Kyle Pearce: This week, we reflect on our experience teaching remotely and realize that while the experienced was and continues to be quite a struggle, with some hardship, comes new learning.

Jon Orr: Stick around as we reflect on the silver linings of teaching during COVID-19 that could easily go unnoticed.

Kyle Pearce: All right, let's get ready because... here we go.
(Singing).
Welcome to the Making Math Moments That Matter Podcast. I'm Kyle Pearce from TapIntoTeenMinds.com.

Jon Orr: And I'm Jon Orr from MrOrr-IsAGeek.com. We are two math teachers who together...

Kyle Pearce: With you, the community of Math Moment Makers worldwide, who want to build and deliver math lessons that spark curiosity...

Jon Orr: Fuel sense-making...

Kyle Pearce: And ignite our teacher moves. Welcome to another episode where Jon and I get to do a little bit of riff and back and forth. And in particular, in this episode, we're going to talk about three things we can learn from online learning.

Jon Orr: We are pumped. Let's not waste any more time. Let's dive straight in.

Kyle Pearce: Hey, hey there, Jon, top of the morning to you. How are things going on in your world? I don't know about you, but my body is really, really aching. And I think I actually sent you a message this morning on Slack saying that my whole right side from my buttocks down my right leg is really, really tight. crosstalk. How is your body holding up today?

Jon Orr: It is also quite sore. And we are recording this episode early morning in the summer. We're going to share with you why that's the case, but yeah, we're hurting a little bit here today, but summer's just flying by and we're definitely doing our best to make the most of it, which is part of our big win we want to share with you here this morning before we get into the bulk of our episode. But Kyle, why don't you start off and share your big wins that you've had over the last couple of weeks so far?

Kyle Pearce: Yeah. Thanks. Yeah, Jon. Obviously it is summertime as we're recording this, actually this one will be released in the summer. Oftentimes we give ourselves quite a bit of time, but this one we left a little bit further because we wanted to really focus in this episode. And as you'll hear, as Jon said, as we get into the bulk of this episode, we're going to talk about some of the lessons that we've learned and some of our reflections. But for me, some of the big wins on my mind right now, one in particular from a personal standpoint was exactly why I'm sore today. It was great having your crew over yesterday. And we went out on the lake on Lake St. Clair, which is kind of like a little... It's a big lake, but definitely not a great lake.

Jon Orr: It's a little one compared to the great lakes here in Ontario.

Kyle Pearce: Yeah. It's kind of like a little... we call it the pond between Lake Huron and Lake Erie, Detroit River flows. It flows into Detroit River.

Jon Orr: It's big. You can't see across it, big.

Kyle Pearce: Yeah. crosstalk. On a clear day, we can see across to Michigan. And if we head out on the boat, I've got an old ratty pontoon boat, some people who are close to me know that I call it the ratty pontoon boat. It's about 25 years old, but it does the trick. And we had an opportunity to get out there and do some water skiing, some tubing. And I went down pretty hard at one point-

Jon Orr: You were on one ski though.

Kyle Pearce: Yeah. I went on the one ski and Scarlet, your wife's Scarlet, was on the boat and after she said like, "It was like I got shot in the ankle." And I was like, "What happened?" I don't know if I got caught unaware or something, but I went down in a really awkward way and I'm feeling it right now. From an educational standpoint, it was great for us to get some clarity here in Ontario from the Ontario government about what our back to school plan will look like come September. Here in Ontario, anyway, we go back after the Labor Day holiday, typically. I don't think everyone loves the plan, but I guess for me it's a big win to at least have some guidance, some understanding, some time to wrap our minds around what this might look like, sound like. So again, not really saying that I like it, hate it, but at the same time, I just wanted to have some sort of clarity to understand what's going on. Jon, how about you? What are your big wins lately? And then we'll dive into the episode.

Jon Orr: Yeah. I echo your personal big win. It was really nice yesterday to come on over and get our families together to share some of the summer. I think you don't give yourself enough credit, Kyle, being the great skier you are on the water. You did a great job, even though you fell. I think we all fell eventually, but it was great to get the kids. We've got young kids, but the kids gave it a shot. And it was a pretty fun day yesterday to do that. So, that was a big win.
This week for me, personally, educationally, I think like you said, it's been good to reflect. And I think that's what I've been doing lately. And we saw a message, I think it was on Facebook, it was on one of those memes, and it was like, there's only one month left of March break before schools starts. And I think in our last episode, when we did the back to school episode just a couple of weeks ago, that was released a couple of weeks ago, we talked about August is always the longest Sunday night ever. For us here in Ontario because we go back to school this year right before Labor Day, kids come back after Labor Day.
But it's August where we definitely start to reflect on what the last year looked like. And especially this year, our COVID challenges. What did our classrooms look like beforehand? What did they look like during COVID-19? You start to think about what you're going to do better, what you're going to change. So I think this long Sunday night we're having right now is giving us time to reflect. So that's what's going on. It's a big win for me just because you're thinking about it, even though you're trying to stay in vacation mode, but you're thinking about those big challenges, which we're going to share here today in this episode. That's what this episode is about. It's thinking about these challenges, this reflection, and then how to move forward a little bit. It's an extension to the back to school episode, but more general in detail than just starting the school year off, but thinking about the school year as a whole.

Kyle Pearce: Yeah. I think you nailed it there. When we start to reflect on this very long March break, as you mentioned, for everyone in Ontario they're laughing because right as we went on our March break, that is when our Ontario government announced at the time a two week pause crosstalk. We definitely weren't. And we would only share that with educators because we definitely don't want the public to think that we did nothing over these many months of distance learning and so forth. We know it was very, very challenging, stressful. When you think about it, one of the things that maybe the silver lining... this episode is kind of a big silver lining episode, I think. And it's based on these reflections. I know that it personally tested my own resilience and that was around how I do things. We talk in math a lot about teaching math conceptually and not rushing to algorithms or procedures. Not that procedures aren't important. We do think that. But we don't want to rush there.
And when we think about our own practice and what we do each and every day, there are so many things that we have proceduralized that as soon as we got thrown into this COVID blunder, essentially all those built-in procedures were taken away from us. Like for me, it was very routine. I spoke on a few episodes about this, that I really struggled early on to find my routine. It was like I was committing so much brain juice to trying to figure out like how am I going to start my day now that we're at home, the kids are at home? How are we going to schedule their work during the day? And really, I call it entertaining, but at the end of the day, it's like, how are we going to ensure that they have meaningful days? That we don't look back and regret what they did over this time period? And of course we change a ton of things.
I think the silver lining is, we were sort of forced to think on our feet a little bit, regardless of your role in education, reflecting on things that really work. And maybe some of the things that we thought were working, but maybe now we've been able to shine a bit of a spotlight on that and at least ask ourself the question of what things might we now change as we hopefully get back to this face to face sort of regular or traditional education model.
And I think we're going to talk about three big ideas here, three big reflections that are on our mind. And it's not to suggest like we have answers or that after this episode it's like these ideas or these reflections are going to be fixed for all of us. But it's things that I hope all of us can think more about. And the first one, Jon... and I know you and I have spoken about these ideas throughout the summer, throughout this very long March break as we said, at length a number of times. And the first one that really popped up a lot, and it always popped up in the past, was this idea about engagement. But now more than ever, we think and we realized how important engaging our students was, especially in this distance learning scenario. Jon, what are some of the things that you've been reflecting on when it comes to engagement? And maybe it's like light bulb moments that went off for you, or just wonders that you still have about how that might influence what you do moving forward.

Jon Orr: Yeah, there's this phrase that's been floating around in my head for a little bit. And it was something... I think I had listened to a podcast that talked or replayed commencement address. And then one of the commencement address titles, I think, I can't remember who it was. I think one of the Steve Jobs commencement address a number of years ago to a group of people. But the title of it was that, I'm not going to wish you good luck. And it goes into reasons like why good luck is not necessary because we need to go through some hardships. We need to go through hardships to learn things about who we are and what we can improve upon. That always stuck with me because I always thought going into a school year or talking to a new teacher, you almost want to say like, "I'm not going to wish you good luck. Because if everything was smooth, if you never had trouble in the classroom or trouble in your teaching life, then I have a feeling if I never had that trouble or experienced pushback from students, I would still be an ineffective teacher."
And I know that for sure. So it's like people say good luck. And you really hope that you're not going to have issues in the classroom this year to overcome. But those issues are what I think make us better teachers. So we want to have, like, if you're going to wish a new teacher good luck, you're going to wish a new teacher to have struggles because it's going to make them better teachers. And so when I think about what's happened this year, COVID-19 has thrown us all a loop to think about what's going on in our classrooms. And it's definitely like it wasn't smooth. So it wasn't smooth. So it's definitely given us pause to think about what has been working and what hasn't. And so we're talking about engagement that all these things that we've been doing in our classroom to sparking engagement with our students, like we're using three-act math tasks and we're teaching through tasks to build voice in your classroom.
That gets engagement from kids that might not normally engage or breaking away from traditional instruction. Then it's just like chalk and talk instruction, but we're getting more engagement and more dialogue in our classrooms. And then all of a sudden COVID-19 hits and it's like, "Oh, what do we do now?" And we're starting to move online. That engagement drops off. And so it brings up this idea of what was really engaging our students. And I think Kyle and I we've talked a lot about that in our live Q&A calls with our academy members. We've talked about it on the podcast here before, because I don't think have all the answers. You said that earlier, Kyle, that we don't necessarily have all the answers here in this podcast episode, but it's something that I'm reflecting on like what was working in my classroom. I know my group work at the boards was working for engagement with my students. My students were faster to get to work at the boards with markers, standing in groups.
Now, what does that look like coming into this school year? I don't know yet. I haven't figured out what it's going to look like. What we recommend to do to people when they ask us like, "How does this work in the classroom, Kyle?" When they're talking about any kind of structure we ask them to change. And often we just say, "You got to be brave enough to give it a go and try something."
I don't know exactly what my classroom is going to look like come the fall because according to Ontario's plan right now is I'm going to have everybody normally in my classroom, every day. So I'm going to have probably 30 kids per class in my classroom every day for longer. It looks like it's for longer than normal, like a double period altogether, like a two and a half hour block of one class. And I'm trying to imagine like, "Well, am I going to allow... can they go to the boards and work in partners? They can't share materials. So each of them has their own marker. Are they allowed to share the board?" These are questions I don't have answers to, but it's definitely giving me thought to what is really engaging for my students, because when we moved to online, we know that some of those techniques teachers were using to think they had engagement. All of a sudden this didn't work. And it brings up this idea that we've talked about here before, Kyle, about what type of engagement you are getting in your class.
And that's what I've been reflecting on is, was I really engaging my students cognitively or was I engaging my students behaviorally? Because we know that when we moved to teach more task-based, Kyle, and more student-centered so that the students were working before we were showing them what to do, we talked about... we were in the old method of teaching for us behaviorally engaging our students because they were compliant. Just because they were quiet, just because they were raising their hand when they were asking a question, we said, "Hey, our kids are engaged." But it was really behavior. We were scaring them into responding in a certain way, but we know that we moved somewhat cognitively. But now I'm like, when we went online, a lot of that engagement for us even dropped off. So trying to do three-act math and task teaching, even online, we didn't have the engagement that we were hoping for. And it begs the question, were they really cognitively engaged still? Or were they behaviorally engaged? This is that level of engagement that I've been wondering about.

Kyle Pearce: I know, Jon, for your district in particular, that quad master approach, it sounds like my district will be doing the same. Our area is actually not in phase three yet of the back to... I don't know, back to work plan or whatever it is for Ontario. And we're heading there in the next couple of days, but it sounds like our plan might be a little different based on higher COVID numbers in this area. But when you're saying like quad masters, and now trying to engage kids for a long period of time, like you had just referenced, like for two and a half hours or whatever it is, engagement's going to be even more important.
Not only did we have to rethink what we were doing when we went online, I had a lot of teachers, for example, that I would chat with and they would say things like, "I'm struggling to do what I would normally do in the classroom." Sometimes they would do more of like a lecture style. And online it's even harder for students to stay focused. They've got other distractions in the home. Maybe they're not really that interested in the material as is. And that could be really challenging.
So yeah. So the problem based learning piece, if you're not already teaching through problems, teaching through task, what better time than now to give that a shot. And we constantly say that to our academy members when we do our monthly Q&A calls, we're constantly sharing that. Again, a silver lining right now is that nobody knows how to do this. What we've been doing... No one knows how to do this right. There's never a right or that 100% must be done this way. But at the end of the day, it should open the door for you to be a little more experimental, to be, I say innovative, but not like in the buzzword sense. Try new things and see what works for you.
Hopefully that's like a takeaway you can get from this experience. Again, as Jon and I are reflecting, it's like, "Wow." We have to realize that even at Make Math Moments, when we think about the three part framework, we're trying to create a procedure for how to run our classrooms. But when things change, we have to be able to think about what at its core is really important. And one part that really popped up for a lot of educators here in Ontario, and maybe this might be the same or different where you are from the listener, but in Ontario, from an equity standpoint, when we went to online learning, the government also announced that from that March break point, that middle of March, that we weren't going to allow student grades to drop. And that was a huge challenge for many teachers, Jon and I included, going like, "Okay, what's the impact of doing so?"
Now, we get why we in Ontario want to be very equitable, access and equity is so important. We didn't want any student in the province to not have the opportunity to, or I guess not be punished for having access. And that we agree with, totally get that. We totally understand. But then the part of around assessment that teachers were saying is like, "Now, if kids aren't going to have to work hard to get a higher mark or to keep their mark at what it is now, students aren't going to engage in the material." And we sort of nodded and said like, "I guess, yeah, that is going to be a challenge."
But then when you think deeper, it makes us think about, what does that mean about education in general, in particular in math class and how students look at math class and why they do what they do. And Jon, before you and I went on, I said the metaphor or analogy that pops into my mind right away was, your family came over yesterday. We had a blast on the lake. When we got back from going on the lake, I didn't turn to you and say, "So Jon, how was the afternoon? Rate it from zero to 100, or one to 10, or whatever that scale is."

Jon Orr: You need your Yelp rating to keep it up.

Kyle Pearce: Yeah, exactly. And then we went on and then you stayed for dinner and we didn't ask Scarlet, your wife, we didn't say, "Scarlet, so what do you think?" She'd probably say that was a great dinner, whether it's true or not. She probably would have said that. But at the end we didn't go, "Oh no, but really! What's the point of you coming over if you're not going to give me my grade? I'm after the grade." But when we think about math class, it's framed in that sense. Teachers tell us all the time, if you try to reduce the importance of the grade or the overemphasis of the grade we get.
We need feedback, we need students to know where they are and understand where they are in their learning journey. But this overemphasis on marks and the fact that when the government announced what they did over this COVID period, that there was such a huge drop off for so many students, our assumption is because the mark didn't matter anymore. That really should make us worry about why are we doing what we're doing? We want to learn for the love of learning. And I get kids are kids and they don't see the world the way we do as adults. They don't have the same expertise or experience, but that should at least get us thinking. And again, this is an episode about reflection and thinking about our practices. And to me, if my students are going to essentially completely disengage because there's no mark associated with it, then I feel like I'm missing the mark somewhere. And I say, I'm missing it. It's like we in education are missing the mark somewhere.

Jon Orr: It's definitely something that personally I've been wondering about considering thinking about reflecting on. But like you said, it's almost like our system as a whole has to think about this because I'm a high school teacher, my experience is maybe different than your experience is and also different than an elementary teacher's experience is. We had a high amount of drop off of engagement in high school. I suspect it would be more in high school here in Ontario drop off versus elementary school because of marks seeming to be such an integral part of earning a credit at a high school level. I think more high school students are looking at mark-driven. It seems to be part of the culture in high school to earn these marks and only do things for marks because once I have these marks accumulated, and if they're high enough, I earn a credit and then I don't have to take that course again.
And then that course, I only need so many of these courses to graduate high school, and I graduate. It's very much a system issue to think about marks as a means of currency to graduate. And I think that's really hard and something that we've been doing over the last number of years to try to change that mindset about marks with our students, even though it's still there. And I think elementary teachers, I don't think they have the same sort of culturally market-driven issue that they do in high school. I don't usually hear about my daughters talk about marks in grade six and lower about earning a level on a grade, even though we talk about that, and they know that that's good, but it's not like I got to earn this mark. I don't see them doing a project and then only wondering what grades they got out in the end.
I don't see that from my kids. So on a personal elementary level, that's my experience with elementary right now is only through my kids because I'm a high school teacher, but we had significant drop off in high school. So it makes me think like, "What were we doing? What are you doing in your classroom?" This is the reflection part, wherever you are, in high school, middle school, elementary school. Because I know a lot of teachers who really struggled with like, "Why am I even teaching them if you're going to take the marks away?"

Kyle Pearce: What's the point?

Jon Orr: Exactly. Teachers even asked this question, which made me to have a pause and step back because we know that we've been trying to push no marks for a number of years or not no marks, but think about learning as a whole with the benefit of your growth and promoting growth but teachers saying like, "Well, why am I going to even teach this lesson if I can't grade them or I can't give them a mark?" And so as a teacher, when that switched, I think when... if you didn't already have that mindset with your students, you might've had more drop off. So, because they're like, "Well, I'm not going to do this for marks because Mr. Blank has said everything is for marks all along." I remember, Kyle, saying these words as a beginning teacher and even a few years in, it was just like... kids would say like, "Well, why do I have to do this?" We were like, "So you can get a good mark or you're going to lose those marks if you don't do this activity." It was your motivation. That was your engagement tool.

Kyle Pearce: Tool.

Jon Orr: Yeah.

Kyle Pearce: It was a compliance tool. It wasn't even necessarily an engagement tool. When I was new in secondary, I was a new teacher coming out of teachers college... Well, I don't know if maybe there's something with the dynamic of the students aren't that much younger than we are, and we sort of remember our own experience and our own relationship with learning, but I'm just thinking back to what you had mentioned about your daughters in elementary and how they're not doing it for the mark. And of course they want to do well. They want that feedback.
But at some point, it sort of shifts. And the students who seem to not be as... and I'm just wondering, thinking out loud here, I'm wondering about, let's say students in your daughter's class, I know your daughters are really into school, they really enjoy it. But there's students in that class that don't so much. And at some point in elementary school, as they head into middle school where some students are starting to disengage, it's almost like we start to overemphasize the mark hoping that that's going to dangle a big enough carrot in front of those students who have disengaged.
But in reality, it's not helping those students. Those students typically have already disengaged because they don't feel a level of success. They don't feel like they belong. Whatever it might be for those students. And then the negative of trying to dangle that huge carrot of marks is that it almost trains students like your daughters to want the mark more than the actual learning, which they already had. And I see this with my own son and daughter, my daughter's eight, my son's six. And it has everything to do with the question we ask them.
And it comes back to that big idea around curiosity for us in the three part framework that we always talk about. If I can make that question, I ask my kids juicy enough, curious enough, instead of just a blank naked math fact or whatever it is, if I can just ask them a question that is just intriguing enough for them to think about, they are in. It's like no battle at all. Just thinking about this engagement piece, the first idea, and then assessment, I think they're much more closely related than maybe we realize. And as we start moving into our last piece that we wanted to riff on, I go back to that student in your daughter's class that we just referenced, that student that doesn't appear to really want to do the work, has sort of disengaged.
And when we start to think about why that is, you and I, we would argue that that student has been disengaging because they aren't feeling comfortable, again, belonging in the classroom. That could be, is it related to the color of their skin? Is it because of their family background, where they come from, their cultural background? Is it because they don't fit in socially in the social circles of other students in the class? Or... and I think this more often than not has a huge impact is how able or confident or comfortable they feel in learning the material. And that brings us to our third idea, one of these things we can learn from online learning. And that's kind of the impact on content and really like the content that students bring with them and really their retention of content. So Jon, what are some of the things we're hearing and maybe feeling as well, because I think you're feeling it too, this worry around what are students going to have when they come back to us this coming school year?

Jon Orr: I think teachers and myself, I guess it's a mindset thing that we have to remember that... I guess before I go into what I was just going to say there that if we give some context to this, that when you start a school year, you always have students where you're thinking about your course or your grade level and you're planning out lessons and yet you have to do some anticipation of what students will do on the lesson, or remember on a lesson. And oftentimes students are going to say, "I didn't learn that." Or, "I don't remember that." Or, "I wasn't taught that." And you're like, "Yes, you were here. You're in grade five and this is a grade four topic. And I know that teacher did it." Or, "I taught you last year. You did it."
And the kids are either saying they don't remember, but that summer gap in learning, it's real that students walk away from the course. Or not even summer gap, Kyle, you may might have taught something in the fall or even in the winter and then all of a sudden it's like a couple months later they lost it already. It's like crosstalk.

Kyle Pearce: When you get to the end of a course crosstalk where there's exams and teachers commonly say like, "Well, I'm going to need this many weeks to reteach the entire course." So these are struggles that have happened well before any of this distance learning things sort of happen. But now I guess the question is, what can we learn from this? And I guess, how can we work with what we have in this particular idea or topic?

Jon Orr: Yeah. This is where it kind of brings us back to what I was going to start with. It's kind of a mindset thing in a sense that everyone is going to be in the same situation. Teachers are already worried about... or not worried, I guess, but planning for a recap or a review and you're now going, "Okay, now I have to not only teach my course or my grade, but I'm going to have to reteach a third, or a quarter, or depending on your semestering system a full year or semester.
I don't think we're halfway into semesters in high school here in Ontario. And so you're realizing you might have to reteach a really good portion of that course or grade level. And I think what we've said in our live Q&As with our academy members is that, I think you just have to give yourself permission that it's okay this coming school year that it's not going to be the same again. It's okay that you're not going to cover all of the content listed in the standards or the curriculum guidelines. We always like to say uncover curriculum in your courses anyway or in your tasks. But it's going to be clear again that you were all in the situation again. So it's going to be okay that you got that list of standards and you've got the list of standards that you're going to have to help out with from the kids that are coming in to your class from previous.
So I think we have to band together here and realize that we're all in the same situation. And you know you're going to probably talk to a teacher who's like, "Those kids don't remember this." And I'm like, "Well, no. No one is going to remember this. Everyone's going to be a little bit different."
So some of the reflection I'm having right now, Kyle, is it's giving us, like you talked earlier about the golden line or the silver... golden line, silver lining of some of these situations. I think it's giving us a pause moment to think this is a great time for us to help kids individually and think about what each kid has learned and what each kid's gaps are coming to the table. We've often talked about in the podcast and in our workshop about seeing where students are, meeting them where they are, and then trying to bring them forward. And you can do that through tasks, and listening to them, and observing them and interacting with them instead of planning lessons where no one's in mind. It's like you have this imaginary kid that transitioned from the previous grade with all the content knowledge that they were supposed to have and show it up in your class. It doesn't happen.
And you played a lesson like that. Because I did that for many years. I'm like, "I'm playing my lesson based on what I think they should know from that grade." But then you get into it and you're like, "Ah, this didn't work exactly the way I had planned it." But we've learned over time that we should plan lessons to give kids opportunity to demonstrate what they do know. And what a great time in our history to make that shift. Now, if you hadn't made that shift now to listen to what kids can tell you and then pick up where they are and try to push them along the learning journey, that landscape, it's a great time to do that. So that's silver lining that's coming out of this, I think, it's going to give us an opportunity to talk with our colleagues, to help push them along that path too to help change the way that they had been planning lessons.

Kyle Pearce: And there's a couple pieces. And one in particular, you kind of remind me of one of our most recent webinars where we share at the beginning this idea around how we learn and how kids learn in our classroom. And we have this visual, anyone who's been in our recent webinars would probably remember this visual where we show this line and Jon, you and I both admit we would go in, we would plan our lessons with one particular student in mind, like the ideal student. The one who comes into the class and is like right where we need them to be. And we're going to introduce this new content, we're going to pre-teach them all this stuff and push them along this line.
And we realized that students are at very different places. And sometimes those paths are different as well. And we have this visual of all these different lines and these dots on the line representing the students and where they are in their learning. And they're all over the map. So, while this year it might be more dramatic than in years past, what we have to recognize is that every single year we've taught, there has been at least one student in our classroom who wasn't ready for the content that our curriculum was telling us to teach, for those standards.
And maybe we were well aware of that. Maybe we spent a lot of time trying to help meet that student where they were. Well, now it's almost like what better time than now for us to figure out if we're still on this journey to try to unpack how am I going to meet students with where they are with these low floor, high ceiling tasks, teaching through problem based learning and essentially fueling their sense-making. So, again, coming back to this, while this is going to be a struggle, it's going to be a challenge. This is something that maybe is just what we needed in the math community in particular to help us maybe stop some of those, I'm going to call it a bad habit, but I think it's just what we knew. The way I was taught and the way I taught for so long was, here's the curriculum, we're starting here. We were generous enough at the beginning of the year, we do a couple of weeks of review and then it was expected you either are ready for it or you're not.
And the reality is that that is not a great way to ensure access and equity for all of the students, for all of the learners in our room. We have to understand that students are going to be at different places. They are at different places. And this year more than ever, it's going to be more dramatic. So what I guess we're trying to say here is that this was always an issue. It just might've been easier to miss, or might've been easier to sweep under the rug. And we're now kind of being forced that we're going to have to deal with this thing.
So we don't want to leave you hanging and say, "Hey, go have fun doing it." We want to start thinking about like, what are some ways that we can help folks. I know, for example, some great ways online. You'll notice that there's some great progression videos from Graham Fletcher. And we'll put those in the show notes. That's a great place to start if you're going like, "How am I going to meet a student where they are if I'm like, they're supposed to know how to multiply two digit by two digit numbers without the use of a calculator? What do I do to help them get there if I normally didn't teach that concept in prior years?" Well, Graham Fletcher has some great progression of multiplication videos. And I've got a progression of multiplication blog post that I'll definitely throw in the show notes. And then we've also got some other ways, like if you want to take deeper dives, Jon, what do we have to help folks who are interested in really trying to take a bite into this content knowledge piece? That's going to be so important as we move forward this year.

Jon Orr: Understanding progressions is so important because it not only gives students a map of what they're going to learn, a teacher feels confident once you know the progression of, like Cathy Fosnot would call it, the landscape of learning, or I think she called it a web a couple of times. And it gives you, the teacher, the confidence in those lessons to be flexible. Before, I was never flexible enough if I didn't know the progression of topics on, let's say linear relations. If I didn't seem to know where they're coming from and go where they're going enough, and deep enough, then I had trouble answering questions that kids might have. Your confidence level was shot if you didn't know these things. Especially when you teach a course for the first time, you're not sure exactly that flow of where the kids should be on this learning trajectory.
So knowing that is so important. And we're pretty excited about that because we recognize that. And we've learned along the way where kids gaps exists the most, from like grades three through grades nine. We've put our heads together and come up with a course to help teachers address those learning gaps. And we call The Concept Holding Your Students Back, which it sounds like a mystery because you're like, "Well, what is the concept holding our students back?" And that course that we've put together is all about proportional reasoning. Because as a high school teacher, myself, and Kyle's been doing a lot of learning in the elementary had all, but as a high school teacher, myself, I know that the students that struggle the most end up... it's because of these proportional reasoning concepts and how to model proportional reasoning in the high school level.
It's a foundation of linear relations and so many other functional things in high school. That's where we recognize the biggest gaps. And so this course that we've built inside the academy, we're releasing it to the public right now because it'll show teachers not only how to map this proportional reasoning trajectory, but also give teachers confidence in mapping that out but also all the tasks that you would need to teach it.

Kyle Pearce: Right. Yeah. And we've done so much learning around this. And we've said it many times before Jon and I teaching in secondary for so many years and struggling when students came into our classroom, just like many people are worried about this coming year. Students are going to come into my classroom and they didn't get the same or as good of a mathematics experience as they should have in grade... fill in the blank. Grade five. Now they're coming into grade six, or grade eight going into grade nine.
Whatever that grade level is, teachers are worried about this. And for us, Jon and I would sit there and we would just assume, "Okay, maybe if we say it slower, and if we just slow down for students, we'll just say it slower and we'll say it more often. Maybe they'll get it." And what we realized is that didn't really help. And it was because there were so many foundational pieces missing. But our issue was, we were missing that content knowledge ourselves. I didn't understand. When kids were coming into high school I was under the impression that students should know and be flexible with multiplication, division, also fractions.
These were things that I just assumed should come in. Don't get me wrong. It would be amazing if we can get to that place. We don't want this to always be an issue. But the problem is that that's not the reality currently. Not where I'm teaching, I know not where Jon's teaching, and probably not where you're teaching, whoever's listening right now from the Math Moment Maker Community. So we had to do a lot of learning. And we've said before the work with the landscapes of learning with Cathy Fosnot in episode 24. She talks a lot about that. We've learned so much from her, learned a lot from Van de Walle. My colleague, Yvette Lehman, and I have used this book Elementary and Middle School Mathematics: Teaching Developmentally to learn so much about proportional relationships, but also just proportional reasoning.
And what we mean by that is the journey students have to go through in order to get all the way to this place where they're flexible with functional thinking. So we basically took this and we basically unpacked these concepts way down to pre-kindergarten. So to this idea of spatial comparison, because guess what, when we get all the way into ratios and rates and students, things start to get muddy when we get there. The problem is, we can't just back up one step from ratios. We need to understand what are all the pieces that are missing the squeaky wheels that are going along there. The things that need a little bit more oiling, something to pay attention to.
And back in episode 65, we actually take a deep dive, Jon and I take a deep dive into this idea of proportional reasoning and proportional relationships. And back when we did episode 65, we didn't know that we would be in this COVID environment. So everything we said back then, I feel like it's like amplified. It's accentuated because we're going to have some students who disengaged from learning for the past four months, they didn't have access to the tools. Maybe they didn't feel supported. Maybe they got distracted. There's all kinds of things that are going on as to why students are not going to be where we would love them to be in their journey.
But now we have to figure out, "Okay, are we just going to go and spin our wheels? Or are we going to dig into that content knowledge piece that's going to be so important for us to help students along?" So for us, we've developed this roadmap and we've really tried to unpack this roadmap and to try to make it as accessible for educators to work through. And if you're a middle school teacher and you're thinking, "Well, ah! I don't know if I want to do this whole proportional relationships course and learn about counting and additive strategies," well, there are students in our classrooms that are still wonky in those areas. They're not fluent.
And if we want them to be thinking multiplicatively, there's a nice word for you. But if we want them thinking multiplicatively and we want them fluent with fractional thinking and multiplicative thinking, we need to be able to go back and try to figure out, so what's missing? Why is there such a big chasm between this one concept and the next concept in this roadmap? And we've got strategies there to help along the way. So if you're listening and you're thinking, "Hey, how am I going to support? And I want to learn more and build my own content knowledge," this particular course, I think, the timing is right. And we're just so excited to be able to share it with all of you and give you this opportunity.

Jon Orr: So if you are interested to join us, you can learn more at makemathmoments.com/proportions. The course registration will close Friday, September 25th, 2020, which is Kyle's wife's birthday. So be sure to seek out PD funds from your school or district so you can dive in with us and not miss it. So again, that's makemathmoments.com/proportions.

Kyle Pearce: Awesome stuff. And Jon, I've had a fantastic time here riffing away with you on some of these things, these three big ideas that we can learn from the online learning in this COVID situation. So again, it's been a challenge. It's going to continue to be a challenge for the next foreseeable future, but let's look for those silver linings. Let's look for the things that we can build on and we can feel positively about, because all of us are working so hard. The one thing we do not want is, we don't want us to all get down on ourselves. It's going to be challenging, but just know you're putting in that time, that effort, to work with your students. And we're just thrilled that we can be alongside you and learn with you on this journey.

Jon Orr: Thanks so much for listening all the way through with us.

Kyle Pearce: In order to ensure you don't miss out on any new episodes as they come out each week, be sure to pound that subscribe button on your favorite podcast platform.

Jon Orr: And be sure to wreck that five star rating button, as well as leave us a quick sentence or two in that review box to help us reach an even wider audience.

Kyle Pearce: You can find show notes and links to the resources we've chatted about on this episode and transcripts which are available on the web or downloadable to take with you at makemathmoments.com/episode91.

Jon Orr: That's makemathmoments.com/episode91.

Kyle Pearce: Well, until next time, Math Moment Makers, I'm Kyle Pearce.

Jon Orr: And I'm Jon Orr.

Kyle Pearce: High fives for us. And a high five for you.
(Singing).