Jon Orr: Hey there, Math Moments That Matter, Jon and Kyle here. We've got a great episode for you. We are going to talk about all of the things about starting the school year off, and making math moments from day one, all the way to day 180. And that's what this episode is about.
We're using it now here in the summer, if you're listening to this live, so that wherever and whenever you start your school year, you have and thought about all the things that are needed to go into place to kick off that school year, but also keep it rolling, right, Kyle? The ideas of what we're going to chat about here are we can kick things off in week one, but then it's like, now what?

Kyle Pearce: Yeah, absolutely. And Jon, I'm sure those who have listened to the podcast before, if you're new listener, awesome. Friends, just noting, we are putting this one up on YouTube. We got the cameras on. We're going to do some screen shares as well. So, you might want to dive in on our Make Math Moments YouTube channel.
But like Jon is saying, we've done these before, where we talk about the first day of school, we talk about the first week of school, building that class culture. And we've given you all kinds of routines that are great to really start the school year off right. Well, today, we're going to take that idea, and we're going to leapfrog from that, and start looking a little bit more bigger picture as to what does week to look like?
What does week three look like? And really, all of those things should be happening from day one. So, that's why this episode, we're planning to start on day one. But making sure that we create these routines that aren't short lived. They're not gimmicky. They're how we're going to do things in math class from day one through day 180. Jon, what do you say we get going here?

Jon Orr: Let's do this.

Kyle Pearce: All right. Welcome to the Making Math Moments That Matter podcast. I'm Kyle Pearce.

Jon Orr: And I'm Jon Orr. We are from makemathmoments.com and together-

Kyle Pearce: With you, the community of the math moment makers worldwide who want to build and deliver problem-based math lessons that spark curiosity.

Jon Orr: Fuel that sense making.

Kyle Pearce: And ignite your teacher moves. Welcome, everyone. As we mentioned, we are super geeked here. We're recording this in the summertime. But really, we're hoping that this episode is going to feel evergreen. Of course, I think the most optimal time to dive into this particular episode is as we start planning for a brand-new year, or a brand-new semester, or quad master as we've been doing things here in Ontario most recently with all the COVID chaos.
But really, it is something that you can put into practice at any time. But of course, from the beginning of the year is always best because we can really start things off on the right foot, and ensure that students get a better understanding of what math class is going to mean for them, and what it means to you as an educator. Right, Jon?

Jon Orr: Yeah. Also, just to set the stage here. This is our third installment of how to start the school year off right. And we want to let you know that in our previous two installments from August last year, and the year before, we talked about how to kick off the school year, so that you can make math moments. Like Kyle said, we didn't go into what it looks like past week one.
And so, what we're going to do is encourage you right now, is if you have not yet listened to episode 36 or episode 88, then we're going to ask you to go back there, and listen to that because we aren't in this episode going to spend a ton of time on what we talked about in those episodes, which was really focusing around building culture. What are the activities we do in week one to build the community, the culture, get students thinking?
All the things, all the activities we have, a ton of activities that we recommend to do in week one, week two, or week one and two in those episodes. In episode 36, we talk about what those activities look like, and talk about how we've used those exact activities. What are the resources we have in our classroom, so that we're setting the stage in the routines that we're putting in place for those first few weeks?
And then, on episode 88, what we did is we redid the episode, but because last year, we were facing a pandemic, we redid it. It's like what does it look like to start the school year off in a pandemic? So, that's what episode 88 was all about. And like what Kyle said is, in this episode, we're going to go a little bit deeper in going okay, now, if you've listened to episode 36 and 88, and now we're like, okay, what are we doing next?
And how do I keep this amazing culture and community that we've established in weeks one and two, how do I keep going so that we don't lose some of that? And what are the routines we've put in place? So, also, if you have not yet grabbed the guides, we've got full guides on how to start the school year off, like a PDF downloadable guide. You can head on over to makemathmoments.com.
And there's should be a little pop up that pops up, and you can get the downloadable guide for starting the school year. All right. So, Kyle, let's not waste any more time here, let's head into and maybe what we'll do is we'll just kind of quickly summarize the four big things we're going to talk about in this episode, which are actually going to spur off, or I don't even know if I said that right, Kyle, spur off or spun off.
We're going to spin, yeah, branch off, we're going to spin off this episode into two other episodes, because there's so much to talk about throughout the school year. But the four things we are going to talk about in this episode to continue our journey are specifically about how do we teach problem-based lessons on a daily basis? And how does that fit into our units, and our youth teams for the school year?
We're going to answer questions like how do I cover all the concepts? Well, we're going to talk about spiraling and interleaving. We're going to talk about assessment, Kyle. We're going to dive deep into assessment here in this episode, because I think we've talked about that here in the podcast so much because everything should start with assessment.
And we should be definitely starting the school year off with this assessment idea in mind. I think I did three there, Kyle. Maybe I said four, but maybe it's just three.

Kyle Pearce: Yeah, no, no-

Jon Orr: Well, see, I think we had four because this covering it all idea, I think it's big one. And it does connect to how we organize and how we plan out our school year. So, we're going to talk about these things at a high level. And then, we're going to try to dig a little deeper. And actually, we've planned to go even deeper in a couple future episodes. So, we'll talk about that as we go through this episode.
But ultimately, at the end of the day, yeah, you got to go back, check out those previous episodes, check out some of the resources on the website for some of those culture building activities. Because I think those are really great as a way to get students thinking building that trust, building a non-threatening classroom environment. So, all of those have been talked about and covered.
But then, a big question we often get is, where do I go next? I think a lot of teachers, a lot of educators, I know you and I both have talked about this many times before, where we felt like it was almost like day one. Well, first of all, we've addressed this before. We went from day one was all about the syllabus and rules. And this is how you do things, you don't write with pen, and only use a pencil, all of these things.
And then, we realized after a while that that actually didn't help us build culture. I would even argue, it didn't help us with even necessarily classroom management, because it was almost like we were creating a bit of us versus them mentality instead of a culture of like, we're going to work together, and we're going to learn together.
And then, we shifted to doing some activities on day one, day two, sometimes even all the way through day five. But then, it was like we flipped the switch, then we went back to our old self. And for us, that old self was more of a gradual release of responsibility mode. I'm going to lead this lesson, you're going to watch me do some stuff. And I'm going to ask you some questions.
And then, you're going to start doing that same work. And while that might seem to make sense, in a lot of cases, what we've realized, and we've addressed many times before is we actually weren't seeing our students doing any thinking. So, we really want to get into this problem-based mentality of avoiding that rush to the algorithm.
And really uncovering the curriculum, as our good friend, Alex Overwijk once said, and I'm sure he may have heard that from somewhere as well. So, one thing that we're going to knock off the list right away, is something that I think a lot of teachers feel is automatic during the first week. So, day one, you might have moved past the, "Hey, we're just going to do the syllabus and the rules."
And maybe you're doing some fun activity, maybe one of the activities we've shared in some of the previous lessons like maybe name tense, like Sara VanDerWerf that we've highlighted, or maybe 21, the game of Nim, or any of the other activities, and that's fantastic. But then, if after that first day, or maybe even those first two days, if we flip the switch to review of grade blank-
We have to go back, and review, and preload all of the stuff that I know that they didn't teach, or they're not going to remember from the previous grade. We got to spend a week there, or 48, or three days.

Kyle Pearce: Yeah. And Jon, something else, too, that I think we will dive into a little deeper, as you mentioned about assessment is think of the assumptions we're making when we do the review of blank. And I know that you probably have a long history of like, "Well, I know being that I've taught this grade for 10 years or 15 years that students always struggle with this, this or that."
I'm just wondering, though, if we've ever reflected on how well that review actually worked for us. So, let's say it was fractions, and I'm being very general there, just fractions. So, that could be comparing, it could be ordering, it could be operating with fractions, or whatever. We just say students struggle with fractions. So, I'm going to spend a bunch of time reviewing that.
But then, I wonder, at the end of that work, were students that much better with fractions? At the end of the school year, were you like, I'm good, and next year, the teacher is going to feel like these students are amazing with fractions? I know, for me, I can only speak for me. I never felt that way. So, it makes you wonder how well used was that time.
And when we think about assessing, and evaluating, and really trying to figure out where students are, we made a huge assumption about where they are or where they are not before they even really did any math in our classroom, Jon. So, what do we do instead? What's so whole here?

Jon Orr: Yeah. The idea of moving away from a review is that if we start with, and this is not going to be a shock to avid listeners here of the podcast is, instead of jumping into a review week, what we're going to recommend is you jump right into the lessons, the ideas, the tasks that we are sharing over on our tasks page. But your course, basically, you jump into your course.
But we want to teach through tasks, we want to teach through our lessons that are going to continue to build this relationship and value voice. And why we do that, and why we skip the review part is because if we choose tasks early on that are course, or content specific to our standards, we can achieve a lot of the same things without spending all that time on a review.
We can see what students know, and what they don't know from teaching through problem-based tasks. So, what I mean by that is this is not like, I'm going to jump into day one, I'm going to teach my day one, or my textbook 1.1. And I'm going to teach a I do, you do, we do, or I do, we do, you do model. I'm going to actually ask students to solve a problem that is unfamiliar.
I'm going to set them up with something very curious. We're going to follow the curiosity path that we've talked about here on the podcast. And I'm going to watch and listen to strategies that they work through at the boards, in their whitespace. We talked about that in our previous, how to kick off the school year episodes too of how to set up your classroom so that you're ready to go for problem solving.
We teach through problem solving here as much as we can, because we know that we learn through what the students are showing us. And that's because when we allow them to work, we're going to see the strategies that come out, we're going to see, "Hey, do I even need to start with what I thought was less than 1.1?" I can actually move a little bit forward and get a sense of where we are, and then maybe pivot a little bit later.
But we often share what problem solving, teaching through problems because you can learn so much about what your kids can and can't do. And I think that's where we want to start. But Kyle, it's like after we start that way, because our whole podcast series is about teaching that way. So, it's like we're not going to dive into how to run a lesson exactly like that.
That's actually what we're going to do in episode 142 that's coming up. But it's like a lot of questions come up Kyle about, okay, I'm going to teach this task that you guys have on your website, or I'm going to teach through this problem-based task like you've suggested all these episodes. Okay. Do I do that every day, Kyle? Do I do that once a week?
This is probably one of the most common questions we get is how often are you guys teaching through this problem-based lesson? And once you've stopped that lesson, what do you do on the next day? So, let's chat about that for a little bit.

Kyle Pearce: Yeah, Jon. That is a super common question. How often are we doing this? And the beauty is, so when you think about what we're trying to achieve with this particular episode, those who are watching on YouTube, you can see on the screen, I've got all kinds of problem-based units there. The beauty is, if I start that first week, like you had mentioned, Jon, it's like we don't have to throw out the idea of review.
We can still do review, and I would argue that every problem-based math lesson or unit should be a bit of a review. We don't ever start with a really high floor. We always start with a really low floor, and the intent there is so that we can learn more about what students know and where they are. So, if I'm thinking, my grade nine self, my students may struggle, or may have some struggles with fractions.
I also want to maybe articulate a better way to ask that question or to make that statement is instead of saying, my students may have some struggles with fractions, I might want to change my thinking a little bit to say I wonder what students know about fractions. You see a very slight change in how I'm questioning that from a deficit model of what don't they know to what do they know, and what can I build on there?
So, when I go and I look at my problem-based lessons, I could actually click on that fractions filter. And I can have a look and say, wow, I got a lot of units here that I can look at. And depending on the grade level, and depending on your prior experience teaching that grade level, you might have a general sense of where you want to begin that journey.
It might even be something as simple as representing fractions. I'll argue, my grade nine students, while they may have known how to multiply tops and bottoms, or multiply and flip the other to divide, they might have known some procedures, oftentimes, they didn't actually know how to model fractions.
So, I might actually, during my first week of school, dive into the woolly worm race unit, which you can see up on the screen here, which is all about representing, comparing, ordering, and even adding fractions. It's a whole unit, it would be a fantastic first week review, where students don't realize it's a review.
Think of what that is to a student where you go, okay, week one, we're going to just review what you already did. Half the class is like, I already feel good about what I did last year. The other half of the class is like I didn't really like last year, I didn't really feel confident there. Now, I'm stuck. And then, the beauty, Jon, you're saying is, I'm flowing into my routine for this year, because Jon is saying, how often are we doing problem-based lessons?
Well, I'm going to argue, we're doing them a lot with the caveat that we're giving students the opportunity to do some practice in between, and do some math talks, and some fluency, and even some small group instruction where appropriate. So, with all these units, that is how we have them set up, you can see up on my screen those on YouTube, when you go to day one, you've got a problem base unit.
But then very often, the day after a problem-based unit, we have a math talk set up for you, and some purposeful practice setup for you. So, that you can give students the opportunity to do and explore the context more deeply. And you have an opportunity to be going around, floating around the room, students can be working with partners, you can assign some of it partner work or group work.
Some of it, maybe you want as independent practice, where you just want to get a sense of where students are. And by doing this process, you're constantly collecting information about where students are along their mathematical journey, and where we might actually go from there.
So, I'm going to argue that that week of review, instead of thinking of it as a week of review, you're actually thinking of it as the beginning of your course, which just so happens to have some review built in, because every single unit that we're going to do with our students is going to start in a place where students feel comfortable, and that we can push them inside of that unit.
And we can sort of push some students who need that extra push, we can also assist some students that might need that a little bit of assistance along the way. And really, that's what that true differentiation in the moment is going to do for each of our students.

Jon Orr: Yeah. These are great ideas for answering this idea of how often are we using problem-based lessons? And Kyle is saying we are using them as often as we can. But if you look at our units over on our problem-based tasks page, you can see that on day one, we're doing this but on day two, we're doing something a little bit different, but they all connect together in a nice progression.
And that can help you think about how to set those up in your course. Because every big idea, we start that, and we have a nice progression that builds through that. And we're actually going to talk specifically about those units, those tasks, and how to like set up those progressions for you in episode 142, which is coming up. That's a future episode. So, we'll dive deeper into that.
Those ideas, we're going to open up one of those tasks, we're going to walk through the teacher guide, all of those things in an upcoming episode. So, let's move on here, Kyle, because another big question is, how do these fit into the bigger picture of things? If we're going to set up the school year right, and keep it going, oftentimes, we think about, okay, well, I did a unit.
Now, I've done a progression. I've done a problem-based tasks that had some purposeful practice embedded in it on next day, or maybe I did the math talk on the third day. Awesome. But now it's like, what do I do after that? Do I just go on to the next topic? And this comes up to where we've been dabbling for a number of years now. We've talked about some here on the podcast.
We do have a full course or a full mini course on this called Spiraling, and that we've learned a lot about spiraling, which is really interleaving concepts since we started this a number of years ago. And we've had a lot of success in interleaving our concepts. Basically, what we're saying here about spiraling. And again, we're going to have another full episode on spiraling coming up in episode 145.
Another future episode because we know it's worth diving into. And basically, when we say spiraling, we're talking about not following what I did, especially in high school being like chapter one is all about linear relations. And it's like 1.1, 1.2, and it's all the way there. And then, we never talk about linear relations again in the course ever again, until it's time for the end of the year final test or your standardized assessment.
It's like the next chapter is a whole different topic. So, spiraling or interleaving concepts is mixing some of those concepts up so that we're not just doing all linear relations, and never talking about it again. We are using our problem-based lessons to introduce that. And then, maybe once we get through that small progression, and that might equate to 1.1, 1.2.
All of a sudden, we are now going to... once we've assessed that our students are feeling good on this part of that progression, we might switch to a different strand that we can also dive into. And then, we'll come back to linear relations later in the course. And what that does is help with retention, helps with problem solving, too.
We noticed we get a lot better problem solvers, since we're teaching through problem solving, that students are going to be like, "You know what, in our last progression unit, we did all linear relations. So, on this one, we're just going to do linear relations again." So, it's got to be about that, whereas when we switch to say, geometry, or measurement, all of a sudden, that first problem-based task, where we're asking kids to notice, and wonder, and be curious.
It's like, wait a minute, is this about linear relations? And then, all of a sudden, they have to start thinking about other areas of mathematics to tie into that problem. And we've now really begun problem solving. They're not trying to predict what this math problem is about. They actually have to dive down. So, that's really what we're talking about spiraling.
But Kyle, let's talk about some of the brief changes we made. Because we are going to go into deep on this in the next episode, but maybe give one technique here of what we did to change our spiraling approach over the last few years.

Kyle Pearce: Yeah, absolutely. And when we first began, and we've discussed this a little bit in some of our previous podcast episodes, where we've talked about spiraling with some of our mentoring moment guests. Michael Rubin comes to mind on a couple episodes with him. And that we'll say right up front, there is no perfect way to do it, there is no one way to do it.
There're so many different ways that you can approach this. Early on, you and I took this. Now, mind you, it also helped that we taught a course where a lot of the content was extended in that course. It wasn't brand new. So, I don't think developmentally, it really mattered a whole bunch when we were introducing these concepts. But Jon and I took this approach of, let's just randomly pick a topic and go.
And there were some benefits to doing that. But one thing that we lost in that process was the ability to make intentional connections throughout the course. So, we felt like we were over here in left field one day, and over there in left field the next day. So, what you'll see is that we've actually developed, and maybe refined how we particularly do spiraling. And we do that through our problem-based lessons.
And we tend to do more of a unit spiral, where our units are pretty short. They're about five days, sometimes they span to seven or eight days, but five days or so. And then, we tend to instead of let's say if I was starting off with a unit like the planting flowers unit, which is all about ratios and rates, what I might do, instead of going on to the next problem-based unit related to ratios and rates, you'll see up on our screen here, there's planting flowers.
I might not dive into the next level deeper in ratios and rates, I might actually move on to something a little bit different, but that isn't developmentally inappropriate. So, ideally, I might start with early in the year, I might play with division. And I might play with the sowing seeds problem-based unit, where we explore quotative and partitive division.
And then, maybe I might go off into more of an algebra unit where we start to do one solving, one-step problems where oh my gosh, in the one step, or even in a two-step problem, at the end of the day division comes into play. It's like oh, that's perfect timing. Even though I was playing a number sense with division, now I could go over to algebra.
And when we do two-step equations, and we divide out the coefficient at the end, we can actually explicitly make a connection back to our sowing seeds unit where we explored partitive and quotative division. When you solve this equation, what type of division are you using in order to solve this equation, given the context that we've laid out for you?
And in some of our units, we've done this through a similar context. So, sowing seeds, for example, is one unit. We have another revisited unit, where you will actually be able to solve equations using the same context. So, students feel like they're still dividing, but they're actually in algebra now. So, what you're seeing is, over time, we've tried to refine this process, so that it is clearer to make connections.
But we're still doing a spiral around different concepts, different strands of the math curriculum. Now, for you, you might be teaching a grade where you're going like, "Wow, that's like a lot of work, I might not be able to do this straight up." So, you might want to do some sort of modified approach to this. So, what we recommend that you do is start off thinking about a linear progression.
So, think about your course, and how would you teach it more of like, I'm going to say a traditional, not to make it sound like it's a bad thing. But you might start with unit one, and there's a clear progression from unit one, all the way to unit eight, or nine, or whatever it might be. And what we're going to argue is that, is there a way that I can either take unit one, and instead of it directly connecting to unit two, could I take one of these later units, and do that a little earlier?
And then, maybe I head back into the original unit to where that is a continuation of unit one. So, you've intentionally created a little bit of a space in between that first unit, and that third unit. And initially, you're going to say, but why would I want to do that? Don't I want students to have familiarity with what we were doing in unit one, so that they can leverage it for unit three?
And what you'll find out through our complete spiraling guide, if you were to watch and listen to some of the research there is that actually, it appears as though that is helpful by keeping everything connected and making it really close together. And even this idea of mass practice, or mass learning a concept, but what researchers find is that that's actually really short-lived learning.
Because students are actually depending more on familiarity, the illusion of understanding than actual deep conceptual understanding that's going to last over a longer period of time. So, if you've ever asked yourself, why do students not remember what we did just a couple of weeks ago, or even a couple months ago?
That is one of the contributing factors is that we have this illusion that students have a deeper understanding because we spent so much time talking about it, and exploring it in one big massed chunk. So, the big idea here is how do I break that apart a little bit? Not too much, where there's no connection, but just enough so that it provides us almost like an excuse to have to come back and revisit an idea.
And this might feel frustrating at first, because you're going to go, "Holy smokes, I thought they knew this." And you're going to quickly realize that actually, they were just familiar with it at the time, and they didn't necessarily have a deep understanding like you may have thought. Now, as you do this planning, Jon, I'm curious, how do I know?
So, a lot of people are thinking, I'm planning... if you're listening to this in the summer, before school starts, you're planning this long-range plan, and we tend to try to follow it to a tee so that we could feel like our plan worked. But what are we going to do in order to actually be responsive to student learning, if we're going to use, let's say, more of a spiraled-spaced approach?
Or if we're actually going to try to meet the needs of our students, and not just follow what we said we were going to do in August, before the school year began?

Jon Orr: That's a great question, Kyle, and thinking about when we have to take what we're seeing here, and what do we do next? What are we seeing with our students? And I think that's where we want to bring in this other idea of one of our last ideas here to talk about in this episode. And just before I jump into this, this last idea on assessment, and that's what I'm alluding to.
Here is let's talk about assessment here because assessment can drive all the instruction. Good moving forward. And I think that's such a huge idea to talk about, especially how do you set up your assessment practices early. That's why we want to talk about it here in our summer learning so that we can be ready for it, and how to pivot when needed to.
But before we jump into that last one, I'm just going to circle back here to end our discussion here on spiraling, and if you want to learn more about spiraling, we are going to have a future episode on episode 145. But we do have a ready-made email course, Kyle talked about the Ultimate Spiraling Guide. You can learn more about that and enroll in that right now over at makemathmoments.com/spiral.
We'll also throw a link in the show notes page if you want to learn more about spiraling. And the idea about talking about that right now is so that you can plan your course with the space practice in mind. All right, Kyle, let's jump into this idea of how do I pivot when needed? And that has to bring up this assessment idea.
And when we talk about assessment, we're not talking about specifically like, I need to write a quiz here, or I need to put a test here. Those maybe performs evaluation, but what we talk about assessment, we are talking about assessment for growth. And if you're here with us up on the YouTube channel, Kyle is showing you, we have a full course, seven-module course on assessment.
Everything that we have been talking about here, we've put into a full course, and you've got module one of that course is open, ready to go on assessment for growth. We're going to give you a snapshot here. What we mean by that so that you can start the school year off right. Setting up some of your assessment ideas, and thinking before you go in.
Because once you start a school year, and you say learn a little bit later like, "Oh, I wish I had started this assessment protocol or assessment guidelines earlier, so that my students are ready, or know how to handle, or work through what we're working through, and what are their big ideas there." It's sometimes tough. And so, starting early is really great here.
So, what we mean by assessment, we're meaning by gathering information, so that we can help our students along the learning trajectory that we have set up. So, if you're thinking about those problem-based lessons, and those learning tasks, or problem-based units, and you've already mapped out maybe using your spiraling approach or spaced approach to how those units are going to fit, and when you're going to do them
What we want to do is when we're teaching through these problem-based lessons, why we recommend it is because you learned so much about what your students know or don't know, and you can help them. And that's really what we talk about with assessment is that we have to start with seeing, and listening, and collecting evidence. Now, collecting evidence can happen a lot of different ways.
But what I mean is just observing, and hearing what's happening with your students when they are problem solving. Because with that information, you can then decide on helping that one student in the moment where they need to be, but you also collectively have enough information to decide tomorrow, do I need to continue with this idea along this trajectory, or in this unit?
Or do I have to pivot cycle back? Or can I move on to our next unit, or next lesson in that? Why we say that, it's not such a new idea, but it is a new idea if I'm teaching in that I do, we do, you do model that I taught with for so long, because I had my setting stone lesson, guideline to go here. We're going to do this. And then, we're going to do another unit after that.
And if I know that I'm going to have my assessment set up so that I'm going to listen to students, and I'm going to have engaging conversations, and use that to help them move along the path, I need to know that right off the bat. And so, maybe we want to talk, Kyle, specifically about how to set some of this up, because people are going to want to know that.
So, it's like, okay, well, when you talk about assessment, you're talking about collecting information and learning, but what does that look like for me on a day-to-day basis so that I can be ready starting on day one, but I'm prepared to go the full length of the course this way? Kyle, what do you think that might look like? We do have a full course on it. We'll point you in that right direction a little bit later. But let's give you some snapshots so you're ready to go for day one through day 180.

Kyle Pearce: Well, there's obviously a lot. Assessment is huge, that's why we created a course. Actually, initially, when we were planning it, I remember very vividly, we thought it would be a mini course at the time. And it turned into one of our larger courses that's inside the academy. And the reason why is because everything, everything revolves around assessment and evaluation.
So, there is a lot to unpack. And as Jon has already mentioned, we're going to dive into an assessment episode really soon to dig in a little bit deeper. But I would say probably the most important piece upfront for me, is providing yourself the time for assessment. And you can see up on the screen, those on YouTube, you can see module four in that course.
These are just five of the modules for the course, there's actually more than five. But for module four, it's how to build time for assessment. And if you think back to what we've discussed here today, we have really been trying to create that time through our daily problem-based lessons. Now, that doesn't mean that we never have a day dedicated to more of the assessment.
And I'm going to include the word evaluation process, which a lot of people look at as the same. But to us, evaluation is more of giving students that end goal, like where they ended up as of a certain date. So, that might be maybe an assessment after or sorry, an evaluation after a term, or a quarter, or a semester, whatever that might be.
But throughout every single day, we should be assessing, and assessment is to help both the educator, the student, and their stakeholders, the guardians, parents to understand where they are now, and where do we go next? So, everyone has a role in this. And the challenge is if we aren't using a problem-based model for learning in math class, when do I do that work?
To me, it looks and sounds like, okay, if I'm doing a gradual release of responsibility model, I am forced to essentially use maybe that little bit of time at the end of the lesson where you ask students to do something or do the work. But what typically happens after that model lesson is student hands go up. Because you have so many students who are like, "I wasn't following along at all, and I'm not sure where I'm at."
Whereas, if we're in a problem-based lesson, from essentially the start of the lesson, you are giving students the opportunity to think, and share their thinking, represent their thinking. And you have now built in a daily opportunity for you to assess where they are. Now, obviously, where do you go from there? How do I document this? There're so many different ways you can do that.
And of course, you want to have a plan for that. But your plan might not be the way things will end up by the end of the school year. It's okay for that to evolve over time. But I think upfront, at the beginning of the school year, the most important thing we can do is to craft our routine, our classroom routine in math class, our program is built around a model that provides me with the opportunity on a daily basis to be assessing student thinking, and student understanding.
And when we do that, Jon, we know that that doesn't mean every student is being assessed. It's maybe informally they are, I'm looking around, and I'm making notes, and mental notes, I've written notes, however you choose to do that. You have to decide how that's going to work for you, whether it's a clipboard, whether it's bringing an iPad around, and just quickly documenting a few ideas.
And then, at the end of class, you reflect on that and like, okay, where are we? Who do I need to see tomorrow? Who do I need to ask a specific question to? And the one thing I always ask educators is, at the end of the lesson, are you sure who heard what? And that's a Lucie West quote. And when I heard that, I was like, that's really interesting.
When I leave the classroom, am I confident that students got what I was putting down? Or that they made the connections that we were hoping to make through the consolidation? Or do I need to spend more time here? And I know the way I was teaching what the gradual release model, I didn't understand that. Even if, let's say, I did a ticket out the door, I could do a ticket out the door.
But unless I'm giving students the opportunity to think during the class, it's going to be hard for me to really look at those consolidation prompts, and understand whether students are getting it if they haven't had the opportunity to actually explore these ideas. Jon, what's on your mind when you're thinking about assessment, and how you get started, or how you got started on your journey?

Jon Orr: Exactly. I just want to give one tip here, before we wrap up this episode here on what you're talking about here, Kyle. Because I think teachers are like, well, I want to do this, I want to capture these observations, I want to look at what students know, and who heard what, I want to be able to do that. How do I document? How do I keep that going?
And I think if you're using a model like I was when I was teaching for the first 10 years, which was I have a unit mark on proportions, and then it's out of this much. And it's really just comprised of quiz, test, assignment. That's the way I used to set up my marking scheme. It's like, I have those marks. But basically, if you're going to shift to listening and observing, and you're really concerned about what students know, on what topic, you've got to make a pivot.
And this is what helped us, we made a pivot towards a standards-based grading model, which means basically, now we're not having a mark for test unit, or test assignment quiz from unit one. We actually have specific standards that we are assigning feedback to students on, but also, that's where you can assign a grade if you want, and you can assign a grade that says how is the student progressing on solving systems of equations, or comparing fractions?
You can actually give kids comments on these standards. And if you switch to being standards-based, kids, and parents, and you have so much more information at your hands, to share with them, say a parent-teacher interview to say like, where are we? Well, on systems of equations, this is what I've seen. This is what I've heard. This is where they are, and we want to move them forward on systems of equations.
You've got so much more power to help kids learn the standards if you keep track of where they are on those standards. And I wasn't doing that before. Our unit-based module or assessment was on unit one, we had a mark. But it was comprised of tests, assignment, quiz. Looking at those numbers, I didn't know what the kid can and can't do in that unit.
And I think when we make that switch, and it's a natural switch, when you're teaching through problem-based lessons is because we're actually listening and looking for these things on a regular basis. Like Kyle said, the format you take for that, though, is up to you, and there're lots of different ways. You can use what he said, like a checklist, if you want.
We use a spreadsheet for a long time that we would update on a regular basis for students. They could see that spreadsheet, because we did that through Google Drive. And then, we morphed into some new tools that are coming out, like we've been using FreshGrade for a number of years now. And we go into how to set all of that up, and how to embed all of that into your program into our assessment for growth course, which you get access to as an academy member.
But module one is completely open to set the stage for you right there. So, that's a quick tip, but I definitely would recommend thinking about this now before you start the school year. Because you can start to build this, and think about how this is going to run for you once you start the school year. Because switching an assessment style midway is tough, not only for you, but for the kids too. Because you're changing what you value all of a sudden, and if you want to value growth, this is the way to go.

Kyle Pearce: Yeah, absolutely. So, it's okay if it's not fully, let's say, crystallized as you begin. In a perfect world, it is. You're going to have to take a stance as you go into a new school year as to what is going to happen, and how it's going to happen. One thing I'm going to maybe caution people to avoid is we're human. And humans tend to be very on-off, very digital. Balance is hard.
We want everything or nothing. And when we think about math, think of the false dichotomies that are out there. There's this idea that, for example, we've talked a lot about problem-based lessons. Some people are going to walk away from this episode, and think that they said problem-based lessons. So, that means we don't value students having any procedural fluency, which is actually absolutely incorrect.
We want to use problem-based lessons to build conceptual understanding, to work towards procedural fluency, where students, things become automatic, because they have such a deep understanding of what's going on in the background. The same is true here with assessment and evaluation.
A lot of people believe that if I'm going to go with more of a progressive approach, standards based, this idea of spiraling, and then this idea of assessment for growth, a lot of people think, well, students are never asked to know something by a certain date. And that's actually not true. We want all students to be continuing to grow based on where they are, we just want to do this in a productive way as we possibly can.
So, again, when we think of the reasons why we want to maybe morph a bit of our assessment and evaluation practices, I want you to think about those students who math class hasn't worked for, all right. I had clear dates that students needed to be ready for a quiz or a test. The approach students or the approach I pushed on them was to cram, the night before, did you study?
And really, what we're trying to do is say actually, that isn't all that helpful, because even those students who did cram a year later have forgotten most of what they had crammed. That goes through all the spiraling research you'll find out in our complete spiraling dive that we'll have linked up here. Well, the same is true here for assessment and evaluation.
We want all students to see and understand where they are so that they can take action and nudge forward. That doesn't mean we're going to just say, "Hey, we'll wait for you forever to put an effort in." That is not what we're saying here at all. We want students to just have the opportunity and feel like there's a purpose for them to put in an effort.
Because if they feel like the goal is way too far off in the distance, they're going to just disengage completely. So, this idea is like making a shift. But let's not completely try to pull the rug on everything you're doing. Because oftentimes, you find yourself more lost and confused than where you began. So, keep it productive.
Make sure that you're communicating with people in the community, in the Make Math Moments community, whether it's in our Facebook group, if you're an academy member, obviously, in the discussion area, it's great to be sharing those pebbles in your shoes. Or let us know through a math mentoring moment episode, if you go to makemathmoments.com/mentor.
If there's any of these ideas that are really causing you to reflect and you're thinking, I want to dive deeper here, get to that form, and let us know so that we can pull you on for an episode. And we can dive into that, and really try to help pull that pebble out of your shoe. Let's be honest, if it's in your shoe, it's probably in many other educators' shoes out there as well.

Jon Orr: So, we hope we have set you up for some success and giving you some things to think about as the school year approaches. We're just going to do a quick recap here of some of the ideas that we talked about so it's fresh in your mind as you walk away from this episode. But the first thing we talked about here was teaching through problem-based lessons.
And we talked a lot about this idea of a review week, and probably, "Hey, let's bypass a review week, and teach through problem-based lessons on a regular basis." Because there are a lot of benefits that actually trickled down through some of these ideas that we did discuss here. The second thing we talked about was this idea of interleaving and spiraling space practice versus mass practice.
We're going to have an upcoming episode on that specifically for you on episode 145. It is coming up, but you can get the spiraling guide by heading over to makemathmoments.com/spiral. We briefly talked about that connection with problem-based lessons. And then, we talked specifically here for the last little bit on assessment. And we definitely need to think about that now.
So, that we can start our school year off right on like, I want assessment for growth, and how do I need to set that up? What are some of the things that I need to do? We gave you a few tips to think about, and get ready for the school year off. Because I think if you switch now, you're in a better position for having a great year from day one to 180 by making some switches to a standards-based grading or standards-based grading approach to assessment.
All right, Kyle, that's it from us on this episode. As always, how are you guys going to reflect on what you've heard here in this episode? Have you written ideas down? Maybe you did a sketch note, or maybe you're sending out some tweets. Did you call a colleague? Be sure to engage in some form of reflection to ensure that the learning here is going to stick with you so that you start the school year off right.

Kyle Pearce: Yes. And make sure you open up that podcast platform on your device, hit that subscribe button, and do us a favor, leave a review. We love hearing the feedback through the reviews. If you're on YouTube watching this right now, make sure if you're making it to this point, I think you want to slap a like on there.
And do us a favor, and hit that subscribe button so that we can reach more math moment makers out there in the universe. Friends, show notes, and links to resources from this episode can be found at makemathmoments.com/episode139, that is makemathmoments.com/episode139. And Jon, until next time, I'm Kyle Pearce.

Jon Orr: And I'm Jon Orr.

Kyle Pearce: High fives for us.

Jon Orr: And high five for you.