Balancing Group vs Individual Work

For over ten years now, my classroom has been setup for group work and talk. Currently, I have desks in groups of three and I reshuffle the groups after five class meetings using flippity. One of the courses I teach is called Honors Calculus. It is a differential calculus course that is an option instead of AP Calculus AB. What is typically done be the first week of December in the AB course takes us into May. This allows much more time to review algebra and trig ideas and to really dig into the mechanics and principles of Calculus. I don’t skimp on the level of analysis I ask for in this class, we just have more time to settle in. This year, after a conversation in the first trimester, I settled in to a routine where we have group quizzes – I write five versions of each quiz – but we have individual tests. My hope was that this would decrease the level of stress in the classroom, that it would increase the level of communication between the students, and that hearing multiple voices would increase the likelihood of ideas and techniques sticking with my students. What I have witnessed is that this process has decreased the level of stress overall because a handful of students just don’t worry much knowing that they are paired with confident kids who can carry them to the finish line, the level of conversation HAS increased, but only for a subset of the students who end up in the role of explainer, and ideas are NOT sticking. Mistakes made in November are still being made. Skills practiced (or at least skills that have been available for practice) are not embedded. On our most recent individual test about 15% of my kids did not recognize the need to use the product rule when taking the derivative of a product. I have asked a variation of the exact same question for the last three tests and there is no noticeable improvement in answering that question.

There is another feature of our class that is at play here. In the 2017 – 2018 academic year our department adopted a test corrections policy that I wrote about previously. For the 2018 – 2019 academic year the department voted down this policy. I had spent a considerable amount of time and energy promoting this policy and talking about its importance in the learning process. In the wake of this decision I reached an uneasy compromise with the two courses where I am the only instructor. They can review a test when it is returned and they can reassess on up to three questions from that test with the possibility of earning up to half of the credit they missed. There was a lot of debating in my mind and with my students before we arrived at this imperfect solution. This was in place before the conversation with Calc Honors about group quizzes. Looking back, I feel that the combination of group quizzes AND opportunities to reassess provides too much of a sense of safety net and many of my students are pretty clearly not preparing themselves too carefully or they are simply not practicing much. With the level of practice opportunities provided/the number of times to talk together in class/the class conversations led by me with examples and old assessments offered as practice/etc. I simply should not be seeing the test performances I am seeing. I am clearly complicit in all of this due to the decisions I made about assessment and the decision I have made not to collect or check HW practice. In my last post I thought out loud about the idea of frequent, low stakes, skills-based check in assessments. Had a great twitter chat last night with the #eduread crew (prompted in large part by this article ) and I went to sleep convinced that I need to incorporate some of these ideas into this course next year. I also need to remove the added layer of reassessment, it has not worked in conjunction with the group quizzes. I think I probably still need group quizzes separate from the check-in layer of ways for me to see progress AND as ways for kids to feel that they can buffer their grade with legitimate skill progress. I hope that the combination sends a couple of important messages about what I value. I really (REALLY) like the conversations that do happen in the group quizzes. I am more than willing to write multiple versions of quizzes so that conversations can happen out loud without worrying about giving away information. Our discipline, I think, allows this more easily than some others might. I do not want to collect HW daily for all sorts of reasons, but I think that frequent low stakes check ins send a message about the importance of mastery of topics. I think that I need to adjust my problem sets so that they feature more reminders of topics. My kids know how to take derivatives with the product rule. They probably need to be periodically reminded of it in a more tangible way. I also wonder about balance in point values between these three ways of assessing and reporting on my students’ progress. I do not want to retreat into a mode where I am scaring (or bribing) my students, but I do think I need to be more clear and explicit about what I value and balance it accordingly when/where I can.

As always, any words of wisdom here or over on the twitters (where I am @mrdardy) are much appreciated.

Experimenting with Visible Random Groupings

In some ways I think that I am intellectually adventurous, that I am willing to try something new in my classroom. In other ways I struggle with change. I try to make myself feel better about this by reminding myself that we all struggle with this in varying degrees.

This past summer – my third lucky summer at Twitter Math Camp – I finally committed to trying visible random grouping (to be referred to as VRG for the rest of the post) for this academic year. A little background here.

When I moved up north in the fall of 2007 I made a commitment to not have my students in rows and columns. I no longer felt comfortable with most of my students looking at the back of other students’ heads. So, I rearranged the seats at my old school in ‘pods’ of three or four desks. However, I always let students pick where they wanted to sit. As most of us know, even if WE don’t assign seats, the students essentially do this themselves. I comforted myself by thinking about the camaraderie I saw, by listening in on the lively conversations that did not happen when my students sat as if they were in a matrix, and by the fact that I know that I would have preferred life this way as a student. When I moved to my new school I had two long conference style tables so I had two largish groups of students working with each other. Two years ago I ditched the conference table and went back to pods.

Over the past three summers I have heard more and more conversations about the power of rearranging the students, about shaking them out of these simpler comfort zones and encouraging everyone to be comfortable sharing ideas with everyone else in class. Alex Overwijk (@AlexOverwijk) has been an especially articulate proponent. So, this summer I learned about a pretty cool website ( where you can build a roster for a class and anytime you want this program will randomize your class. In groups of 3 or 4 or 5, by the number of ‘teams’ that you want, etc. It creates a cool visual that you can project and the kids get rearranged instead of staying in their friendly neighborhood comfort zone. I committed to trying this for a number of reasons, the primary one being my experience the past few years in Geometry. I had been teaching mostly AP and upper level honors classes and these students mostly knew each other for awhile and they were comfortable sharing ideas and debating/challenging each other at times. Not true of my Geometry class. Even last year’s class which was outgoing, chatty, and engaged. They did a great job in their pods discussing ideas but did not do a good job projecting those ideas out to the class. They always wanted to filter ideas through me and, over the course of the year, inevitably fell into some ruts about who took command when I asked them to work together.

Now, enter VRG. The strongest proponents discuss doing thisĀ every single day to continually shake things up. I got a little scared of this because I really value the sense of camaraderie that I have seen developing over the years, so I came to what seems like a nice compromise. On the first day of each week, I shuffle the class. I am now ending the fourth week of the school year and I have some observations I want to share. I am particularly motivated to do so by a twitter chat this morning.

There is sound research in the field about VRG and its effects. This research suggests that the positive effects of this practice are most clearly seen when this happens every day. I do not want to discount this and I do not want to feel like a contrarian. What I want for my classroom is for my scholars to not only know everyone else and hear the ideas of their peers, but I want them to be in a zone that feels comfortable and safe. My prejudice is that this zone is more likely to happen if I have some time to get used to my new teammates. What I have seen in four weeks can be summarized as follows (and I will make separate remarks for my AP Calculus BC group and my Geometry group)

  1. In BC Calculus I have also been incorporating whiteboards that the pods write on together. The combination of whiteboarding (and presenting the ideas of the pod) out to the class along with VRG has been pretty spectacular. Again, these are kids that know each other well, but I have been seeing active conversation across table groups to former teammates that is lively. I can step out of the way and let them bounce ideas around as I wrote about yesterday.
  2. In Geometry we have not done as much whiteboarding, I want to improve on this. What I have seen is students talking to people they did not choose. I see them making guesses to/with their neighbor. I have seen students more willing to stand up and talk. I have heard some lively discussion between students and I know it is not just with their good buddies unless they all magically happen to love each other.
  3. I have been able, in both classes, to call on a wider variety of people because even the shy/underconfident/nervous kid has someone in their group whose ideas they can paraphrase. In the past few years I felt that there was more of a posture of looking to one person in each pod to be the spokesperson. I see less of that now.


When I tweeted out my happiness about weekly VRG I was promptly congratulated AND reminded that this would be even better if it was done daily. I may get there, but I kind of feel that this is my 10% moment. That place where I am making a change I know is for the better but I am limiting myself in my own discomfort a bit so that I can still feel sane and effective in other arenas.