Episode #254: When Students Are Missing Valuable Background Knowledge – A Math Mentoring Moment
On this episode we speak with Jason Garner, a veteran 5th grade teacher of 15 years. Jason joined us on episode 127 and we’ve brought him back to provide an update on his journey.
After spending the last two years being more intentional in his problem based lessons Jason seeks guidance on how to help students stick with problems a little longer when they lack the prerequisite skills needed to succeed. Join us to discover Jason’s big a-ha moments and hear the answer to this common math classroom issue.
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.
What You’ll Learn:
- How we can teach problem based lessons when students don’t have the mathematical background to engage in productive struggle;
- Why planning and posing purposeful questions is essential to ensure that the struggle remains productive during the problem solving process;
- How we can give ourselves permission to teach when using problem based lessons;
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00:00:00:08 – 00:00:17:16
There’s those kids that they’re a little more comfortable with math just in general for whatever reason. And they have some of that maybe more number sense and things like that and not afraid to come up with interesting ideas. But then they’re working with somebody else who’s like, have no idea what’s going on. So they do all the work.
00:00:17:16 – 00:00:22:19
So I think what to do when strategies or thinking is not emerge.
00:00:22:20 – 00:00:44:11
In this episode, we speak with Jason Gardner, a veteran fifth grade teacher of 15 years, and Jason joined us a while back almost two years ago on episode 1.27, and we’re bringing him back for a math mentoring moment. Update to figure out where he is on his journey and see if we can rattle around a few pebbles and kick him out of those shoes.
00:00:44:13 – 00:01:09:02
Amazing. Here we are over 100 episodes. Later on episode 254 and Jason spent about two years being more intentional. And let’s say it another way, because the reality is he’s likely been an intentional teacher his entire career. However, he’s spent a lot of time two years ago in our online workshop and he’s been really honing in on problem base lessons.
00:01:09:04 – 00:01:34:04
And today, Jason shares that update, but then also asks for some guidance or some suggestions on how we might be able to help students stick with problems a little longer when they lack the prerequisite skills needed to succeed. Join us to discover Jason’s big AHA moments and hear the answer to this common mathematical classroom issue.
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This is another math mentoring Moment episode where we chat with a teacher just like you, a math moment maker who is working through some problems of practice, and together we brainstorm ways to overcome them.
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All right, friends, let’s hit it.
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Welcome to the Making Math Moments That Matter podcast. I’m Kyle Pearce.
00:02:06:15 – 00:02:09:00
And I’m Jon Orr, we are from makemathmoments.com.
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This is the only podcast that coaches you through a six step plan to grow your math program whether at the classroom level or at the district level.
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And we do that by helping you cultivate foster your mathematics program like a strong, healthy and balanced tree.
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If you master the six parts of an effective mathematics program, the impact of your math program will grow and reach far and wide.
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Every week you’re going to get the insights you need to stop feeling overwhelmed, gain back your confidence, and get back to enjoying the planning facilitating of your mathematics program for the students. Or if you’re a district leader, the educators user.
00:02:45:18 – 00:02:50:05
All right, friends, let’s dig in here and get an update from Jason.
00:02:50:07 – 00:03:11:22
Hey there, Jason. Welcome back to the Making Math Moments That Matter podcast. It’s been a minute. It’s been a while. We had you back on episode, I believe, 127. By the time this airs, it’s going to be over 100 episodes later. So that’s a couple years worth of episodes. So folks, if you haven’t listened to Jason’s first episode, episode 127, we encourage you to go back.
00:03:11:22 – 00:03:28:03
Listen to that, because we’re going to chat about where you been, Jason, and what’s been going on with you. And we’ll dig into a little bit of Pebble, what’s going on with your shoes right now, But give us a little snapshot. Remind everybody where you’re coming from, what your teaching might have changed since the last time we chatted and how you been?
00:03:28:05 – 00:03:36:11
Sure. Yeah, well, yeah, it’s been a couple of years. I’m still teaching fifth grade here in Illinois, north central Illinois, Ottawa, Illinois.
00:03:36:13 – 00:03:37:22
00:03:37:24 – 00:03:58:11
Yeah. It’s my 16th year. I teach fifth grade. I’ve taught fourth and fifth. Kind of my sweet spot, I think. And yeah, I mean, over the last several years, I’ve really been trying to work on I teach everything for sub, so that’s tricky in itself, but I’ve been really working on over the last several years, changing the way I teach math and the way my students learn math.
00:03:58:11 – 00:04:10:03
And a few years ago I participated in the workshop that you guys have kind of got hooked on that I’ve been really trying to dive deeper in and some of the strategies and things. So yeah, that’s where we’re starting school next week. So.
00:04:10:03 – 00:04:10:23
Right, it’s coming.
00:04:11:00 – 00:04:41:22
Be coming up. Yeah, that’s exciting. Exciting times. So it has been a little while since you’ve not only been on the podcast, but also since you are a part of our online workshop, one of our online programs that we offer through our online platform. And I’m wondering what would you say based on the learning that you had back then and where you are now, What do you think has had the greatest maybe impact on your teaching practice from some of the learning that you did in that workshop?
00:04:41:24 – 00:05:03:14
Yeah. So one of the best things I think that came from it is just the curiosity tasks kind of starting with those units. That’s something I’ve really been doing the last couple of years, especially that we’ve been here at school in person, been a lot easier to to try new things. So I’ve really become a lot comfortable with that and even kind of created some my own.
00:05:03:14 – 00:05:21:05
And I’ve seen a lot more engagement with the kids doing those tasks in particular. I even had some kids say last couple of years at the end of the year. When you ask of what they enjoyed about fifth grade and a lot of them will say I noticed the wonders they had, they enjoyed doing those because it was more fun than it would be.
00:05:21:07 – 00:05:43:21
So that’s been something that even kind of created some of my own. You know, some of the best ones have been simple ones. I took basic word problem about writing expressions and just put three clip art images, a shirt, a hoodie and a pair of shoes and Adam do a notice and wonder. And then it turned into a little more just revealing about the problem.
00:05:43:21 – 00:06:05:18
And then they they solved it in groups. And then I challenged them to write an expression to represent how they solved it. That’s what the goal, the lesson was. And that one just little way we started it allowed it to be more engaging and interesting for the kids and challenging because it wasn’t just, Here’s what an expression is now we’re going to write a bunch of them.
00:06:05:22 – 00:06:11:24
They had to really think through it and apply that. So I feel like I’ve come a long way with with with that in particular.
00:06:11:24 – 00:06:35:02
Yeah, that’s great to hear. And I think like a lot of educators who have come out of the workshop said those same things, that they’ve felt engagement change heavily in their classroom experience from the learning that they did other than, let’s say, kids saying they’re having fun and you’ve got that engagement in thinking happen in your class. What else would you say is in a huge shift or benefit from the students?
00:06:35:02 – 00:06:38:10
What are you seeing as a change in students over the course last couple of years?
00:06:38:12 – 00:06:54:12
Yeah. And I was also going to mention I’ve been trying to get them up at the whiteboards and things more often too, so I actually purchased some of those. I don’t know if you still promote them, but the white books versus a few of those last year, check it out. And so we have some limited white board space in here in my room.
00:06:54:12 – 00:07:21:24
And so they’ve been up kind of working on those more. And that has kind of shifted things a little bit too. But yeah, when they’re working in those tasks, they just see a lot more thinking on their part compared to just waiting for, Hey, he’s going to show us how to do everything. And I know the last time we chatted, the biggest takeaway was the choosing task with more intention, and that’s something I’ve really worked on a lot as well and think I’ve done a better job with.
00:07:22:01 – 00:07:44:14
So instead of just, Hey, there’s this one task I have that I found, it’s going to be fun, it’s going to be engaging. I’m really focused more on choosing ones that there’s a purpose to it and the kids are. If I want to try to see something come out of this, what is it? And and so I’ve seen a lot more of that with them and challenge them to do more of that thinking and having that intention with the task.
00:07:44:16 – 00:08:03:09
Yeah. On the intentionality How do you feel like that focus and thinking about every lesson you’re thinking, okay, we’re going to do a curious task we’re in do a task where students are going up the walls thinking and doing mathematics. How would you say has that focus been for you too, on, let’s say, your unit plan or your course plan?
00:08:03:09 – 00:08:21:23
How does that help? Is it streamline things or is it allowed you to speed things up or capture making sure that we get to the curriculum when the only reason I ask is folks get worried about if I go down that pathway, if I start to change my instruction so that students are being more curious and more engaged, will I cover the curriculum?
00:08:21:23 – 00:08:32:19
That’s always a big concern. And what is your experience been, especially now that you’ve been more intentional with the task of the day and what the learning goal is for that particular task?
00:08:32:21 – 00:08:54:12
Yeah, so kind of go back to the one I mentioned before with the expressions. So like I said, I feel like that’s been one of the my most successful ones that I’ve done, and I present that task without giving them a lot up front. And then what happens is from there, when we get to the expressions part, they don’t know what the expression is at that point in fifth grade with me.
00:08:54:14 – 00:09:18:02
So we do a little bit of, Hey, here’s an expression, here’s some examples, and then I challenge them to write it, and then I see some of their struggles kind of come to light and can then tackle that from there. And I think what I’ve tried to do is as far as the curriculum and covering the concepts, I’m kind of of the mindset that there are concepts need to be covered in fifth grade.
00:09:18:03 – 00:09:56:23
I also understand that and this could just be me. It’s just not sometimes going to be possible to cover everything. So I try to look at we have a subscription to Excel and there’s good and not good to it. So I’ve tried to actually take some of the concepts that maybe are I don’t want to sound to that some of the concepts that maybe don’t need a lot of focus with me as a group like Measurement conversion or naming a points and lines and segments, things like that that aren’t necessarily a problem solving, just kind of some of those basic vocabulary or things.
00:09:57:04 – 00:10:16:05
And I’ve tried to put those into during our guided math time that we have. Those are like individual tasks that they accomplish and I can keep track of that, where then I can focus on more of the major concepts that I want to focus on. When we get to division, It’s big thing in fifth grade is dividing larger numbers and multiplication and fractions and things like that.
00:10:16:05 – 00:10:39:21
So I really try to just focus on that and my mindset is always if I can get them thinking and solving problems and learning new strategies and things like that, then we can cover those concepts and dive deeper into some of the more important parts of them, but not spend a whole bunch of time on certain things that maybe aren’t as critical going forward.
00:10:39:21 – 00:11:04:14
And yeah, now I’ve got visual in my mind that when we say that there’s standards or that curriculum that we need to cover or the reality is these are things like we need students to engage with, but the level at which we engage with them can be different. So I really like how you’ve taken sort of an approach where you can still actually provide students with an opportunity to engage with some of these content pieces.
00:11:04:14 – 00:11:25:23
It’s not all equal. We don’t necessarily have to dig in and have a formal lesson about every single piece. We want them to be able to do those types of problems and explore those concepts, but it can be done in different ways. So I really like that in some places, talking about call it the essential standards, right? Or what are the enduring understandings that we want students to walk away with?
00:11:25:23 – 00:11:44:02
And I think that’s something that is hard for educators to kind of think about because you’re scared to miss something, right? I don’t want any of our students to miss out on anything. But oftentimes what that leads to is doing a little bit of everything and maybe not going to the depth that we need to with some of the more important topics.
00:11:44:02 – 00:12:04:08
So I’m wondering, you’ve shared some of your journey here over the last couple of years, the learning you’ve been doing, some of the benefits that you’ve seen from actually engaging in some of this work that you’ve been engaging with. What’s on your mind lately as you look forward to this school year. This episode will be going live when the school year is in full motion.
00:12:04:14 – 00:12:22:10
But right now, as we’re chatting with you, we can see that you’re at school getting yourself ready, getting your game plan together. What’s on your mind now that maybe it’s a pebble that’s kicking around in your shoe that you’re still kind of wanting to work on and hoping to be able to address over this new school year?
00:12:22:14 – 00:12:42:17
Yeah, well, there’s lots of pebbles. There’s always a problem. So I tried to narrow it down. I tried to find the biggest one maybe that’s kicking around in there. So like I said, I feel like I’ve made some good progress with getting the case up and working on solving problems and having more of that responsibility and that intentionality on my part as far as the tasks.
00:12:42:17 – 00:13:04:14
And that the biggest thing every year I always come across is those kids that and sometimes it’s a lot of the kids because of come from not having the background or the strategies that you hope that they have. So that expression staff, for example, works great every time because they start it gives them all a chance to kind of dive right into it.
00:13:04:14 – 00:13:19:10
And then when the expression part, it clicks and makes sense in a way. But when you’re thinking about, okay, in this lesson, maybe there they’re in this task, maybe there may make a number line or maybe they’re going to make a model in that. But the reality is sometimes with my students is they don’t.
00:13:19:14 – 00:13:20:11
They don’t actually do that.
00:13:20:15 – 00:13:39:22
The number line, they’ve never actually had a chance to make a model that ever sometimes you don’t see anything emerge. And I think there’s those kids that they’re a little more comfortable with math just in general for whatever reason. And they have some of that maybe more number sense and things like that and not afraid to come up with interesting ideas.
00:13:39:22 – 00:14:09:08
But then they’re working with somebody else who’s like, I have no idea what’s going on. So they want to do all the work. So I think what to do when strategies or thinking is not emerging and then kind of a thing that ties into that an offshoot pebble from that is then how to keep them engaged, especially during the consolidation time when we come back together and those same kids that maybe were quote lost in the productive struggle are then also lost sometimes during that consolidation.
00:14:09:09 – 00:14:28:20
They’re not maybe paying attention. And then I feel like sometimes they’re not getting even though the intentionality is there. And what I hope that sometimes, even after the lesson, they’re still like, mm, I don’t know what’s going on, and they’re holding back from participating and sharing their ideas and things like that. So I think what to do when strategies don’t emerge and then you feel like the jump in.
00:14:28:20 – 00:14:46:11
And now I was just going to say you did articulate a few pebbles there, but when you say specifically when they’re in the productive struggle stage, so this is like we’ve given the problem, we’ve got them into it, and now they’re kind of trying to grapple with the mathematics or with the problem at hand. Are you saying that you’re not seeing kids?
00:14:46:11 – 00:15:03:02
Maybe your purpose was like, I’m going to use this model in this strategy to go do this, but then no one is showing you that inkling of that strategy, the model, or you’re hoping that they come up with a number line, like you said, or an area model for a particular task. But they’re not doing that. They’re maybe just going straight to algorithms or that kind of thing.
00:15:03:02 – 00:15:23:07
It’s like, that’s one image that I got in my mind. But another image I got in my mind from Your Pebble is that students aren’t sure what to do at all. Right? So it’s like, I have no idea how to engage in this problem. Another one that I got an image from is that students, maybe they’re not engaging because they actually don’t have the skill set coming in to fifth grade.
00:15:23:07 – 00:15:38:20
I thought they would be good with this topic already, and it’s clear they don’t actually have that skill set in terms of preparedness for the content I thought I was going to teach. So all three of those are what you’re experiencing or more one in particular.
00:15:38:22 – 00:16:00:05
So it’s more the last two that you mentioned. Sometimes they come in without the skill set and then also they don’t know what to do it. And it’s not necessarily based on the task. It’s just as you guys know and other teachers that are on your podcast know that what I’m trying to do is a struggle sometimes because they don’t come from that idea that might sometimes.
00:16:00:07 – 00:16:12:14
And so like when you propose a problem to solve. And so it’s not necessarily like I’m looking for something in particular. The first thing you mention is more like some of the kids just don’t know what to do. They don’t have strategies to pull from.
00:16:12:14 – 00:16:40:20
So I’m thinking about, say, some possible next steps here for you. And I’m wondering, you said that this comes up every year and I think every teacher who tries to do these strategies, this comes up every year for them as well. So I’m curious, what have you been doing so far when you encounter, say, this issue? So kids come in and give them a problem and they’re not grappling with it the way I thought because they don’t really have the skill set.
00:16:40:22 – 00:16:52:23
They’re not actually sure even how to get into this. And it’s like last year we didn’t do any of this. So it’s like, Well, what am I supposed to do here? What am I expected to do here? So what have you done to kind of help this pebble already know?
00:16:52:24 – 00:16:56:21
Or maybe hunches what you might be able to focus in on?
00:16:56:23 – 00:17:16:14
So one of the things I do try to do at the beginning of the year is I try my best to set a mindset of this is going to be a little different this year. I try to start with a task at the beginning of the year, a problem that I know they’re all going to kind of be successful with, but it kind of follows the path that we’re going to go down throughout the year.
00:17:16:18 – 00:17:48:06
So something I know they’ve done in fourth grade, I know they’ll have some entry points. And so that does help kind of set that tone, I think. And then when it comes to seeing kids struggling and not really participating and not knowing where to start, sometimes I’ll just like any teacher I think would do, is sometimes kind of go back to the drawing board as far as, okay tomorrow, whether it’s try this task again or maybe pose another problem and go through it again, but with a little bit different kind of approach from my part.
00:17:48:06 – 00:18:09:18
So just typical what a teacher might do is go back and rethink about any barriers that were there for some of the kids. I think in my mind as I’m thinking through this is there’s always those kids who are able to jump in, like I mentioned. So it’s not like a whole class thing. It’s more sometimes it’s a few kids that just maybe a really struggling and they don’t know where to start with anything.
00:18:09:18 – 00:18:31:00
They don’t have ideas of. Sure, they’re to maybe lack the confidence to share their ideas because of that, don’t have as much background or. And then the one thing that we do have, like I said, is guided math. We’re kind of supposed to do that as much as possible. And one, can you say like a hunch that I have is heading in this year is maybe thinking about.
00:18:31:03 – 00:18:55:08
But there’s those students who are really struggling with a task and that is trying to maybe pull them off to the side during that guided math time and not just sitting there and doing, here’s how we’re going to do this, to do this, but maybe in a smaller group, another kind of task that goes with that to kind of relate to what we were doing and here’s what we were trying to do and make those connections to that full class lesson or something like that.
00:18:55:08 – 00:19:03:13
So that’s one of the things I’ve been thinking about doing, is trying to differentiate in that way, even though I haven’t worked it all out. You hope that.
00:19:03:15 – 00:19:20:23
Yeah, well, I think you’re saying a lot of really good things here and I almost want to take what you’ve said and maybe have us think as a group here a little bit more about if, let’s say, and you are obviously going to look at this a little differently, you’ve been in fourth and fifth grade for quite some time.
00:19:20:23 – 00:19:44:12
Be adventurous. Kind of like your wheelhouse, right? Which is great. And that means, you know, some of the patterns throughout that course. Right. And you’re going, hmm, there’s certain areas of that course where I’m going to guess even without even meeting my group yet this year that we’re going to probably have a student or two or maybe a group of students that kind of struggle with this concept.
00:19:44:12 – 00:20:13:20
Right. And I’ve typically done it maybe this way. And I wonder if taking what you just said about your guided math and you were to think about what’s the guided math version of that lesson that you can do in the moment with those students? So what I mean by that is it’s almost like instead of thinking about it as a completely separate experience, I wonder if we were to look at tomorrow’s lesson in our minds and go, okay, I’m anticipating.
00:20:13:20 – 00:20:40:17
So now I’m thinking about where might some students maybe fall off the wagon? Or maybe better stated, where might some students not be able to even get on the wagon? Right. Is it right away or is it later deeper in the lesson? And what would be that question, that wonder? It could be, like you said, it could be giving them a slightly varied or differentiated sort of look at that particular idea.
00:20:40:17 – 00:21:02:11
And really what I’m thinking about here is if I could take my actual task that I want the entire class to do, and then I was to think about it and say, Let’s pretend the entire class got stuck. What would I do next? And it makes me think that I go, It doesn’t matter if one student or 30 students all get stuck.
00:21:02:13 – 00:21:41:06
If I’m thinking ahead like that and going, okay, at this point, I’m anticipating that at least one student might blank. They might not be able to get started. They might not maybe fully understand the context or what’s being asked of them. And if I was to kind of paint that picture in my mind of what that looks like and sounds like that might position you so that when you go into that classroom, when that student does start struggling, that you’re not necessarily ad libbing in the moment, which I remember doing for many, many years, I always felt like it was like an ad lib.
00:21:41:08 – 00:22:19:08
Now it’s almost like, Aha, you did exactly what I thought you were going to do. You hit this bump in the road and I’ve got this little tiny next step question for you, right? Does it mean changing the problem slightly for this student to help bring them back on board? Or does it mean just asking them a certain thing, asking them to draw it in a different way, but thinking about those key little moments might position you so that when those bumps do arise, you sort of have this we’ll call it the magic, the tool in your back pocket to kind of come out and go, you know what?
00:22:19:08 – 00:22:55:10
What about this? And it’s like you’re asking that purposeful question at that time so that students might be able to go, hmm, get to the next step, and then you get to kind of continue roaming and come back to check on that student So are you in your mind I’m wondering where is your head at? They’re maybe already doing some of that work, but can you envision how some of that thinking that anticipating might be a way to sort of help yourself kind of in the moment deal with those students who are like, I’m not sure what to do or they haven’t started or they’re really struggling and spinning their wheels.
00:22:55:16 – 00:23:16:14
Yeah, I think that’s a great idea. There is some of that going on as I prepare for the lessons in that. I think one of the things and this goes along with what you’re saying is I try to do sometimes is I don’t know if it’s for better or for worse, but sometimes when I do see them not having kind of that entry point or whatever, I will oftentimes come around.
00:23:16:14 – 00:23:41:10
And if they’re working in groups or whatever and say, Hey, maybe you could try it this way and not not showing how to do it, but maybe getting them scaffolded a little bit with a model or something like that, How about trying to draw this first and then let them kind of go from there? So I do do a little bit of that, but I do like what you said about thinking ahead a little bit more sometimes with some questions and things like that for that next step and.
00:23:41:12 – 00:24:00:19
I got a couple of curiosities still kind of rattling around in my brain. So because you’re focused on your intentionality and thinking about my learning goal at the end, I’m curious about cows talked about the anticipating pebbles that students are going to have and trying to make sure you hit them head on in the planning process before we get into there.
00:24:00:19 – 00:24:21:16
But also in that planning process, that anticipation is I often think about the journey that I want students to go on while experiencing this task and then how the journey ends, right? So I know that this is the beginning of the journey and I’m anticipating the hiccups, the problems here, and I’ve got those back. QUESTION those magic questions that I’m going to prod and get them to do something.
00:24:21:16 – 00:24:44:05
But I often go, okay, well, what happens if I do have a bunch of students who aren’t getting into it or I miscalculated the floor and I didn’t have the floor low enough to kind of get people into it. And so I think about that journey, and I often plan the end when we get to the end, what are we doing to kind of tie things with the bow, right?
00:24:44:05 – 00:25:18:20
Because we picked the task for the intentionality and at the end we want to make sure the learning goal comes out from the shared experience that students have been in. So, Jason, tell me a little bit about what the ends of your lessons have looked like in the past and then maybe that can help steer the ship a little bit to help with what we’re doing in the middle to kind of keep that journey going so that we can still go, Hey, some students were struggling here, but we still modeled over here and everyone still coming out the other end with that learning goal being very clear to everyone.
00:25:19:01 – 00:25:26:18
Yeah, So the way we have it set up, I’ve got about, I would say about 70 minutes or so for me each day.
00:25:26:19 – 00:25:28:02
That’s about me. That’s about me.
00:25:28:02 – 00:25:57:14
And it’s broken up into two class periods. So part of my struggle in the last couple of years is having to try to balance the okay, I’ve got to have the guided math so that sometimes those lessons are pretty short. I kind of do the guided math at least a few times a week. I try not to do it every day because I sometimes I want just more time for the whole group type of lessons or during those whole group types of lessons where we are doing some kind of task or whatever.
00:25:57:15 – 00:26:23:08
In the end, my goal is to bring them back together, discuss certain strategies that I’ve seen that I think would be good ones to share. And then I do think to your point about how that lesson ends, usually my goal is to try to make connections between a couple of those strategies that they used and try to bring out what we were trying to get out of that lesson that day.
00:26:23:08 – 00:26:57:15
But sometimes it carries over the next day and then I feel like it carries over and then you might have to kind of restart just a little bit because they are fifth graders. Sometimes there is that effect. And in my mind, I know one of the things that I also continue to work on is trying to make sure that when we do wrap up, whether it is that day or that the next day, that next lesson before we move on is really trying to get them to move in from that, to move to a little bit of independent practice with it.
00:26:57:17 – 00:27:31:00
And I actually listen to one of the podcasts was on recently that you did about someone who was struggling with balancing individual and group work, and that was actually one of my pebbles. But since I just happened with that, I changed a little bit. But I did kind of from there. I really like the idea of if there’s kids that are getting it or they maybe had those strategies, kind of allowing them that option to kind of go back and hey, you can work on these follow up tasks independently, whereas the other kids that maybe struggled maybe need a little bit more of that time.
00:27:31:03 – 00:28:03:06
So I think at the end of lessons this year, one of the things I’d like to implement is kind of similar to what you guys suggest with that is if that learning goal was achieved already by some of those students and they’re comfortable with it, go ahead and continue. And then those kids that are still struggling with that learning goal, maybe they haven’t quite gotten that learning goal even when we came back together and did some of the consolidation to try to maybe whether it’s pulled them over in a small group or there’s a lot of them, let them continue to work together at the boards and things like that.
00:28:03:06 – 00:28:12:15
And so I think that’s one of the things that kind of stuck with me listening to that and also kind of relates to, I think, your question at the end of the lesson. I think that’s something I’d like to try to implement.
00:28:12:17 – 00:28:34:07
Yeah, I think one of the biggest challenges that we all experience at being a facilitator of math and learning is the different stages and kind of helping or maybe zooming out to recognize what stage of the lesson you’re in. We started with the conversation around the productive struggle and trying to keep it productive, right? And we want it to be a legitimate struggle.
00:28:34:07 – 00:29:07:08
If a student’s not able to enter into a problem, to be able to have anticipating along the way that there’s going to be someone who’s stuck. What’s my next move? What’s the purposeful question that I can ask that student to keep it productive? Not necessarily with the goal. And this is hard for us to recognize that it’s possible that at the end, before I’m ready to consolidate or before we allow students to maybe do a gallery walk and share with each other, we may not have all students at the exact same place right.
00:29:07:08 – 00:29:28:11
And that’s a part that I think is hard for us to accept. But the reality is we know coming in to every lesson that’s there, some students at different places in the journey. So it would seem logical that by the end of the productive struggle phase in my lesson that I might not have every single student at the exact same spot.
00:29:28:13 – 00:30:07:22
But what we may have and what I want to keep it at is as productive as possible so that all students have entered into the task. Some students are finished the task and they’re already making connections and extending like you’re saying. But when I bring them back together at the consolidation, it’s almost like if you were to look at that phase as the opportunity for the students to grapple with the idea, and then when we come back to consolidate, this is where I’m just going to be 100% as explicit as I can be to make sure that all students now see a path to get them from here where we started, which is a problem
00:30:07:22 – 00:30:35:05
I’m not sure where do I begin to an end goal here? The big idea, the strategy or strategies and the model that we’re trying to reveal. And it’s okay. And this is a permission that we have to give ourselves. It’s okay if not every student was able to get there themselves by the consolidation point. And this is an area that I think it took me a very long time to come to that realization.
00:30:35:05 – 00:30:53:04
I wanted every student to be 100% successful with the problem. But what ends up happening when I did that was that it would stretch over the day or I may not be able to tie it together and still at the end, some of those students didn’t make it to the place I was trying to get them to. So there’s a bit of this balance.
00:30:53:05 – 00:31:17:09
We’d certainly don’t want to rush it to the point where it’s like, All right, you know, no one’s getting it. Let’s just consolidate it together. I want to make sure that I’m helping every student make some progress towards the goal. And then when you feel that they’ve had enough opportunity to grapple to work through to problem solve, and then you’ve given them the opportunity to walk around the room and even look at some of the other strategies some students are doing.
00:31:17:09 – 00:31:40:11
And there might be a student who’s looking and sees John’s solution and it’s done and it makes sense to everybody else in the class. But to this one student, it’s still not there yet. That might still indicate, hey, this might still be the time that we’re going to have to consolidate this as a group. And then now in my mind, I’m going, Oh, there’s my three students that I have for my guided right.
00:31:40:11 – 00:32:02:04
So when we break and we go, okay, here’s your consolidation prompts and everyone’s going to go over there and I’m going to go and sit with maybe those three students to again reiterate, have that next task that may even lower the floor just a little bit further from the initial task to make sure that they’re making some headway in that area.
00:32:02:04 – 00:32:31:24
And ultimately, at the end of the day, it’s a really tough job to be doing in the moment to really recognize where am I in the lesson progression and at what point is it productive versus unproductive? And it can be that way in two ways. It can be unproductive very early in the lesson. If I don’t have those purposeful questions, an idea or a model or a something to give those students, but it can also be very unproductive if they’re just spinning wheels and they’ve been grappling, grappling, grappling.
00:32:31:24 – 00:32:51:22
And that’s not very helpful either. So it’s finding that balance. It’s not like I can set the timer in my pocket after 5 minutes, we’re going to call it quits. Every day is going to be different. And there’s this feel that you get in the classroom and you can sort of start seeing. And the goal isn’t necessarily for them to all be 100% successful on the task.
00:32:51:22 – 00:33:19:08
It was to give them the opportunity to grapple and maybe even the curiosity or the thirst for the math. Right. And now you get to be the magician and go to to look at this and hey, friends, it’s okay if you didn’t get there, because guess what? The person you could cite, the mathematician who came up with this approach and you can say it took them years to discover this, and I only gave you 10 minutes to grapple with it.
00:33:19:08 – 00:33:35:05
Right. But we’re going to dig into it. Do you see why it works? Do you see how this makes sense? And I wonder, let’s try a different problem together and then, hey, you go and let’s see if you can apply this to a different scenario, a different context, and we can grow from here.
00:33:35:07 – 00:33:50:21
Yeah, I like what you said about, okay, if you don’t understand it, and I always try to encourage that with my kids too, is if we have to wrap things up for for the moment and move on in tomorrow, or I’ll say to them, it’s okay if you don’t get it right now, we’ll get there at some point.
00:33:50:23 – 00:34:13:23
And sometimes they might believe me and maybe not, or we’ll get there, you know, and I’ll even say to them, I encourage them. I know some of you don’t get it. I can see it. You can see it in their faces. And it’s hard. There’s no doubt about it. It is a fine balance of trying to keep moving forward that are ready and then to try to keep working with those kids that aren’t ready for it either.
00:34:13:23 – 00:34:39:17
And and sometimes I think to as you’re talking and a lot of times I try to encourage the kids that during the process it’s okay if you don’t get it. And sometimes I’ll even ask them if you’re still struggling, it’s okay. And let’s go work on something, you know? And sometimes that works, and sometimes there’s just kids. They’re understanding, like, I’m not getting this right now, and there’s kids who maybe they’re a little more like, I don’t want to say I don’t understand it or whatever.
00:34:39:17 – 00:34:41:04
So I like what you said, but.
00:34:41:07 – 00:35:01:10
Yeah, it sounds like you have some good next steps to think about with your focus on what happens during that lesson. And I think you said that out loud here, and I liked how you just said that because sometimes it’s okay to struggle and telling kids it’s okay that you’re still struggling. The struggle is really important. It’s really what you do next.
00:35:01:10 – 00:35:22:04
Once you’ve identified this is the metacognition skill we need to help our students with. Right? Is thinking about struggle is really important for you. And when you recognize that you’re struggling in most important thing is what do you do next? Do you just quit and or do you just cross your arms? Do you not say anything or do you ask or talk?
00:35:22:04 – 00:35:40:14
It through? These are the skills that we as math teachers take for granted and miss. And focusing on that is really helpful for students to continue that. Hey, like what you said, this mindset at the beginning of the year is really important. We’re going to be struggling throughout the year with different tasks. The most important thing is what do we do once we realize we’re struggling?
00:35:40:17 – 00:35:59:03
And actually to John, I just wanted to throw in there. It’s like if at the end of the day, too, when we consolidate, it’s okay if we say to students, it’s like, you know what, we’re at a great spot as a group. You’re at the exact spot I wanted you at because I think you’re ready for me to show you.
00:35:59:04 – 00:36:19:14
Right. And I’m using that word very intently. I feel like a lot of times we think it’s got to be the kids that come up with it every time you can say it. If you know that this lesson is a tough one for you to get. But you’re at this perfect moment where I think you’re going to see the connection between where you are now and the next step here.
00:36:19:16 – 00:36:36:19
And boom, here’s the big moment that we can share. And it’s like and I’m going to share that with you here today because I am a teacher. I’m allowed to do that, too. It doesn’t always have to emerge from students. So I think getting comfortable with that and even just how we approach it when that happens, it’s not.
00:36:36:21 – 00:36:55:06
I used to think it’s like, Wow, you all got stuck in, You didn’t get there. You used to think of as a bad thing. Now I look in and go, Wow, there’s some amazing ideas here and I want to build off of this idea and this idea. I don’t want you to tell me if you can see your thinking and what I’m about to do through this strategy over here.
00:36:55:08 – 00:37:09:09
And sometimes that experience can be like, Oh, and you’re like, Hey, I just wanted to cut a couple hours of work out of your way. Are you okay if I do that for you? Because, like, I could let you go all day if you want, but do you want me to help you see it? Because I think you’re ready for it.
00:37:09:09 – 00:37:41:07
You’re ready for it. And just think about that experience where a student’s leaning in going like, Yeah, this is kind of frustrating over here, and I wonder what that might look like. And there’s a lot of great ideas here that are kind of floating around in this episode. So I’m wondering as we kind of wrap up here and you look forward to this next school year that you’re about to begin, what would you say is maybe your biggest takeaway from the conversation today and how might it impact your next steps here as you plan for this new school year?
00:37:41:09 – 00:38:05:02
Yeah, well, I really like what you just said because it got me thinking. I think I tend to do that sometimes is think about, Oh, I want them to all have this by the end of this. But actually it’s okay to show them a little bit too. When I started out, like I said a few years ago and over the last couple years trying to make math more open and you’re going to come up with ideas and strategies and things like that.
00:38:05:04 – 00:38:16:24
I think, you know, the reality that I need to keep reminding myself of is what you just said is sometimes maybe they don’t. And it’s okay to say, Hey, I’ve got this really cool idea that maybe we could try.
00:38:17:01 – 00:38:37:10
I love that. And I almost want to build on that and say, even instead of saying just a little bit, I’m going to say we have to tell our kids a lot. But it’s just one right. And I think in your mind, you to be looking at yourself and we always called it the real flipped classroom, right? Our old models, like we’re just going to tell you right upfront, here’s how to do it.
00:38:37:10 – 00:38:54:14
Go do it or here’s how to do it. I’ll show you how we do it. Now you do it. And we still need to tell them a lot, because the reality is, is that and there’s going to be, I would say, the rare cases when the whole class everything progresses perfectly and you’re like, this is a dream. Holy smokes.
00:38:54:14 – 00:39:14:16
Amazing. They all walked away with the big idea. But more often than not, I would say the majority of the time it’s on us to help get them as close as we can before we tell them. And I think that’s a part that, again, we’re trying to say it more and more on the podcast because I think we are always talking about this balance thing, right?
00:39:14:16 – 00:39:32:07
And we always kind of it’s like, tell them nothing or tell them everything upfront. It really is somewhere in the middle. And once you get to that place where they’re ready to experience it and again, we do it in a way that’s very accessible and we do it in a way that’s welcoming so it’s not like, Hey, I know it all and you don’t know anything.
00:39:32:07 – 00:39:48:18
It’s like, Wow, you did a ton of great work. This is exactly how I wanted this lesson to go, even if it’s not right. Been there before, but you tell them that you’re at the perfect spot for this. And I want to share something with you. You okay? If I share that with you now and it’s like, now they’re ready.
00:39:48:18 – 00:40:17:05
They’re in this moment. It’s almost like we often hold ourselves back because we’re trying to pull it from them, when in reality there is the role of actually telling, We do need that. We need that explicit instruction to come out. It’s just deciding when that moment is. And I would argue even when those kids solve the whole problem nicely, imperfectly, I still want to be super explicit because some of those kids got there, but they don’t recognize why they got there.
00:40:17:05 – 00:40:38:04
Right. Or they don’t see it as this is something I can replicate in a different scenario. So that’s a massive, big takeaway and I hope some others who are listening in the math moment make her community are feeling the same way as they’re thinking about this school year and trying to continue refining their practice. Jason, it’s an honor to have you back on here.
00:40:38:04 – 00:40:56:05
It’s great to chat with you again and we’re so proud of the work that you’ve been doing over the past few years and the growth that you’re making in your classroom. And the fact is, is that, hey, great teachers never stop growing so good on you for that. And we’re looking forward to checking in with you again, maybe nine or 12 months into the future.
00:40:56:07 – 00:41:00:22
Thank you very much. I appreciate you guys everything you guys do and for having me on again.
00:41:00:24 – 00:41:11:09
Awesome. Awesome stuff. Yeah, we’ll reach out. We won’t let it go. I think two years this time, we’ll make sure we reach back in about a year. But thanks, Jason, so much and good luck as you start school next week.
00:41:11:13 – 00:41:12:07
00:41:12:09 – 00:41:46:20
Chat soon. DJ Take care. Well, friends, there you have it. It’s been over two years since we chatted with Jason and always a pleasure. What a dedicated, reflective educator who continues to strive to do better for their students. Just like everyone who’s listening to this podcast, you are all math moment makers. Who cares so much about reaching every single student in your classroom and you’re not going to stop until you do, which is such an honorable thing and such a motivating thing.
00:41:46:20 – 00:41:57:11
So thank you so much for the energy that you put into your classrooms, just like Jason’s putting into his year as he looks forward to another brand new school year.
00:41:57:11 – 00:42:20:10
Yeah, and in this episode we think about our six parts of the mathematics classroom tree. When we talked about thinking about a lot of the anticipation stages, and I’m thinking about what a student’s going to do, what can we anticipate strategies that they’re going to take that anticipation stages. One of our key teacher moves. It’s in our mathematics framework for make math moments, as we call that the before moves.
00:42:20:10 – 00:42:46:18
There are a certain amount of before moves we want to implement. And then there’s during moves and there’s after moves. Those three categories of moves, they all fit in that certain area of our classroom tree, which is the branches of our tree, which are our pedagogical moves. It is important for us to think about and plan for those types of moves, those pedagogical strategies, so we can bring our students along the mathematical trajectory for that key learning or those key learning goals.
00:42:46:18 – 00:43:09:23
So Jason’s on his way, shifting those branches around, trying to strengthen those branches as much as possible, because if you strengthen those branches, you’re strengthening your resources, which are the leaves of your tree, and then that will trickle back down to the trunk of the tree, which is our leadership in our classroom culture. And then also the limbs of your tree, which is your pedagogical or your professional development plan.
00:43:10:00 – 00:43:17:03
There’s so much that Jason’s been working on, so a great job. Jason, we look forward to checking in with you in another year and see how you’re shaping up.
00:43:17:05 – 00:43:47:21
Oh, that’s awesome. So if you’d like to hop on, just like Jason, keeping in mind that these calls are really about coming together, sharing common struggles, and really working through them together as a team to try to get to the next place, head on over to make math moments dot com forward slash mentor and you can be on a upcoming math mentoring moment episode again that’s MC math moments dot com forward slash mentor and we can’t wait to chat about your common math class struggle.
00:43:47:23 – 00:44:08:12
And if you’re looking to continue strengthening these six parts of your classroom tree, then don’t forget that in November, November 17th, 18th and 19th of this year, we’re holding a free online conference. We call that to make math Moments that matter summit. This will be our fifth summit, fifth free summit that we’ve hosted here at MC Math moments.
00:44:08:12 – 00:44:28:20
We’ve had thousands and thousands of teachers each year join us for that free summit. We have ten featured speakers this year and so many other featured speakers, classroom teachers from the Math Moments community. And we’ll be headlining this again like we did last year with a joint session with Kyle and I and Peter at Little at all. So join us.
00:44:28:20 – 00:44:34:06
We are super excited. Head on over to McMath moments dot com for that summit and get yourself registered.
00:44:34:06 – 00:44:53:24
Hey there friends and also make sure that you help this reach this podcast reach a wider audience That’s a huge huge huge help that you can do if you find this helpful for you and your practice. I’m sure there’s other educators out there who feel the same way. If they had the opportunity to listen. So do us a favor.
00:44:54:04 – 00:45:15:04
Whatever podcast platform you’re listening on or if you’re watching on YouTube, rate review, follow comment, whatever the action is on that particular platform, we ask that you do it because it goes a long way. And also it’s super inspiring to us when we see the impact and influence we’re having on. So many thousands of listeners each and every week.
00:45:15:09 – 00:45:26:05
Shownotes And links to the resources you heard here today. Folks can be found over at McMath moments dot com for such episode 254 McMath moments dot com forward slash episode 254.
00:45:26:07 – 00:45:30:21
Well until next time mouth moment maker friends I’m Kyle Pearce.
00:45:30:21 – 00:45:32:01
And I’m Jon Orr.
00:45:32:01 – 00:45:34:23
High fives for us.
00:45:36:14 – 00:45:38:20
A high five for you.
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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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