Danitte Kozai: Just the engagement piece is not there the same way it is person. I mean, this isn't something that I think that any sort of engaging math can fix. But I find a lot of the times the kids are just signing into the Google Meet and walking away. Because I call their name and they just don't respond or they don't go to the breakout room. Especially with applied classes, I didn't have any this semester, but I'm thinking like, "I'm glad I had some students who are really game to do stuff," but a lot of them weren't, and how can really fix that? How can I translate, just do it"? Like just do any sort of thing the they we were doing before.

Kyle Pearce: Hey Math Moment Makers. Today we are speaking with Danitte Kozai about how to prevent that student who shows up to your online class for attendance and then immediately just inaudible and walks away from the computer. I think we've all been there before. I'm not even-

Jon Orr: Are you there? Are you there? Are you there?

Kyle Pearce: Yeah, I'm not even full time in the classroom right now. But in all the classes I go into, I love co-teaching with teachers. I come into their classroom and I can tell that we've got students in the room that are doing just that. Today we're going to brainstorm with Danitte on how to engage students while teaching online through the use of low floor and high ceiling tasks.

Jon Orr: Yes. I'm super excited for this one. This is another Math Mentoring Moment episode where we talk with a member of the Math Moment Maker community who is working through struggles and together we brainstorm possible next steps and strategies to overcome them.

Kyle Pearce: All right. Let's hit it. Welcome to the Making Math Moments That Matter podcast. I'm Kyle Pearce from TapIntoTeenMinds.com.

Jon Orr: I'm Jon Orr from MrOrr-IsAGeek.com. We are two math teachers here 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: Fuels and spanking.

Kyle Pearce: And ignite your teacher moves. Welcome, everyone, to another Math Mentoring Moment episode, where we get to chat with a fellow Math Moment Maker from around the world and work through a struggle.

Jon Orr: Before we dive in here, we want to make sure that you folks have taken the time to explore some of our most recent full units of problem-based math lessons.

Kyle Pearce: Right, Jon. We've been busy adding full units to our Make Math Moments website. That's makemathmoments.com. We are really excited to share one of our 60 units. This one's called the Wooly Worm Race, and it was created specifically to help educators address teaching and representing fractions and adding and subtracting fractions. But also, we sneak in decimals and percentages conceptually.

Jon Orr: We've also tossed in some more context-rich problem-based math lessons with our unit called Snack Time, where students will explore the TapIntoTeenMinds.com classic 3 Act Math task, Cheese and Crackers to use part of the division and partition and distribute slices of cheese to a specified number of crackers.

Kyle Pearce: Yes, that's definitely a classic that I used with many of my classes, except now with this whole unit of connected math talks, math and sense-making prompts, purposeful practice, and a summative assessment. It's all straight there from the web browser for you to explore at makemathmoments.com/tasks.

Jon Orr: Super exciting. See you over at makemathmoments.com/tasks to run one of these awesome problem-based units in your classroom right now today.

Kyle Pearce: All right, my friends. Let's jump into our conversation with Danitte.

Jon Orr: Hey, hey, there, Danitte, thanks for joining us here on the Making Math Moments That Matter Podcast. How are things going up your way? I say up, it's like Northeast-ish from where we are, but just a few hours up the road. How are things going in your world?

Danitte Kozai: Yeah. Things are good, thanks. Not really much to do with the lockdown and whatnot. But things are good. How are things going with you?

Jon Orr: Good, good, good. You know what, Kyle, it's almost been a year now where we've asked that and people definitely bring up, "Oh, we're in COVID. It's lockdown. We're not doing a whole lot." And that's true. We're not really going anywhere. We're just hanging out. That actually gives us time to chat with you.

Kyle Pearce: Jon, actually, I think we're almost moving in on maybe a third of the time that this podcast has been out, we've been in lockdown. Is that true?

Jon Orr: I guess, yeah. By the time this airs, it will be like two and a half years of podcasts and-

Kyle Pearce: It's going to be almost more than a third.

Jon Orr: Yeah, almost a year. Yeah.

Danitte Kozai: Really?

Kyle Pearce: crosstalk.

Jon Orr: Those are numbers sets coming in, right? Yeah.

Kyle Pearce: Yeah. I'm going to model it-

Jon Orr: You send the picture over. We'll have a peak.

Kyle Pearce: Because everyone's like, "It's a podcast, Kyle. We can't see it."

Jon Orr: Danitte, well, welcome. We've met a few times through conferences when we were allowed to see each other face to face. But tell us a little bit about yourself. Tell our listeners where you're coming from, how long you've been teaching, and what's your journey look like?

Danitte Kozai: Sure. My name's Danitte Kozai. I'm a teacher in York Region District School Board, which is just North of Toronto and the GTA. This is my fifth year of teaching. I'm teaching at a school in York Region District School Board called Dr. G. W. Williams. It's in Aurora. Nobody's heard of it. Anyways, this is my fifth school in five years. As a new teacher, I got bumped around a lot. But I'm the assistant head of the department here and I'm really excited about that. So I think I'll be staying here for at least the next few years, or as long as my contract goes.

Kyle Pearce: You actually brought back a memory because I know we were chatting on Twitter back when you were applying for this position as the assistant department chair, I think you said, or department head. And that's so awesome. I totally forgot about that and it just popped into my mind. How did you land yourself in the teaching profession in particular with mathematics? What's the story there?

Danitte Kozai: I guess I'd always considered it at the back of my head to maybe go into teaching. I tutored my brothers when I was in school. I was remembering just grade eight math class, where there was like a circle of girls sitting around me in the hallway and I was explaining what a variable is, things like that. But I was always like, "I don't really want to do the same thing over and over again for my entire life." I felt like that would be boring.
Teaching, thankfully, has been nothing like that. So that's good. I only really started to think about it seriously when I was in my second year of university. And so, I started tutoring on the side just so I'd make a bit of extra cash while I was a student. I ended up really enjoying that more than my major. And so, I switched program tracks from straight up computer science to be in computer science and math, so I would have a teaching track with two subjects.
Then in my third year of university, I got to be a teaching assistant. So I had my own little classroom twice a week for first-year students, and I loved that. That's when I really made the decision that I was going to go through with it and go to teacher's college and do the whole teaching thing. I've listened to a few of your episodes of your podcast, or I guess maybe more than a few. And so, I feel like my teaching journey is a little bit different than a lot of other people's because a lot of people have like, "Oh, I was a traditional teacher and I discovered Thinking Classroom.
I actually haven't been around all that long, I guess, because I learned about the two of you, Jon and Kyle, as a student teacher through my host teacher. She was already doing like 3 Acts math problems and stuff like that. So, in a sense, I got a bit of a head start that I got to watch her really do the Thinking Classroom for six weeks straight and just be there every single day and just see what it's like without having to figure it out while I'm already in the job. That was pretty great.

Kyle Pearce: Yeah.

Jon Orr: But that does sound interesting. We've always said that we wish we could go back in time. And I think a lot of teachers later in their careers wish they could go back in time and use the knowledge and the experience that they've learned along the way to restart. It brings up actually two ideas that just are popping into my mind about that experience that you just said.
One is your starting out feels like where we are. So it's like you're starting out at that time where it's like, "We wish we could go back in time and reteach all the kids that we taught for 10 years through a Thinking Classroom, through our spiraling program, using our tasks to engage our students and fuel their sense-making." You get to start there, and that's such an exciting opportunity, which brings the second issue, or not issue.
Second great thing that I'm thinking about is what is your career going to look like then 10 years down the road? If we've changed our thinking modified at 10 years in or at 12 years into our career, I'm wondering like 12 years into your career, or even maybe a little farther since you're already five years in, is what is it going to look like for you? That's an exciting thought for me.
I'm wondering just about that, but I'm also thinking about your past. There's a lot of thoughts flowing. But if you listen to episodes before, you know this one's coming. It's what's your math moment? When we say math class, if you think back to your experience, what is that defining stick in your brain math moment when we say the math class?

Danitte Kozai: I always thought about this question, like if I ever got asked. And I'm really excited I get to answer it now. I was like I shouldn't share this story, but I'm going to share it because it's the only one that really sticks in my mind.

Jon Orr: It sounds exciting.

Danitte Kozai: Yeah. It's not such a positive one, but there's a silver lining, if you will. And so, when I was in high school, so I was in the regular stream academic math in Ontario in grade nine. Then I discovered there was an enrichment class that I was not in, and that made me very jealous. And so, I was like, "I can do this. I'll sign up for it for next year." And so, the grade 10 enrichment class was a whole other level.
From what I can tell from afterwards, it was not a normal class. Our teacher taught us imaginary numbers in grade 10, which is way beyond what we were really supposed to learn and things like that. And so I think it was a defining moment for me because I really struggled with that class. This was the first time that I really questioned whether I enjoyed math and whether I felt like I was "good at math" was in that class because I was just like having such a hard time with it.
I don't really hate when my students do this, but I just feel like, "Oh, what a shame, all that marketing." But every time I got a quiz back that I didn't do well on, I would crumple it up and throw it out immediately. And so, the boy who sat next to me was trying to convince me not to do that. Then I felt like, I guess, I was just alone in this really difficult class and everyone else took grade nine enrich math, so they must be doing really well.
Then one day our teacher let us do a quiz rewrite, and I guess it didn't go well for other people too, during lunch. And so it was optional. So I walk in and over two-thirds of my class was there doing this rewrite. That was the first time I felt like, "Oh, maybe I'm not the only one." And then, later on in the year, I just felt like I didn't really belong in that class. And maybe I really didn't. I didn't feel like I knew enough math or I was good enough at math. And so, I really wanted to do well and to understand it.
Then my father, who's an immigrant as well, was trying to teach me about senos and cosenos. And I was nodding and nodding. In the end, I studied really hard for the final exam and I was surprised with my results. I did really well. I guess the silver lining of the story, I was just thinking about it. I felt like I didn't belong in that class and maybe I'm not good at math, because I found it difficult. But in the end I was able to understand it.
I feel like I want to bring that into my own teaching, that really anyone can learn. I don't really want to set that bar of like, "You can't do this," because I think that students can do it. And the growth mindset is foundational part of learning math.

Jon Orr: That's such a interesting story. And like you said, there's definitely a silver lining there. This has come up quite often when we've had guests on the show share a math moment. Sometimes it's like one of those moments where, let's say, it made the person feel like they weren't a mathematician or they didn't belong. You had mentioned that a few times in your little share out there. Part of me thinks about what that actually teaches us.
I know that struggle is never fun when it's happening. I'm wondering about that. Clearly, you're reflecting on that. You're thinking about how that might influence what you do in your classroom. And it makes me wonder what details you pay attention to in your class to try to ensure students feel welcomed and feel like they do belong even when there are struggles.
Then there's this other side too that popped into my mind around, "I wonder if maybe by being in that classroom, you were finally able to see that actually anything worthwhile is difficult and it's hard." I just wonder sometimes about how we do this thing called school. Again, it's the mindset I had when I was teaching for my first five to eight years. I was trying to make math class easy for everyone. I was trying to make sure that every student got a good mark.
When I look back at that, I was really good at it. I was really good at helping kids memorize stuff even though they didn't know what they were doing. And I just wonder if some of my students were to go into a class where the math is actually challenging, because realistically math is challenging. It is complex. I just wonder about that, when sometimes I think we go at math wrong when we try to make it easy for everyone, instead of, again, trying to find that productive struggle.
You didn't mention about what that teacher you had did in order to meet students where they were. So maybe there was some differentiation skills that maybe weren't there or whatever it might be. But I think that rigor piece is really important. And then, obviously, finding ways to ensure that when students are struggling, that they aren't feeling ostracized or that they don't belong. So that's a really great story. It really makes me reflect on how we do math, how we teach math and trying to find that happy balance there.
We're really eager to hear about what you're currently working on right now. I'm wondering, do you have any positive quick wins for us, we'll say, like from this school year? From the beginning of the school year till now, is there any quick wins that come to mind that we can flip back to the positive and start thinking of some of the good that's come out of this experience teaching online?

Danitte Kozai: Actually, yes. I've been fortunate to teach the grade 10 math course for most of my career, actually. I think I've taught it almost every year since I started teaching, well, applied academic multiple times. And so, the one thing that a lot of the times got me was similar triangles, and I didn't really have a good way to teach it. So I ended up showing them how to do it and set up a proportion and all the little steps.
And so, last year I was just hunting around because I was like, "I can't really do this anymore. I want to do better than that. I think I can do better than that." I found this really great lesson. I wish I knew who to give credit for for this, but it's definitely not mine, that connected similar triangles to Pythagorean triples. And so, the activity is basically I show them what a Pythagorean triple is and I say, "At your boards, find as many as you can."
And so, with COVID restrictions, this was in person before we got shut down. And so, we have alternating groups of 15 kids in the class. And so, I did this in person on the last day of our in-person rotation with my classes. And so, that I had groups of two. I was in a computer lab, so not at the boards, but at their own tables. And I said, "Find as many as you can." And so I found out two kinds of patterns emerged and it was just really fun to see them working because, first, they find a few and they're really struggling to find more. They're testing out different numbers in their calculators.
And so, they find a couple of them. Like the three, four, five is the first one we look at. Five, 12, 13, seven, 24, 25. And then some groups just start exploding because they find all the multiples, that like a three, four, five triangle and a six, eight, 10 triangle, and so on and so on. And so the groups, when I did this last year, but the vertical bars, they would just look over at each other and be like, "How are they finding so many?"
It was harder with everyone just being seated at their seats this year. But I felt there was that still same energy. And then I made it into a competition and I said whoever found the most gets some sort of prize, which is usually stickers. And so, then we talked about the connection between like how do you find more Pythagorean triples from other ones? And so, they came up with this idea that was basically a conceptual understanding of the scale factor.
I feel like it really helped them understand similar triangles a lot more, that they're not memorizing definition or same angles, different sizes kind of thing. They could really see how one similar triangle is related to another. And then, later on I connected that with, Jon, your lesson that connects the tangent ratio to similar triangles. And so, I felt like that was a really big win in my grade 10 academic class.

Jon Orr: Yeah. You remind me actually also of another lesson I'm just going to throw out there for folks who are gobbling up the resources which we'll all throw in the show notes. I think Kyle has found one here. He's putting in there show notes already about similar triangles and Pythagorean triples. That is a link to one. It reminded me of one from Al Overwijk and his work on spiraling problems through task, which is, Danitte, where I started my similar triangle lesson, which is also looking at, say, families of triangles.
We looked at like three, four, five, and then we showed like the six, eight, 10. Then we said the 12, 16, 20, and the 15, 20, 25, we said, "They're all a family." And then we looked at why are they all a family? And then they all start to look at the patterning and then we branch off from there, similarly. So we'll throw that also link in the chat on that lesson, because I think that's a winner. But I really appreciate you sharing your lesson for us to dive into and think about, and I think that's a great one to start.
We'll also shared the one that you mentioned about how I've taught how similar triangles connect to trigonometry, like the beginnings of trigonometry and how we can do that through slope. That was also a good pivot for me when I changed that lesson, instead of just saying, "Hey, here's trigonometry. Here's the sin, cos, and tan, and we're going to do it this way." So it was a nice way to do that.
Thanks for that big win. But now let's pivot a little bit. Let's start to think about, what's a pebble in your shoe lately. The whole point of the conversation is that you're here to chat with us so we can brainstorm something that you can take back to your classroom and work on and help your students out. So what's that pebble in your shoe that you could pluck out of there and that might make walking a little bit easier?

Danitte Kozai: I guess, probably right now, the biggest struggle I find is really engagement with the online classes. When I originally wanted to be on your show, my struggles were really COVID was way far ahead all crosstalk-

Jon Orr: Felt like a whole different world, right?

Danitte Kozai: Yeah. It was a whole different world. So I haven't even been considering this. And so, I have a pretty good idea and a good program for a spiraling and stuff. And especially grade 10 applied, I've done a lot of work with that course. But just how do we adjust that to online? It's like I found that, when I talk with other department members who are also like I was starting, various stages of implementing Thinking Classroom. So people have been doing different things.
And so we've had like some success with breakout rooms, but I guess just the engagement piece is not there the same way it is person. I mean, this isn't something that I think that any engaging math can fix, but I find like a lot of the times the kids are just like signing into the Google meet and walking away because I call their name and they just don't respond. Or they don't go to the breakout room, especially with applied classes.
I didn't have any this semester, but I'm thinking like, "I'm glad I had some students who were really game to do stuff." But a lot of them weren't. And how can I really fix that? How can I translate, "Just do it. Just do any sort of thing the way we were doing before," and make it engaging online from home in 40 minutes or however many minutes they give us?

Kyle Pearce: Engaging students face to face is a challenge. This is a topic that has come up so many times on the podcast. And it's so important because we've said it a billion times, like without the attention of the learner, and not meaning attention, like sit there and just listen. But without them actively engaged in what it is that we're trying to explore and investigate, really, it doesn't matter what you do after that, if they're not giving it a good go.
It makes it really challenging when you're teaching a course where oftentimes you have some students who typically haven't felt like... It brings me back in a different way to your feeling in that enriched course where you felt like you don't belong. Like oftentimes the students who disengage in a face-to-face environment are feeling the same way. They feel like they aren't able to do the mathematics or they weren't born with the gene or whatever the reason that they're telling themselves or that they're feeling they're being told that through some grades or actions by others, it's a real challenge.
I know even here at home, my whole family is online right now. My son's in grade one. We had another call from the teacher today and Landon was watching YouTube. He's in grade one and it's like, "Oh goodness." Hey, he's in grade one, and I'm thinking to myself, "Yeah, I guess if I was in grade one and, heck, if I was in grade 10, it'd probably be even worse." So this is a huge challenge.
I don't know whether we can do a whole lot about students who, let's say, are logging in and walking away. That is definitely a challenge. I mean, reaching out to the student and parents and maintaining some sort of communication is definitely key there. But when it comes to those who are there, I think there is something we can do in regards to that engagement. Jon, what's your thoughts, because I know you've had some challenges with this too just with your own groups, right?

Jon Orr: Yeah. With my groups, I guess, I wanted to just address the statement that you just made, Kyle, about we might not be able to help the kid who just walks away. We would argue against that in class, Kyle, right? Like we would say if the kid's sitting in class and they're pulling out their phone, that's the same kind of analogy of saying like, "They've got their phone in front of them." You can't really fight that or we can't really help them if they're going to look at their phone.
I think we can help kids that are walking away from the computer, by trying to give them a reason to not walk away from the computer, like not pull out the phone. That's our battle. It's like, "What can we do?" I don't think we're going to win this battle. I'm not saying we are going to win because this is a huge battle.

Kyle Pearce: You're going to go to war though, right, Jon?

Jon Orr: Exactly. I think so. That's what I want to do. It's like, I'm not going to just roll over here and say, "I'm just going to go back to teaching the most boringest way online as possible." I know there's a lot to do, and I know... Because I've been teaching online too and I know that it's real easy to cue up of YouTube video because someone else made that lesson that was very just like, "Hey guys, we're going to learn how to solve equations. And you just do this and you bring this over and you do this."
There are a million videos out there that do that, that you could just go click, click, put that in your Google classroom and say, "Guys, watch this video. And here are your homework questions." And then you sign off for the day. That is not going to get that kid who's just turning on the Google Meet and then walking away. They'll be like, "Why do I need to sign into my Google Meet if I'm just going to be told to watch a video anyway? I can do that later tonight, or maybe I could just do the homework questions without doing all of this."
We've got to have something if we want to continually engage our kids in mathematics as a discipline, as a thought, as this thing that mathematics is bigger than just learning procedures. It's about problem solving. It's about curiosity. It's about sparking something with inside us. I think we can do better than that. But I think there's a lot to that.
So I'm curious right now, Danitte, to what have you done so far to... I know that you're asking about applied level students, but I think what's going to work with applied level students is also going to work with the academic students that you've been teaching. What are some good practices that you've been using so far? Maybe start with, like you mentioned, breakout groups, and some folks are like, "Yeah, I've heard about breakout groups," or, "I've tried a breakout group. Just didn't go great for me."
Maybe do you have some tips there to kick things off to say, hey, what's been working for you maybe in breakout groups? And then maybe we can go down that path to figure out like, what could we do to battle this?

Danitte Kozai: Sure. I guess, the closest I can get to simulating online what I used to do with vertical boards or try to do, is with the breakout rooms, it's basically some of the apps like zoom and Google Meet have it built in. There are others where there's tons of Chrome extensions that you can find to do it. But basically puts them into a random group of however many students, you choose.
And so, I'll admit that I haven't done this very often because I've been stretched crazed. Then with this semester, I have two new inaudible. I got four days notice that I'm teaching computer science this year after really not having taught it, being part of the math department for the past four-ish years. So that was a bit of a surprise.
But when I did try, for some of the things, well, I think what I first started with was a trig identities in grade 11. That was the thing that I really wished that they could really work together on because you often need more than one perspective when you're doing something like that that's a little bit more of a puzzle, as opposed to like, "Here's the process," where everything has a process. But identities aren't really something where it's like the same steps over and over again.
Anyways, so the breakout room. So I put them into groups. If I tried to aim for two or three, maybe a couple more, because some of them don't necessarily engage. I made a Google Jamboard, and each group, whatever your group number corresponded to your slide number. And I put the same question up on each board. So there was some response to that. Some of the groups, the students were actually... Like I'd pop into the room and I'd hear them talking. And one person would be writing with either a mouse or if they had a tablet or a phone, then they can write with their finger. And so they'd write on the board.
Then I could see their work. It was kind of the same with vertical boards where you can see what everyone's doing at once. It's just that the students couldn't really see each other, hear each other. So they're missing out of that. But I found there was some success with that. But I found some groups were reluctant and when I walked in... Not really walked in, but when I entered their breakout room, it was just completely silent and it's like nothing was happening. Nobody was writing.
And so, I asked, "What's going on?" And they told me, "Oh, we're each solving it separately and then we're just going to put up one of the answers." And so that seemed like it defeated the purpose. I think the nice thing was I could look at all the boards at once and flip through them. So if a student's talking to me and I'm listening to them, I can also be looking at the other slides and seeing where everyone else is at and not seem like I'm rude by not looking at them. So that part was kind of nice.
But I guess, like how do we get students to buy in? Because they don't really want to do anything. They feel like they're online and they don't want to do it. Whereas in person, if I just give them a marker, then they're already there.

Jon Orr: Right. They've got the pressure of everyone is here and we're all together. Well, I've got to do this.

Kyle Pearce: I even think, too, going back to when I first started trying to do vertical, non-permanent, it wasn't like a first day of school thing. It was midway through the year when it came across my radar and I was like, "I'm going to give that a shot." I remember there being a reluctance then as well, and we talk a lot about the culture building. I know it's, again, extremely difficult to build culture in an online environment in comparison to in a face-to-face environment.
But I'm wondering, what does a prompt look like, sound like to get them started? For example, I know you use the trig identities as an example, which I agree that's something that you can work together and talk through and look at it a few different ways. That's always super helpful. But I'm wondering, what might it sound like when you're about to get started on that activity? What does that prompt sound like to get students going?

Danitte Kozai: I guess I'm thinking just normally, like in a regular class. I try to leave it open and give them something that they can fight with. It's hard to do with depending on the class period. Like right now our periods are 40 minutes long, so there's not a whole lot of time to do anything with that. It's either I'm going to attempt this breakout room thing and it's going to take the whole time or there will be a lesson. But there probably won't be time for both.
Well, the prompts I would have used, I guess, I did this in person. But with the Pythagorean triples, just show them a couple, and then how many can you find? I keep it like just they're the ones figuring out what they need to do. And they need to talk to each other to figure out where to go from there.

Jon Orr: When you did your Pythagorean triple lesson, how was the engagement there? When you put three numbers up on the board or you talk about it and then say, "Hey, go and find more," what did you find about engagement there? Same as, say, compared to the trig lesson. I know there's different classes, but like the trig identity lesson, or do you feel like there was a different buy-in there?

Danitte Kozai: I think there was more buy-in. But also I guess I have to say that the Pythagorean triples was in person. So there were less people. There was only 15 of them. But there was definitely engagement across pretty much everyone, I'd say, that they were all working on it. Maybe there was one group where they weren't really talking to each other. And so I tried to encourage that. But I also can't tell them to get any closer to each other. So that was difficult.

Jon Orr: That was in class?

Danitte Kozai: That was in class.

Jon Orr: Yeah. So you didn't try that lesson specifically while online yet though?

Danitte Kozai: No, I haven't.

Jon Orr: No.

Danitte Kozai: Let me see what else I did. Oh, I did do one thing that completely flopped. Should I just talk about that?

Kyle Pearce: Oh, for sure. Yeah.

Danitte Kozai: This is a thing that I love to do in person. And so, basically I think I actually got the idea from your workshop. You showed us like two squares and one of the growing patterns, and now draw the next step. Then we looked at all the patterns and then draw the next step. Like you remember that?

Kyle Pearce: Yeah, for sure.

Jon Orr: Yes. We show the first two and then you had to draw the third?

Danitte Kozai: You showed just the first one. And you said, "What does term two look like?

Jon Orr: Oh okay. Right, right, right, right.

Danitte Kozai: Then we look at all of them and say like, "Just all of these are great. Here's the one that we're going to look at today." And then I show term two and term three. And so I've done this with linear patterns, quadratics. The quadratics one has always got them because they just don't expect it to look like that with a cube and a line and the square.
And so, I did this with... It was intro to quadratics. Over at Google Meet, I did the same thing. I was drawing the next step and I had them type in the chat, what do you think the next step looks like? They don't really like to talk with a microphone. I mean, so I got some answers. I find that I'm usually getting the same six to eight people who are always the ones typing the chat, who are usually always the ones with their hands up in person.
So I got some engagement with that part, was like, "What does the pattern look like?" And then the next step I go to from there, I was like, "Show me a table of values, equation, graph, that whole deal. Like, "What does term 17 look like? Which term has 500 tiles," or whatever it is. And so, I put them into breakout rooms and I think they just did not know what to do and they were just silent.
So I went from one to another and I tried to help them get started, like just, "How would I make a table of values? Tell me what to write." But there wasn't really a whole lot of time to really talk to everyone.

Kyle Pearce: What we're hearing, and again, things are... It's just so different in the online world. Like you're saying, I'm seeing that a lot as well when I'm going into different classrooms. I get to go in and co-teach with some teachers and I'm seeing a lot of the same students responding and turning their mic on or responding in the chat. So definitely a challenge there.
I'm wondering about if we were to think about, I guess, a couple of things. First off, obviously, you know us well. You've been to a couple of our workshops and presentations. Something that we really spend a lot of time on and we try to put a lot of effort into is that idea of sparking curiosity. In an online world, I feel like we almost have to pay even more attention to that, to get that ball rolling, to start that snowball effect.
I wonder if maybe some of the hurdle's in the way with the technology. Like your mind is in so many places. You're trying to set up breakout rooms, you're trying to monitor a chat, you're wondering whether Tommy's actually at the computer or not. There's a lot of things going on, a lot of distractions. I'm wondering, and I know I do this a lot when I'm presenting, doing a webinar. Jon, I'm sure you would relate.
We do a lot of these webinars together where you're talking to a screen and sometimes you're wondering what the facial expressions on the other end are doing. Their cameras aren't on. In your head, it's like your mind's telling you a story about what may or may not be going on on the other end. Typically, I read a book. I can't tell you what book it was, but it said that your brain is never giving you or your rational brain is never giving you good ideas. It's constantly sabotaging you, your inside voice.
There's almost this natural tendency to move quicker when you're talking to a screen. I wonder about the idea of sparking curiosity if maybe, if we were to zoom out a little bit, I'm wondering if you could reflect on maybe this patterning lesson, for example, and reflect on the amount of time and care we put into that lesson upfront when we're face to face versus in the online world. Is it possible that maybe we're pushing it a little bit too fast?
You had mentioned, I think you said 40 minutes. That doesn't sound like a whole lot of time either. Tell us a little bit more about that. Let's zoom in on that part of the lesson, because I'm feeling like that's the make or break, whether a student's going to walk away or whether they're going to be like, "Oh, I don't want to leave because this is actually kind of interesting." It's like you want to get some skin in the game. So can you tell us a little bit more about that? Especially like the starting, the prompting to get going on a task.

Danitte Kozai: Yeah. I guess I've thought about this and I'm ashamed to admit I've done more traditional teaching than I've ever done in my career this year. Just been really thrown for a loop with this online stuff because I have to like, "How do I teach and be engaging and do it all in 40 minutes?" That's been the problem. And so, what I did when I did have some of the lessons that really... I was like, "There's no way I'm going to take this engaging lesson from face to face and make into a boring thing online where I just show them how to do it."
The way I thought about doing it is usually we have like, "What do you notice? What do you wonder?" Like a think pair share. Students share their answers with the class. We write them all down. Then they get to the problem solving part, and then some sort of consolidation. And so, the things I really had to cut short were like some of the beginning stuff with all the wondering.
And so I didn't want to speed through things because I've noticed even when I'm teaching just a boring old lesson, sometimes my students type "Wait" into the chat. It's kind of hilarious. They'll type, "Wait". Basically, I was like, "What am I waiting for?" I'm waiting for them to finish typing because they have a question or something. I'm like, "Oh yeah. It takes a lot longer to ask a question when you don't type 200 words a second or whatever it is a minute.
And so I try to cut down on one of the things and just take it out, so that the students have more time for one of the others. So like maybe we'll only do questions instead of notice. And that way, at least I can get them thinking and not have to rush, rush through each of the parts so that I get to check them all off.

Kyle Pearce: Right. I think when we have the longer time to keep the floor low, if we get our students to have that low floor, than the entry level into the mathematics, into the thinking, is easy for everybody to get into. It can prevent the person from over there tuning out. I think that's true online too. The challenge is, how can I keep my floor low enough so that I can bring everybody in, but I also can make sure that I do what I need to do in the timeframe that I have? I guess that's your big challenge. Would you agree to that?

Danitte Kozai: Yeah, I think so. Yeah. The time has definitely been a challenge.

Jon Orr: I think so too. It's like I have to ask myself that too. I have all day with my students, but I have to... That's still for... Because I'm in a quadmester, this situation where we have all day, but I've broken it up into blocks, periods of the day. And so, like you've experienced teaching online, someone just told me that you're going to move through material much faster. But because I want to keep them floors low enough, and get the engagement, and get kids to respond and have our conversations, it actually takes longer like we've just talked about, because I think someone who said it's going to be faster is just going to be like, "I'm just going to show you or I'm going to give a video, I'm going to move on."
So I guess, since the challenge is, how can we keep that floor low enough, what are you thinking? If you could imagine a magic wand that we could wave over this and say, "Hey, the answer looks like this," what do you think that magic wand is showing us?

Danitte Kozai: Yeah, there has to be something there in the beginning that gets them because otherwise they're just going to walk away. In person, it would be really a question that anybody can answer. That's why the notice and wonder is often really good. So start with that. And usually I'll play a video like three, four times just so that everyone can see it and figure out what's happening. Yeah. I think that's good.
I don't know what else to... Just where do we go from there? How do I just see that students were actually not tuning out when I'm explaining the instructions? And then they're whispering, "What do we have to do?" But there's nobody to whisper to. They're online.

Jon Orr: Right. I think getting action is quick and getting action from them as often as you can, is really key. And how you can do that can be in lots of different ways. But keeping that floor low enough is super important. One way I did that this week was... And I shared this in a video recently about the activity I've used many times in class, which is Truths and Lies. I used to call it Two Truths and Lies, which both said there's only two true statements in one lie. And then it was easy to pick out the lie or a true.
But I changed it to Truths and Lies because they could all be true or they could all be lies. Let's make it a little bit more interesting that way. And so, when we tried to engage our students, I find that I, especially, and especially in lots of different grades, not, say... And this works great especially in higher grades because there's less and less, say, real world problems out there to engage our kids with at an abstract level, is doing a Truth and Lies activity, which is an activity that's really low floor for everyone to get into and you can bring out great discussion and great thinking at the same time.
And so, one way I did Truths and Lies this week online was I showed two equations, and it can be just any old equations. It can be whatever you're working on. It doesn't have to be equations. It could be lots of different things. But it kept the floor low enough because it was just right down, it was like, "What are some true statements? What are some lies about these equations?" Having kids make up their own, instead of me saying, "Hey, here's are some truths and here's some lies. Verify which ones are true, which ones are lies."
That turns the math dial right up real fast, and where if you keep it low floor enough, that you can get kids to say... It could even be like, "I see a 2X. That's true." That's almost like a notice and wonder at the same time. So I guess the point I'm making here is that the activities don't have to be, say, video always the time. We can bring in other activities that generate discussion and good thinking to keep the floor low enough. Then it's like once truths and lie statements come out, we can share them back and forth. Then we can also introduce more complex ones.
Like I've done the breakout groups where everyone got a set of equations, a graph maybe if it was a different problem. And they had to create their own two truths and lies and then post it on a Padlet board for everyone to verify. But some kids will create really easy questions and then it's like, "Okay, you created the easy set. Now create the hard set. And so, it's like you can now go to the high ceiling. So I think the lower floor is our key, but how can we keep the floor low enough and get that discussion going?
The magic wand I think is keeping that floor low. How can we do that? We've got to get that discussion happening, get action in and then move them up slowly.

Danitte Kozai: I like that, and I like that it can work at any level too. That could work as easily in a grade nine class, as a grade 12 MHF calculus or a calculus class type of thing. So that's cool. I like that idea.

Kyle Pearce: I'm thinking as well, estimating is big as well. I find getting everybody estimating, asking them. And when no one's responding, asking questions that almost make them accidentally respond. For example, if three people make an estimate, then picking one of them and saying, "Oh, there can't be anybody here who estimated lower than this." And then all of a sudden, two more trickle in. How about anybody higher than this? Okay."
I'm trying to model it on a number line using Brainingcamp or a document camera, and trying to, again, get really loose conversation going and letting everybody have that voice and doing that early and often I think is really important. Then the other piece too, and this is I guess coming in near the end of the lesson, is trying to think of... I know in a face-to-face environment, lot of teachers do like a ticket out the door type thing.
That's something that I think in the online environment, even if it's one consolidation prompt, when you go on our Make Math Moments problem-based units and lessons, we usually have one or two consolidation prompts, which is essentially just a quick gauge for us to get a sense of who heard what. All right? That's like a Lucy West quote. She says, "I need to know who heard what." And even collecting that.
Not suggesting that every day you're doing a full assessment/feedbacking everything, but just to get a quick glimpse of where everyone is at. When I see that there's some students that either aren't submitting, which, again, they're not engaging in the lesson, maybe they are walking away, whatever it is. This is part of what I think Jon's getting at as well is like, "Okay. So we want to find ways to keep them there and make them want to participate."
But then if, let's say, they're just not even giving it a chance. They're logging in and they're going on YouTube like Landon. At the end, you're looking at this and you're looking to see who heard what, where is everybody? And then if I'm seeing there's five, six, who knows, however many students, that aren't submitting this, that's where I think investing a little bit of that extra time...
I know nobody wants extra on their plate, but to be able to reach out to the student and the parent and just touch base and, "Hey, what's going on? Are you with me? Was the internet down? What's happening here?" And trying to keep that communication line open to try to hopefully nudge that student to engage because, had we not gotten a phone call today from my son's teacher, I would not have known that he was in the middle of a very, very important YouTube video during the morning lessons.
So those are things that I know it's like, "When are you going to find the time to do that?" Everybody's working really hard right now. But I think that is something too that we don't want to forget, is that keeping everybody in the loop, keeping that student in the loop, oftentimes, especially high school students, I know I was this kid, I would try to cram. I would do little during a unit of study and then I would wait until it mattered.
Trying to keep that culture in your class, that everything we do is assessment and it goes towards evaluation. Like it all matters. And if all I have is just a couple things once every week or so, or two weeks, then it's just not enough, even if they're really good at it. They're really good at last minute studying or whatever it is. We want to encourage students to see that, you know what, there's a payoff for participating here.
So hopefully you're enjoying the lesson because we're trying hard to get you talking and engaging. But then also that I'm going to recognize, and I'm going to use that information, that data, to help inform what you know and what you need to work on moving forward. I'm going to pause there, and we're getting close to the end here. So I'm going to pause and ask you for some final thoughts, maybe any takeaways from this particular conversation, that is circling around in your mind that you might want to give a little bit of thought to in order to try to put into practice.

Danitte Kozai: I really liked all of it. I think that just getting them... Like we've been doing this this entire time. It just online changed all of the rules. But I think that idea of just things like Truths and Lies and those other kinds of prompts so everyone can answer this question or everyone can come up with something, so they feel like everyone's included, are really good and they work at any level.
I think it is really hard because the time is just so difficult. Just our own time too, that I feel like I'm doing 10 times the amount of work I was doing last year and stuff like that. But I think that just through the semester, I've learned to like spend more time on some things than other things. Like in my computer science class, for example, just made it up as I was going along in the beginning. One day I decided, I was like, "You know what? Exercises, like the small programs that you're doing as you're learning how to do something, you can submit as many times as you want, I'll make it summative. It'll count for marks and you can just redo it as many times as you want."
And so, that's how my students learn to become programmers. So I invested the time on marking those little things that they kept resubmitting, as opposed to marking a big project. I feel like just taking that approach where the learning is ongoing like you were talking about with the consolidation prompts and stuff like that, I think it's worth having that conversation over and over and you can get more out of that, than out of one big test after a few weeks.

Kyle Pearce: Right, right, right.

Jon Orr: Before we take off here, I'm wondering if you would compare how you were feeling before you came into this call about online learning and your struggle and your pebble in your shoe and then how you're feeling right now.

Danitte Kozai: I feel good. I feel like I'm inspired to get to work and just really try some of these things. And so, thank you. I appreciate it.

Kyle Pearce: We've had an awesome, awesome chat here, and please know I know there's so many people listening going, "That is exactly what I'm struggling with right now. This is a struggle." Like Jon said, we're going to battle it. All of it's not going to go away necessarily. Think about it. We're all first-year teachers at teaching online. Really, when you think about that, you go, "Holy smokes." You could be a 30-year experienced vet, or you could be fresh out of teacher's college, everybody is battling with the same sort of scenario and didn't even have an opportunity to practice, teach this way.
So you're doing great work. We can tell you're really invested. We always knew that about you, the times that we had an opportunity to meet and chat with you. We just want to let you know that we're rooting for you and we're so happy that you spent some time with us tonight in the Math Moment Maker community. Our last question for you is, is it okay if we maybe check in with you down the road, nine to 12 months from now, and see how things are going in your world?

Danitte Kozai: I would love that.

Jon Orr: Awesome stuff. That would be great. We'll reach out to you to set up a time on that. But definitely want to thank you for spending some time with us here on the Making Math Moments That Matter Podcast. We hope you have a great rest of the school year.

Danitte Kozai: Thank you so much. Likewise.

Kyle Pearce: As always, friends, both Jon and I learned so much from these Math Mentoring Moment episodes. But in order to ensure we hang on to this new learning so it doesn't wash away like footprints in the sand, we have to reflect on what we've learned. An excellent way to ensure this learning sticks is to reflect and create a plan for yourself to take action on something that you've picked up here today.

Jon Orr: A great way to hold yourself accountable is to write it down, or even better, share it with someone, your partner, a colleague, or with a member of the Math Moment Maker community by commenting over on the show notes page, or tagging us @makemathmoments on social media, or get over in our free private Facebook group, Math Moment Makers K to 12.

Kyle Pearce: Yes. And friends, if you haven't headed over to the makemathmoments.com/tasks page, we've got all kinds of problem-based lessons and full units for you to explore. Day one is fully open, including the teacher guide for you to explore. So head on over and check it out. The rest of the unit is still there available for you to use. But again, academy members will be the ones who can access the actual teacher guide. So go over there, dive in, and explore some of those tasks over at makemathmoments.com/tasks.

Jon Orr: Also, if you're interested in joining us for an upcoming Math Mentoring Moment episode, where you too can share a big math class struggle, apply over at makemathmoments.com/mentor. That's makemathmoments.com/mentor.

Kyle Pearce: Show notes, links to resources, and complete transcripts to read right from the web, or you can download and take them with you, head on over to makemathmoments.com/episode117. Again, that's makemathmoments.com/episode117. All right. Math Moment Maker friends, until next time, I'm Kyle Pearce.

Jon Orr: And I'm Jon Orr. High fives for us and high five for you.