Episode #245: Balancing Group Dependence & Independence – A Math Mentoring Moment
This week we spoke with Lauren Sawyer, a middle school math teacher from the Chicago area. Lauren has been implementing Peter Lilijedahl’s work Building Thinking Classrooms and is trying to find the right balance between collaborative work and individual think time.
In this episode we help Lauren limit the illusion of understanding students may get when students are working in groups, determining the right time to schedule individual think time in her lessons, and how she can truly assess her students.
This is another Math Mentoring Moment episode where we chat with a teacher like you who is working through some problems of practice and together we brainstorm ways to overcome them. If you have a math class “pebble in your shoe” you’d like to work through, take less than 2 minutes to book a Math Mentoring Moment Call with us and before you know it, you’ll be on a call with us to chat all things math!
What You’ll Learn:
- How do I balance individual work time and group work time?
- How can we limit the illusion of understanding some students may have when working in groups;
- How can I truly assess students’ understanding when working in groups;
- When is the right time to schedule individual think time in a Building Thinking Classroom; and,
- How I can offer opportunities for students to think collaboratively AND independently every day.
Attention District Math Leaders:
How are you ensuring that you support those educators who need a nudge to spark a focus on growing their pedagogical-content knowledge?
What about opportunities for those who are eager and willing to elevate their practice, but do not have the support?
Book a call with our District Improvement Program Team to learn how we can not only help you craft, refine and implement your district math learning goals, but also provide all of the professional learning supports your educators need to grow at the speed of their learning.
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Take two (2) minutes to book your Math Mentoring Moment call and let’s work together to shake that math pebble out of your shoe!
00:00:00:06 – 00:00:21:03
Skill checks are. My rebranded term for quizzes, and skill checks are not assigned any type of grade. There’s no letter grade or no check plus check minus. I give feedback and it’s branded in the way that this is for you. This is for me. This is for your caregiver or whoever supports you. You just want to know where you are.
00:00:21:06 – 00:00:22:24
At least I think it’s low stress.
00:00:23:05 – 00:00:45:19
But this week we spoke with Lauren Sawyer, a middle school math teacher from the Chicago area. Lauren has been implementing Peter Little, The Hall’s work behind building thinking classrooms and is trying to find the right balance between collaborative work and the much needed individual think time.
00:00:45:21 – 00:00:58:24
In this episode, we help Lauren limit the illusion of understanding students may get when they’re working in groups, determining the right time to schedule think time in her lessons and how she can truly assess her students.
00:00:59:01 – 00:01:21:19
This is another math mentoring Moment episode where we chat with a math moment maker just like you, who’s working through some problems of practice. And together we brainstorm ways to overcome them. If you have a math class pebble in your shoe, or maybe it’s a district level pebble in your shoe and you’d like to work through them, it’ll take you less than 2 minutes to book a math mentoring moment.
00:01:21:19 – 00:01:44:11
Call with us, and before you know it, you’ll be on a call to chat with us. All things math here on the podcast. Let’s do this. Ooh.
00:01:44:13 – 00:01:48:19
Welcome to the Making Math Moments That Matter podcast. I’m Kyle Pearce.
00:01:48:19 – 00:01:50:17
And I’m Jon Orr, we are from makemathmoments.com.
00:01:50:17 – 00:02:00:03
This is the only podcast that coaches you through a six step plan to grow your mathematics program, whether it’s at the classroom level or at.
00:02:00:03 – 00:02:07:17
The district level. And we do that by helping you cultivate and foster your mathematics program with a strong, healthy and balanced tree.
00:02:07:19 – 00:02:16:19
If you master the six parts of an effective mathematics program, the impact of your math program will grow and reach far and wide.
00:02:16:21 – 00:02:38:03
Every week you’ll get the insight you need to stop feeling overwhelmed, gain back your confidence and get back to enjoying and the planning of facilitating your mathematics program for the students or educators you serve. Hey there, Lauren. Thanks for joining us on the Make Them Have More Moment That Matter podcast. We are excited to dig in to all things math with you, but how do you do it?
00:02:38:04 – 00:02:39:10
I’m great. How are you?
00:02:39:12 – 00:02:57:03
We are exceptional. It’s summer right now, and as we just jumped on here, we do a little bit of podcast recording on some days like we are here this morning, but we love to kind of get up in the afternoon and do summary things with our family. So we’re looking forward to that. Fill us in. We want to know a little bit about you and what your current role is.
00:02:57:03 – 00:02:58:20
Where are you coming from and what you’re teaching.
00:02:58:22 – 00:03:22:24
Yeah, so I’m a middle school math teacher for grades five, six, seven and eight and a private, independent, progressive school in Chicago, Illinois. And then I also had a little side hustle, I call it where I work as a lead teacher for math circles of Chicago, which apparently is one of the largest math circles in the world, which is pretty cool.
00:03:23:01 – 00:03:34:15
Ooh, tell me more about that. What is happening over there? I mean, most people are like, we know how it goes in a middle school, private, independent school. But tell us a little more about math circles here.
00:03:34:20 – 00:03:57:14
Well, so the math circles isn’t connected to my school. That is just kind of an outside organization I help with. But they provide afterschool enrichment for students centered on just kind of doing math in a way that. Well, I mean, we would say we should be doing in the classroom, but in a way that a lot of students aren’t getting in their classroom.
00:03:57:17 – 00:04:04:09
So kind of serving a lot of different populations in the Chicagoland area, which is kind of cool.
00:04:04:11 – 00:04:26:24
I love it. I love it. That is awesome. And before we start digging in here and chatting about what is on your mind lately, we’ve got to ask you this question. It’s a question we ask every guests on all 200 plus episodes of the podcast, and that is what is the math moment that you remember from your learning experience?
00:04:27:01 – 00:04:57:13
Yes. So I’m going to echo everybody who has been with you in the past. I absolutely anticipated this question, and I have thought a lot about it. But I think that the moment that I wanted to highlight is actually something that happened pretty recently to me as a teacher. I was working as a fourth grade math teacher about a year ago, and we were entering into a unit on measurement and we were starting with kind of thinking about units of length.
00:04:57:15 – 00:05:28:18
And after kind of reviewing the lesson plan, I saw that it really was just asking me to create a table with the students. So it was here is the unit name, here is the abbreviation here, the typical conversions. And then let’s find a benchmark object for that unit. And the questions were very narrow in the lesson plan, just kind of funneling the students to just like, let’s fill this table together, right?
00:05:28:23 – 00:05:32:14
Just do this thing. Yeah, we’ll all do it stuff.
00:05:32:16 – 00:05:59:19
Yeah. Like, you know, a thing you don’t know. I’m going to tell you that thing. So it didn’t resonate well with me. It was kind of typical of all the lessons from the curriculum that I had been teaching. But I must have been feeling exceptionally petulant that day. I would echo my five year old son who has recently taken to the I don’t have to if I don’t want to, and I felt like that after looking through that lesson that like I don’t have to if I don’t want to.
00:05:59:19 – 00:06:22:21
So I decided to hit up the storage closet and grab a handful of rulers and some yardsticks and just started off class. I was thinking like Oprah Winfrey, like you get a ruler and you get a ruler and you get a ruler and we all get rulers. And I remember my students looking at me like, Well, no one’s ever given us a ruler before.
00:06:22:23 – 00:06:24:12
What am I supposed to do with this thing?
00:06:24:12 – 00:06:26:16
And a sword fights ensued right there.
00:06:26:16 – 00:06:27:14
Like we’ve never.
00:06:27:14 – 00:06:29:09
Actually had these.
00:06:29:11 – 00:06:54:16
Yes. And I had to go through the these are math schools, not toys speech. But after kind of working through, you know, what we do with the rulers, they’re like, what do you notice what you wonder about this object that I just handed you? I sat them off on the task of I want you to measure things around the room that would make sense to use these units of length.
00:06:54:16 – 00:07:19:17
And I want you to find a unit, an object that is equal to or almost equal to that unit. And so, I mean, you can imagine with a group of fourth graders, nine year olds. Right. The most interesting thing to measure is height. And we had a lot of students who were asking about, I want my height measured, and then how tall are you?
00:07:19:17 – 00:07:44:01
And then it went into, well, so-and-so’s taller than me, and who’s the tallest in the class and who’s the shortest in the class? And we had uncovered all this extra learning, right? They were collecting data and they were comparing their data and they were arguing with each other. Any time there is any discrepancy that happened, like, Oh, no, you’re doing it wrong, you’re doing it wrong.
00:07:44:01 – 00:08:06:03
And so they had to satisfy that base. And it was the first time we had ever done something like that in the classroom. And if you are familiar with the scope and sequence of curriculum, you know that measurement doesn’t come early in the year. It comes later. So it really was the most alive that we had been in the math classroom.
00:08:06:03 – 00:08:16:04
I felt alive. The students felt alive. It hadn’t been a really great year. And so that was kind of one of those just uncovered this thing and it was really, really fun.
00:08:16:06 – 00:08:29:11
Right. And so that experience obviously sticking out to you because you’re making a change or how often are you trying to do that now with your students versus the way you were doing before?
00:08:29:13 – 00:08:52:10
Exactly. And unfortunately, I am going to give a twist to the story in that there was kind of aftermath of the lesson when I met with my math coach who was there to witness the lesson. Right. I’m feeling like I’m on cloud nine. I’m feeling really good. It was the first time I kind of walked in like, yes, something good happened and we started talking about the lesson.
00:08:52:10 – 00:08:59:10
And I remember the question that she asked me was, Lauren, were you trying to follow the lesson plan?
00:08:59:12 – 00:09:15:24
Oh, did they have the lesson plan in their hand? And they’re like, this person is not even coming close to what is described here on this document. So they’re thinking this is a complete failure because it’s not matching what you intended to do.
00:09:16:01 – 00:09:16:23
00:09:16:24 – 00:09:18:22
So what did that conversation look like after?
00:09:19:03 – 00:09:40:06
Well, I did a little bit of a student thing where I had the lesson plan, too. And I pointed here and I was like, it says that this part may take longer. So we technically did the lesson plan in the sense that we did fill in the table that was being asked. But I know I coach No writers.
00:09:40:06 – 00:09:48:09
No. You all can guess when they say it may take a little longer. It’s going to be a couple minutes longer, not 60 minutes longer.
00:09:48:09 – 00:10:13:11
Yeah, well, but ironically, I would argue if you want to do it well, it probably will be a lot longer. That’s the part that I think lesson planners might say, hey, do this short little activity. But it’s like if you want to actually do it in an approach where students are in charge of the learning and actually allowing them to make the connections, it’s not just a couple minute experience.
00:10:13:11 – 00:10:35:13
It’s not a, Hey, compare these two things and then back to the table and everything will just roll along smoothly. I can appreciate where the coach is coming from. A we’ll call it planning perspective that, hey, maybe in the future I want to maybe more document or script out or point form, describe what that might look like and sound like.
00:10:35:13 – 00:11:02:18
However, I guess a little bit disappointing, painted a little bit maybe is an understatement that they couldn’t recognize probably the connections that students are making. If I’m envisioning it the way you’ve described it, I’m seeing students making comparisons now. The part where the lesson planning piece could be beneficial is if I put down a couple key big things I want students to take away and I’m going to try to get them there.
00:11:02:18 – 00:11:24:05
So, for example, if let’s say we’re using nonstandard measurement tools and you have this thing is this long and the other is half of that length, the great discussions that could be had if John is ten of this thing and your 22 of the one that’s half the size and students have to kind of compare and then land on this unit conversion thing, like why it matters.
00:11:24:07 – 00:11:48:07
But ultimately, at the end of the day, what it sounds like is that you sparked curiosity in students, right? You created an opportunity for them to investigate and you gave them the opportunity to do some of that learning and you still brought them back. And through the student learning, you were able to explicitly address the learning expectation that the lesson was after.
00:11:48:09 – 00:12:09:16
My wonder for you is how does that style of lesson compare to how you remember learning as a student? Was it the way the lesson was supposed to be taught? Is that how you remember things, or did you have any teachers that were trying to do what you were doing in that lesson? Where does your head go? When I mentioned that.
00:12:09:18 – 00:12:34:14
Oh yeah, I mean, none of my teachers were anywhere close to kind of what I was trying to do in that moment. So I think that the way in which my coach had looked at the plan and kind of looked at the script that was written for me, that was what she expected me to be doing. That’s what I would have expected me to be doing, as well as what as a learner.
00:12:34:20 – 00:12:51:08
I would have seen from my teachers. But yeah, I don’t know what came over me. I do have more of a background in science, so I wanted to be doing more hands on learning and it just felt like kind of the right thing to be doing at the time.
00:12:51:10 – 00:13:12:24
What was the feedback that your coach gave you about that lesson? I’m just curious. Mostly because you had a scripted lesson plan. You didn’t follow it and then did they say, Oh, you didn’t follow it, you should follow it, And then maybe they didn’t give you that feedback. Maybe there was other feedback they gave you. I’m just curious about what objection was.
00:13:12:24 – 00:13:14:17
Hear from the coach.
00:13:14:19 – 00:13:42:12
Yeah, I mean, ultimately kind of the next step was going through the rubric again of how I was supposed to be approaching the lessons, the curriculum and reading the curriculum. And I know from the lens of the coach, they had just gotten this new curriculum that year. And so they were working pretty She had a coach that she was reporting to, so I’m really far down the line.
00:13:42:14 – 00:14:06:21
She had a coach in that person probably was reporting to somebody else and it was kind of a launch of a new curriculum. And so I think probably the agreement when they took on that curriculum was that we would be following it with fidelity that so that whatever results kind of came out of it, it was like, well, look, this curriculum does X, Y and Z to the students and these are the results.
00:14:06:21 – 00:14:14:10
And so I think she was more, I don’t want to say disappointed, but probably concerned that I hadn’t followed it.
00:14:14:10 – 00:14:35:22
And so yeah, from a data perspective, if they’re trying to track the success of the curriculum to decide whether the curriculum is useful or not, I could see that. However, what they’re doing right, they’re experimenting with a curriculum on the backs of students in realizing you quickly realized that this lesson for this group of students isn’t going to work.
00:14:36:03 – 00:14:57:09
And instead of sticking to the script to prove data wrong, you’re like, I actually have to rescue these students. So that their math connection to measurement is saved. Instead of trying to serve the data that the district is trying to collect, I could see that that’s another ballgame, another level we have to address. But so, Lauren, what’s on your mind?
00:14:57:10 – 00:15:10:01
Thanks for sharing that story with us in your experience around that lesson. But what’s on your mind as well? Like what else can we dive into? What’s a current pebble that’s rattling around in your shoe, as we like to say?
00:15:10:06 – 00:15:21:04
Yes, I actually had to think about this quite a bit because I’ve been on summer, so all the pebbles that usually collect during the school year, they don’t exist anymore.
00:15:21:06 – 00:15:28:21
You know, they disappear. You know, you took that shoe and you just put it in the closet for a little while. They’re all in there. You just kind of put it in the closet.
00:15:28:24 – 00:15:59:13
Exactly. So it took me a moment to unearth Why I had kind of reached out to you guys in the first place and what was really on my mind at the time. And so I unearthed this idea. I’m trying to grapple with this idea balance between individual independence and group work dependency, just like how do I build more individual independence with my students, especially in a more collaborative environment?
00:15:59:15 – 00:16:20:19
Very interesting. Can you paint us a picture of what does that look like in your classroom? And I guess where are you seeing maybe some of that dependance that some students are showing? Where is it emerging? Is an emerging in the group work? Is it emerging also when they go to the independent or do they have those opportunities?
00:16:20:19 – 00:16:26:09
What does it look like in sound like on a typical day in your classroom?
00:16:26:11 – 00:16:54:24
Yeah. So I think the foundation of the classroom and this is my first year kind of doing this this past year, so obviously I’m still kind of working out the kinks, but we use a lot of the thinking classroom as well as open mindset tasks. Everything was very collaborative. We were communicating with one another, lots of discussions, lots of reflection, working together.
00:16:54:24 – 00:17:28:07
I really can’t think of a time where there wasn’t some type of buzz, where the students weren’t talking with each other and talking through things with each other. And so that was really exciting. Oh, this is exactly what I want to be seeing. But I did notice, and this is kind of where this have all kind of surfaced is that when I was giving my weekly skill checks, skill checks are my rebranded term for quizzes, and skill checks are not assigned any type of grade.
00:17:28:09 – 00:17:54:18
There’s no letter grade or no check. Plus check minus. I give feedback and it’s branded in the way that this is for you, This is for me. This is for your caregiver or whoever supports you. You just want to know where you are. At least I think it’s low stress. But apparently it seems kind of stressful because what I’ve noticed is students, when they have their skill checks, they can’t help but try to whisper to each other a little bit.
00:17:54:18 – 00:18:16:24
I don’t feel like I can fault them for that because we’re not ever quiet in the classroom. And then whereas during our tasks, I’m not the answer machine anymore, they go to one another for help. But during our skill checks, I have a line of students just coming up to me asking me like, Is this correct? Or they’re telling me they don’t know how to do it.
00:18:16:24 – 00:18:37:00
I’m okay giving them questions just to refocus their thinking, but I believe in them. And so it’s just I don’t know if we’re doing too much together and where is that balance between where I should be having them? I don’t know. Is it the purposeful practice or consolidation of learning?
00:18:37:02 – 00:18:59:11
Continue to paint us the picture of I know you said you’re following building thinking classrooms. Is the entire period a collaborative experience? And then where the disconnect happens or the independence happens only on the quiz? Or is there a mix already in place? And you’re just wondering what the right balance is? Are we full to one side versus the other?
00:18:59:11 – 00:19:17:24
Because I can imagine my experience is probably similar to your experience in the way I taught for a long time was full independence. It was like teacher at the board. I teach you copy notes now it’s work time, but don’t talk to anyone else. Get your work done, get your homework done. It’s all independence. And then sometimes we tend to swing from one sided to the other.
00:19:17:24 – 00:19:37:20
Now we could go full group and it’s no independence. So I’m curious, is there a mix already or is it we’re full building thinking because when you read Peter’s work in building thinking in classrooms, he gives off the impression in the book that the whole time everyone’s at the boards, everyone’s working together, and then notes happen at the end.
00:19:37:20 – 00:19:45:15
When you say make a point to do it or we do it together for notes. So I’m just curious about what your balance looks like currently.
00:19:45:17 – 00:20:07:08
I mean, I definitely think we’re leaning more towards the group work that even in an opener where it’s like, okay, take 5 minutes and try this on your own much just get ourselves set for the class time. They know that at the end of that 5 minutes we will come together and kind of share our thinking. And the same goes.
00:20:07:08 – 00:20:28:06
Or if I launch a task, it’s okay, well, let’s take some time. You try the task first, and then I start putting them into the random groups and sending them to different spots around the room. And it’s like, okay, so now start talking with each other and sharing your findings. And then that obviously goes into the bigger classroom where, okay, now these groups have talked.
00:20:28:06 – 00:20:51:23
Let’s all talk with each other and discuss and reflect what has happened. So I feel like there’s very minimal parts where it is independent and I do feel like there’s that safety of I will eventually go off and talk to somebody else, which like I don’t know, I’m not being tested individually every single day. It’s just like one of those things.
00:20:51:23 – 00:21:13:16
I know tests exist placement exams and fortunately aren’t thing and I want to be responsible in preparing the students for that so that when I’m giving a skill check or, or if you guys have suggestions on other things that they could do by themselves, they’re not, I don’t know, freaking out or losing confidence in themselves.
00:21:13:22 – 00:21:53:17
I think you bring up a really valid point and that’s this point of in the real world, it’s like we don’t typically sit down and quiz ourselves on things. However, through the learning process, I would argue if we can potentially re-imagine why we’re doing that and that it’s not necessarily for a test for a grade, your check ins are great how you have them, but I wonder if in order to make that process more of an independent experience for students, we also need to throughout the week, have opportunities for them to essentially practice that skill.
00:21:53:19 – 00:22:10:19
And it’s not. And I would argue if we can reframe it and if we can imagine and I’m picturing on your board somewhere in the room where there’s almost like the structure of the learning and it doesn’t have to have times on it, it’s not about time how much time you have group work and how much you’ll have this.
00:22:10:21 – 00:22:36:16
But it’s like to have a time in ideally, it’s not always going to be perfect, but if, let’s say in every math block, there’s a time for students to go and independently challenge themselves on what they gained from the experience. So Peter addresses that through your forgetful note to yourself, which I think is a great skill to help students build on.
00:22:36:18 – 00:23:18:00
But I also think that we need students to actually engage in some of the problem solving that we just experienced. So your example earlier in the math moment, that activity maybe doesn’t lend itself as easily. However, if that table if the purpose of that table for measurement and conversions was for students to recognize that here in Canada that there’s 100 centimeters in a meter or 12 inches in a foot, that we then give them some reflective questions to actually apply that learning on their own, not as a judgment for you or for their parents or guardians, but for them to recognize that, hey, when I was in that group, because what we notice will happen.
00:23:18:06 – 00:23:53:17
So when you’re in a group and you’re hearing people talk, you’re doing a lot of learning, which is great, but only when you have the opportunity to actually leverage or utilize that skill, that strategy, that model, that big idea. Only then are you actually growing your brain to be able to do that thing again in the future. So I guess what I’m saying is to go from, let’s say, a really helpful learning conversation over here and turn it into true learning so that they actually know understanding can do that thing.
00:23:53:19 – 00:24:12:00
Often times as humans, we have this thing called the illusion of understanding. And the illusion of understanding is the thing that tells you that you’re ready for the test and then you get into the test and then you go blank. You thought you knew it, but if I actually did some of these questions last night, I would have recognized that.
00:24:12:00 – 00:24:31:11
I don’t know as much as I know, and I think the same is happening in our collaborative experiences. It’s amazing to ensure all students can enter into that conversation so that all students can do some learning. But naturally there’s going to be some who are doing a little more of the thinking, maybe a little more of the doing.
00:24:31:13 – 00:24:54:00
The reality is this what we want to do, this is for the students, but also for us as the educator is giving them that opportunity so I can observe what they’re know. It’s great in a group. I can listen and observe, but when they’re doing it independently, just to observe who’s doing what and who actually got what, I was hoping they were supposed to get right.
00:24:54:00 – 00:25:17:18
So if that big idea is like I want them to notice that if you double a number, double a factor, then the product doubles. If that was the big idea, we were trying to reveal in my mini lesson, I want to give them an independent opportunity to do so. I can’t just be confident that just because the whole group in my math talk is kind of following along, that we got it because a lot of kids didn’t get it.
00:25:17:18 – 00:25:45:21
They got that one question, but they didn’t get the goal. The point right. The big idea that we were trying to land on. So my wonder is I want to flip it back to you and get your thought on that. If you could imagine you’re doing this collaborative work and we don’t want to shut down the collaboration. But if our students knew that, hey, we’re going to take some time to do independent time for your own consolidation of this learning so that we can all understand where we are.
00:25:45:21 – 00:26:07:19
And so me as the educator, so I know where do we go next? That’s how I can truly see is like, Ah, John, he picked it up today. Awesome. But oh my gosh. Lauren, I thought had it in the group, had it but actually missed the point. Kind of missed the point of the activity. She came up with the answer and her strategy worked.
00:26:07:19 – 00:26:34:21
And I thought based on her strategy, that she understood the underlying conceptual pinions here that could be applied to any other scenario like this. But I just gave her another one like it, and she couldn’t replicate that. So it’s like, Hmm, that’s interesting. So I can learn a ton by giving those students that independent time. And it’s at that time where you can kind of lay down some of that groundwork of, Hey, I’m still not the answer giver during this time.
00:26:35:01 – 00:26:50:19
I want to see what you got. And then we’ll come together and it’s like, this is for you to know where am I along this journey and what else can we do or what else do I need to do as the learner in order to get myself to the next place in the journey?
00:26:51:00 – 00:26:57:11
So I’m wondering with that, I guess kind of look like an exit ticket in a way.
00:26:57:11 – 00:27:16:14
It could look like an exit ticket. I think the way I structured that is during, say, our block of time together, we’re doing that same building thinking classrooms we consolidate. What Kyle is saying is we’ve got in these groups, we’ve consolidated, we’ve tied a bow as a teacher, we’ve taken this and this, and we’ve said this is the learning goal for today.
00:27:16:14 – 00:27:36:17
And we pulled this person’s work to show it as an example. And this is the example we’re going to show. But this is the expectation from today. Sometimes for me, what I do next is I purposely try to make sure that we do have individual work time. But a lot of times I leave it as a choice for some students.
00:27:36:17 – 00:27:57:04
So for example, once the bow is tied, we’ve got some time left to do that practice. That’s individual. But I also say, you know what, You could do these practice questions which are carefully designed to elicit the learning goal that we’ve got here today to keep going and practice it on your own. But you may choose to go back to your boards and work as a group.
00:27:57:06 – 00:28:13:22
You could switch teammates if you want to go to a different board and work that time as a group, or you can come back to your desk and do that individual work time by yourself. And so that gives that self-regulation to going like, I need to know, I need to go back and do this myself so I can prove to myself I could do this.
00:28:13:22 – 00:28:42:05
Some students might be saying, I’m not ready for that, but there is that expectation in our room that there will be like that transition. Does have to happen to say everyone’s going to have that time. We do need to be able to know, understand and do these things and you can still do the exit ticket after that. But I tend to kind of rely on a little bit of a choice there when I give that choice, especially at the high school level, a lot of students will go back and do that individual practice time and then they kind of bounce ideas off each other at the desks.
00:28:42:05 – 00:29:04:08
They can go to the boards if they wanted. There space to be individual, but I think the individual is a necessary inclusion of the work that you’re doing, especially when you’re doing so much group work. I tend to think we tend to tend to structure our lessons too, generally, especially in group work. Reward the extroverts, the people who are quick thinkers, the people who have no trouble interacting with other people.
00:29:04:08 – 00:29:28:21
Now I’m saying that group work is super valuable and we want to keep that going. But there are that group of students who would be like me that gets a little bit stressed when being at the boards because one, I’m maybe a little bit more introverted, but on the second is my brain might not be able to think as quickly as someone else’s or as I need to have that more careful, slow, thoughtful reflection before I’m ready to respond with my thoughts.
00:29:28:23 – 00:29:55:11
And that group work. Standing at the board sometimes is intimidating there because some other people might be quick to respond with their thoughts. And I’m still trying to figure this out before I respond. And so it sounds like you’re got that think time happening at the desks or individual already, which is great. But I think I always want to kind of include that other are think time as well at the end for that purposeful practice because some of those students are craving that part of the lesson as well.
00:29:55:17 – 00:30:15:18
Now one thing I want to do is just I’m going to quickly share my screen. Those people who are listening or watching on YouTube will be able to see it. We’ll do our best to kind of describe it for our audio listeners. But if you head over to our Web site, make math moments dot com and go to the tasks area, you’ll see that our tasks typically we have a full unit there.
00:30:15:20 – 00:30:37:17
However, day one of every task is fully open for people to engage in and they can dig into without being an academy members. So I’m looking at covering ground right now. This is all about area of a triangle, an area of a parallelogram, and you’ll notice the way that we have it structured, you’ll see along the sidebar here that we have our intentionality of the lesson is clearly stated.
00:30:37:23 – 00:30:56:21
So that can be seen here and we can leverage what is it that we’re trying to accomplish here. So those are the main goals and it’s like I need to give students in my mind and in a math moments lesson, we’re going to give them the opportunity to investigate, to collaborate, to do this work together, similar to how you’ve been describing them there.
00:30:56:21 – 00:31:23:21
Lauren And ultimately, at the end of the day, once we consolidate some of this learning, so they go through and they do a curious task this one’s all about. There’s a graphic of basically a yard that’s being landscaped and we’re trying to figure out how much is patio and how much is grass. And it’s a triangular shape. They estimate they do all kinds of great things and then we give them an actual struggle prompt.
00:31:23:23 – 00:31:50:20
We have different student approaches that of how they might go ahead and actually approach solving this task. So those are there for you to see as an educator. But the part I want to highlight to you is after the consolidation, when we get to the reflect and consolidate prompts, you’re going to notice these consolidation prompts. Typically we assign them more independently because what we’ve done is we’ve investigated as a team, we’ve solved collaboratively.
00:31:50:22 – 00:32:14:04
It could be at the whiteboards, it could be at table groups, it could be however you choose to do that work. And then we consolidate that. Consolidation is where I as the facilitator, I’m going to take whatever student knowledge and strategies and I’m going to try to link them together to get us as close to the learning objective as I possibly can, making sure that it’s super explicit for everyone.
00:32:14:04 – 00:32:42:03
So there’s not a chance that you’ll leave that consolidation circle without knowing what the purpose was up. The lesson less important is the answer. More important is Wow, any time I have a triangle, if I find the area of the rectangle and take half of it, I’m good to go. It’s like, Oh my gosh, that makes sense. And we’re not just saying, Here’s the formula one half B times H It’s like, No, no, we got a rectangle and we took half of it.
00:32:42:03 – 00:33:15:15
And here’s one example. These consolidation prompts give them a few more triangles for them to work on. So you could say it’s a garden, you could say it’s whatever. But the goal now is I want to see who heard what, because you’re going to find that you thought your consolidation was amazing. You delivered it perfectly. Everybody is going to be the triangle area master, and then you get to the consolidation promise and they do this individually, and then you start to see, oh, maybe they missed something.
00:33:15:15 – 00:33:37:21
Right? And that can only really be explicit when we give them that opportunity to do this independently. And sometimes they need to experience that, that they’re like, wait a second, I thought I got it. Maybe I don’t know it as well as I thought I did. And that’s not to shatter their confidence so that we can then help them to truly understand this content.
00:33:37:23 – 00:34:00:08
And in our lessons, you’ll notice when you go in to day two, usually day two is building on day one. So there’ll be a math talk in there. You can hop into the day to math, talk more purposeful practice opportunities, maybe four centers or however you choose to do it. But you’ll notice that there is more independent time for students to do some of the learning.
00:34:00:08 – 00:34:25:00
So for us, while it’s not a rule we would like to say when we’re introduced an idea or a concept or a big idea, we want to make it a collaborative experience. We want to give students the opportunity to problem solve and struggle together. But then we want to start building and refining that skill more independently. It’s almost like we’re starting in a group setting and we’re working towards more independence, right?
00:34:25:02 – 00:35:06:24
I want to work with you and make sure that you’re good to go, but eventually I need to let go of the seat of the bike and let you bike off without the training wheels. Right. And let you do that independently. So it’s not an either or. I think it’s a both. And it’s thinking to yourself about how can I intentionally do an offer opportunities for kids to independently think every day, not to boycott the collaboration or the discourse or any of those things, but just to ensure that they do have that space in that time to think and for them to recognize where they truly are and that they’re not necessarily maybe accidentally riding
00:35:06:24 – 00:35:21:17
the coattails of another group member. Right. The group member explained it all and say, Yeah, that makes sense. Great, I’m good, but could you do it the next time? Only when they have that opportunity can we truly feel confident that they’re going to be able to run off with it on their own.
00:35:21:20 – 00:35:27:12
Learn Where’s your head at so far after kind? I sharing all of these ideas on the idea of balance.
00:35:27:16 – 00:35:48:18
So I think I had already gone and was going into this coming school year with the idea that consolidation and purpose will practice were a couple areas that I wanted to find to and a little bit more. And I feel like this past year I was really fighting the battle. They had a very traditional teacher prior to me and so I was really changed.
00:35:48:19 – 00:36:00:15
You know, this is our new norm and this is what we do. And trying to correct the mindsets that I was seeing in the classroom. And so I think I might have overcorrected a little bit. And then.
00:36:00:15 – 00:36:01:17
Now you’re just human.
00:36:01:17 – 00:36:25:18
Like, yeah, I don’t know. Only so many messages that a middle school brain is really going to latch on to. So I think this coming year I realized, yeah, we need to now start to emphasize that while collaboration is fantastic, we want to be able to work together. There have to be times in which we do things for ourselves and where are we going to get the fire?
00:36:25:20 – 00:36:47:01
Where can my students find that fire and drive that like, Yeah, I want to do this for myself because that’s the right thing to do. I’m excited about learning. I want to do things for myself. But right students are always so excited to work with each other and help each other out. But now I think the messaging has to be like, How are you to help yourself out?
00:36:47:01 – 00:36:48:24
What types of things do you need to do?
00:36:49:03 – 00:37:05:14
I think you just nail that. As humans, we are kind of all in all out type species. We want to do a new idea. It’s like we’re on to do all of that. And then sometimes we kind of maybe forget some of the other pieces that could be helpful or we didn’t recognize were helpful at the time. And I know I was there.
00:37:05:14 – 00:37:35:19
John had mentioned it earlier in the episode that he was there as well, where we kind of like you go all in on something and it’s almost like, how do you do that without maybe going all out on something else? And it sounds like you’ve kind of landed in this place. And I’m picturing starting off this new school year coming up and almost like helping students from day one understand that your goal is for them to become collaborative learners with the goal of ensuring that every student here can do this work on their own.
00:37:35:21 – 00:38:01:24
So if you imagine that as a classroom pillar that you want to set with those students, you don’t have to say like, you know, we’re all about collaboration or we’re all about independent, we’re all about that. We want to get you the whole goal. All is so that each and every one of you can leave this room. And if you’re on your own, sure, if there’s a neighbor around to work through a problem with, you can do that in the real world.
00:38:02:01 – 00:38:24:14
But I want to make sure that you’re equipped so that if you’re alone, that you can be doing some of that work on your own. And it sounds like you’ve got some ideas. So I’m wondering what would be your immediate next step, your big takeaway? Where is your mind that as you look to the rest of the summer and you know, you got to pull that shoe with all those pebbles back out of the closet at some point soon?
00:38:24:15 – 00:38:45:11
Yeah, I mean, I think my immediate next step is going to be to look back through the math mindset that we have kind of written in our classroom. So when we start off the year and with that understanding of what the norms are in the classroom, I don’t think I ever use the word independent doing work independently before.
00:38:45:11 – 00:38:50:09
And I guess you were probably trying to break it, right? It was like everything we did, we did too much to say that.
00:38:50:09 – 00:38:54:20
We did too much of that already. You already do too much. Yeah, we’re going to go here, but we need that balance.
00:38:54:22 – 00:39:18:01
Right? Well, and they were really trained well for independent work. Right? It was hard to get them to actually talk to each other. Oh, no, no, don’t just talk to each other about whatever you want to talk about. Please talk about math. But I think I will have to go. I like that idea of like, we will do this stuff collaboratively, but we also want to ensure that individually we can do this on our own.
00:39:18:01 – 00:39:34:02
And whether or not that means that you have the drive to want to do that independently on your own, or you’re going to help encourage one of your classmates that, yes, you can do this on your own. I think that’s going to be kind of a good focus of messaging as we start the year.
00:39:34:04 – 00:39:54:12
Awesome stuff. Awesome stuff. We are actually eager or excited for you to kind of try that out in this coming year. And also kind of we’re hoping that you could check back with you say next year and see how things went over the course of the year and how that balance came to be in your classroom. Are you open to kind of joining us again in a year to kind of fill us in on the details?
00:39:54:14 – 00:39:59:05
Wow. Well, I’m here today, so I will be here next year. All right?
00:39:59:07 – 00:40:10:10
Love it. Perfect. Love it. Thanks so much, Lauren, for joining us here on this episode. I think a lot of folks had the same pebble you have on balance and lots of takeaways as well as the same as yours.
00:40:10:12 – 00:40:28:15
Right. Thank you so much for having me. And really being a part of this community has been a lot of fun and listening to you guys, whether or not it’s the podcast or even right now, which was kind of scary going into not as scary and the aftermath. So thank you so much for having me.
00:40:28:17 – 00:40:40:01
That’s awesome. I can tell we can tell the passion in your voice and how much and how reflective you are. It’s going to be a great year for you and your students. Thanks a ton. And hey, don’t be a stranger, right?
00:40:40:01 – 00:40:42:01
00:40:42:03 – 00:41:24:09
Well, there, John, after this conversation, I thanked Lauren after the call because I think her challenge is a common one. And whether you’re listening to this episode and you’re recognizing that that’s a challenge or maybe you haven’t recognized that that is a challenge you will endure if you are taking on more collaborative approaches, problem solving, task based learning, problem based learning, whatever it is that you’re doing in your classroom, we tend to try so hard to overcome that vision in our mind of a quiet, independent role of desks in that math classroom that we worked so hard to get rid of it that we almost like throw it right out the window.
00:41:24:11 – 00:41:56:20
And I was really happy that Lauren came in to sort of, I guess, uncover or to wonder, is there enough or am I doing enough to ensure that students are getting what they need to also be independent thinkers? It sounds like her students are becoming great at collaborating. They’re becoming problem solvers, are doing all of these things. But it just seemed like maybe not quite enough opportunity for them to then take that learning and then go and feel what it feels like to productively struggle on my own.
00:41:56:20 – 00:42:18:12
And when we think about our tree and six parts of our an effective mathematics program, the branches of our tree are the teacher moves that we’re doing in the classroom and sometimes that anticipatory move at the beginning of like, what am I students going to do should be paired with when am I students going to do that? If I’m going to plan out group work, I should also plan out that individual time.
00:42:18:12 – 00:42:36:12
And what do I anticipate to happen at the individual work time as well, so that I’m prepared to help them when they need help there, but also help them kind of steer the lesson to get to the learning goal. So thinking about branches of our tree and our teacher moves, our pedagogical teacher moves, we have to think about all aspects of our classroom, but also all learners.
00:42:36:15 – 00:42:54:08
Are we rewarding students who are quick thinkers, extroverts? Are we taking into account students who are more introverted, a little bit slow, more careful thinkers? We do. We need to think about all learners in our room. And you only know that when you get in down and dirty with your students so that you can feel what they’re feeling.
00:42:54:08 – 00:43:15:09
You see what they’re seeing, you’re listening to them. You got to get to know your students and that’s a teacher move. So that’s part of our branches. So folks, if you thought about some of the takeaways you had yourself from this episode, did you write them down? Did you share them with someone? Lauren Sounds like she was taking notes along some of the ways or some of the episodes change that in her journey.
00:43:15:13 – 00:43:29:02
Maybe you are also taking notes. Maybe you’re taking notes in different ways. We’d love to hear about it. You can reach out to us on all social media platforms at make math moments and let us know where are you consolidating your learning?
00:43:29:04 – 00:43:52:17
Hey friends, The rating and review on your podcast platform is the best way that you can help us reach more math moment makers from around the world. So if you want to have an impact or an influence on the students, you teach, just imagine if you could bring in more of their educators into this experience and we can all learn together.
00:43:52:17 – 00:44:04:24
So hit that rating button and leave a short review on Apple Podcasts, Spotify, wherever you’re listening. That goes a long way to ensuring that the podcast reaches a wider audience.
00:44:05:00 – 00:44:23:10
Folks, this was a mentoring moment episode, and if you want to be our next guest, then we encourage you to head on over to make math moments dot com forward slash mentor, fill out a quick form. You’re basically picking a time slot for you to join us. You’re going to enter in your pebble. What’s going on right now that you want to discuss with us and boom, we’ll have a chat.
00:44:23:10 – 00:44:33:12
And by the end of that chat you will be feeling a lot better about that pebble, just like I learned it after this call. So head on over to make mathematics forward slash mentor and chat with us.
00:44:33:14 – 00:44:51:11
Hey friends. Shownotes resources and complete transcripts over app make map moments dot com forward slash episode 245 that is make math moments dot com forward slash episode two for five and friends until next time. I’m Kyle Pierce.
00:44:51:11 – 00:44:52:11
And I’m John aware.
00:44:52:14 – 00:44:55:14
High fives for us.
00:44:55:16 – 00:45:02:09
And high five for you.
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Each Teacher Guide consists of:
- Intentionality of the lesson;
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Each Make Math Moments Problem Based Lesson begins with a story, visual, video, or other method to Spark Curiosity through context.
Students will often Notice and Wonder before making an estimate to draw them in and invest in the problem.
After student voice has been heard and acknowledged, we will set students off on a Productive Struggle via a prompt related to the Spark context.
These prompts are given each lesson with the following conditions:
- No calculators are to be used; and,
- Students are to focus on how they can convince their math community that their solution is valid.
Students are left to engage in a productive struggle as the facilitator circulates to observe and engage in conversation as a means of assessing formatively.
The facilitator is instructed through the Teacher Guide on what specific strategies and models could be used to make connections and consolidate the learning from the lesson.
Often times, animations and walk through videos are provided in the Teacher Guide to assist with planning and delivering the consolidation.
A review image, video, or animation is provided as a conclusion to the task from the lesson.
While this might feel like a natural ending to the context students have been exploring, it is just the beginning as we look to leverage this context via extensions and additional lessons to dig deeper.
At the end of each lesson, consolidation prompts and/or extensions are crafted for students to purposefully practice and demonstrate their current understanding.
Facilitators are encouraged to collect these consolidation prompts as a means to engage in the assessment process and inform next moves for instruction.
In multi-day units of study, Math Talks are crafted to help build on the thinking from the previous day and build towards the next step in the developmental progression of the concept(s) we are exploring.
Each Math Talk is constructed as a string of related problems that build with intentionality to emerge specific big ideas, strategies, and mathematical models.
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