The Ideal Group Size for Your Secondary Math Classroom

Welcome to Solving for the Undefined Podcast. I’m your host, Johanna, founder of Miss Kuiper’s Classroom, the place that equips teachers and creating a healthy math classroom where students can thrive, no matter their academic abilities. But it’s not always about the numbers. And that’s why I’m here, bringing you the formulas to solve your problems, math and otherwise, plus strategies on cultivating that necessary math mindset. And that’s what you can count on.

Alright, hello, hello. Welcome to Episode 32. Now, in the intro of this episode, I asked you to think about the setup for your favorite and least favorite class. And there’s a reason for that, as I was planning this episode, talking about the ideal group size and how to create groups, I was wondering what changed, because when I was in high school, I had maybe one class that utilize groups. And I don’t remember it being the entire semester or year that we did groups, it was maybe a few days here and there. So I was wondering what changed, because I have so many parents come to me complaining that math itself has changed. But I argue that overall the way we teach has changed. And maybe because I was a student and then a teacher, I didn’t see when the shift happened. But I think it’s very interesting how education itself has changed over the years. And as a young teacher, I feel like I’m learning new things all the time to better my practice as a teacher. And what I’m going to talk to you about today is one of those things that I’ve learned that has dramatically changed how I run my classes. And I don’t mean that dramatically, although I kind of do. But it is seriously changed every component of how I look at my class, how I plan my lessons, and everything about it. And if you’ve listened to the past episode or two, you’ve kind of heard me talk about this book that I’ve been reading called Building thinking classrooms by Peter Lilienthal. And in this book, he talks about how to create an ideal classroom where students are thinking on their own and becoming independent learners. And one of the things that he talks about very early on in his book is the use of whiteboards, specifically vertical whiteboards, or non permanent surfaces, which we covered in Episode 31.

And the next thing he talks about is groups. When I first started student teaching, my junior year of college was the first time I was introduced to the idea of students working in groups. Now coming from my background, my classes were always in a row. That’s how we learned. But the classes I worked in for my junior and senior practicum, we’re always in groups of four. And I could see how much more collaboration was happening with those students with the math. So when I got my first job as a classroom teacher, I knew that I wanted to do groups. 

But unfortunately, the classroom I was given had these giant tables that were made for two people. But when I tried to turn them around and make them groups of four, the way that my classroom was, which was really long and narrow, it didn’t allow for me or students to really move around the classroom at all. So I was kind of forced a little bit to do just rows. And I was able to do groups of two and have them strategically placed where students could turn around to make groups of four, but not in every classroom. Because one of the classes I had my first year of teaching had 35 students, and I had 32 desks. Like that’s insane. And I know that they can’t control everything, but I was a little salty about it. Eventually I got to move into this classroom that I have now that I am absolutely obsessed with. I have whiteboards on almost every wall. I have ample space to turn my desks into groups of four. However, that’s not what I do. When I first started in this classroom, I did groups of twos in rows facing the front, this was partially because of COVID regulations as well as me wanting to still maintain the sense of control. I feel like I have like a smidge of type A and me where I need everything to be nice and orderly, as well as being able to feel like I can control the situation. And when I had my groups of four, it was a lot harder to feel like I was in control of my classroom. So what I do is I’d have pairs of two and when I really wanted them to be in groups of four, I’d have the first to turn around and do a set of four. But then the desks always got put back into those rows of twos. And here’s what I noticed about the two versus the four. When I had students working in pairs, they rarely worked together. It was usually like two separate people working together occasionally checking in with each other. But it wasn’t a collaborative effort. Whereas with a group of four, it was a collaborative effort. But there was more socializing than there was academic work, which is why I tend to steer away from groups of four because it was harder to manage as a teacher.

So when I found Peter Liljedahl, who does work on groups of three, I was thrilled. And while he has his research in his book Building Thinking Classrooms, I heard him talk about this on a podcast episode, he was talking about why groups of three were ideal, for upper elementary and older. And the reason why he says upper elementary and older. And I know most of you listening, don’t teach littles. But he says pairs are ideal for kindergarten, first grade, second grade, because those are the grades still learning how to be human or to be social. And so once you get to like third grade, they’ve developed that social aspect. And so groups of three begin to be a better or more ideal setting for students. I’ll link the podcast episode I was listening to in the show notes because he says it really well. But I’m going to do my best to share his thoughts. And the reason why groups of three are ideal is because there’s enough redundancy and diversity. Now redundancy refers to the things that we have in common with each other that allow us to connect and converse with each other. And then diversity is the things that make us different from each other. He goes on to say in the podcast that groups of four added that social layer to it that became too variable to predict the redundancy and diversity of a group, which kind of matches up with what I saw with my groups. When I did groups of four there is that social component that made it hard for groups to stay on task. One thing that came out of the research of groups of three was this idea of not allowing students personal think time, because it was found that when you posed a problem to a group and gave students time to work on an on their own before coming together with the group, because of the variety of ability levels inside of these groups, it created way too much diversity for the group to be a functioning team, which I thought was so interesting, because as a teacher, I’ve always given students private thing time or personal think time first, before turning to a partner and discussing it. But now this idea that it creates too much diversity was really fascinating to me.

Are you so ready to be done with this school year that you want someone to plan your last couple of weeks of school? If this is you, I’ve got you covered with the End of the Year Survival Pack. Inside of this survival pack you will receive 10 different activities! My favorite being the Summer Vacation Budget Project. In this project, students are actually budgeting out a one week vacation to anywhere they want. Looking up the real life prices of things. I do this every year and it’s a blast. 

Also included in this end of the year bundle

• (3) Guess that Slogan activities where students match a brand to a slogan
• (3) Academic Vocab Word Searches
• A game of spoons using proportional relationship
• A game of spoons using systems of equations
• Ultimate Tic Tac Toe using solving equations

And here’s a bonus for you. If you use the code “SURVIVOR” at checkout, you’ll receive 20% off your purchase. So now you can make the end of the year about thriving, not surviving.

So now that we’ve talked about this idea of using groups of three in the classroom, let’s talk about how to create those groups. And this idea has possibly become my absolute favorite thing I’ve ever done as a teacher. And it’s this idea of visibly random groups. Now, most of us use a seating chart within our classroom. So students come in, they find their name on the list, and that is where they sit inside of the classroom. And whether we do that for three weeks, or we do that for a semester, we use a seating chart to group our students I use to labor over creating the perfect seating chart for my classes, I had to find the exact way to position some students in the classroom, because depending on who they sit by, they’d either work or talk the entire class period. And so I’d have to make these strategic decisions about how I’m going to set up a group of 28 students, when I have 32 desks, like how am I going to strategically place people around the classroom to make this a healthy environment. And then along came this idea of visibly random groups. Now, this idea is very much as its title, visibly random groups. So you group your students randomly, so that students can see it. So this isn’t you creating a seating chart with like, sticks of fate and putting students where you think they should go based on the random pulling of their names. This is students coming into the classroom and seeing that the group they are sitting in is completely random and chosen by random. It eliminates all bias from you as a teacher, and students from choosing where they want to sit. And I’ll share more about why or the research behind why we do this. But here’s the logistics of how I do this. I use a deck of cards. And I portioned it out for however many students I have in the classroom. So one of my classes is 24. So I need eight sets of three cards. And each card whether it’s the 10, or the aces or the Kings corresponds to a group of three within my classroom, I have the fourth card of that set taped to that group. So when students receive the card, when they walk in, they know which group they’re going to sit in. And I let students choose their card, like pick a card, and then they’ll just pick one from the hand. They don’t know what it is their cards are facing me. I found the cards facing me little sneaky teacher stuff for you. If the cards are facing me, when students pick, I see what card they get, and therefore know what group they’re supposed to be sitting in. Because some sneaky sneaky little students will try to change it in order to sit where they want. And it’s like, Ah, I saw what cards you pick, you didn’t have a king, you had an ace, go sit at the Ace table. I know better. 

Anecdotal Evidence

Anyway, before I go into the research, I wanted to give you some anecdotal evidence I found as to how random grouping has changed the dynamics of my classroom, I have found that in these random groups of three students are way more willing to work with whatever group they’re given. Because they know that tomorrow, they’re gonna be with a different group. It’s eliminated about 95% of students asking to sit somewhere else. Like that’s a huge number. I remember when I would give students independent work time, the amount of students asking to move was huge. But now when students are given work time, they don’t move, they just stay inside the group they’ve been given. Granted, I rarely do independent work time at as an individual now, but still, they don’t move anymore. Another thing I’ve noticed is that my classes to become more of a community than just a classroom of students. Because so many students are working with each other on a weekly or monthly basis. They have now become this close knit or seemingly close knit community of students. And this really ties into Michael Grinder’s idea of a healthy classroom.

Scientific Research

Now let’s go over some of the research that was found about using visibly random groups. Number one being that students seemed more agreeable to work in any group, which is what I saw in my classroom. These social barriers that students seem to have whether it’s cliques or friend groups or something they seem to eliminate as time went on using these random groupings. So students became more willing to work with anyone, as well as the social barriers kind of dropped. And with this, students started to rely more on each other than on the teacher, like one of the things that I really strive to do in my classroom is to not tell students whether they’re correct or not. Because I find that that leads to them relying on me for their confidence rather than themselves. And me giving them a yes or no of whether they’re correct or not, doesn’t really help them in the long run. Because what if they just guessed that number, or they took it from someone else, there’s no way for me to know that that’s truly no or just took from someone else. And let’s talk about how I deal with those situations now, in a later episode. But students have stopped coming to me for me to check their work, they’ve relied on each other inside of their group of three, to get that confidence. And with that students are beginning to become better at math, and more confident in math. Because of that, and because students are gaining more confidence in their abilities and understanding and math. They have more enthusiasm for math class in general, and higher engagement in the math tasks or the math problems we do. And that’s something that Liljedahl found in his research inside of these, I think it was 400 classrooms that he studied and did this in that students seemingly enjoyed math class more, and then hence, increase their engagement.

Next Steps

And now that I’ve dumped all this information on you, what could be your next step? Well, first, if this is something that you want to try in your classroom, just do it. Don’t wait. The end of the year is always the best time to experiment, because you only have a few weeks left. And change can sometimes bring that extra engagement or hook that you need from students and those last few weeks. I mean, that’s what I did. I think it was maybe March-ish, that I was just like, Alright, I’m changing this up. We’re doing groups of three, we’re getting random cards to choose your seats, we’re doing this.

And that kind of leads me into the first question, or the first FAQ Frequently Asked Questions. How did students react? I think at first they were very hesitant, because this is not something they’ve ever done before. I don’t think there’s another teacher at my school that has ever done random groupings like this. So it was brand new to them brand new to me. And I definitely got resistance from certain students. To start off with, I had a couple of students asked me, Is this how it’s always gonna be? Can we maybe do it like every other day. So we have some similarity between days. But I went all in every single day, we do different random groupings. And it’s been what three months of me doing this, and I haven’t gotten any complaints in maybe the past month and a half of doing this. So I think the consistency of doing it every single day has been really helpful.

The second FAQ I have is Do I ever let students work alone? No. The reason why I say I don’t let students work alone is because inside of a group of three, that’s their best chance for success. And when I’m talking with a student about this, I asked for the reason behind why they want to work alone. And I address that, if it’s Oh, I don’t know the people in my group. Alright, well, let’s fix that. Let’s do maybe a whole class team builder, so you can get to know your small group before you begin working with them. So addressing the why behind they want to work alone, I found has really benefited me in the long run with these students.

My next FAQ is what if I have a class that isn’t divisible by three, the next best would be groups of two. And with this, the reason why I say don’t go to groups of four is because a lot of times when you have a group of four, it will devolve either into two groups of two, or one group of three and one outsider. So then splitting into two groups of two, or having a group of two will be more productive for your students. And the way I accommodate this with my Karnes is by having two of each kind in my hand, and as students are coming, I’ll add a third into my hand at a time. So I know maybe it isn’t fully random at some times because of that, but that’s how I do deal with sometimes not always having group sizes divisible by three. And I feel to that that is better. Because I don’t want to if I have one extra student come in, after I’ve set up all groups of three to then pull someone to then make a group of two, I don’t feel like that stays true to the idea of visibly random groupings. So I just account for that inside of the cards as I hand them out to students.

And the last FAQ is what about when you have a sub one, I’ve had a sub, I’ve done it two different ways. One, I just put explicit directions in the sub plans of how to do this with students. And the other is I have a trusted student do it for me. So maybe a student who always comes on time or is always the first in the classroom, I will then ask them if they are willing to be the card holder for the day. So then they would pass out cards to students as they come in. I do remember when I first had a sub after I started these visibly random groups, I asked my classes, would you rather me have a sub slash student handout cards? Or would you like me to make a seating chart just for the day, and all of my classes, thankfully, said that they wanted to have visibly random groups. And that was really nice. And I know that the sub or student may not hold true to the validity of visibly random groups. But it’s better that way than me putting bias into the situation by creating a seating chart.

I know we’ve covered a lot of information today. And if you were like me, when I first heard this, this is new information that I’ve literally never heard of before. I mean, I wish this was the case when I was in school, because I think it would have been amazing, I was a very shy and introverted child, I think I still have those tendencies. But I just think of the amazing social benefits this would have had for me, like being put into a group with people I may not have been good friends with yet. And every day, meeting new people working with new people, I think would have really grown the community in the classroom. So when questions arise about what we’ve talked about today, please send me a message on Instagram. I’ll leave my Instagram link in the show notes. Just click on it, send me a DM, let me know that you listen to this episode. And what your question is. I’m happy to answer any question you have about this or anything else you’ve heard in any of my podcast episodes. And with that, thank you so much for tuning in today’s episode, and I’ll calc-u-later. 

Thank you so much for tuning into today’s episode. To find all the links and resources to things talked about in this episode, head on over to misskuipersclassroom.com and click on “Podcast”.

Transcribed by https://otter.ai