Episode #177: Making The Consolidation Count – A Math Mentoring Moment
In this Math Mentoring Moment Episode, we speak with Jeremy Sarzana, a high school math teacher at a Vocational High School in Boston, Massachusetts. Jeremy has been putting all kinds of great pedagogical practices into play including students working in randomized groups to engage in problem based lessons and is having success. However, when it comes time to consolidate the lesson, the student participation quickly fades.
This is another Math Mentoring Moment episode where we talk with a member of the Math Moment Maker Community who is working through problems of practice and together we brainstorm possible next steps and strategies to overcome them.
- How can we consolidate the big idea in our math class so that students are engaged;
- How to be flexible in your lessons so students feel heard;
- What is really important when monitoring, selecting, and sequencing;
Are you a district mathematics leader interested in crafting a mathematics professional learning plan that will transform your district mathematics program forever? Book a time to chat with us!
Jeremy Sarzana: So in my classroom, I've been having the students do one problem and go deep into it. So when we're in the working groups, so when they're in that stage, that's when the best learning is going on, like the group work. There's student discourse. They're using different strategies. And I'm walking around just to make sure that everybody is... Some people might need a little nudge or some people they just might need a little help to get going or I want to make sure they understand the task. So that's great, but then as soon as we come back together...
Kyle Pearce: In this math mentoring moment episode, we speak with Jeremy Sarzana, a high school math teacher at a vocational school in Boston, Massachusetts. Jeremy has been putting all kinds of great pedagogical practices into play, including having students working in randomized groups to engage in problem-based lessons and is having quite a bit of success. However, when it comes time to consolidate the lesson, the student participation quickly fades.
Jon Orr: This is another math mentoring moment episode where we speak with a member of the math moment maker community, a person just like you, who is working through problems of practice and together we brainstorm possible next steps and strategies to overcome them.
Kyle Pearce: Hey, math moment maker friends, before we dive in, have you submitted your math class pebble in your shoe? If you haven't head on over to makemathmoments.com/mentor so that you can hop on the show just like Jeremy has hopped on today, so we can talk about your current math class struggle. Once again, that's makemathmoments.com/mentor, and let's do this.
Welcome to the Making Math Moments That Matter Podcast. I'm Kyle Pearce.
Jon Orr: And I'm Jon Orr. We are two math teachers from makemathmoments.com who together...
Kyle Pearce: With you, the community of math moment makers worldwide, who want to build and deliver problem based math lessons that spark curiosity...
Jon Orr: Fuel sense-making...
Kyle Pearce: And ignite your teacher moves. My math moment maker friends, we are looking forward to diving in with a fellow math moment maker to discuss the current pebble that's kicking around in his shoe.
Jon Orr: Yeah, definitely. And this is a common pebble that many teachers have. We've talked about it also on previous episodes. We've talked about it, Kyle, in our Q&A sessions monthly that we've hold with our academy members. This common problem what happens at consolidation times? How do I do that part better?
I think a lot of the community right now, Kyle, throughout the work that we've been sharing and the work that we've been getting from lots of folks like in this episode, you're going to hear Peter Liljedahl's work, the thinking classroom reference. We've talked indirectly about the five practices for orchestrating productive mathematical discussions. There's so much great work out there that are helping teachers get lessons started, put the right things in place to make it successful for your students. But then the consolidation comes and it's like, "Well, how don't I keep that engagement going? And how do I do that well so that kids aren't like hitting the snooze button again like they were maybe before I started making these changes? I want that piece to be better." So we talk about that here in this episode, and you're going to get a kick out of it.
Kyle Pearce: Yeah, absolutely. We are not going to tell you too much more, but do pay attention. When we start talking about maybe some of the pieces to be thinking about before the lesson and some of the really intentional moves that we're going to suggest that Jeremy makes during the lesson in order to set himself up for a really awesome consolidation, which can look a few different ways. So let's not waste any time there, Jon. Let's dive right in and let's hear it here from Jeremy.
Jon Orr: Hey there, Jeremy. Thanks for joining us this week on the another episode of Making Math Moments That Matter Podcast. How are you doing Kyle?
Kyle Pearce: Oh, goodness gracious.
Jon Orr: Now this a little bit weird right now. We're starting the podcast episode, and if you're watching us over on YouTube, because we're going to leave this in. There's a cat that just jumped up on my shoulders. Oh my gosh. Okay. Sorry about that, Jeremy.
Kyle Pearce: What's crazy is Jon doesn't even have a cat. Where did the cat come from? No, I'm just kidding.
Jon Orr: Sorry about that, Jeremy.
Jeremy Sarzana: No worries.
Jon Orr: How are you doing this evening?
Jeremy Sarzana: I'm doing excellent. And I'm very excited to be on the podcast with you guys.
Kyle Pearce: Fantastic. So we need to know before we get going, we always want to get sort of a sense of who we're chatting with. And of course the audience wants to know who we're chatting with. So give us a little heads up like where are you coming to us from? What's your current role? And I guess what got you into this crazy world of math education?
Jeremy Sarzana: Okay. Yeah. So I'm coming from Boston, Massachusetts and I teach at a vocational high school. It's called Madison Park Vocational High School. It's in Roxbury, which is a neighborhood in Boston and I'm a 10th grade geometry teacher. So I also co-teach. So there's two math teachers.
Kyle Pearce: Very cool.
Jeremy Sarzana: Yeah. So it's an inclusion classroom. So there's some students in special education with some modern disabilities. So I have a math license, but I also have a special education license as well. I went to Berklee College of Music. So I'm a guitar player.
Jon Orr: Oh, nice.
Jeremy Sarzana: I just face the music. Yeah. Basically, my partner, her name is Theresa, she's my fiance, and we have two greyhounds.
Kyle Pearce: So if I had to guess, we're not going to see a Greyhound jump on the back of your chair? Like Jon has got the cat rocked in.
Jon Orr: It just jumped off and shoved the table.
Kyle Pearce: crosstalk was roaming around recently. So who knows? She might show up. But who knows there? I got to ask you about Berklee because Berklee is a pretty prestigious music university college. I know-
Jon Orr: The music geek is going to start coming out, Jeremy.
Kyle Pearce: Yeah, I know. All growing up and when I was playing in a band and stuff, I would always look at Dream Theater and I loved like John Petrucci and that whole group. I feel like the whole group was from Berklee. I think maybe Ian Thornley from Big Wreck, I think may have went to Berklee. I'm not sure, but fantastic.
Jon Orr: That's your band.
Jeremy Sarzana: Sure.
Jon Orr: That's your band, Kyle.
Kyle Pearce: Tell me a little bit about that. So was that the plan? Were you thinking like, "I'm going to go and do some crazy music"? Was it music education? I'm just curious more as an aside here.
Jeremy Sarzana: Since I was a young kid, like nine years old, I played guitar and I grew up watching MTV. So I was all into those hair bands and all that stuff. By the time I got to high school, I started really getting into the guitar and I just said like my senior year, I was like, "Oh, let me just apply to Berklee." And I got accepted and it was a great experience. Just being in the classroom, like for four years and just soaking in all that information, it was like an unbelievable experience. I loved it so much.
Jon Orr: Awesome.
Kyle Pearce: I'm so jealous. Good for you.
Jon Orr: Jeremy, can you pivot for us a little bit here? I am always curious on back stories, before we get into the deeper conversation, but music, student, becomes math teacher. Can you fill us in on that part of the journey? How did that occur? Where did that pivot happen for you? It's foreign for me and Kyle because both of us studied mathematics and then went into math teaching. So it's foreign to me to hear about a music teacher who's like, "You know what? Math teaching is my calling."
Jeremy Sarzana: Yeah. I mean, so basically I graduated college. I never wanted to be, or I never thought I would be a teacher. It wasn't like, "I want to be a teacher." I was just literally like, went to Berklee and I was playing in a bunch of bands. So I was having a lot of fun playing gigs at night and everything. And then I was like, "Fine." I was like, "I guess I'll get a day job." It was like-
Jon Orr: This sounds like... Wait, Kyle. I think they made a movie about this. It was called School of Rock.
Kyle Pearce: Yeah. I love it.
Jeremy Sarzana: Yeah, exactly. And it's funny-
Jon Orr: You were a supply teacher filling in for some other supply teacher?
Jeremy Sarzana: Well, literally though, I graduated... I got a bachelor's degree. I had a friend that was substitute teaching in Boston Public Schools. So he was like, "Why don't you look into that?" And yeah, I did it and I liked it right away, like working with the kids. Yeah.
Kyle Pearce: Fantastic. So I'm wondering too, so I think there's a huge advantage to those that bump into teaching maybe later because they fall in love with working with the kids, which is something that I think I was missing initially out of the gate. I know I was one of those teachers that I was like, "I like math." And it was like, "I'm going to teach math," but it was more about the math and then it was like I learned to love teaching the kids. And it's almost like you kind of maybe got a little bit of the opposite where it was like, "Hey, I like working with kids and it seems like maybe math kind of settled in."
But I want to go back to your experience here a little bit in the math classroom, I'm wondering. So you went into music, you studied music, post-secondary. I'm wondering how about you as a math student? What math moment comes to mind when you think about your experience? Was it a positive experience for you? Was it a negative experience? Did it just even... Some people are just like, "I don't really remember much at all." It just isn't something they think of. When we say math moment to you, what pops into your mind from your own personal experience?
Jeremy Sarzana: Yeah. So I think I was a pretty good math student. I was very good at the procedures, the algorithms. So I could do all the algorithms. I could do the long division. But the problem is I had no... Looking back, I had no number sense. Kyle, I know you mentioned that if you had given me as a kid 1,000 minus 997, I would've stacked them up and did all the crossing out then got three. But I wasn't able to think about the relationship between the numbers. And a number line, maybe just three away.
Kyle Pearce: Right. Just such a common thing that I think... And as a musician too, a lot of people always say like, "Oh, math and music are really tightly interwoven." But I also had this experience as a guitar player, bass player where I was more of a memorizer. I don't want to say that was the reason that I couldn't do something bigger with music, but I now realized I was like, "Oh, just the sense, like the musical sense itself wasn't kind of there." I would memorize how to play the song versus feeling the song. Like the same idea in math.
So I was kind of like that. Was that the same or different for you as a musician? Did you memorize more so or did you feel like it was more of like a mix of both? Or what was that like?
Jeremy Sarzana: Yeah. I would literally memorize the song. So every song was just like a new thing. When I went to Berklee, I was starting to make those connections being like, "This is just this core progression." But before it was just like, everything was completely new every time. So I just had to memorize the song.
Jon Orr: Right. Yeah. I can see that translating into math because when you were speaking about that, I think we're all on the same page that way. We all, I think were memorizers and kind of regurgitators and the fluency for us wasn't really there until later. It wasn't developed at that time, because it wasn't developed for us back then. I didn't feel like we'd put an emphasis on fluency as not a memorizing, but a way that we confidence in moving with numbers or moving with expressions or having that like I have fluency. When I speak fluently or I play music fluently and interpret songs or I listen to a song and play it, I know that I tried to learn in the guitar and I could never do that.
I was like, "You guys, I tried to memorize the progression and then just try to repeat that." But that fluency wasn't there for us I think. And I think that's an important thing. So I'm wondering, Jeremy, how does that moment of your memory of being that memorizer? How does that influence your teaching today?
Jeremy Sarzana: I mean, when I first started off, I was very just teaching my procedures. That's all I knew and I didn't have that conceptual understanding. But I mean, one thing I do want to say is that in eighth grade I was taught how to use the area model like when you're multiplying polynomials. But I didn't realize that it was like an area model. I was just basically-
Jon Orr: Box method.
Jeremy Sarzana: Yeah. But that method was able to help me factor just in my head or at least there was that.
Kyle Pearce: Yeah. I definitely can relate as well. And I looked at them again as all strategies and all these methods to me were all very isolated events. So going back to your chord progression idea where it was like, "Oh, this song, you do this and this song you do that." Like not being able to see that like, "Oh, actually, this song is very similar to that song and the chords progressed this way versus that way." Same idea. I used to use these methods for factoring having no idea that what I was doing was essentially the same thing that I could have been doing for whole numbers or making some of these connections that now seem so obvious or so intuitive to me.
So I want to start digging into this conversation. You are on a math mentoring moment episode. So I think it's only natural for us to flip it back to you and get a sense of what's on your mind lately in the math classroom. There's always something that we're thinking about, but what's on your mind right now. What's that pebble that's kicking around in your shoe that we might be able to shake out together here tonight and try to help find some next steps for.
Jeremy Sarzana: Yeah. So in my classroom I've been doing just having the students do one problem and go deep into it. When we're in the working groups, so when they're in that stage, that's when the best learning is going on, like the group work. There's a student discourse. They're using different strategies and I'm walking around just to make sure that everybody is... Some people might need a little nudge or some people that just might need a little help to get going or like, "I want to make sure they understand the task."
So that's great, but then as soon as we come back together as a whole class, like you guys said, it's like, sometimes it's like crickets, right? It's crickets. And also somebody is speaking, it's kind of like the sense-making goes out the window.
Jon Orr: Gotcha. And you're trying to like, "Hey, how do I make that better? How do I keep the engagement going during that portion?" Is that the real issue that's happening there?
Jeremy Sarzana: Yeah. Because it's like, it was just great learning going on. And then we're trying to wrap it up and then people start going on their phones.
Kyle Pearce: It's like, "Oh, now he wants to say something." And all of a sudden, now everybody stops doing the thinking.
Jon Orr: Gotcha. Jeremy, let's go back just one step here. Could you think back to a recent lesson, maybe one that you did and just walk us through? Feel free to tell us the topic, feel free to tell us maybe even what the prompt was that you're working on. Just give us a picture.
Jeremy Sarzana: Yeah. So we were working on transformations and multiple transformations. So it was just a very simple task. There was a content, but I don't think I'm in context, but I don't even think you really needed the context. It was just a triangle that was going to be reflected over the Y axis and then translated two units up in three to the left. And then the main idea we're talking about like I guess things being congruent.
So the main idea of that lesson was like is the pre-image congruent to the image, the final image. When I set up that lesson, I was basically having them draw each transformation. So I was trying to make that concrete. They were drawing. So about the end of the lesson and they were able to notice that it's just the same shape that's just reflected and translated up.
Kyle Pearce: So I'm wondering and I'm getting a good visual, so I really appreciate that. So getting a sense and it is a geometry class as well. So on some recent episodes, we've discussed this idea that sometimes things can be when they get abstract. Sometimes context becomes maybe a little bit more difficult to create or emerge in a situation. So I'm envisioning students working on this and I had a vision of you as you mentioned going around and it was like almost... You're kind of like listening in, monitoring and you had mentioned like maybe nudging this student. So it might be like asking the students something specific about what they did or you saw them do something and you might ask them like, "Hey, why'd you do that?" Or this student over here looks like they're not really moving yet, and maybe it's like asking them in another way.
Right, like rephrasing the prompt or, "Hey, what do you think might be a good first step." So I'm pitching all of that. I'm wondering what does it look like or sound like when you make that transition?" So I'm going to guess here that you've looked around the room, you see that some people have either... They're either in the process of doing some of these transformations. So maybe there's a student who's like halfway there like he did maybe the first two.
So he shifted it this way and he did whatever the first two translations were. And then these groups are done. What does it look like when now you want to bring them together? Because this is kind of like... We call it one of the most important parts of the lesson where it's kind of like trying to... And it's the hardest part of the lesson too. I would argue. Right? It makes sense that you're kind of like, "I'm not sure where do I go next with that?" What does that look like or sound like when that is happening and then I guess when it goes to crickets? Is it sort of like, "Hey everybody, it's time to share out"? Or what does that sort of look like and sound like as we start to shift towards that part of the lesson where we bring it all together?
Jeremy Sarzana: Yeah. So we do have just like a timer in the room. When I launch a lesson, I'm going to be like, "Okay, we have 15 minutes and go." And then when that timer goes off, I know where everybody is. So sometimes I'll be like, "Okay, we're going to do another five minutes," and I'll set the timer again. But then once I feel it's time to wrap it up basically wait for that timer to go off. And then I just start talking to the class. I'm like, "Okay, guys. Why don't you focus your attention up here?"
And then sometimes we have the students bring their whiteboards up to the board. So then sometimes I just try and talk about the main idea that we were trying to get across.
Jon Orr: Right. Okay. So that paints us a picture and I think I get the timer because I don't actually set a timer visually for the kids. I monitor the time on my end and go, "Okay, look." Because we've talked about that in the past too, on past episodes where sometimes teachers think, "Okay, well, I'm going to do this problem-based lesson. I'm going to get the kids thinking." And then we ran out of time or it went too far and it's like, "I didn't get to talk about the big idea before we left." And I get that why you might want to put a timer is because we want to make sure that we're going to, say, wrap this up and make sure we got some consolidating happen before they walk out the door.
Especially at a high school environment, I think that makes a lot sense. I'm wondering in that same lesson, could you paint us the picture of what that, "Hey, we wrapped up, now, we're here," what that looks like for you? What does that consolidate look like for you? When you said let's talk about the big idea, can you maybe describe how you've done that in the past?
Jeremy Sarzana: Yeah. Basically, it hasn't really gone too well. I'll just say that.
Jon Orr: No worries.
That's why we're here. We're going to make it better.
Jeremy Sarzana: But I envision like I did just finish the building thinking classrooms book and what I envision is that just everything that he talks about that you launch the lesson when everybody huddled around you and then they go to their whiteboards. And then when it's time for the consolidation piece, you do that gallery walk. As you guys say that, you're thinking about which pieces of the student work you want to look at. So I mean, that's what I envision, but I'm definitely not there yet.
Kyle Pearce: Yeah. And trust me, I'm having visions of my own many years of like not really... To be honest I didn't know-
Jon Orr: And not feeling comfortable in that piece. Right?
Kyle Pearce: Yeah. And I almost feel like I-
Jon Orr: When you're starting that, it feels uncomfortable.
Kyle Pearce: I ended up essentially skipping that for a long time just because I just wasn't sure what to do. So I mean, trust me, we're with you there. We totally get that feeling of like, "Okay, things are going on." And I guess what I'm realizing now as we're going around and as we're asking these question and as we're nudging students, it's like at the same time, and I guess before the lesson as well thinking about what is the big idea that we're hoping to kind of reveal. When we talk a lot about the curiosity path and the curiosity path is a way to engage students.
So to get students to come with us on this journey, because at some point we want to reveal some mathematical truth, right? So it's almost like in my mind before the lesson begins and when we craft this prompt or it might not be a prompt I've created, maybe I found it or the textbook had a great prompt there. And it's like, when I bring that prompt here, it's almost like what is it that I'm hoping that I can share to the group or that I can ask specific enough questions where I can emerge it through the questioning to the group.
So it's kind of like in my mind, you're going around the room and you're seeing all the student work and you're seeing where students are like where maybe some of the hiccups are, but then you're also seeing some of the successes. And maybe the groups that have had a lot of success I'm in my mind going like, "Okay, I'm probably not going to give them the floor too early in this process because I don't want them to sort of come in and sort of rob the thinking of the whole group." But what I might want to do is it's like I want to ask a question to the entire group and I want them to turn and talk.
So this is where maybe the crickets might go away a little bit where I think about like, "Okay, I saw the entire group was able to do the first two transformations or the first two translations." And I'm like, "Okay, I want them to turn and talk and I want you to explain how," blank. And then, again, that sort of like keeps that fuel going where it's like, "Okay, there's still a little bit of talking." And then you get to listen in still and then you go, "Wait a second, wait a second. Hey, Samantha, can you share what you were all talking about in your group?"
You're almost tricking them into... They don't feel like they're sharing out to the group. They're turning and talking to their individual groups but then you sort of, you don't ask them. Now you're saying, "Hey, I just heard something really cool over here. Do you mind sharing that out to the group?" And it's like you're using them as a means to scaffold towards this bigger idea. And it might be maybe where some of the groups sort of fell off. And then that's where the other two groups that maybe had a couple steps ahead where you can maybe have them and say like, "Well, I noticed that you did this or you were able to get from here to here. I'm wondering, what did that look like when you were discussing this in the group? How did you know to do this or to do that?"
So it builds on what you were already doing in the group, but it's in order to, again, get you closer to that big idea, that mathematical behavior that you're hoping to emerge. For example, you had mentioned congruence was a big idea here and it's almost like you could have this great prompt around, "What do you think?" So depending on what translations you gave, you could pause and say, "At what point did you know that the image was going to be congruent or wasn't congruent or whatever. Thinking about these prompts about, at what point, what told you..." And some kids might be like, "Well, I knew right from the start because I was going to be scaling this point by whatever value." But I wasn't scaling this point or whatever that might have been.
So I'm going to pause there. I just want to get your thoughts there, because I've got this vision of your class and I'm picturing you at this place where it's almost like, rather than it being like a hard stop, which maybe even trying to keep the timer to yourself or something where now it's like you just start reframing the questions. I'm wondering what your thoughts are on that. Does that make sense or is there something happening else that we're not aware of that maybe might hinder that idea? But what are your thoughts there?
Jeremy Sarzana: Yeah, I think that's perfect. It's just kind of like instead of that hard stop, as you'd say, it's just kind of like almost they don't even know that we're transitioning. Just basically like, okay, I would say something and then give them a prompt and then have them turn and talk. Just keep that going.
Kyle Pearce: I love it. And something I love being able to do as well is like at some point when sometimes some days it might happen early, some days it might happen later, but it's always nice to eventually have something for you to add that raises or elevates the conversation. I think sometimes we worry that it's like, "Well, it's not supposed to be teacher centered." Right? Well, your whole lesson wasn't teacher centered. You did such a great job making it student centered. And it's like at the end, it's almost like, "I want to on what they said, what they said, what they said." Do you notice what's happening here? And that might be the part where you kind of emerge this generalization where you go, "Wow, based on what you just said it sounds like what you are saying is..." And then you get to kind of reiterate that.
That might be the point in which where everybody goes, "Hey everybody, that note to your future forgetful self that Peter talks about, that might be that point where you go, 'Wow, that's something, I think we got to get this down because I don't think I'm going to remember that couple weeks from now.'" Like what you just said. Can you say that again? And then you can reiterate it with them and sort of get the whole group where they feel like they're truly contributing some of these main ideas while you're there, you're still the mastermind sort of like molding what that looks like or shaping what that conversation looks like because you knew that we were going to talk about congruence and about why this series provided that these steps made it congruent at the end or they didn't.
And then maybe having, again, another prompt ready as well. We call them consolidation prompts. So it's like, "What about if this one was congruent, in your groups, I want you to take some time and talk to your neighbors and I want you to create a series... Start with a free image, and I want you to create a series of transformations that are going to produce something that's not congruent." How could you guarantee it's not going to be congruent? And I want you to write about that. Right?
So it's kind of like that shifting towards instead of it being like about getting the right answer to the problem, you were like, the whole point of this was for us to come up with this generalization, this behavior of mathematics that now you're like, "Oh." Again, it's like that chord progression. Right? You're like, "I now know the chord progression. I don't just know the song. I know something deeper than that."
Jeremy Sarzana: Yeah. And I like how you like kind of asking specific questions like you said, when did you notice that it was going to be congruent and as opposed to just being like, are these congruent?
Jon Orr: Yeah. And another thing is that since you're setting off at the beginning of this task to know what big idea you're trying to emerge and also at the same time, you're trying to think... And I know that we have it in our minds. Sometimes you have people write them down. Sometimes I don't, or some people don't. But in my mind I definitely like, "Okay, when I know my students have captured the big idea, what does that look like?" Right.
I will know this group of students or this student has the big idea or the skill. Maybe it's the skill based lesson. Right? And that's what this will look like. So sometimes it's going to depend on your lesson, what that consolidation might look like. So for example, I've had lessons where I was doing a thin slicing type activity with like, out of Peter's book or like a problem string, and I wanted students to solve equations and the equations were... Create it very carefully to lead into the next. And by the end, you're solving more con complex equations.
By the time you get there and you're seeing students and working with students, it's almost like I know this group has got the big idea. They are solving two-step equations fluently, consistently. And now it's like, I don't need really to consolidate as a whole group now if I'm moving from group to group going, "I know that group's good. I know that group's good. Oh, they're finished that part." All right. Here's your next step to keep going on these ideas while I'm over here with this group trying to consolidate with them if they need it."
So there's that type of lesson where you're kind of like... Sometimes it's not a whole group thing. It can be just making sure everybody gets to where they need to go in the time that you have. So I've definitely done that whereas I don't think I need a full group here because we all got there and that's sometimes that fluency on the fly, like fluency for us in this way we're doing this. I sometimes plan, I'm going to have that big consolidation if all of a sudden, a lot of groups don't get it. And that big consolidation might be, "Okay, we're going to come back to the board. The timer went."
We're going to come back to the board and maybe I'll have a small little math talk and I'll say, "Okay..." Like what Kyle suggested. It's like, "Oh, you guys were doing... Can you guys tell me or share that strategy?" And then you're mimicking on the board for everyone to see. And there's that kind of whole group consolidation. "Hey, that strategy worked here. Does it work over here now? Hey, let's try another one. Everybody, grab your marker, grab your pencil. Let's try it this way on your page right now or my desks or dry-erase desk. So we write right on the desk, which is really nice.
So it's like, that can work that way. And by the end of maybe just these prompts that was now all of a sudden the whole group, because you needed to bring the group back together. Then giving them small prompts too instead of asking questions for like, "Hey, can you tell me? Raise my hand. Here, raise my hand. Oh, I know. Oh, it's me again. I know it's me again." Right?
Instead of that, being more active then saying like, "Okay, we just saw that strategy. Now everyone try this one." And then you walk around a little bit more. So you could even send them back to the wall space at that point. So I've definitely had lots of different experiences where the consolidation can happen at the board with a small group. It can happen in the big group and we go back to the board or it can happen individually as well.
So I think it depends on you knowing or remembering what is the learning goal I want. What does that look like when I know it's a success? And then making sure that I take lots of different ways that I can move lots of different ways to make that happen for my students.
Kyle Pearce: And there was something that kind of popped into my mind as you were talking there, Jon. I'm glad you mentioned that too, because that is so true that sometimes like the mini-consolidation, especially in a case just like Jeremy is finding himself and sometimes where it feels like crickets. It's like those students might be hearing you better. You might do the same mini-consolidation in four different groups as you're walking around the room. Right? Where it's sort of like it's hard on you because you're like, "I feel like I just said this three times." But they're looking at you, and we all know that the smaller the group, the more people feel like you're actually communicating with them and they become less anonymous. Right?
Peter talks about that in his book, this idea of the anonymity of sitting in a desk, in a chair. It's like, when you have that small group and you can look, there's three kids and you can keep looking them each in the eye, it's like, "I'm talking to you. All of you." And that conversation might be more fruitful that way. Something I'm going to throw out there too, just as you get these lessons going, it sounds like you've got a great thing going with the thinking classroom idea like getting kids actually thinking, working in groups, maybe standing up at the boards, all of those things.
And it's almost like always thinking before the lesson about like, "Why does this lesson matter?" When you just ask yourself that and sort of go like, "If I don't teach this lesson, what are kids not getting?" And I think it's really easy for us to look at the lessons more from the skill based side of things, especially as we get in the older grades where it's like a lot of things feel skill based, but it's like, there's always something there, I think that we can like latch on to.
So whether you choose to do it in the mini-consolidation groups or whether you decide to do it as a larger group, it's so like to highlight something, it might be the model like the mathematical model that was helpful. It might be a strategy like a strategy you see emerging or that didn't emerge that you want to make sure they now see and have and encourage them to try it. Or it might be a behavior of the math like a mathematical truth that like, "Wow, when this happens, when I do this, I can expect that to happen." And it's sort of like, those are kind of the things that beforehand helps you with setting up your prompts, but then also bringing it out at the end versus if I go in and I kind of just only see it as a skill-based lesson. And I don't think about these other pieces that are underneath the surface.
It can feel more like, again, it was like a problem to get done versus we did this set of learning. It was less about the answer you got and more about the realization we just had where we're like, "Oh, that is what's going on here. That's that, to me, the end of the curiosity path is when they go, "Oh, something here just happened." And that's like the fun part for you as the educator is try to tease that out. And sometimes kids land on it and that's awesome that you feel like a superstar when that happens. You're like, "I didn't even have to say anything."
But then there's lots of times where it doesn't, where it goes right over their head and they get an answer. But it's like, they missed this pattern that is right before their eyes. So we're going to pause here. And what's going on through your head right now? There was a lot said, a lot shared here, but we want to make sure that like, how are you feeling right now when you think about this and think ahead to maybe some of your lessons, how this might influence maybe some of your planning and delivery of your lesson?
Jeremy Sarzana: Yeah. I really like what you said how like kind of thinking not as a get done thing, but more of like a bigger idea or maybe finding like a mathematical truth or something like that. I guess in this particular lesson we were talking about congruence, but I think that the task, it was just kind of like at the end they were like, "Oh yeah, they're congruent." But it's just like, I think could have gotten more out of that lesson.
Jon Orr: So you're wrapping your mind around thinking about the big ideas here and I'm wondering here, Jeremy, if you think about some of the suggestions we've had, I'm going to push you to be a little bit specific here and thinking of like, "You went back to the class. What is a change? What is something that you're going to like put into place from this conversation to help with that consolidation piece starting, say, tomorrow?"
Jeremy Sarzana: Yeah. I mean, I may... Well actually, yeah.
Kyle Pearce: Like now.
Jeremy Sarzana: I think, yeah, I'm not going to do that hard stop. I'm going to maybe just give them like have them do like a quick turn and talk. And also I'm going to be thinking in my mind as the students are working, like maybe specific students and specific work like, "Could you share what your strategy?" as opposed to forcing kids to share their ideas there.
Jon Orr: I've done that one a lot. And I think kind of an add-on to what I've done is if we do pull them back to a whole group because you want to highlight, you want to make it very clear. It's like, "This is a strategy that can work well." But having a kid explain it to you and maybe you want to emerge a model or maybe you want to get one of these big ideas is one that I've used a lot is when the kid is explaining it to the group. It's like, "Could you just talk to that strategy?" I model it on the board in live time.
What I find is beneficial there is because if we go over to that board, that work is already done, right? It's already shown in full solution, format and everyone else is seeing it that way. You're explaining it, but it's still a full solution.
Kyle Pearce: It could be like overwhelming. Right?
Jon Orr: Yeah.
Kyle Pearce: Like to see it done.
Jon Orr: So we might do that, but then when we come back, and I have a blank board in front of me and they ask them, "Hey, can you just walk me through?" We are solving proportions today. So it was like, "Okay, you know what?" It was a unit rate problem to start. And I wanted to show the model of a double number line and show this... I wanted to... One of my big goals with my students solving proportions is I want them to be very fluent in moving along the number line with a multiplication type strategy. Some kids are doing additive strategies still. And I'm like, "Let's move along the number line here in this way. Let's make sure that we can see the relationships along that number line."
So when the student was explaining this strategy, they had found a unit rate to help solve this problem. And so I said, "Okay, let me model your thinking here up on the board." So then now the whole class can see that solution unfold using a diagram that I was trying to emphasize as well. So it's kind of like they see it in live time instead of post solution time when you're kind of outlining it that way too.
Kyle Pearce: I kind of picture it and I'm making a lot of these like musical artistic references, but it's like, I picture, especially, with your background there, Jeremy, it's like, this is your opportunity throughout the lesson to really be an artist, right? Where it's like you might have had in your mind planned it a certain way. So you should have a plan coming in, but it's okay if that plan doesn't happen that way. Right? So it's like, "You get to pivot. We always talk about pivoting the plan because of what's happening in the classroom."
But what we don't want to do is come into the lesson and just hope that it'll all kind of come together the way it should, quote-unquote. But what does should even mean if I don't know ahead of time of like... So you have almost like your plan and you're like, "Okay, I'm thinking kids are going to merge this idea, this idea, and I'm going to highlight this idea. But then as the lesson happens, it's sort of like, you get the freedom to kind of... As Jon mentions you get to go to that group and say like, "Hey, can you share?" And we always advocate too, for asking kids to share something specific about what they did instead of it being... Because you had also mentioned we used to like... It's like a show and tell when you kind of go around like, "Hey, group one, share what you did."
And it's like, they could potentially talk for 10 minutes. Right? It's almost like, I think that also inspires the crickets because a lot of kids are like, "I don't even know where to start. We did a lot of stuff." So then they start from the beginning and it's like you hear a lot of the same things being repeated over and over. "Like that group, like group one and two, like group one, two, and three, we did this." So it's almost like you were like, "I saw right here." And you could literally point to it and be like, "Right here, tell me what was happening here."
And then as Jon mentioned that might be where you're modeling over here, and this is that artistry piece where you're going, "I like a bit of that and I like a bit of this." And when I bring these two things together, it's going to help me get to this place where I can show that behavior or whatever it might be. So lots and lots going on here. I hope you're as excited as we are about it, but I'm excited for you because I feel like you've got some things to chew on, probably too much to chew on.
So don't try to make it all happen exactly in one way. But just by thinking and reflecting on some of these pieces, I feel like you'll be in a good position to at least keep that conversation going in your classroom and get the kids turning and talking. So I heard some big takeaways from you already. I think that's great. I think by maybe hiding the timer a little bit and playing with that transition a little bit, I think you're going to find something that works really well for you and your students.
So I'm wondering here, before we sign off, what would you say is your biggest takeaway from the conversation and what are you most excited about your next lesson when you try to apply some of these ideas?
Jeremy Sarzana: I think my big takeaway is asking a student a specific thing to share, and I think that's going to just help me so much in the class. So I'm really excited about that.
Jon Orr: Awesome stuff. That's great to hear. And actually, Jeremy, we'd love to check in with you say next year. I know it sounds like far away, but maybe in 12 months reconvene back here and see how you've progressed using these takeaways. And then also probably, obviously, you're going to learn so much more in the next year as we always do from year to year. So what do you say to that? Are you up for checking in next year on this?
Jeremy Sarzana: Absolutely, yes. I'd be very happy to. Yeah.
Kyle Pearce: Awesome. And of course we will be in touch. I know that you've been doing some awesome work inside the academy and doing all kinds of learning in there and doing some sharing in the forum, which is awesome to see. So we will, of course, still be in touch and sort of alongside you on that learning journey. But just for those who are listening to the podcast, be great to get you back and sort of... I got a funny feeling there will always be another pebble, right?
So we can always talk about where you've come, how things have changed and then what else is sort of kicking around in those use. But I got to say it's been a pleasure. I met somebody who went to Berklee now, like virtually. This is super cool. I love it. Hope you have an awesome, awesome... We're heading into our spring break shortly. I'm sure you are soon too and we will definitely be in touch and we'll see you around in the academy.
Jeremy Sarzana: Right. I'm looking forward to it. Thank you. Okay.
Kyle Pearce: All right.
Jon Orr: Awesome stuff.
Kyle Pearce: See you soon.
Jon Orr: Awesome stuff.
Kyle Pearce: Well, math moment makers, as we mentioned in the intro, I hope you found that this episode has been helpful. It was great to bring on a math moment maker who's doing some pretty awesome things in the classrooms, getting his kids talking, selecting and sequencing student work as they're going, and helping to nudge some students and help to kickstart some thinking over in different groups, doing all kinds of great things. But just like so many of us, that consolidation is a doozy. It is, I would say one of the most challenging, but most important parts of our math lesson.
And the reality is it can look a few different ways as we discussed here. So hopefully you found that there was something of use there that you can grab something to bring into your own classroom. We'd love to hear from you. So make sure that you're reflecting on what you're doing and maybe go ahead and share some of those reflection with us by commenting on the blog post that goes along with this episode or under the YouTube video or on social media at Make Math Moments where we like to engage with all kinds of math moment makers just like you.
Jon Orr: Yeah. That's a great recommendation there, Kyle. And if you are also looking to chat with us about a pebble in your shoe, just like Jeremy did here, then don't forget that you can fill out a form and apply over at makemathmoments.com/mentor. The form is really a chance for you to just share what is that struggle that you're working with, that you want some feedback on. And then that just comes to us. And then we see if that fits. We don't pick one that comes in, but just because we want to keep a variety going. But hey, throw that in there. You never know. We'd love to chat with you about your pebble. So again, you head on over to makemathmoments.com/mentor, fill out that form and we'll chat soon.
Kyle Pearce: Awesome stuff. And friends show notes, links to resources, and complete transcripts to read from the web or download and take with you can be found at makemathmoments.com/episode177. That's makemathmoments.com/episode177. And of course, if you're watching this, be sure to hit that subscribe, hit that notification bell on YouTube and we will be in touch with our weekly YouTube videos.
Jon Orr: All right, folks, as we normally wrap up our episode with Kyle and I doing our high fives for us and high fives for you, Jeremy here from this episode wanted in on the action. So awesome stuff, Jeremy. You're going to take my place in that. So Kyle hit it. Kick us off.
Kyle Pearce: Here we go. Well, until next time, math moment maker friends, I'm Kyle Pearce.
Jeremy Sarzana: And I'm Jeremy.
Kyle Pearce: High fives for us.
Jeremy Sarzana: And high five for you.
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