Episode 146: How To Reach More Students After The Toughest Year Ever

Sep 13, 2021 | Podcast | 0 comments



As we start/continue another school year during this pandemic we might find ourselves asking: What should I focus on most? How can I help my students get ready for the next grade level? Do I have time to teach through activities or should I just teach with direct instruction? What resources can I use so that I cover the curriculum and still teach deep learning? 

As we are both practicing educators they have been asking themselves that all summer and have prepared this webinar event to help you answer those exact questions.

[This episode is a recording from their free webinar]

You’ll Learn

  • Where you fit on the “math class lesson spectrum” and how you can use it to help your students succeed by learning math through sense making; 
  • After teaching a year in the pandemic where should we go now, where we should focus our learning; 
  • How to find the right balance between a “back to basics” and a “sense making” tug of war; 
  • The concept that holds your students back the most and what you can do to address their needs; and, 
  • How to help students develop a sense of their own mathematical identity and feel more confident in math class.
Start your school year off right by downloading the guide that you can save and print to share with colleagues during your next staff meeting, professional learning community meeting or just for your own reference!


Kyle Pearce: Hey, hey, math moment makers, as we start another school year here in the northern hemisphere, anyway during this pandemic, which doesn't seem to be going away, unfortunately, we might find ourselves asking, what should I focus on most? How can I help my students get ready for the next grade level? Do I have time to teach through activities or problem-based learning, or should I just teach with direct instruction? What resources can I use so that I can cover the curriculum and still teach deep learning?

Jon Orr: As Kyle and I are both practicing educators, we've been asking ourselves that all summer long, leading up to this point, what you're about to hear in this episode is actually a recording of the webinar we hosted just the other day at the time of us recording this. We chatted with a great group of educators from all over the world about these topics that Kyle just talked about. So we wanted to replay that here for you on the podcast, but just keep in mind that this was a live webinar that we talked to the audience. We had the audience interact. We shared some visuals.
Also, if you're looking or if you're interested, you can see those visuals over on our YouTube channel. So we'll definitely put the links to the YouTube channel in the show notes page. You can actually watch the video version of this podcast on the show notes page. So we'll be making sure that you get that. But Kyle, are you ready to get into this?

Kyle Pearce: We are ready? Here we go.
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 math moment makers worldwide, who want to build and deliver problem-based math lessons that spark curiosity, fuel sense-making and ignite those teacher moves. Friends, welcome to another episode of the Making Math Moments That Matter Podcast. We are super excited to share. As Jon mentioned right before the intro here, that we've got an audio version of this particular webinar that we just did just a couple of nights ago as we're recording this. But remember, if you are listening on the podcast right now, of course you're driving to work or on a run, of course, listening, you're going to gain some new insights and some different perspectives.
But if you've got access to your eyeballs right now, you might want to head over to YouTube, hit the subscribe button and hit the notification bell. And you can grab the video version, which has all of the visuals that go along with it. So today, what we're going to try to do is we're going to try to help you figure out where on the math class spectrum you fall and how you might use it to help your students succeed by learning math through sense-making.

Jon Orr: And after a year of teaching in the pandemic, we have these questions about where should we go, which should we focus on. Should we be resorting back to basics, or should we move forward? We got this time factor that we feel like we have to fill gaps. So we're going to talk about that and what should be the right thing we do here to help our students the most.

Kyle Pearce: Awesome. And then finally, we're going to be exploring a concept that might be holding your students back and we're going to talk about something pretty precise, but then sort of a zoom out a little bit. So we're super excited. So sit back, enjoy, and let us know, leave us a comment on whatever platform you are listening or watching to this webinar on. We really hope you'll enjoy it and we'll see on the other side.

Jon Orr: All right, let's get into it. We are super excited to chat with you this evening, all about how to reach more students after such a tough, tough year last year. I know I say after a tough year, because I feel like it's still going on. Right, Kyle? It's still a tough year coming into this new school year, even though we just started this week here in Ontario, Canada.

Kyle Pearce: Yeah, you're absolutely right. It's been, I guess, reminiscent of last summer. I know during summer break things felt like we were getting back to normal and now we're starting to see this fourth wave talk going on. So we know that people are feeling like, "Holy smokes, when is this going to get behind us?" And really tonight, what we'd like to do is we'd like to take some time to help you with reaching more students. When we say that, we're not saying that you're not already reaching a lot of students because trust me, we know you're putting in your 100%, but ways that we might be able to do this without taking on more stress, more anxiety, more even, dare I say it, guilt.
Because I think sometimes as educators, we put that on ourselves and we know it has been probably the toughest year ever from just a general education standpoint, and you folks deserve as many opportunities to just keep on pushing and helping as many students as you can. So that's what we're going to do tonight. But, Jon, we're not just going to leave people empty-handed, are we?

Jon Orr: Right. No. And if you've been with us for a webinar before, we've been doing, I guess, like not quarterly webinars, it's like we do almost three webinars a year, like three live webinars here a year for the last, it's got to be going on three years, Kyle was we're just chatting that we were like, "Maybe we should keep our slides in that tells them all about the chat feature." And we're like, "This is old news to them."
But when we first started this, we had to tell you how to use the chat. But hey, let us know in the chat right now. If you've been with us a webinar before, let us know if it's one, two, lots. I don't know. Maybe it's your first. I'm really excited to see this might be your first webinar to join us. But if you've been with us before, you know that we give away some stuff at the end and we are going to continue that here.

Kyle Pearce: It really makes our heart feel great when we see people that are coming back to keep diving deeper with us because as we always mentioned, we will never be down this journey now being a true lifelong learner, learning how to teach math, I don't think you'll ever get there. There's no such thing as being at the end where you sort of have all of that knowledge. I used to think that, to be honest. I thought I knew enough where it was like, "I didn't need to learn anymore to teach math." My world has totally been flipped upside down since diving in on this journey with Jon to my... Well, I guess on my screen to my right.
So let's talk, Jon about what we're going to do tonight, the first thing. And we want you to hold us accountable. Those who have been with us before, we want you to hold us accountable that when we say you're going to get something that you're going to see it emerge from this particular webinar here. So the first one is where you fit on the math lesson spectrum. And maybe you haven't been thinking about this yet. We're hoping to help you see that a little bit more clearly and how you can use it to help your students succeed by learning math through sense-making or maybe just pushing that sense-making a little bit more than maybe we have in the past. Jon, what else are we going to do here?

Jon Orr: Yeah. So we talked about this right off the top, but after teaching a year through the pandemic, I know that we taught in face-to-face, online, back to face-to-face, back to online. Some of us are doing that now. After teaching a year in the pandemic, a lot questions are circling around, especially we're starting the school year. We just started this week, but where should we focus learning so we can find the right balance. We're going to talk about this back to basics, kind of idea, this push to fill gaps versus this inquiring conceptual understanding. It's like there's a tug of war.
Especially when we face adversity in this kind of pushback, we're like, where should we go? And we want to talk about that and help you with that idea this evening. Kyle, what else?

Kyle Pearce: Absolutely. We're feeling it as well. People are feeling crunched for time, and I think when we get into time crunches really kind of pushes us to one end of that spectrum. So we're really going to dive into that and really try to emerge that idea tonight. And then finally, the last thing is we're going to try to help emerge... I'm going to say tonight, it's going to emerge part of a concept that holds your students back the most and what we might be able to do to help address those needs, so we're going to talk about something specific math focused a little later, but then we're also going to show you how it connects to something that's much bigger in something that maybe we don't even realize is there.
So super excited to be here with you tonight. I want to take just a quick moment for those first-timers who may have not really known who you or I are. Jon is my colleague and good friend. mrorr-isageek.com is a website that Jon has had brewing and really just journaling your experiences as a high school math teacher, really trying to figure this thing out we call math education. That's how I bumped into Jon looking on his website, realizing that we were teaching some of the same courses, and that's how we sort of connected online through Twitter.
Jon's also got a really cool project called mathbeforebed.com. He has three girls and doing the whole reading thing at bedtime got Jon thinking, why am I not taking an opportunity to bring in this subject that sometimes gets, maybe ignored a little bit at home math and bring it to the bedtime routine. So Jon started putting together some prompts that are very open and really a low floor of entry for students, for children of all ages. So go check out all those prompts over at mathbeforebed.com.

Jon Orr: Thanks, Kyle. And I want to introduce Kyle Pearce, the other co-host here with us this evening. You, I'm sure have bumped into his websites. He's got such a vast resource over at tapintoteenminds.com. Lots of lessons, lots of ideas from what he was doing in the classroom to ideas on elementary learning. So much great stuff. A search engine for 3 Act Math Tasks is over there. And maybe you bumped into that and discovered his stuff over there. Kyle also, he's a K to 12 math consultant for his district, is ventured deep into the elementary program. He's also creating and still creates many resources on the website, mathisvisual.com, which he's dedicating his awesome skillset on animation to making do some abstract math concepts like dividing fractions, or adding integers or subtracting integers. You want to make those visual for you and your students.
So for your students, you can use them in your classroom, these videos and lesson ideas, but also for you, because it's really important to understand how this works and the videos help you do that too. So check out mathisvisual.com, if you haven't already. Kyle's got some great stuff up there. I don't know if you know also about what we do together. Obviously, you're here. You know about make math moments. But it's also possible, you don't know that we have a podcast.
So give us a shout-out in the chat if you've listened to podcast episodes. We put out every Monday morning, we release an episode on any podcast platform. So Spotify, Apple Podcasts, Google Podcasts, all of those. If you can subscribe to our podcasts, we chat with teachers in the field. We chat with big names about math education. Kyle and I also chat with each other about what's going on in our class. So we love hosting that podcast. We love chatting about math. Hey, we're here with you. We love doing these kinds of chats. If you haven't yet get over there, do that because I think, you're here, obviously, here with us, you're going to love some PD over there too.

Kyle Pearce: As we mentioned earlier, the YouTube channel is something we are doing lots of work on. So definitely check that out. We've been on this journey. We continue to try to unlock different ways. And with every concept, we try to tackle in mathematics. For me in my role right now, I get to go in many different grade levels. So I'm looking at all kinds of different concepts at different parts of where these concepts emerge and where we kind of dive in deeply into some of these ideas.
What we realize is that it's not luck to have a math moment in your classroom. We can create these. Now, we're not going to tell you. We're not going to lie and say that every single time Jon leads a math lesson that a math moment happens. But more and more often, they happen because of the elements that we try to uncover, and many of the ideas that we're hoping to share with you today.
So as many of you probably know, the people who are on our podcast and listening or on our email list, we are totally all in on problem-based learning. We try to make every experience as problem-based as we possibly can. And this is something that I think a lot of people are feeling is harder to do these days due to the pandemic and due to something that some districts are calling learning loss, or they're calling these gaps in their learning. However, you want to name it.
The reality though, is that we still learn in a pretty specific way. So if we get into it a little bit here, Jon, and we talk about this, this is something that we have seen, and we're going to expand on this a little bit because in some of our previous webinars, we like to start here because I think it's really important for us to understand if all of these dots are students that many of us begin our careers. And maybe some of us still feel that we're at this point now where we think that students are supposed to come to us with a certain amount of knowledge and understanding, right?
I'm a grade seven teacher. They should know grade six material. When in reality, we realized that this isn't actually the case, right? And students aren't just going to move along a straight line to this new knowledge and understanding. It would be helpful if it was just like this, where you're just spread out on a straight line. It's like, "Okay. Well, I'm just going to meet this student here and this student here."
But the reality is, is that it can look much more complex and students will be at different places along this learning journey because not every student has the exact same experience. They don't have the exact same background. They don't have the exact same way of thinking. So while we can find trends and we could try build on those trends and those trajectories, the reality is, is that learning is actually pretty dynamic, and it's actually pretty hard for us as educators to try to meet these students here where they are.

Jon Orr: Yeah. We're going to kind of dive into that and talk about how we can do that with our students. But I want to bring up this idea that math educators are also on this journey and we also are on this kind of spectrum. What I mean by that is when I think about my teaching when I was first starting out, I had this thought, this deep belief that I had to teach a certain way to get the results that I really wanted. When we have this spectrum, if you think of this spectrum, there's these books that I remember when I was a kid. Right, Kyle? The Mr. Books or little Miss Books.
When I think about myself as a starting teacher, I was like, I have to be Mr. Strong. I have to be this in order to be a high school teacher and get this rigorous math program. I have to be the guy that doesn't smile. He's almost like a robot. He's not interactive with the students. I thought I had to be this super strong character that wasn't myself. If you think of this spectrum that we are all on, on our math lesson journey, think of that being one end of the spectrum of this super rigorous teacher, this direct instruction, front-loading skills all the time. Come in. This is the way we vision math class. This is the way we taught for a number of years because after speaking with Kyle, he taught that way for a long time too.
But on the other end of the spectrum, there's this imaginary view that when I had, when I first started teaching that if I'm not Mr. Strong, I'm Mr. Messy. And Mr. Messy was this chaos classroom down the hall. It's this classroom that it's like, there's no rules. It's This classroom that is like, it's all play, right? And they're like they're not-

Kyle Pearce: The kids are walking all over him.

Jon Orr: Exactly. He had to be one or the other instead of this actual spectrum that exists. We try to find ourselves as we learn. Year to year, you learn where you fit on this spectrum between these two end point. What I realized after this year, that's been the toughest year ever is that we've moved up. We're not completely, "Hey, there's no chaos here. It's not chaos in my classroom?" I'm not that. Mr. Strong anymore. I'm actually a human being in my math class. I see my students as human beings. We're not doing this direct instruction, but there's this nice mix of this inquiry based learning of this problem-based learning that we're going to talk about a little bit later. I'm going to show you some math lesson that fits along that spectrum.
But what we noticed and what we've heard after this tough year is, and this is natural after any setback is that you resort back to what you were originally comfortable with. And this happens for a lot of teachers. It happened I think I was really drawn back to being Mr. Strong when we had to teach through this pandemic. And starting school year, we had that poll too. It's because we have this idea that, "Hey, we have to go back to the basics so that we can fill these gaps for our students."
I heard that in my school. I heard that from parents. I've seen that in the community. We see that on social media that we have to go back to this basic idea of filling these gaps. We have to front load these skills because kids are missing so much. Kyle, looks like you want to jump in here.

Kyle Pearce: The part that what's hitting me as you're saying that, Jon, and I think it's something we all have to reflect on is like, "What does that even mean or look like when we say like, "I've got to go back." It's like, "Okay. So there's a couple of different things we could do." But I think the interpretation, at least, I hear, and I think Jon, you hear, and I think many of us hear, when we think about that is that if I want to go back to the basics, that also means the way we deliver our lesson has to also be very traditional in its approach.
The reality is that, if I don't believe that that approach was working well, two years ago, or five years ago, I have to really stop and think about whether that is going to help us in this time as well, or whether there's another way. Right?

Jon Orr: Right. It's really just a belief, right? A lot of people are just believing that that's what we're supposed to do. We actually don't have a lot of data ourselves, or information to be like, "I know that going back to this way of teaching to fill these holes is the right move." Even though you feel this draw to do that. When I think about that, when I hear those polls from the community and other people, I actually read this book in the summer, and I felt like this went hand in hand with some of the thinking along this line, because there's a belief that we have to catch kids up by going back to these basics.
There's this book called Think Again by Adam Grant. Adam Grant is a researcher about behavioral economics mostly. But in his book, Think Again, he starts the book with... And he basically uses this foundation of these four mindsets for the whole book. The book is about rethinking different things, and this brought this up because we're under this belief that we have to go back to the basics to catch these kids up or fill these gaps. But Adam argues that in any conversation, argument, discussion you have with other people, it could be on social media, it could be face-to-face. It could be at the dinner table. It could be in your schools. Any kind of conversation you have, we take on one of three personas.
I know I said four mindsets here, but I'm going to say three personas right now. The first persona that some of us might take on, and we all do this at different times, and we all take on these different personas depending on the time or the moment. The first persona he describes is the preacher. The preacher is like you take on the preacher persona when you are promoting values, you're promoting this idea.
So as you think of anything that you're trying to share this idea out, you're preaching the idea out. It's almost kind of like we are doing that right now. We're sharing this idea out. This webinar is almost like we're going to share some ideas out today. You're giving this sermon and you're promoting ideas. A lot of times we do that at, say department meetings, or you're telling us all about this movie that you saw, you're promoting that movie. That's the preacher.
The second persona that sometimes we take on is the prosecutor, which is... Usually this comes up when you disagree with someone. And when you disagree with someone, what you're doing is you will try to shoot down their ideas or you use arguments to prove them wrong so that you can win. So that's usually in that discussion is that you will take on this prosecutor role to shoot people down.
The third persona that we take on is the politician, which is that the politician is the people pleaser. This is like, we take on this persona when we're just trying to get the approval of the other person. So we would take on these three roles at different times, and sometimes in a combination in the same conversation, anytime we really talked to the other people. However, when we think about convincing people or the right thing or truth, what happens here is all three of these ideas bring up something, we call... Sorry, behavioral economist and behavioral scientist call confirmation bias.
Confirmation bias basically means that you seek out information or facts or things to help you seem right. You've got this idea that your right. These are your ideas, and you only look for those ideas to confirm that you're right. You leave out ideas that say, "You might be wrong. There might be something different to think about here." So those three roles actually lead to confirmation bias.
So in his book, he sets the whole book up with this other fourth persona that we should take on, and not a lot of us do this, which is the scientist. The scientist is the role that we will then seek out, form hypothesis before we make conclusions. We run experiments or we consistently rethink things and we want new information so that we can make good decisions. That's what the scientist does.
When I read this book and we think about this push back to basics, right? If we're being told that there's this belief that we go backwards so that we can fill this tough time and catch kids up, then we should be acting as a scientist. We don't know if that's true. We need to gather information. We need to actually see what our students know.

Kyle Pearce: I was going to say, Jon, when we're looking at this, I think when we take on this mindset, when we think about being the scientist and actually seeking this information, forming hypothesis, running experiments, what it tends to do is it tends to find the important pieces that these other mindsets were putting out there anyway. Right? So I'm sure when you're the preacher, you're throwing out some good ideas or when you're the politician, you're throwing out some good ideas for people to consider, but maybe conveniently leaving out some others.
And that might push you to go maybe one end of a spectrum versus something that's a little bit more balanced where with the scientist, when we approach this and we grab data and we look at it, what we start to realize, we start to emerge, especially in the math classroom is that it's not a dichotomy. It's not an either or. In our messaging earlier when we said like a lot of people feel like, "Hey, we've got to get back to the basics. We don't want to ever leave the basics."
That should never be a thing, but I'll be honest and say that there was a time for me where I thought like, "I'm just not going to worry about that stuff. I'm going to just focus on problem solving and that's it." Now I realize, "No, no, it has to be both. It has to be all of these things and how we seek this out might be a little bit different."
So what I want to do right now, Jon, is it okay if I share a short little clip and a couple images for the room. And I want you friends in the chat, just tell me what you see. I'm not too concerned about what you notice or what you wonder at this point, but I do want you to tell me what you see, because we're going to try to be the scientist here, and we're going to start trying to seek answers. We're going to try to seek information, seek data. I'm going to show this to you. It might be a little choppy, so don't worry too much about that. But what do you see? Just share it just in the chat.

Jon Orr: Fancy.

Kyle Pearce: Big old explosion in the chat. Don't have to hold back. What do you see? Jon, what are people seeing?

Jon Orr: A lot of waves, trees, beach, ocean, water, sand, shells. A wide expanse of water. crosstalk

Kyle Pearce: I saw ebb. I love that.

Jon Orr: Pebbles. Volleyball, that's-

Kyle Pearce: The ebb and flow.

Jon Orr: Yeah.

Kyle Pearce: Fantastic. I love it. You can keep those coming what you see. What I want to share with you though is I'm going to take a closer look at the beach here, and I want you to think. What really hit me was when I was walking along this beach with my children and my wife this summer, and my children kept coming up to me and they had something in their hands. When I'm looking at the beach in front of me, I just see a bunch of stones. I see some seaweed. I see even some litter.
But they had in their hands, all kinds of sea glass, or beach glass, whatever you want to call it. They kept coming with more and more of it. It was interesting to me because had they not brought it to my attention, I didn't see any beach glass on this one.

Jon Orr: Yeah. What I'm looking at right now, Kyle, it's like, where's any beach glass?

Kyle Pearce: Absolutely. It was like only then when they said, and they said, "Dad, can you help me?" And to be honest, I was like, "Oh, geez. I'm going to have to bend over and find some beach glass." But I said, "Okay, I will." But I wasn't going to like stress myself out over trying to find it. But as I was looking, it took me a little while, but it was like, as soon as I started looking and then I knew what it was I was looking for, I could start to see beach glass emerging.
I don't know about you if you can see in these pictures, but there's a lot of beach glass that was all around me. I've got another shot that has some, if I back up a little bit, there's some over here and there's some right there, it is literally everywhere on this beach. What I want you to think about when we bring this idea up is the fact that when students walk into our classroom, think of the assumptions that all of us as educators have made about students because of what a year we've had.
We've made a lot of assumptions that students are coming to us with deficits. This may be true. We don't know. But if we are a true scientist. What we want to do is we actually want to find out whether that's true or not. You might already see that from day one or two, and you might see some of these things. But the reality is, is that until we get to know our students and get to know our learners, it's really hard for us to make these assumptions. Then also to decide that I'm going to teach, let's say a back-to-basics in a traditional format style lesson.
Because oftentimes I know, Jon, you would agree with me when we were teaching the way we were taught, we didn't know a whole lot about the students in front of us until we gave a formal test or an evaluation. What we want to do is flip this on its head and start looking for the beach glass every single day of our school year. I think there's a way we can do this. Right, Jon? How do we actually find these pieces of beach glass every single day during every single lesson?

Jon Orr: So what we're going to argue is in order to be a good scientist, like Adam Grant would say, in order to find the beach glass every single day, instead of teaching that direct instruction, like Kyle said, it's like, we rarely would know who our kids are or what they could do until that test came out. We know from what we've been doing for the last few years and all of the teachers, the educators that we have helped through our programs, our PD programs, we know that teaching through problem based lessons is like an assessment goldmines.
What I mean by that is that when we teach using our three-part framework, by listening, observing, interacting with our students, before we inject the do it this way, when we listen to what our students are doing, following this framework, we learn so much about them. And that's us being the scientist and looking for the beach glass.
Because if we do that, if we can follow that and get in there and listen to them, then we're going to learn what they actually need. And they might actually need these back to basics programs, or they might actually need small group instruction, or they might actually need more direct instruction or they might actually need, "Hey, we actually love the exploring part of this mathematics lesson that we did."
We don't know that until we actually get in the classroom and listen to what our students are doing. For us, teaching through problem-based lessons has allowed us to do that and do that on the time we need to do that. Most teachers will say like, "I don't know if I can do that and fit it in my year schedule, my course outline. I'm worried about time." We've always experienced more time than we actually need when we go this way.

Kyle Pearce: Absolutely. So what we're going to do is we're actually going to dive into a problem-based lesson. We're going to uncover some mathematics through this exploration. As Jon mentioned, it isn't an either or. It's not a, "Hey, we do a problem-based lesson," and that means that there's no explicit instruction because that's something that I think we've made that mistake many times before. We actually, at the end of our lesson, have to be very explicit. That's what we call ignite our teacher moves. And throughout the lesson, as students are doing the work and fueling that sense-making, that's where we're essentially searching for the beach glass.
We're trying to figure out like, "What is this student bringing to the table?" And we're trying to avoid what they're not bringing. We're trying to get to what are they bringing? Because here's the crazy part, my older mindset, and I say my older, my earlier mindset in teaching was coming in and looking for deficit, looking for what the students didn't have.
You could do that. But the problem and the challenge with that is when you find what they don't have, it's really hard to figure out what they do. But when you figure out what they do have, that's when we can start crafting the experience to nudge them a little bit further. So when we do bump into those cases where a student might not have an entry point into a task that gives us the information so that we can adjust the task. We can adjust the prompt or the questioning for that student to ensure that they're going to get a rich mathematical experience.
So today, what we're going to do, we're going to dive into a lesson. The topic, because you're educators, I am convinced that you are not going to struggle with the actual calculation of the mathematics we are going to do today. But what I do want you to be focusing in on is what is under the hood? What mathematics, what concept is emerging here? What idea? Why are we focusing on this? And how might that impact you as a classroom teacher?
This is true whether, if you're a primary teacher, if you're a middle grades teacher, or even if you're a high school teacher. I believe that the concept that are going to emerge today is really going to maybe fascinate, maybe surprise you in some ways in how it emerged and how all students could access this particular task. So Jon, why don't you-

Jon Orr: Yeah. I'm excited.

Kyle Pearce: ... lay out a framework for us here? What are we going to have them do? Let's talk about the hats we like people to wear.

Jon Orr: Yeah, let's do that.

Kyle Pearce: And we're almost going to like rush. It's the first week of school for us, right, Jon?

Jon Orr: Yeah.

Kyle Pearce: So like laying the groundwork of like, how do we do math in our Make Math Moments classroom?

Jon Orr: Yeah. We're actually going to ask you to wear two hats. One hat is your teacher hat. You already have that hat on. And Kyle said, you're going to look under the hood. What are the teacher moves that are being made? Can I reproduce that in my classroom? What's that look like? These are the kinds of questions you want to have when you're wearing the teacher hat. But we also need to experience the students' side? And that's why professional development we've been in, that was fantastic, we always knew it was fantastic after, because we were put in the place of the student.
We experienced that learning, those curious moments, those aha moments. We want you to do that too. So we want you to wear the student hat. We're going to get you to answer some questions here. You're going to, I guess, notice some wonders from you. So we're going to start off that way. So get your self in the chats. We're going to ask you to notice. Kyle, glimpsed a little already. He's going to show you an animation. We want you to type in the chat, things you notice and things you wonder. Kind of like what we did with the beach. Hey, Jon's already in there. He's got beans.
But get yourself in there. And then he's going to play the full thing. We haven't played it yet. That will be you being the student, right? You're going to be the student hat and we'll get going here. Kyle, ready to go.

Kyle Pearce: All right, let's do it. All right. What do we have? I see the chat is going on fire. I can't really see it, but I see it scrolling, which is great. Okay. Let me see. Jon, do you have anything to read out there?

Jon Orr: I'm seeing the animation. I'm seeing lots of stuff. Green, grams, 30 grams, 30 grams, 30 grams. Spacing tables, garden beans. I'm sure they're going to come in as more of this animation unfolds here in front of us, measurements. Somebody is seeing a table. Shannon says non-GMO, so does Stacey. We see some seeds and heirloom. Capacity of the container. Planting, instructions for planting. I think I'm way behind. Here we go. How many will germinate? There's beans going into a container. I'm seeing, "I wonder how many seeds are in the packet?" How many beans in 30 grams? How many beans are left in the bag, Kyle? Is that all of them that have been poured out?
As our teacher hats go back on, I just did... Yesterday was our first day in our classroom. I noticed some wonder math problem. I had done a measurement problem with my students, the R2D2 problem, Kyle. When we do this with our class, I wrote all of these down on our board, in our room and put names attached to them, make sure that every voice gets heard. We filled that board up. It's important. Like you said on day one, the first time you do this, make sure that you're setting the stage right for your students to feel like their voices are valued.
That's different than the way I did it when I first started teaching. So it changes some of the dynamic in your room and that's what we would do. There's a ton going on here, and we would put as many as we can up under the two headings, notice and wonder. All right, Kyle. We've got lots there. What's next as a teacher?

Kyle Pearce: I love it. I love it. I'm seeing even like Beth has some suggestions like writing them on stickies and then having them paste it. All kinds of ways. And then also, I think what's important to note here is that sometimes we look at these types of problems or prompts and some people look at them as warmups that are disconnected from the real math in class. And the reality is what we try to do is we try to take these types of prompts. We try to merge them with the lesson.
So this is our lesson. This is where we're going, and this is leading us down a path that we're hoping will not only spark curiosity, but also fuel students' sense-making. So we have tons and tons of things that are noticed and wondered. People are saying like, are you going to plant these? The question is yes. Or sorry, the answer is yes. Also, we like to frame out a little bit of a storyline too. So you can make these up on the fly. You can connect it to what they're saying, whatever, but I would say we plant a bean garden every year and we've only got space for so many or whatever your storyline is going to be to really get students to lean in.
But the question I'm going to have you start with here and it's really going to involve, you're going to have to shake off a bit of your summer brain for those on the west side of the world or the northern hemisphere who are just coming off summer break, I need you to do a little estimating for me. What I'd like you to do is I'd like you to have a look at those beans. That's all of the beans.
I know like the view, your angle, your perspective, isn't perfect here, but I do want you to have a look at that and I want you to use your spatial reasoning to first make an estimate. We'll have you freely share those in the chat. Now for you today, I'm going to have you just go ahead for any estimate. Now, depending on the grade level of your students, so if I'm with younger students, I'm definitely going to want to have them estimate like a low, a high and a middle.
Today, because I know you friends probably are going to have a pretty tight range based on your spatial understanding or awareness. I might not need to do that today.

Jon Orr: I was going to say that, Kyle.

Kyle Pearce: So that's something that you need to determine, right?

Jon Orr: I was going to say that if you're doing this with students, I would definitely... If this is the first time to do a too low, a too high, give them three numbers. Have them give you three numbers too low, too high to help frame in that. I do that as many times as I can. And then sometimes like we're doing here, once that framing is part of your routine, you can take that too low, too high away, and it can speed some things up. We are going to do that here just for timing purposes as well that Kyle said, we are all. But keep in mind, we do that in the classroom too low, too high. crosstalk

Kyle Pearce: Yeah. So, Jon, I'm wondering, what do you have for too high, too low? What do you see in there?

Jon Orr: Yeah. I'm going to do a two high as a range of your best guesses. So I think the highest right now I have seen is a 300 as a too high. But then also our too low is like, I think I'm seeing 50 is a too... I don't think I've seen anything less than 50, Kyle. So that's a pretty big range, right? Huge range between 50 and 300. In the conversation I had with my students yesterday on the different problem about this, and I've shared this in our previous webinars too when we talk about estimates. Think about the power of mathematics right now. Anybody can guess.
We've got this huge range between 50 and 300 per seeds, and what we can do is anybody can make a guess, but with more information and tools at our disposal. So ideas and tools. We can take these ranges, these huge ranges of just pure gut estimates. With that information and ideas and tools and resources, we can shrink that gap. And that is the power of mathematics, right? That's the power of having more information and tools at our disposal. And that sets the stage for all the math you're going to learn is you can always relate it back to be like, "Hey, anybody can make a guess, but let's narrow this gap and be very precise, as precise as we can.

Kyle Pearce: Awesome stuff. As you were talking there, I was just tossing in a few of the responses that I saw. And you'll notice here, these are all sides. They're not really the main focus of our webinar tonight, but it is something that I think is worth mentioning. When we are taking these estimates down, we do want every student to feel like their voice is valued. We're not going to discount, "Oh, 300, that's way too high. Or 50, that's way too low. We're going to include everybody here because everybody is making their estimate. They're using their own spatial sense in order to participate.
I'm also throwing down a couple names so that they can feel this sense of being heard. Right? So they know, and they feel like, "Okay. My voice matters here." It's worth participating in this classroom. Here's Stephanie here. And I don't know if it's just where I am in the chat, but it looks like we've got quite a range here, it appears. I'm sure there are some more higher ones as well. We do have a classroom of, I think, over what. What was it there, Jon? Over 200 friends here.
So we've got a lot. And of course in the classroom, every single day, we're not necessarily going to put down every single estimate, but early in the school year, we're going to really try our best to put everyone down so that we can feel like, "Okay, if he is listening, they do care about my voice." And then maybe later it might be, "Hey, why don't you as a table group, decide on a number." And then you might share out six from different groups or whatever you choose in order to keep that process moving along.
But Jon, I'm seeing a range here that really... it's pretty tight there. The beauty of mathematics, we always recite or say this in our sessions is just how... The whole goal of what we're going to do today is to see if we can tighten this up. Are we all off? And it's like closer to out here, or is this telling us something about where we might land today?

Jon Orr: Right. We're going to gather some more information to help do that. So one question that we would ask our students, and I think for time purposes, we'll give you some information to help you change that prediction. But we always want to ask our students, put them in that place, right? This is that moment, I always find in my class, this is the moment where this task, this problem-based tasks is the assessment goldmine. Because when you ask students, what information would you need? And then they tell you, I want to know blank.
Then I just say, and what would you do with that? Then when you listen, they're going to tell you the strategy. And you want to listen to those strategies because students are communicating mathematical ideas that maybe they don't even know is the mathematical idea that you're looking for that day. But you want to listen because they will share great insight on their thinking that's going to help you help them at a later time or even that time.
So that's the assessment goldmine piece is to hear what they have to say at that moment. And that can be in small group, that could be in the full class. Lots of different ways to do that, Kyle. So let's give them a little bit more information to move this along.

Kyle Pearce: Yeah. I love it. I love it. So I'm looking at your estimates. We see a range of 50 to 300, but we see a cluster between this 50 to 150 range. So I'm curious if we might be able to get a little bit closer. Now, one thing I'm going to do right now is I'm actually going to reveal, we're going to celebrate our closest estimate here. And then I've got a bit of a follow-up prompt for you. I'm just going to lay these out. I'm going to lay these out on the table here. You can't really see it very well. Let's throw them down there.
Depending again on your grade level, you're going to decide how you do this. If I'm in a younger class, I might have students count this or have them estimate. I might even pause here and say, "Okay, well-"

Jon Orr: Right. You can print it out, right, Kyle?

Kyle Pearce: Yeah.

Jon Orr: And you can cut it out?

Kyle Pearce: Exactly. If this is 10 beans, how many do you think it is now? Right? And maybe you want to update your estimate in the chat. We would encourage updating estimates as we go. We're seeing this tighter range forming. I see 90. Lots of 90s, 95, 100, 80, 87.

Jon Orr: We're tighter already.

Kyle Pearce: Just seeing it tighter already. As we give you more information, you can see that. Of course those estimates are going to get tighter and tighter. Our intent here is to get students to not only participate in what we would consider to be a pretty low floor first experience here. Oh, is it actually 90? Nice work everybody.

Jon Orr: 90.

Kyle Pearce: Oh, it isn't 90.

Jon Orr: 91.

Kyle Pearce: 91. Awesome, awesome. If you were close... Look at how people were like 87, 92, 90, 91. It's 91. Awesome, awesome stuff. On the count of three, we're going to do one clap. Everybody should celebrate. One, two, three. We're all a little delayed.

Jon Orr: We're all over the place.

Kyle Pearce: But that's okay. Here's what I really want to ask you. And what we're going to have you do right now is I want you without the use of a calculator, and if you, let's say know this fact to memory already, I want you to think of how you would do this if you didn't have this as a known fact. The question I have for you is that I am in fact going to be planting these beans, all 91 of them, but here's the deal. I actually have seven pots. Okay? I have seven pots to plant my 91 beans in.
My question for you is how many beans did the gardeners sow in each pot? Now I see people sharing in the chat. What I'd like you to do is I'd like you to pause from the chat for a moment, and I want you to pull out a piece of paper or maybe digital tool. I want you to come up with a convincing argument. I want you to use a model of your choice. In the chat, we're seeing lots of symbolic sort of forms, which is completely fine. But I wonder, is there a way that we might be able to leverage other mathematical models to assist us here as well?
Here's the deal. I always tell students when I'm working with them, I'm a really hard person to convince. All right? So sometimes I say that, sometimes their strategy, it might be super clever and I might not actually be able to catch on to that strategy. So what I want you to do is I would like you to model this. And there's going to be something happening in the background here. Maybe you want to start thinking about it, but there's something happening here that is more complex than maybe some of us realize when we actually assign a problem like the one we see here. All right?
So we're going to pause. We're going to give you some time to think. And as you're working, we're actually going to encourage some of you to take a picture or a screenshot of your work and share it with us through the Knowledgehook snapshots tool. So I'm going to leave this up on the screen for you. And what I'm going to do is I'm going to open up a Knowledgehook snapshots room, and we will give you some further instructions once your model is ready. So I want you focusing on the math for now, and then we will take a moment to share the steps for you to share your work with us.

Jon Orr: All right. How are we doing there?

Kyle Pearce: Good stuff. Yeah, lots of good ones coming in. Lots of good ones. Loving it.

Jon Orr: Right. All right.

Kyle Pearce: Loving it. Loving the creativity. Now something that's interesting, Jon, I'm going to quickly share this Knowledgehook tool. Again, not really our intention of focus on the specific tool let's say, but it is a tool that we find really helpful. Right now, I'm just going to hide names, but I have all these different solutions coming in. Something I noticed right away when I go to this tool, when I'm asking students, especially in the online environment to share is I start to see more visual and more different models instead of when we're typing in a chat, what you tend to see is people just talking about adding, multiplying, dividing. Just operators.
That's great and all. We want to have those discussions too, but also we want to have an entry point for all students. So when I look at these, something that really pops out at me... So first of all, I want to, in my mind here be... Again, we talked about searching for that beach glass, right? So I'm looking right now for different types of beach glass. I don't want it to all be the brown beach glass, I also want to find some of the green beach glass.
I want to find some of the clear beach glass. I want to find different solutions and I want to see how they connect together. I want to select and sequence them much like our five practices, friends and authors tell us to do so during the math lesson and something I would maybe start with is when I start to see... I saw these arrows and that popped out at me. I haven't looked at this closely yet, but right here, I really liked this.
Jon, I'm wondering you're looking at this for the first time. I'm wondering what about this pops out at you? What are you thinking when you see this initially? You go, boom, I see beach glass. What's happening here?

Jon Orr: So honestly my first thought was I'm seeing threes getting put in there. So my first thought was like, "Maybe this person put in threes and they kept putting threes in." It was just like, "How many threes can I put in?" But then I saw the tens I glanced up and I was like, "Oh, there's already 10 in each of the seven jars already." It makes sense. Right? You should be able to fit 10 in each because we have 90. That would use up 70 already. And then this person put in threes.
I guess my wonder at this point to this student might be like, "How did you know the threes were going to fit?" How did you settle on grouping by three? Because my gut might be like, "I might just go with twos or ones. How do I know groups of three are going to fit in each one?" This solution works out perfectly for threes here.

Kyle Pearce: I love how you're asking that, Jon, because again, the only thing you and I can do... and here's the tough part, as an educator, most of us are teaching by ourselves in our classroom. Right? Some of you might be blessed to be able to team teach with someone. But if let's say you're by yourself, you're basically making assumptions until we ask that student, right?

Jon Orr: Right.

Kyle Pearce: Until we actually have that conversation. So this is that data. We're being the scientists like Jon had mentioned earlier. We want to find out more about what the student knows. And again, we're going to make an assumption here and say, "Yeah, it looks like they fair share 10 to each pot, takes that 70. It looks like they may have drawn out the extra 21 here and then assigned three to each. So it's almost like maybe they had them drawn out and then they circled it.
And they're like, "Well, if there's seven pots, I can circle one, two, three, four, five, six, seven." All of that is just an assumption. Until that student tells us exactly how they were thinking, we may never know. Right? So that's how important it is for us to get a better sense. Now, I love this because the arrows here really signify and share the strategy that we're using for this particular problem.
Now, in some classrooms, in our younger classrooms, students might not even realize that what they just did is division. Some students might not realize that. But what they've done is they've used a strategy here and it becomes very obvious when we use this model that it is like what we call a fair sharing model. Like one for you, one for you, one for you. Except I went 10 for you, 10 for you, 10 for you, and then went three for you, three for you all the way through. So that's actually kind of like a more advanced, fair sharing strategy. We can see this done in a variety of different ways. Look at that.

Jon Orr: Yep. There's another one.

Kyle Pearce: So we have some different approaches to it. So again, trying to highlight some of our student work here. I like the connection to the symbolic here, which is nice. I give this a click. So you can see similar strategy and look at how this particular student is able to actually articulate or explain their thinking that yes, it's in fact division and they're actually breaking down the 91 into two separate quantities.
Whoops, I want to go back here. And this actually has a special name. This is a special name. This is called partial quotients, where when I'm using division and I actually take the dividend, 91 seeds, and I actually partition this into more than one quantity, so that they're more friendly for me. And this particular student even says, "I know that something times seven, or I know that 70 divided by seven equals 10." That's why they've selected 70 as their dividend here and the remaining dividends.
So really, if you look at this, for those who want to get technical, I could even introduce brackets here to really explicitly show students who are working on order of operations. Actually, we're working backwards here. We're actually saying, "You know what, I'm going to give you brackets because it's going to make life easier." When a lot of times we teach students when we get in the middle grades, "Hey, when you see a bracket, get rid of... Simplify everything on the inside, because that's what we're supposed to do." When in reality, this student just said, "You know what? We're going to do the exact opposite. We're actually going to introduce brackets because my life is way easier. 70 divided by seven plus 21 divided by seven is way easier to me than 91 divided by seven." crosstalk

Jon Orr: Keep going in a moment here, but I'm going to interject. There's a couple of common questions here in the chat that we usually get when we talk and introduce tasks to teachers. And the task is also found on our website, which we'll share a little bit later. That question is like, what grade level would you aim this at? I think there was an earlier one that I didn't bring up just yet, but it was like, "Is it for grade four? Or would you stop earlier?" There's like a lot of like, "When do I use this?" You know what, that's a common question because on our tasks, we don't say grade levels and there's a reason for that.

Kyle Pearce: I love it. And Jon, I think these solutions... Actually, I want to high five everyone because you're making our job so easy right now. I want you to picture that you can deliver this task in a grade four class. You could deliver it in a grade, I promise you, in a grade two class. You could probably do this, and students would do it. They would use much lower level strategies, right? Their strategies would probably be limited to fair sharing, and they may not be able to go beyond that. But I would go all the way up into my middle grades, and even in Jon's grade 9D stream math class, this task could be helpful because the students in his class, Jon knows that some of those students aren't very fluent and flexible with their order of operations, with operations in general, maybe with their math facts and with their ability to model their thinking.
So I see this other student here who very wonderfully has shown us symbolically what happened when we broke down our 91 into 70 and 21. And then they actually use the opposite. They actually didn't even think division here. They said, "I'm going to think of this as multiplication and I'm going to use partial products in order to get to the same place that this last person did, who use partial quotients."
These are strategies that we want students to have, and we want them to build. I know Jon for you, as you get closer to algebra, there's a model called the area model that you find really, really helpful, because as soon as variable is introduced, like let's say I don't know what seven is. That becomes an X. Now we have 10 X's and we have three X's, and in total, we're going to end up with 13 X's in total, if the seven was unknown in this particular case.
So when you look at how wide this particular task can be leveraged, and the beauty is, is that we're meeting the needs of every learner in our classroom. They all can enter this task where they are. And I learned something valuable about each and every single one. So if I have three students in my class doing fair sharing, and that's where they are, and then I have other students doing an area model, and then here's another model that's really helpful later is going to a ratio table, a student who's going to a ratio table.
You have all of these models. You have students across this entire spectrum and we can help every single one of them by helping every student see and make a connection to one other model. It's a bonus if they see other models. But if they see that, they can then see this particular task as something more than what they probably thought it was initially.
I could keep going, Jon. I don't see double number lines here, but this is such a great way for us to summarize. And something I do want to say for those who do use our task off our website, we give you a visual animation of a lot of these models. The model we really wanted to elicit today is the area model, but the beauty is a student did it for me. So I don't even have to show this because the student in my classroom gave us the model that I was hoping to emerge here.
Something really important that we need to be clear on is that actually, there's something really interesting happening here when we solve this particular problem, this is division, but it's actually a specific type of division that reveals a specific quantity, no matter where you encounter it in the entire universe.
I'm wondering in the chat, if there's any brave souls out there, does anyone have any experience with the different types of division? Because I'm going to tell you right now, whether a student is in grade four or in grade nine, if they're unaware that this is a specific type of division and that it happens about half of the times you divide, and the other half is the other type, that could be one of the reasons why students are struggling so much with what we call the basics.
And you are absolutely right. We've got some friends. You're all my number one math moment makers, dear friends. The part of division is what we're revealing. We're actually giving students a quantity and we are partitioning it into seven groups to reveal a rate. And the rate we received here is 13 beans per pot. So I want you to think all the way down the spectrum. If I'm a grade four teacher, maybe I'm not worried so much about the rate idea. But if I'm a grade nine teacher, I should be thinking if I'm using a rate of change in my grade nine class, and I'm not talking about how part of division is the reason it happens, then I'm totally missing that beach glass.
If I'm looking for beach glass in my class, and I don't know what the beach glass looks like, that is where we really run into some hard work as math teachers. I'm going to be honest, Jon and say, I was searching my metaphorical beach for a glass. Every class I was looking for this, but I didn't always know exactly what I was looking for. And that's something that I think you and I have really learned a ton over these past five, 10 years is that there is so much rich, conceptual understanding to be had from what seems to be a pretty basic problem, but yet can reveal so many key connections that were all not maybe super strong with yet.

Jon Orr: Yeah. For sure, Kyle. I think this outlines, like you just said, if we're going to be the scientist, we're going to look for the beach glass. We do have to stretch ourselves so that we can understand these concepts at a deep level so that we can know what to look for. And when we know what to look for, then we're in a better position to help the students. We're in a better position to write those report cards because you see it, you can experience it, you know how to help them. It helps with a lot of our teaching. And if we think back to that assumption that we were making at the beginning of the discussion, I was like when we're teaching through this tough year and going, okay, we got to fill gaps.
But hey, we can't build those things until we know what we're looking for. So we have to give kids the opportunity to demonstrate learning in different areas and then we collect that information, but we got to know what to look for, which is so important here, Kyle. And I think we're ready to do a little giveaway. Are you ready?

Kyle Pearce: Yeah, absolutely. I want to make two points, before we go ahead.

Jon Orr: Yeah, let's do that.

Kyle Pearce: Something really important in the chat. Someone had said, "I tend to use the two types of division more with division." And I think that's more of you on your own learning journey. The reality is, is students won't care about the two types of division if they can't see it with whole numbers. So we've got to make sure that we're really being explicit. In our unit, this is day one of the unit I want to be clear.
Somebody else asks, "Well, what about the other type of division?" Well, on day three of the same unit, we introduce bird seed. And through that prompt, we actually have students filling bird feeders. So we tell them the rate. We tell them how much bird seed can fit, and now we want to know how many groups we can create or how many bird feeders we can create. Then we compare and contrast both types of divisions. So I just didn't want to leave anybody hanging on that, but we are running out of time.
So yes, we are going to get to a giveaway. And before we do, we want to make sure that you, friends are holding us accountable for what we said you'd learned today. Right, Jon?

Jon Orr: Right. Let's go back over that. And then what we'll do is we're going to ask you for your biggest takeaway. Then we're going to share a little bit of information about the giveaway, which actually leads you, the giveaway is a great resource for you to actually dig deeper and help youth go further with some of these ideas, but also know what you're looking for, looking for that beach glass.
So Kyle, let's head back to the top here because we said we were going to do these things. We said we would help you see the math class spectrum and how you can use it to help your students succeed by learning through sense-making. Give us a yes in the chat if we helped you kind of see that spectrum and what we should be doing to help kids learn through sense-making? Oh, I see some good stuff.

Kyle Pearce: All right, sea glass.

Jon Orr: I was worried there for a second.

Kyle Pearce: I know. It's always scary. It's always scary when it goes quiet. After this year in the pandemic, we also said we wanted to help you with where should we go now? I even saw someone say this confirms and gives them some affirmation as to what they were doing with their students, because I'm sure you're hearing people saying like, "I can't do that this year. Not after all of that, not after all the school students were missing."
So finding the balance between the back to basics and the inquiry and the conceptual understanding tug of war. I want you to pause for a second. Do you think you saw that today? We took division. If you want back to basics like division, operations is back to basics, but we'd still did it through an inquiry and conceptual understanding lens ensuring that students can enter the tasks from anywhere along the trajectory. How are we feeling about that there? Been looking good?

Jon Orr: Absolutely. Yeah. Give us a yes.

Kyle Pearce: Give us a yes. All right. There it is.

Jon Orr: And the last thing, give us a, "Yes, we hit this one." We wanted to talk about the concept of hold your students back in the most... Or holds your students back the most and what you can do there, the rest of their needs, we're going to talk a little bit more about that being a specific concept, which is actually related to our giveaway here.

Kyle Pearce: Absolutely. So just to lead us in there, what we're getting at here today is we're actually going to be doing a giveaway for you that's going to help you build your own understanding, so you can better see and search for that mathematical beach glass like we had mentioned at the beginning of this session. Because guess what? Today, we looked at one type of division, and we're not talking about giving away more information about just division itself. We're actually talking about something bigger. And in the chat, feel free to share like, what do you think we're after in this particular visual here? What are we seeing?
I'm going to be honest, there's so many real and so many correct answers to this question because it is so open. I see ratios. I see multiplication I saw up there. We saw, oh my gosh, capacity. Here's the crazy part. If you say ratios, or if you say rates, or if you say multiplication, or you say division, guess what? They're all so interlinked and interconnected. They aren't separate. What we just did was a problem that is a part of a proportional relationship.
And every single one that you're seeing up on the screen has to do with proportional relationships and proportional reasoning. So what we're going to be giving away to one of you, friends who shares your biggest and best takeaway from tonight is share what your biggest giveaway is what I mean. I'm just searching for a slide here is we're going to be giving away a course that unpacks all of the interconnected proportional reasoning concepts.
Now, some of you might be thinking, "Okay. So what multiplication, division. Someone said ratios. Well, someone else mentioned measurement and non-standard measurements. Well, all of you are right because proportional reasoning concepts develop, and they begin with spatial reasoning. This idea of composing and decomposing visualizing. We have measuring in there, unitizing, comparing quantities and change.
This interconnected web is what we unpack in one of our courses, which is called the concept holding your students back. We've really built this course off of much of the research that's cited in this paying attention to document that was released by the Ontario Ministry of Education. What we've done is we've really kind of constructed what we call the roadmap to proportional relationships.
So built off of both that proportional reasoning document and a lot of the work from John A. Van de Walle. We have unpacked a roadmap and we take you through nine modules starting with comparison. This is at pre-K and working our way through all the way through our middle years into the muddy land of ratios and rates.
So for you, friends, what we want to do is not only share this course with you so that you're aware that this is something that you'll be able to become a part of, but also we want to give it away to someone tonight so that you can take a deep dive into proportional relationships with us.

Jon Orr: Yeah. We're really excited for that. So the course is open. It actually opened for registration just earlier a week or so ago. We run this course only once a year. So we run a different course at different times a year, but this one only runs in the fall. We ran it last year. We've had a lot of success with the teachers who have been through this program. It's one of our, we call this, flagship program because it's a 12-week course. It's going to start at the end of this month. Even though if you register now... One of you is going to get in right now.
But if you register now, then you have access right away until the middle to end of December. It's a 12-week course. So we're super excited to offer this. It's an asynchronous course. However, it's a little bit of both. Right, Kyle? We run it for 12 weeks because we want everyone to move through the modules roughly about the same time. So it's like a start date and an end date. However, you are free to move through the learning asynchronously at your own pace, but every single module is built to do a few different things. Right, Kyle?
There's a slide down... I know that you're controlling the slide deck, which is your next step. It's got our downloadable guides. These are the common things of our flagship programs is that we not only teach you the concepts about how to teach proportional reasoning so that you can do it from the progression from low grades even into high school like we've been mentioning here, but we give you the resources and the tasks and the ideas and the lessons that help you do that as well.
With all of our flagship programs, you get access to our monthly live sessions. We were just chatting with Jon here. I'm sure there's lots of other ones of you that have been through those here with us from our other programs, but we have live monthly chats to help you get what you need. There's videos. They're all closed captioned as well and certificates and PD credits, if you need that type of thing to move up in the scale. So we've had a ton of teachers through these, our professional development programs. Kyle, I think we've touched on some ideas, but what's module one, two look like.

Kyle Pearce: In module one really just unpacking what proportional reasoning is because I'll be honest, I taught high school math for over a decade without really knowing what it was. What is it? What isn't it? So we spent some time going in there, and then we start talking about in module two, how measurement is really a proportional reasoning sort of activity in order to be... You might notice... I know in my district measurement tends to be something we struggle with on many of our standardized tests. And oftentimes it's because we look at it as something separate instead of something that should be really tied closely into this idea of multiplication, division, and ratio and rate.
We then go into comparison and we start getting into the types of thinking additive and multiplicative thinking. Then we start moving into the heavy stuff, ratios and rates. I'm going to tell you right now, we don't have time for it right now, but if we were doing a session on ratios and rates, and if I asked everyone to tell me, what is the difference between ratios and rates, we would come up with a plethora of different ideas and different definitions, because even different curriculum have different definitions of what is a ratio and what is a rate. Some keep it simplistic. Some is much more complex, but the reality is it's a very muddy area.
So what we try to do is we try to unpack what is really going on under the hood, and then we start diving into how am I going to spark curiosity in proportional relationships and how might I use this in order to put it all together? So this course is something that's we love running. It is one of my favorites. It's been sort of a... I'm going to say like a bit of a pet project for myself over the past couple of years where my mind just continually got blown.
If you think partitive, quotative division is something that's mind-blowing, this course really will surprise you at some of the things that have been laying underneath the surface that you may not have noticed.

Jon Orr: Yeah. Awesome stuff. I'm really looking forward to the group coming through this cohort, coming through. I was going to say that last slide there is that with all of our programs, we do have a full refund guarantee. So for example, if you're on the fence, because you're like, "I'm not sure my district is going to cover it, or I don't know if it's for my grade level or I'm going to learn something of value." If you get to the end of the course and you're like, "Hey, man. That wasn't for me," let us know and we will make sure that you get what you need back so that you can do that.
So there was another slide there that many of our educators that take our actually don't pay with their own money. They get it funded through their district or maybe their federation or even their school principal might pay for that. So there's the cost associated with the workshop alone. But one of you will get this for free... Sorry. There will be a professional development credit. So sometimes we need that to move up the ladder on our pay scale, and we provide a certificate that says, "Yay. You engage in 30 hours of professional development here with us and we'll send that off to you."
So your next move, if you have not yet... you've got two moves. Actually, if your next move has not yet buttoned to put what your biggest takeaway is in the chat, because Kyle's going to do a scroll and pick, then your second move is to head on over to makemathmoments.com/nextmove. And from there, you can get a certificate for tonight. There's a 75 minutes certificate that says, "Hey, you were with us tonight for 75 minutes." You can get on and get off that over there. You can learn also more and register for this new course that we're running this fall... Or not new course. We ran it last year.
But what I mean is new cohort. You can get in register right away and get your seat. As I said, you get access right away to the course as soon as you register. You can do that too tonight, get in and register so that you can make math moments with your students and make sure that we're not leaving them off on that concept that can hold them back.

Kyle Pearce: I think it's time. I just want to give a heads up. Some people were asking about the tasks. Most of our problem-based tasks are open on the web. Jon will type it into the chat here in just second for you. Head to makemathmoments.com/tasks. You can access that if you want all of the downloadables and the full unit downloads.

Jon Orr: Right. It's not fully open.

Kyle Pearce: You can join for just the tasks. Only membership. Someone was asking, "I just want the tasks. How do I do that?" So Jon's going to hook you up with that in the chat right now. I'm going to go ahead and do some scrolling and I'm going to stop there. I am pointing at Lynda, L-Y-N-D-A, who says, "Be more specific to use student reasoning through these tasks as the formative assessment. Thinking that like the scientist analogy is spot on." Lynda, if I could gift one big takeaway to everyone, that is one of our biggest messages that we always want to consistently share is that we can do formative assessment every single day, if we're giving students mathematical tasks that are going to allow us to actually see what they can do with mathematics. And that is such a big takeaway. So Lynda, congratulations. You my friend are going to dive into the concept holding your student back.

Jon Orr: All right. Awesome.

Kyle Pearce: The Last thing I want to say because I saw someone who commented about district leads and I do want to say a message to our district leads. We try our best to stretch district PD dollars as far we can. So if you want to get a group of your educators going, shoot us an email. What we try to do is we try to extend as many licenses to as many educators in your district as possible. So let us know. We have many districts coming on board, especially given the challenging situation we find ourselves in for PD, face-to-face PD is becoming harder and harder to do due to the pandemic.
So reach out to us, just hit us up on the website, makemathmoments.com and hit the little chat bubble at the bottom and say, "Hey, I want to talk about district pricing and we will get you hooked up. We want to spread this knowledge as far and wide as we possibly can."

Jon Orr: All right, everybody. Thanks for joining us here this evening, or this morning, if you're over on the other side of the world, but thanks so much. Go and make some of those math moments with your kids, would you? As always, Kyle and I often reflect on the learning that we engage in while we have the webinars like you just had, but also any of these podcasts episodes. So we want to know have you written any of these ideas down that we shared? Have you drawn a sketch note? Maybe you sent out a tweet. Maybe you called a colleague or email the colleague to talk about or share some of these ideas. Hey, you should be sure to share or engage in some sort of reflection so that learning here sticks with you.

Kyle Pearce: Absolutely, absolutely. Remember, in order to ensure that you don't miss out on any new content, make sure you hit that subscribe button, whether it's on Apple Podcasts. Or if today you're hanging out with us on YouTube, keep in mind all the podcast episodes do go up to YouTube as well. We release weekly video content, which are extra goodies that you don't hear here. So hear here. Listen to that. So make sure you head on over to YouTube, hit that subscribe button and let us know what you're listening or tuning into over on Twitter or other social media platforms.

Jon Orr: Show notes and links to resources from this episode can be found at makemathmoments.com/episode146. Again, that's makemathmoments.com/episode146.

Kyle Pearce: All right. My friends 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.

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