Episode 145: What We’ve Learned About Spiralling
Jon & Kyle share insights on their journey with spiralling their math lessons over the last 8 years. They dive into what spiralling is, why you should consider this structural change in your classes, and how they changed to this model from their mostly traditional approach to math lessons.
You’ll also learn what they changed along the way in their journey as well as how to get started so you can save valuable time and maximize this approach.
- How spiralling can help you and your students learn math at a deeper level;
- How you can get started with spiralling;
- How you can build retention with your students so the learning sticks;
- What are the pitfalls of spiralling and how you can avoid them.
- HOW WE LEARN: THE SURPRISING TRUTH ABOUT WHEN, WHERE, AND WHY IT HAPPENS By Benedict Carey
- Make It Stick: The Science of Successful Learning Hardcover – by Peter C. Brown (Author), Henry L. Roediger III (Author), Mark A. McDaniel (Author)
- Spiralling Mini-Course: https://makemathmoments.com/spiralling-guide/ 3 videos to check out and downloadable pdfs to get you started
- Episode #40: How Do I Know When To Proceed Or Pivot My Plan? – [Math Mentoring Moment]
- Episode #42: How Do I Spiral My Math Standards Without Spiralling Out Of Control! [Part 2 of A Math Mentoring Moment]
Kyle Pearce: Hey hey Math Moment Makers, it's Kyle here, I've got Jon right next to me if you're watching on YouTube.
Jon Orr: Woo, right here.
Kyle Pearce: Some of you are listening on your favorite podcast app, today we are so geeked to dive into a deeper discussion about spiraling our math curriculum. A few episodes back, we were chatting about problem-based lessons and the topic of spiraling came up and we promise that we would dive a little bit deeper on YouTube. Some of you are listening on your favorite podcast app. Today, we are so geeked to dive into a deeper discussion about spiraling our math curriculum. A few episodes back, we were chatting about problem-based lessons and the topic of spiraling came up and we promise that we would dive a little bit deeper. And for those of you who have actually kind of followed us on our spiraling journey, there's a lot for you here. We're not just going to give you the same old, same old, we've got a lot of things that we want to do, including some of the things that we're doing a little differently than when we began this journey. So Jon, what are we aiming to do here? What are we hoping people will hold us accountable to when they listen to this episode?
Jon Orr: For sure. So we're going to get right into it, but we're hoping, and we're going to share with you how we began the journey so that if you've listened to podcasts episodes before on spiraling, that might be a little bit of review, but it's good to kind of talk about that because it's going to lead into what we've learned along the way. So some of the new stuff is that we are still both practicing teachers and we are learning things, modifying things, changing things, and then how we've changed that approach to spiraling. And then more importantly, how you can get started and kind of skip the pitfalls that we fell into and you can speed things up. So that's what we're going to be doing. Pal, let's get to it.
Kyle Pearce: Welcome to the Making Math Moments That Matter Podcast. I'm Kyle Pearce.
Jon Orr: And I'm John Orr, we are two math teachers from Make Math Moments and together...
Kyle Pearce: With you, the community of Math Moment Makers worldwide, we all want to build and deliver problem-based math lessons that spark curiosity.
Jon Orr: Fuel sense-making.
Kyle Pearce: And ignite your teacher moves. So as folks, all you Math Moment Makers heard in the intro, we're really eager to dive into kind of a quick summary of our own spiraling or interleaving journey. Talk about some of the things that worked for us as well as what inspired us to get on this journey. Some of you might be wondering, "Why would I want to do this in the first place?" And also what we've learned along the way and some of the things that we're sort of tweaking along the way as we always do, pivoting our plan and trying to continually improve our practice. So today, we're going to dive into that and we can't wait to dive deep into spiraling here.
Jon Orr: Yeah, let's do that, Kyle. So let's start off with how we began but also, in this part, we should talk about what spiraling really is for the folks who are, maybe you just tuned into our podcast and is your first episode and you're like, "What are you guys talking about? You're going to talk about like what you've changed along the way, but I don't really know what you're referring to in terms of spiraling." So it's also possible you've called it something different. Maybe you're calling it interleaving lessons or interleaving practice. We've been calling it spiraling after our good buddy, Alex Overwijk from Ottawa and that's where our journey began right Kyle?
Kyle Pearce: Yeah, absolutely. I feel like Alex and both you, myself and actually a bunch of educators from Ontario, many of which who have joined us on the podcast, we were all in this place where we're trying to figure out, how do we improve retention? So we came across and it seems like everybody came across maybe different instances of it. You can kind of think of spiraling as just mixing it up, in general, mixing it up. And there's so many different ways we could do that right Jon?
Jon Orr: Yeah. And if you think where it's maybe easiest to think about spiraling is think about what spiraling isn't what we used to do with teaching our lessons. And we were calling that in, and even on our spiraling course, our getting started spiraling course, we'll share a little bit about that a little bit later, but we were normally a textbook or a lesson guide, your unit plan or your course plan, your grade level plan, your scope and sequence. A lot of that would be the topics, the strands are generally, for me, and this is specifically for me. And I know for Kyle, because we taught at our grade nine classes like this for a long time is we were teaching those strands in silos. This is the term that we've used a number of times. It's like chapter one is all about measurement. And then when you're done measurement, you move on to say proportions. And then when you're done proportions, you move on to say linear relations.
And you never go back, right? For a long time, we never went back and did measurement and talked about the measurement ideas until maybe we brought that into some linear problem solving a little later on, spiraling is doing that on a regular basis. But generally we would never go back and talk about or do more problems on measurement until the end of the course when you're getting ready for your final exam or you're kind of summarizing the end, "Here's what we did. Here's our course review." We might've done that in September and now it's the end of the semester, it's January and we're reaching back and we always had those kids be like, "I haven't done measurements since September, it's been like five months." And we were like, "Yeah, we got to remember this so that we can do well on the final exam." And so that's siloing, this is like how we used to taught.
So spiraling is interleaving those strands and bringing measurement back a little bit later, not too far later. And interleaving linear relations maybe earlier than what you did before or it's kind of mixing up the strands so they're not taught in silos.
Kyle Pearce: Absolutely. And I would even argue too, we talk about this often on the podcast, nothing in life is sort of like an on or off, a yes or no, every textbook, every curriculum out there is probably doing some form of spiraling or interleaving, it's just at varying degrees, right? So for example, I remember teaching a grade 10 course where in the textbook, there was two quadratics units. There was sort of like your intro kind of graphing all of those things, and then there was a unit, they had it later in the textbook that sort of dug deeper into quadratics. And I remember early in my career thinking like, "Why did they do that? They should have put them back to back because then it's more fresh in my students' minds." And some textbooks do do that very thing.
But now we realize that actually having this opportunity for students to sort of come back and revisit and kind of dig a little bit deeper is actually a really helpful thing. So as we dive into spiraling again, there's sort of extremes, there's the, "Hey, take everything and throw it in the blender," which John and I have both tried that method. And there were some benefits we saw based on how we were teaching, but we've learned a lot since then so we'll dive into that as well and talk about some of the drawbacks of taking that approach. And then there's the other end of the spectrum where it's like, "Let's do everything as developmentally sound as possible. So if we start with measurement, we're going to try to hit every measurement idea in one big chunk. And then we're going to move on to like something completely different on the other side of mathematics, in a different strand. And we're going to kind of build from there."
So there's these extremes, we're not going to tell you today that there's one spot that you have to be in. You're going to have to analyze and assess where you fit, where your students fit, where the course material fits for you. But we do want to promote at least some of the pros and cons to doing things in different ways, based on some of our own experiences. But before we do, let's talk a little bit about why would we want to do this anyways? So again, we already talked about, we've got this spectrum and you're on the spectrum somewhere, right? There's some form of spiraling or interleaving, it might just be like very little or maybe it's a lot. And it might just be a product of how the curriculum that you were gifted from your district or from your principal, how well that was done for you and you just sort of follow through, but why were you and Jon, what got us on this path? What wasn't working for us or what did we feel we needed to improve in our own classrooms?
Jon Orr: There's a couple of things, and I think one main thing that I think got us into this pathway was that kind of feeling at the end of the course, we were teaching semesters in high school and when we were looking at the end of the chorus, we were having these kids who couldn't, you were like, "Oh, we have to stretch back to September and think about these concepts again." And it's like, they're gone. You teach something and then don't touch on it again, and by the time you get to the end, it's like we have to almost relearn it. And you were thinking, we're almost cramming for this test because we actually forgot a lot of the material when we have to kind of re bring it back in. And it was like, "How can we fix that? How can I get actual, deeper learning so that it's not just, I now need to mass remember this so that I can just do well on a test and then forget it again."
Kyle Pearce: Yeah, in something I remember vividly myself is like, so back to this idea that at the end of a course, when you really pause and think about it, if you supposedly taught something, students did this evaluation and I'll call it an evaluation because that's how we used to assess and evaluate our students, it was like, "At the end of the unit, we're going to evaluate where you are with this thing called a test and that's going to be the mark you get there and that is who you are as a mathematician for that concept this year." And really, the only thing that could influence that would be how they did on this thing called the exam at the end of the year.
But as many teachers who are listening, anyone who's ever had to do a standardized tests, which many of our American friends would know. Anyone in Ontario who teaches grade three or grade six or grade nine, we have standardized testing in those grades. And then any high school teacher who has exams, they're dealing with this sort of end of the year crunch time. And I guess what we eventually did was we sort of paused and we thought to ourselves, if students supposedly, and let's just pick a random student in your class who received an 80% on unit two, they got an 80%. But at the end of the course, it appears as though they know nothing about that idea, right." They come and they sort of go, "I don't remember any of this." It really should cause us to pause and wonder how useful is that form of evaluation being used in our course?
And now, Jon and I, we do more assessment than evaluation throughout the experience of a course. We assess for growth, we don't just evaluate an peg a number anymore. We still have grades, but we use them as a means to determine where we go next. And at the end of the day, we sort of went, "Okay, if I'm reteaching this, how long after this test is that going to be useful for?" So I would take like, I remember in some classes two weeks at the end of the year and I would just regurgitate, I would stand up there and I would lecture my students, and this is in high school, and I would basically reteach everything. And I remember it being one of the worst times of the year. And I feel like a lot of teachers feel that way because you feel like, "What the heck did we do this year if I'm up here, sort of reiterating everything we did in order to get these students to supposedly achieve?"
And then the very next year, I remember I had a class of students in the spring and it was a grade nine course, and then I taught the grade 10 course in the fall, and it was essentially the same group of students. And when they come back and you sort of think to yourself, "How "hard" we all worked in grade nine and how little was sort of there at the beginning of this grade 10 course," I really paused and I thought, "We're going to have to dig deeper here and figure out how can we help with this retention thing?" So for us, it was all about retention, and Jon, we learned about all kinds of things. What was one of the books that we sort of picked up and it kind of opened our mind to how the brain works and why some of these things were actually happening in the first place?
Jon Orr: There's actually two books. I think that kind of helped us wrap our minds around this and also kind of give us proof, give us the science behind why spiraling works at a deeper level for learning and retention. The one book is How We Learn: The Surprising Truth About When, Where, and Why It Happens by Benedict Carey, that's one book about how we learned specifically. But the other book that I think helps understand this interleaving approach mostly, which is called, Make it Stick: The Science of Successful Learning by Peter C. Brown, and there are a couple other authors there. But those two books, I like the support that goes, "Hey, what we're trying here in our classroom has some scientific evidence to kind of support these ideas," which gives us a push to keep moving. And we go, "Oh, that's what we wanted to try and there's evidence to help us kind of keep moving along that.
So those two books are kind of help us keep moving but I think what you're saying hits the nail right on the head Kyle with this idea that retention. But the other idea, I think why you might want to try this approach is this idea of problem solving and building better problem-solvers. I think as a math teacher, most teachers want to say, "I want to create better problem solving with my students." And I think when we get to the end of the course or the end of the unit, you want your students to be able to apply the concepts that they've learned in different situations. They have to be able to bring those ideas back. And I think the spiraling approach, and also how we're going to kind of show you what we've realized along the way of which is the next part we're going to talk about, that realization of how to teach topics so that you maximize the spiraling concept.
Because I think there's a way to do that right Kyle? There's all this proof that says, "Hey, interleaving things work, except that I think from what we've found out, it's kind of for maximizing problem solving, there's a way to do this well and I think a way that kind of leaves some learning on the floor."
Kyle Pearce: Yeah, and one thing that popped out to me in these books is this idea of the illusion of understanding. And if we go back to that unit two test where a student gets an 80% or 90% or a 75% or whatever it is, they talk about this illusion understanding where it's like we've pulled the wool over our own eyes because the content is so familiar that it's really in your short-term memory and you're kind of relying on that understanding. Now there's some students in our courses that they didn't grasp onto that, so even though it is familiar, it is recent, they're still not at a place where they can hang on to that learning.
And that could be because of a learning disability, it could be because maybe they miss some or maybe they just don't have that short-term memory working on the same level as another student in the class. But either way, this illusion of understanding is something that really got us thinking about, "Okay, we're going to have to like change this." So when we began, we took our very, we'll call it procedures first sort of approach to teaching. We used a gradual release of responsibility model where I would teach the concept, I would give some examples, I'd be asking students to participate. The same five kids would participate during my lesson, and then we would have them go off to the races and sort of mimic what we were doing up at the board.
And if that's the approach we're using, which we were using, and all I'm looking to do is to try to get a little more retention of the steps and procedures, which is really what I was after, at the time, that was sort of what I thought was important. Then mixing it up can actually be helpful with that. But something that can actually hurt is maybe mixing it up too much where there's actually not enough time for students to sort of hang on to anything, right? And I think you've had some experience with that, and I know I have. Should we unpack sort of how we began this interleaving process?
Jon Orr: Yeah. Let's do that before we get into some of the modifications we've made along the way based on what you're saying on this illusion of learning. But the way we first thought about spiraling and what we thought it was was just that, let's switch things up. But when we said, "You know what," and I've often referred to it as we put all of our lessons into a big one, think of like a t-shirt cannon, and we fired them into the stand. That's kind of like we load them up and it was just like, boom, and we just fire them all into the page of like, this page is going to hold all of our lessons, but then it was like scattered, right? It was like, that's how we almost like playing 52 pickup, right? So we throw the cards down and we pick them up in different orders and wherever our lessons fell, that's where we did it. And then we were like, "Okay, well wait a minute, but we should maybe put this one and this one together because those two are closely related.
And I think that's how we've actually evolved is that we just randomly threw lessons down, but then realized if we're going to teach linear relations, we should probably make sure we do some proportion work first. If we're going to teach measurement, we should probably do the 2D stuff before we do the 3D stuff, right? So there's some of that going into play about where you want to design your course plan. But that's how we did it, it was kind of like we just scattered them out and around and then we taught the lessons and it was just this interleaving idea because we would do some little bit on measurement and then go, "Okay, well, we've had a couple of days on measurement, well, let's just jump right over to proportions and let's just jump right over to linear relations.
And I'm using the topics from our grade nine curriculum because this is where we first did, is in our grade nine program. Kyle and I shared our thinking back and forth together on where these lessons would go, even though we don't teach in the same class or we don't teach in the same district even. But right Kyle, we just kind of scattered things out and then what we did is after iteration and iteration of teaching the same course is when you start to realize, and this is where you guys can benefit from us is that we start to realize what lessons might go well together and then we started to make more of say these mini-units, right Kyle?
Kyle Pearce: Yeah, absolutely. So you can see up on the screen here, and we'll be sharing a ton of resources here. Those who are watching this on YouTube, you can see a screen share, I've just got kind of this spreadsheet where we would take lessons and basically we would try to kind of do a little bit of mixing and matching. You can kind of see the strands here, these different colors are representing how we've mixed things up. Something that I think we did well at that time John was, we did it developmentally appropriate and we did try to keep the floor low enough so that no matter what, it wasn't like we just picked up and sort of went full steam ahead, we made sure that students were with us there. But you could see how that could be challenging, especially for educators who are starting to spiral or dab with spiraling for the first time. What should I do first? Where should I do it?
So we found that this method, while it can be effective, I found that we had to do quite a bit of tweaking along the way, and it was kind of hard also to determine like what tweak would actually have an impact because we were tweaking so many things it was like, when things were going well, what was it that was doing it? Was it the order? Was it how we taught that lesson? Was it something else?
And something else we should also mention too, this course that we began spiraling with was a course for students who had typically struggled in the previous few years of schooling, likely had struggled for many years prior, so a lot of the concepts they had at least experienced in some way in some shape or form. So I think that changes things as well. When it's new concept that maybe a student hasn't explored at all, we want to be a little more careful with how we mix things up. And we would maybe say, "Take that t-shirt cannon and maybe put it to the side and maybe start with these chunks in more larger, more succinct chunks and do some spiraling in that way."
Jon Orr: Yeah, and I think the planning process is super important and definitely what you want to do this with a peer, a partner, a team, to kind of go through this because I think that is for teachers, the most rewarding part of this journey on spiraling because it not only helps you kind of see where things get placed, but you start to develop this deep understanding of the standards, right, the curriculum concepts, and you know when to look for them, that's one of the biggest pieces that we've kind of realized where we had a lot of success is not because we just interleaved. Because I spoke with the teacher who says, "You know what, spiraling, okay, let's try this. Well, what do I do?" A very traditional teacher is like, "This is the way I do it. I teach the same way you did well, how do I get into this?"
And then at the time we felt like, "Hey, if you're just going to interleave, you could take lesson 1.1 and then go 1.2 and then, well that's enough and then go to 2.1 and then 2.2 and then do 3.1 and then stop and go that's a unit." And then this teacher was like, "I'm going to test now on that unit." So there was nothing different about the style of teaching, it was just the same lessons just interleaved in different ways. We found that the success that we experienced, because we weren't teaching lessons the same way we were before, we were actually teaching problem-based lessons before we spiraled, right Kyle? So we're teaching through problems to start and we just interchanged our problems, which is what Alex Overwijk was doing. That's where it kind of landed. It was a natural progression for us to do that.
However, to ask a traditional teacher who teaches very procedurally to change, they might not get a lot of that same benefit we got with the deep learning, with the interleaving, with the remembering, with the retention, because like you said, this illusion of learning is going to happen because all we're doing is now if we're doing 1.1 and 1.2 and two point, all of a sudden now it's a whole whack of just not connected ideas that it's almost like it reinforces this math has just a whole bunch of stuff to memorize if you just do it that way.
Kyle Pearce: Yeah, exactly. And you might see, depending on how big the chunks are, the way I had taught for many years was that's what I'm after, I'm after you to be able to do problems that you had seen before or very familiar problems. And once in a while, I would throw in more of a challenging problem. We would always get slack from students that we had never taught them that so that was unfair to put that problem on there because we didn't teach them. But that was sort of what we had trained our students to believe. But even if I'm teaching in that way, if I do space out my practice, if I do kind of come back to ideas a little bit later, you're probably going to see some retention improvement.
But again, at the end of the day, it's still a bunch of memorized ideas, which will eventually fade if we're not using them and we're not making connections to them. So what we had realized over time, at the same time, Jon and I were experiencing with these things called three-act math tasks, we've talked on the podcast many times of how we fell on our face many times with those types of lessons. We usually use them as sort of like end of the unit summaries or something to get kids interested. But then we would kind of go back to that, "Okay, now here's the steps you need to memorize."
And I think the big aha moment we've had over these years is by all of the different math educators who have influenced us, many of which, who have been on this podcast. So you've got Dan Meyer on there, you've got Marian Small on there, you have Cathy Fosnot on there. There's so many educators who have come and we've taken different ideas and we've started to make sense of where this fits. So this spiraling idea and this problem-based lesson idea and making connections and building conceptual understanding has really come together and sort of dovetailed nicely to create an up on the screen for those who are watching the YouTube video, you can see these little spirals, we now kind of are back to calling them units, we do these many units of study, but we mix up when they might happen and we try to keep it developmentally connected because there's something that I think we lose if we take that t-shirt cannon of concepts and we just sort of fire them everywhere.
It can be really hard unless we're very intentional for students to make connections even if the teacher's working really hard to make those connections and help students make them, it can be really hard for students to kind of make sense of it. Why is this happening? Does this connect to this lesson or does it connect to that lesson? So we're now in this place where we try to keep our little spirals or our units are more like four, sometimes all the way up to eight day chunks of ideas that emerge over a few days. But then after that work we'll maybe move on to a different area of the curriculum, as long as it's developmentally appropriate, right? We don't want to just pop around to any random unit, we want there to be some logic and rhyme and reason to why we're doing that, and then we might come back.
So if let's say I was working with part of division, I might be working with that idea and then maybe in the next unit, maybe I go into a fractions unit. Then I come back and we start looking at quoted of division and start referencing, "Wait a second. How is this different from partitive division?" And making connections that way. So you can see how there's still a spiral happening, but we're trying to keep the chunks more recognizable, we want to make sure that students are making sense and given an opportunity for some purposeful practice throughout. And then something that I think is okay to do a little bit more randomly, like the t-shirt cannon, would be some of that purposeful practice or some of the assessment pieces that we give students.
So I could give them something that we haven't looked at in four or five weeks, just to see where they are with that idea. Are students develop? Has that idea crystallized? Have they conceptualized it? Or is this something that, oh, we might need to pivot and come back and continue going a little bit deeper with that idea?
Jon Orr: Yeah, and another great thing that I think we realized as we kind of got deeper and deeper into spiraling is the benefit of those tasks and those kind of mini-units and trying to find those mini-units that have multiple standards that you can touch on in that same progression. And they're sometimes hard to create or hard to find but one that you can go, "Okay, well, you know what, in these group of three lessons, we use the same context, but we touched on these three different strands, we brought them to the forefront." And I think that's one of the big benefits of spiraling where you can save a lot of time is that you get to kind of expose or merge those ideas and then they're out in the open and you talked about different strands all in the next in those couple of days, but then when you come back to it, after you went somewhere else, you come back to it, you can start to strengthen some of those things up.
And that's where that retention, things start to build is that we spaced those ideas out, we brought these ideas up to the forefront. Maybe the learning goal for that day was on this one thing but we also touched on these other two things. And when we come back to it, we can go, "Okay. Our learning goal now is on this thing, and we touch on these things." When you have multiple content strands where a content standard's kind of emerging in the same lesson or progression of lessons, I think we saved a lot of time on our end because you can talk about those things in that day, but that's where we strengthen a lot of ideas up.
Kyle Pearce: I think one piece as well, that I think is really important for us to mention here before we start talking about maybe some of the next steps, some of the getting started ideas that some of our listeners might want to explore is just the idea of how the problem-based lesson approach really helped us with getting to what we were after, which was students being able to solve problems, being resilient problem solvers, persevering through problem solving and relying less on this idea. I used to always think if there was a problem that we hadn't "covered" yet, I was always concerned that I was like, "Well, we can't do that because we haven't done blank yet." We haven't explored fractions yet, so that's not something we can do.
But through a problem-based model, where the task is so low floor, that gives students an opportunity to enter where they are, and that's what gives us an opportunity to assess where they are and determine where do we need to go next? Where should we be focusing? And that to me, I think, is really important because if I am teaching procedures first or maybe procedures only where students are memorizing things and they're not really conceptualizing them, then it is a siloed, it is an isolated idea that they won't be able to necessarily apply to another area of mathematics. So for us, I think that piece is so key. And I would say that that is one of the most important lessons that we've learned along the way is that spiraling can be really helpful, especially interleaving in spacing practice.
But the reality is, is changing how we introduce math concepts so that when students come into this, their first response isn't, "I don't know where to start." When students say, "I don't know where to start," that usually means one of two things. It means either, "I don't understand what the context of this problem is, right? So I don't understand the problem itself, or I'm trying to think of a formula or a step or a procedure that will do this work for me and I just don't know which one it is," which again, I think is kind of related to the first problem, "I don't understand what's happening here."
Through a problem-based lesson, students are understanding the context and they're allowing the context to sort of dictate what strategies and models they're going to leverage. And as they do this work, that's what's going to trigger some of the previous mathematics they've explored. As they start modeling it, that's where they might go, "Oh, you know what? I'm seeing a relationship between these two quantities. I think this is a ratio that we're working with and I know these things about ratios, for example." So those I think are the big, big pieces.
Again, no matter where you are, I think getting started can look very different for one person to the next one. Thing we would advocate you not do is sort of taking what you're doing now and just sort of trying to go all the way to the extreme and doing like the exact opposite, because you're probably not going to see much success there. Yeah, you'll get burnout. You might almost feel like, wow, this is like, things are going to happen and the results are going to be less impactful than the method that you've been using because you've been working with that method for a long time and making tweaks and changes along the way.
So whatever it is that you choose to do, we encourage you to do things slowly and methodically. We want you to feel like the change you're about to make is going to have a difference because blank what's that hypothesis you have as to why what you're about to do is actually going to improve learning for your students. And if you're not sure what that is, then maybe you need to do a little bit more reflection on that or maybe a little more reading or a little more thinking on that. And I think that's what we want to share with you now, before we wrap up, right Jon? Where could people start if let's say they've heard, they've listened to our story, maybe they see themselves in their students in our story a little bit? And they're wondering, "Okay, I want to get started, but I also don't want to completely overwhelm myself or my students along the way. What could we do?"
Jon Orr: Yeah, and so we're going to share our spiraling guide link in the show notes page, we'll toss it out here in just a moment after we kind of share these kind of getting started tips. But I think there's a couple of ways we can get started if you want to go, I want to go in, like Kyle said, you don't want to slowly do that, but it could be taking your units and consider switching the orders of some of those units. And that gets you into this place where you're doing a little bit here, you're doing a little bit there, and you're doing a little bit later on. Keeping in mind that I think what's really important though is to do that with teaching this developmentally, thinking about those progressions and also with this idea of problems first approach.
This is why all of the tasks that we've created on our Make Math Moments website makemathmoments.com/tasks are problem-based to start, and a lot of them are now full five-day units because there's that progression. And then consider taking one of those, doing the five days, I think the five days Kyle is also built on almost if you have 60 minute learning periods. And then maybe switch to another unit and then try that and then come back, you'll see some overlap, right, with strategies with models, but then you're covering different areas, so you might want to consider that. That's probably how we would definitely recommend getting started is switch those units up, but then make sure that you're doing developmentally because you don't want to go back to being like, "we didn't see any benefit, we saw them actually worst results because we were still teaching procedurally." So I think if you're going to make a switch that deep, you have to do both at the same time.
A couple other ones that we recommended that are really easy switches to get into, to kind of dip your toes in, which is seeing some benefit of the retention side of interleaving, which is partly also how we kind of maybe even started before we did our problem-based lessons, which is using some warm-ups, like small things at the beginning of your lesson, math talks on different ideas not related to today or those learning goal that you're planning on that day, maybe you're going to do a math talk here on this idea, then next day, you're going to do a little warmup idea on something that's coming up. A lot of preview is really nice too because you're like a touch on idea and then you go and do the learning goal for that day. And then it comes back later on. So those are some easy kind of not technically, I would say, spiraling ideas, but interleaving ideas.
And I think another one we've heard from many teachers who have kind of ventured in this as this idea of lagged practice. If you are say making the switch into this idea, but maybe you're like, I don't want to go full in yet, you might want to consider any practice ideas, purposeful practice ideas you give to your students. You might want to mix some of those up, which means like today, you're going to do some practice on today's learning goal, but also you're going to do some on yesterday's learning goal or a month's ago is learning goal, and then that kind of keeps things rolling. So there's some interleaving, there's some space practice versus mass practice happening.
Those would be some kind of getting ready, getting started ideas. Hey, and if you've started already and you've got different ideas, we want to hear about it. You can get onto the show notes page, put a comment in there of how you got started and maybe recommend for other people. Kyle what's our mini course link and I know that you've been sharing some resources here up on the screen as I was talking. So if you're watching this over on YouTube, you can kind of go and watch some of the video, the visual support here that we're providing over on YouTube. But Kyle, where can people go learn more deeper than this particular episode on spiraling?
Kyle Pearce: Yeah, for sure. We've got, first of all, in your podcast app, have a look, there's a lot episodes in there where spiraling does come up when we're talking about planning and so forth. So episode 40 and 42 are great episodes where we dive into this idea of planning and spiraling your plan. So you can definitely check those out. We have a full guide at makemathmoments.com/spiraling-guide, or even if you just hit Google and you just type in spiraling guide math, it will pop up. So again, makemathmoments.com/spiraling-guide.
And for those who are in the academy, you've got kind of an extended course inside the academy where we kind of build on our spiraling guide and we've got some case studies and all kinds of other goodies in there as well. So if you're not a part of the academy, you know what, this is the time of the year where people are thinking of new ideas, come join us, you can sign up for 30 days, you don't pay a cent, dive in. And if you want to stick around, awesome, if not, you cancel out your account and you are good to go.
But you know what, we've got hundreds of members inside there gobbling up amazing ideas and sharing them in the community area. So if you want to be a part of that community, head over to make mathmoments.com/academy, and just know that we'll have all of these links in the show notes for today's episode. So hopefully this serves as a nice idea on what spiraling is, why we want to do it. And again, most importantly, some of the big things that we've learned, you can access all our problem-based lessons up on our site, makemathmoments.com, so check those out because it's kind of how we're doing things now based on everything that we've learned over these years. So we hope you've enjoyed the episode. And Jon, what do you say we wrap this thing up?
Jon Orr: We are wrapping things up. We also touched on that we are going to throw in the show notes page a couple of episodes in the past from podcasts, we talked about episode 40, which is how do I know when to proceed or pivot? And then episode 42, how do I spiral math standards without spiraling out of control? Which is part of that case study that we mentioned that you can listen to those episodes there. But Kyle, let's wrap things up because as always, our episodes come out every Monday morning and we want you to make sure that you subscribe. If you have not subscribed to this podcast, hit that button now. Maybe this is the first time you listened, maybe this is the hundredth time you've listened. Maybe it's the seventh time, but hey, subscribe so that you don't miss out our episodes. We release them on Monday mornings so do that on your favorite podcast platform.
Kyle Pearce: Awesome stuff my friends. Head on over to the show notes page at makemathmoments.com/episode145 or episode 145, makemathmoments.com/episode145. Until next time my friends, I'm Kyle Pearce.
Jon Orr: And I'm John Orr. Hi fives for us, and hi fives for you.
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