing in our groups tomorrow. But at the very least, it’s a really powerful way to spend 50 minutes on a mathematical goal while you are inculcating your class with a more “hidden curriculum” goal too.

I also think that a class, collectively generating groupwork norms (and the teacher adding missing but important ideas) could be a powerful exercise before engaging in this activity the first time. And using those norms as the lens to which to watch and critique students.



  1. That would have driven me completely bonkers as a student, especially the being too quiet part. I didn’t shy away from participating, I was usually quite outspoken, but what worked best for me when working was to be quiet and concintrate on my work, and figure out mistakes by myself. I have very good number sense, and worked much faster than my peers. Waiting for them so i could move on to the next problem would have been insanely frustrating. I could see junior-year me skipping class in that scenario, easily, and I was a dilligent student.

    1. Yes, I know what you’re saying. I myself was like you too. However, there’s a time for being an individual working on math, and there’s a time to really be collaborative and work with others and be part of a team. (Both have benefits.) I know my kids can learn from others – whether they know more or less than each other. If they know more than someone, they have some knowledge they can impart. If they know less than someone, their questions can challenge that kid to really think through how well they know something, and think about the nuances.

      I agree, it will be harder for some of my kids than others. But the more I’m teaching, the more I realize that most kids are not like me when I was in high school, and most of my high achievers actually enjoy the chance to work with others — and do actually recognize the benefits they receive from it. Actually, they share that with me explicitly, especially when talking with kids in my calc class who do standard based grading.

      Maybe others who do more groupwork in their classrooms have ideas on how to engage the high achiever who wants to work alone?

    2. Just a few thoughts for students who would rather not participate in an activity like this:

      Lots of kids, having to sit quietly and work alone drives them nuts. Some kids, being required to not sit quietly and work alone drives them nuts. Sometimes at school we ask kids to work outside their comfort zone. It’s uncomfortable by definition, but you also gain new capabilities that will serve you well. Collaboration is a powerful force but it’s a skill that takes practice.

      Also: sometimes you think you understand something, until you try to explain/teach it to someone else. The mental organization required to teach it to someone else will benefit your depth and clarity of understanding. You’re not just helping a group member, you’re benefiting too from the interaction.

      Anyway, that is how I would try to convince a recalcitrant learner that this activity is worth their time. I would also try to sit them with an actual friend in the class they could be productive with, hoping if they weren’t enthusiastic about helping someone they didn’t know, they could be persuaded to be helpful to their friend.

      And if they still didn’t agree, some noogies are tough noogies.

      1. Having one kid tutor another is ok on an occasional basis. But when a kid is asked to be a tutor day after day, there is some question about when he or she gets to learn something for a change.

      2. I agree, Kate. Group work is beneficial for all involved. I have seen many students who do not want to participate (either for shyness or feeling as if they don’t need any help). However, the purpose of education is to produce functioning adults, is it not? I know I have had to work with people in the past whom I did not like. Do you think my boss cared? Absolutely not. I even told my students last week: Deal with it!

    3. A couple of norms that I stress early on to try to help with this issue is that the “Norms Managers” can give the group some quiet individual think time if it’s needed – that’s something that the group should negotiate together and manage as part of the process. Also, another key idea that takes a while to teach is that waiting for everyone before moving on doesn’t mean that the first person that’s done is sitting, twiddling their thumbs while waiting for the others to finish. It’s important to be able to listen to others and hear what they’re thinking. So the ones still working are responsible for putting their thinking out there – the hope is that either the others might suggest a more efficient method if it’s appropriate, or better yet, the ones who might have finished first hear an approach that’s different from what they originally did. I’ve personally seen both happen and think it’s more important to provide the opportunity for this to happen. The net result is that students gain more respect for each other and it builds community in the classroom. It’s hard to put one’s thinking out there because it’s a vulnerable position to be in as you wait for your peers’ reactions – my goal is to make sure those groups of 3-4 is a safe place to do that and eventually the trust/safety becomes class-wide and our whole-class discussions become much more productive.

      A unit that always catches me by surprise is the unit on trig identities – each of the last two years I’ve taught PreCalc, by the time we hit this unit, the class has pretty much internalized these norms and the way they approach the problems – especially because there are often multiple ways of proving identities – lead to rich discussions about advantages and disadvantages of various approaches. And those discussions are usually student-led, where I’ll interject occasionally, or ask a question to get them to think about something more deeply. During my first three years of teaching PreCalc, it was pretty much individual work and by the book. The difference I’ve seen is astounding and I always feel like tracking down my old students, especially from those first 3 years, and profusely apologizing for not doing a better job for them.

  2. I don’t have a smartboard, but this could be done with Google Docs. You could put the GDocs spreadsheet up with the group names in one column. I would love to see a picture of her smartboard to see how it is set up so I could mimic it in GDocs. There are not drop-down choices but you could have positive and negative attributes that you check off in subsequent columns. And, you could type in columns as well.

  3. I’m afraid I’m with jameson on this one also. Not only would this have driven me nuts, it would drive my son nuts also. Group work only works well when the task is big enough to be more efficiently done by several people than by one person. This sort of synchronization slows everyone down to the speed of the slowest student in the group. That can be a disaster if the students are not all very closely matched.

  4. I’ve tried similar things in the past, so here are a few notes/warnings.

    1. Not recommended if you (universal you) feel iffy about management. Remember that writing something on your laptop that is projected on a computer screen is a rather indirect method of getting teenagers to accomplish something.

    2. This focuses the class on the process of group work. This might be important at the beginning of the year. However, in general, students are not interested in how this process works. Hopefully, students will be interested in whatever math topic you’re trying to teach.

    3. What Sue said about complex tasks.

    4. Anecdote: I had a new student this year who seemed to know how to solve every problem I through at him. I thought he might prefer to work alone, so I gave him his own work. This was a misstep (another student asked, “So is working in a group optional?”). It worked better when there was a problem he didn’t know the answer to. In that class I ended up with some skill-based groupings.

    1. (Just a quick disclaimer about my comment that follows – it is largely based on my experience with PreCalculus, AP Calc, and a “pre-PreCalculus” course – I’ll find out this coming year how Algebra 1 will respond…) The indirect method of writing notes on the doc cam has been effective for me in getting students’ attention. I write “good” comments in green, comments that need immediate attention in red, and “suggestions” in blue. I’ve found that they usually look up at the projected comments either (1) when they’re stuck and not really making any progress, (2) are at a good “pause” or transition point in their work, or (3) doing something they’re not supposed to be doing and seeing if I notice. I think it’s effective because of the immediacy of the feedback and that it comes at a time when they’re able to do something about it. Hopefully the positive behaviors and process they learn gives them the framework in which productive discussions about the math can take place, and one in which everyone gets an opportunity to contribute and be heard. I try to do one of these at least every 2-3 weeks for the entire year.

  5. Here is a description of my first properly planned and organised attempt at group work with a class 35 language students.
    During a “Learning English with Films” experimental blended course where the main aim was the promotion of films as multifunctional language learning aids, 10 groups of 3-4 students highlighted, analysed, and explained the language content of a 5 minute film excerpt of their choice. The wiki tool in the Moodle open source learning management system was utilised as both the group database management and project presentation tool. Despite initial difficulties in adapting to ICT based study, a notable increase in classroom interaction and improvement in study organising skills were evident throughout the course as several peer teaching and language practice opportunities presented themselves in the form of language analysis, wiki planning, and problem solving. Although each group member had they’re own individual task; grammar analysis, new vocabulary, pronunciation features etc, they were expected to read and edit each group member’s work where deemed necessary, Indeed, the students took this a step further and began to “peek” at the work of the other groups to steal ideas on layout etc. Wonderful.
    It was a very satisfying course, I think, for all involved, in which the students, from the weakest to the strongest, displayed passion, precision, patience and pride in their work. The only noticeable negative side was the occasional student expressing discomfort with being so “exposed” to the scrutiny of the rest of the class. I had no answer to that, to be honest, and basically ignored the complaint as the benefits most certainly outweighed any such negative aspects.
    I was immediately converted to group work after this experience. I am sure something similar has been done with a maths class although there is no need to use a wiki tool to do so, of course. Saying that, it helped no end having the wiki “open 24/7” and in particular aided the group editing and presenting of their work.
    It was clear to see that this group based approach made it easy for individuals to help each other and themselves, and the class move forward and outward together. Long live group work!

  6. Doesn’t being able to explain something require a deeper mathematical grasp of the topic than just being able to do it yourself quickly? I think there is great value in using this kind of task as part of your teaching toolbox.

    1. Yes, good tutoring requires a deeper understanding than just being able to (barely) do the problem. It also requires a large number of other skills that have nothing to do with math (like being able to model other people’s mental states, being able to read body language to know whether you are going too fast or too slow for the person you are explaining to, and so forth).

      Some of the best math students may need explicit coaching in these techniques—think how much time is spent on them in teacher training! I’m not sure that just throwing kids cold into a tutoring role is valuable for them or the students they are supposedly helping. The support needed for turning them into useful tutors may be better spent teaching them more math.

  7. New to math blogs … glad to have found this idea since I love new ways to promote high level thinking in groupwork. Sharing with students what I heard and observed will be very helpful!

  8. I’m going to “offer” the participation quiz in my 2nd-year Spanish class tomorrow. It should be interesting. I saw a version online that had students rationing their contributions by moving post-it notes from aft to fore on their desks as they commented, but this version seems somewhat anti-thought to me. I’m going to use the version that you’ve described.

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