Carmen Sinatra: I'm thinking about the fact that I'm not sure if they're going to be saying, "Okay, this child has to sit in this seat only." But again, if I only have 15, I could theoretically set up my classroom, so that perhaps in a corner, there's an area for small group instruction and nobody sits there until they have to, I guess. I'm not really sure, because I'll have to figure out how movement around the class is going to work.
I like the idea of giving them some independent journal time. I haven't heard exactly about this consolidation prompt, although I kind of get it. I may want some clarification on that. Actually, crosstalk.

Jon Orr: Today, we speak with Carmen Sinatra from Richmond Hill, Ontario. Carmen is gearing up for her new school year during the pandemic. And like many teachers, she's asking questions like, how can we safely use vertical non-permanent surfaces in our classrooms? How do we create groups and how do I plan a 2.5 hour math block?

Kyle Pearce: Whoa, this is another Math Mentoring Moment episode, where we talk with a member of the Math Moment Maker community, who's working through some struggles. And together, we brainstorm some possible next steps and strategies to help overcome them.

Jon Orr: Let's hit it.

Kyle Pearce: Welcome to the Making Math Moments That Matter podcast. I'm Kyle Pearce from tapintoteenminds.com.

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

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

Jon Orr: Fuel sense-making...

Kyle Pearce: And ignite your teacher moves.

Jon Orr: Let's get ready for another jam-packed episode. But first, we'd like to give a shout-out and a thank you to all of you Math Moment Makers from around the globe, who've taken the time to share feedback, by leaving us reviews on Apple Podcasts.

Kyle Pearce: Yes, Jon. This week, we want to give a shout-out to mathminded18, who gave us a five star rating and review that said, "Best find of COVID-19."

Jon Orr: "I found this podcast during the pandemic and have not stopped listening since. The conversations are so thoughtful, practical and inspiring. I leave each episode with reignited passion for the amazing work of teaching math and the new ideas to try in my classroom. The guests on the show are my longtime heroes. Thanks, Kyle and Jon for articulating the ideas that have been ruminating in my mind for quite some time and pushing my thinking in new directions as well."

Kyle Pearce: That is awesome. We can't thank mathminded18 enough for taking the time out of their busy day to not only listen, but to help us reach an even wider audience. And we are on that 200 rating mark, and we are hoping to rise over 60 reviews from around the globe.

Jon Orr: If you haven't taken a moment yet to give us an honest rating and review on Apple Podcasts, we'd really appreciate it. It helps us get the word out, because we want to help as many math teachers change and make math moments for their students. Because then we get to help students from all over the world too.

Kyle Pearce: Absolutely. That makes us feel amazing inside. And you know what, while we're talking about helping students, we also love helping teachers. And right now actually, as this episode goes live tonight, we have one of our three repeat webinars going on. We are doing this three times, we did one last week. And now we have one tonight and another later this week. We are looking to help teachers start the school year off right during this COVID-19 experience.
So whether you're going face-to-face or whether you've got a part online, part offline face-to-face experience, asynchronous or synchronous, we're hoping to help you out with this webinar. What are some of the things we're hoping touch on there, Jon?

Jon Orr: Yeah, we know it's a Wild West of what the classroom is going to look like, or online learning is going to look like for districts and provinces and for states. Everybody seems to be doing something different, but what we're looking to do in our webinars is to help you navigate that.
So we're looking to help you inspire curiosity, not just to start the year, but also through the year, synchronously or asynchronously. We're going to look to help you build trust in your students from afar, but also could be in class. Or how do you handle situations where the students are supposed to social distance, but you want group work to happen? What do those essential first day lessons look like for your classroom?
So we are super pumped to have this webinar series or webinar sessions going. You can register right now, which we're going to send you a link. If you're going to get on tonight's episode, you're going to head over to makemathmoments.com/webinar. Register there, you'll get a link, choose the appropriate time slot for you. We are going to see you in that session.
If you are, say, listening to this after these dates and when you get to that page, we are sending out replays. So register anyway.

Kyle Pearce: Yeah, definitely get in there. That's makemathmoments.com/webinar. We are also going to be looking at some steps we can take to help address some of the concepts holding our students back the most. So dive in with us, makemathmoments.com/webinar. If you register and you can't make the live viewing, or if it's past the live viewing, definitely do so, so you can access the replay. The replay will be up for a week afterwards, before we toss it into the academy.
All right, my friends, enough about that. Let's jump into our conversation with Carmen. Good morning, Carmen. Thanks for joining us here. This is actually an early morning recording episode. We are all doing a little bit of yawns over here on the Making Math Moments That Matter podcast.
But you know what? We all sound pretty chipper this morning. So how are you doing? You sound awesome. How are you doing and tell us a little about yourself

Carmen Sinatra: I'm doing pretty good. It is pretty early in the morning for me, that's for sure. Well, same as you guys, because I'm in the same area.
A little bit about myself. Well, I've been teaching for about 23 years and I can't believe I say that, because it's never a dull moment. I always knew I wanted to be a teacher. It sounds kind of funny, but it's almost pretty true. Literally, I was about 15 and I was like, yeah, I'm going to be a math teacher.

Kyle Pearce: And you knew math as well.

Carmen Sinatra: Yeah, I did. I knew math as well. I did. I know it sounds strange. I always was the person in class who had the friends come and gather around my desk, help me.

Kyle Pearce: The teddy bears.

Carmen Sinatra: Yeah. And I just loved it. I loved helping them. I loved the math.
I think the thing that really set everything in stone for me was a friend convinced me in grade 11 to go on a university tour, which was unheard of for grade 11s to go, because at the time, we still did OAC. So we had another year to think about things. And they said, let's go to Waterloo. I'm like, okay, sure.
So I went there, knowing nothing really about Waterloo, and they split us up into different areas of what our interest was. So first, I went to math and this sounds good. There's a math faculty. I like that. And then they further split us up into would you like to look at teaching option or stats or whatever it was, computer science? And I was like, oh, teaching option sounds good. I listened to their little presentation. I was like, yeah, okay, sign me up. And that was it.
I graduated, then-

Jon Orr: You're a teaching option graduate.

Carmen Sinatra: I am.

Jon Orr: I am also.

Carmen Sinatra: I thought you were.

Jon Orr: That exact same program, exact same school. So we have a little history there together. We're coming from the same alma mater, same school. Awesome job.

Carmen Sinatra: Yeah, just loved it. That's what I've been doing ever since. I've haven't worked in a lot of different schools, although as you know, co-op takes you to a lot of different places. But eventually, I ended up at Richmond Hill High School in Richmond Hill. I've been there actually since 2001 and have loved it there. It's fantastic and ended up making it my home and became assistant head and now I'm the department head. I've been the head for a while now. I want to say about eight years.
I have a great team, great admin that's really supportive. The team is just, it's amazing, because we're doing a lot of building thinking classrooms and the three act math idea. Not everybody, of course, but change takes time. It's been fantastic.
And my concern with all of what's going on is keeping that ball rolling under the circumstances.

Jon Orr: This question popped into my mind, it's not one that we ask, but since we're all high school teachers here, Carmen, I'm wondering out of the courses, you're in Ontario, if you're from outside Ontario listening right now, we've got a variety of different high school courses, where grade nine is not just say algebra, like it is in the United States. It's algebra, it's geometry, it's measurement, it's got a wide variety of subjects. We do that all the way up, even up till about grade 12, where we start to branch off to do more specifics.
But Carmen, I'm wondering what is your favorite course to teach from the catalog and why is it? From the catalog.

Carmen Sinatra: Wow, I'm one of those teachers, to be honest, you could throw me in anywhere and I would love it, but if I really had to pick, I love data management, MDM for you, just love it.

Kyle Pearce: I thought that I was going to feel a little left out in this episode, having gone to the same school, having the same program and going through, but data management, I was tossed that one, that tends to be a course that-

Carmen Sinatra: Not everybody likes.

Kyle Pearce: It doesn't tend to be the favorite.

Jon Orr: Yeah, we'll give it to the new guy, give him his feet wet with his university bound course.

Kyle Pearce: Absolutely. Folks that have been on my website, tapintoteenminds.com, will see that I have all my old notes. And that was back when I was teaching what we tend to call, Jon and I tend to call traditionally, very gradual release of responsibility. But I still have all that stuff up there. I really can't wait to get back into that course with a new perspective on it.
So I'm wondering, before we ask you our next question here, what about it, what do you like about it? And sometimes that's hard to define. But what gets you excited about that course? It sounds like you like them all, like you said, but that one has a special place. I know it's got a special place in my heart, for sure.

Carmen Sinatra: Yeah, it's so different. I love doing the projects. There's such a variety of kids who come in there. Because you've got the prerequisite, isn't 11 university, it's 11 mixed. So you've got those students in there, you got like, every kind of student in there. Some who really love math and some who are just like, okay, I need a U credit. And this one looked good.
But I find it's a great opportunity for so much of the out of the box thinking or the problem solving. I love combinatorics. I know not everybody says that. But it's just such a great opportunity.
I actually taught it last semester when things went pear shaped, but for the first month, things were going fantastic. And a lot of stuff I did was not so traditional for the students and some of them were really thrown. But it's so different and you can have students who traditionally get really good marks the traditional way, I guess, and they come into data and they're just like, what is this? It's so different.
And so it's a challenge, right? And I love the projects, it's just such a great course.

Jon Orr: It is a really great course. And it gives you an opportunity to talk about the wonders of mathematics and how it connects together and how it's different from... that we don't always have to think about functional math. But you can tie the functional math in, and you can talk about probably one of the most useful or most used topics from high school mathematics of being probability and all of these wonders that come in, it's just a great course.
Carmen, I'm wondering, having talked about this favorite course, we also wanted to ask you about your favorite or your most memorable math moment. And that doesn't have to be as a teacher. Usually, people stretch back to their beginnings, to think about their history of, what is something when we first say math class, what pops into your brain or your mind? So would you fill us in on your most memorable math moment for us, please?

Carmen Sinatra: It's a tough one, because I know I've listened to your podcast and people talk about a great math teacher they had in the past, and not that I didn't have great math teachers, but it was very traditional. Everything that I learned, the way I learned, it was very traditional.
I'm actually going to maybe talk about a math moment for me that was in my teacher education, if that's okay. But really, it wasn't that long ago. I was attending a workshop with Dr. Peter Liljedahl. I don't know how to pronounce his...

Jon Orr: It's a mouthful, for sure.

Carmen Sinatra: It is, it is. And it was such an eye opener. I had done a lot of the things that he was talking about, but I hadn't been able to put everything together. He was just putting things together in such a way that it made so much sense and I want to say this was maybe about five years ago-ish. I had been building up to trying to do group work and trying to do this thinking and getting that into my class.
And after years and years of what felt like tortures, PD was so refreshing. I came back to my department, and I was like, that's the best PD I've ever had. I was so excited about it.
I remember thinking to myself, I got to get this guy in here. I want him to talk to my department. And not only did that happen, that we managed to get him just by stroke of luck, our math consultant, it was such a positive experience that he managed to get Peter back in the following year, in May. I had seen him in October, and he ended up coming to my school and presenting to about 60 teachers for two full days. It was just amazing. Just loved it.

Kyle Pearce: That's fantastic, what an awesome, awesome math moment. I know, as you're describing that PD, I recall the first time that I bumped into Peter's work first, it was online, and you don't get the full story from just a blog post or reading an article or a white paper. But getting to actually see and hear Peter live is something that really resonated with us as well.
I heard a success in that math moment as well. Usually, we ask you for a recent success. I heard that in your voice that you had a lot of these pieces out there, and they're all scattered there. There's ideas, there's things you know you want to do, and being able to start putting them together is really important.
And a lot of Peter's work, we lean on his work as well as so many others when we talk about the math moments three part framework. It's because it is so actionable and it's so quick to spark some change, right? And just the idea of vertical non-permanent surfaces is-

Carmen Sinatra: What a difference.

Kyle Pearce: Yeah, what a difference, especially if you're coming from, sometimes people get a little scared off when Jon and I talk about problem based lessons and flipping the order in which we do things. We tend to give students an investigation or an inquiry experience through curiosity. And then we work our way and then we tie those ideas later. We tie them together in the consolidation.
And that can be very scary, but just to get students up and problem solving is such a great thing to start doing. So for those listening, if you haven't heard Peter Liljedahl's episode, he was on with us back in episode 21. So definitely check out that podcast. We had him as part of our virtual summit. He intends to join us again this November, for the next virtual summit as well. So those in the academy can dive into his replay session we have in the academy. So lots of love for Peter here.
And now I'm wondering, why don't we start shifting here? Because this is a Math Mentoring Moment episode. And let's shift to maybe some of the challenges or struggles that we might be currently experiencing or we're thinking about, we're recording this in the summer as we're approaching another school year. What's on your mind lately that we might be able to dive into together as a team, both you and Jon being co-learners at Waterloo? And you and I being co-MDM for you teachers with data management?
I think we've got a pretty good team vibe going here. So what's on your mind lately?

Carmen Sinatra: Well, returning to school with a blended learning environment. We've gotten our details and it's pretty daunting, I will have to say. I'm in York Region board and the structure, hopefully it doesn't change, but it's now August 19th. I certainly hope not.
We're going to do a live class in the morning for two and a half hours. So it's two periods, like a normal two period. Well, that's not normal, right? And then in the afternoon, the rest of the classes are online. And they're synchronous online, and they're 40 minutes. And the live classes will only have 15 kids.
And then the following day, it's the other 15 kids from your class, and then it rotates through, so that all of your classes have a chance to be live. Basically, what it amounts to is, I will physically see my students nine times out of the semester for two and a half hours each time. And the rest of it's going to be online.

Jon Orr: Because you're also in, correct me if I'm wrong here, Carmen, a quadmester situation.

Carmen Sinatra: I'm not actually.

Jon Orr: You're not.

Carmen Sinatra: Exactly. So we have to do all of the classes at once.

Jon Orr: You're in a regular semester system or you're all year?

Carmen Sinatra: Yes, a regular semester system.

Kyle Pearce: You're going to do like an A/B schedule? Are you going to be like two classes one day for two and a half hours, two classes the next day?

Carmen Sinatra: So that's what a lot of boards are doing. But what we do is, so in the morning will be let's say your period one class for two and a half hours. In the afternoon, the other classes, so from a student's point of view, I guess, the other classes are online. And then the next day, it's the other half of the period one class that will be in the morning, and still the other classes in the afternoon are online.
And this goes on for I think, a period of two weeks. Then it flips to period two in the morning, live. And then the other classes are all in the afternoon.

Jon Orr: Wow.

Carmen Sinatra: It's confusing for me. It'll be confusing for students.

Jon Orr: So period one for two weeks?

Carmen Sinatra: I believe so, yes.

Jon Orr: Kyle knows and maybe other listeners of the show know I'm not an auditory learner.

Carmen Sinatra: I know, you need the visual.

Jon Orr: I'm trying to process this while listening in and I need like this diagram. So for example, you're going to see the same group in the morning, period one-

Carmen Sinatra: Every other day though.

Jon Orr: Every other day. And then I'm wondering, from a kid's perspective, they're going to go to their period one class, which might be math, and then and when do they do science?

Carmen Sinatra: So then they would go home after that class, and then they would have their science class online.

Jon Orr: But then when do they see the science teacher, like you, you're a math teacher.

Carmen Sinatra: Later in the rotation. So perhaps two weeks from then, they would see their science teacher or it's going to be longer, because it has to rotate through the five periods of the day.

Jon Orr: I see.

Kyle Pearce: And then also I guess a clarifying question for myself, because Jon and I listen to so many audio books, but I'm just realizing now that there's probably so many things that we listen to, that goes right over our heads, because it's just so hard to think about complex things when you're listening.
So half of your period one class is Monday, for two and a half hours, and then they go home, they do their other classes in the afternoon. Then tomorrow, Tuesday, the other half of your period one class shows up for two and a half hours.
What it sounds like and I guess there's no hard, fast rule here. You can structure how you want to deliver the content, but in my mind, I guess the first thought was, okay, I'm going to deliver probably the same we'll call it lesson or lessons, because two and a half hours might be multiple lessons, broken up some creative way in your face-to-face environment.
And then tomorrow, I'm going to repeat that face-to-face lesson for the second group, or you have to do some creative way to help everyone, because that is interesting, that's a good one. I like this.

Jon Orr: Carmen, what's so challenging about this?

Carmen Sinatra: Oh, my gosh. One of the things is, just like Kyle was saying, I don't know how we're going to do that part. If I just repeat, then I'll get half the course done. And under the circumstances, I am not going to pressure myself to get the whole course done. How I'm going to cram it in, if I have to do every other day, I'm not sure.
I had one of my colleagues talk to me the other day and he said, I'm going to see if I can try to set up, like turn on a Google Meet while I'm in the middle of my class and have it on for the other kids to see. But I just don't know how that's going to work. Because if I'm walking around the class, and then there's social distancing, as far as I've read everything that we can't have the students be closer than two meters to each other. They have to be two meters apart. So how do I do that?

Jon Orr: Why I think we're asking you to outline your timeline or schedule, and what that looks like is because it still seems very different than say what Kyle's school board is going to be doing with their high school students, what I'm doing, like we're in a different area. So it's a different plan. But we're back every day, I'm going to see the same group of students for 2.5 hours. So that part's the same for us.
But then I'll see them the next day and the next day and the next day. I'll see them every day, but I only see them for say nine weeks straight, and then they're done. And then they don't have math anymore. The quadmester is over, so like we're supposed to be able to get a course in there, because we're going to see them every day, but that timing, that 2.5 hours can be I think just initially, even if we just take away the whole social distancing, if we take away the, what do the bathroom breaks look like? And we take away all the other things. And we just think about the 2.5 hours, that itself can be scary for many of us, just thinking like, oh, I'm used to planning 60 minute lessons or 75 minute lessons. And now there's 2.5. How do I tackle that?

Carmen Sinatra: Exactly.

Kyle Pearce: Let us not forget that we're teaching and we're talking about high school, so grade nine through 12. I remember it being very difficult when I did... I'm sure you folks at Waterloo had similar night classes where you'd have this three hour night class. You're essentially doing one of these three hour night classes.
I remember, in my mind, I thought it was the best idea to do a night class, because then I would only have to go once that week instead of twice.

Jon Orr: Get it all in one shot.

Kyle Pearce: You go all in one shot and I tell you, by the middle of those classes, I was spent. That was in the classes that I was trying hard in, right? I'm going to be honest and say that I in university did not enjoy the learning process. I really struggled with it. Obviously, the model or the mode wasn't ideal, just a lecture style.

Jon Orr: I'm imagining, Kyle, sorry to cut you off there. But I was just imagining that, I had those same night classes, but they were exactly lecture style, right? It's like how can you sit for three hours, and just take notes on someone just talking?
I think parents right now are thinking that's what school is going to look like. Or some teachers.

Kyle Pearce: I guarantee that's what it will look like in many class, right?

Jon Orr: This is what we're worried about. If I'm a teacher who has done one lesson for the 35 minutes or 40 minutes, and then work time, and then it was homework time, and then I would do that the next day. Do I just do that twice? If I do that twice, when do they do their homework? Do I give them double the amount of homework then after?
And so I think a lot of teachers are thinking like, that's what I'm going to do. And if you do that right now, I'm going to tell you, you're going to have that experience Kyle's suggesting about, hey, we're done after the one, because all we did was sit here and take notes.

Kyle Pearce: And I have to assume, honestly, Jon, our Math Moment Maker audience are probably not the people who are planning to do that style. But I'm sure that everyone listening knows many teachers who they almost guarantee will be doing it that way. Because that's how they did the shorter classes.
And I guess it makes you really have to, in your mind, and it sounds like Carmen, you've already mentioned this where you said, you're coming to terms with this idea that you're probably not going to get through all of the content. I think we always talk about depth first breadth. We always talk about this idea of like, did we cover it? Can we check it off the list, versus did we actually engage with that content deeply?
I think that, for me anyway, and it sounds like for you as well is going to have to be central to your planning. We could talk a little more about what that flow might look like, in just a little bit. But for those listening and wondering and thinking, I'm just going to have to. I hear language from teachers feeling like they are forced into this corner, where they're going to have to do that three hour lecture, like I experienced in university, because of the situation.
And I personally don't think that's actually the case. I think doing that might make you or might allow you to say you got through it, but I don't think it's going to help students with any more understanding. People are so worried about, well, if we don't cover it all, then we're going to have issues later. Well, we can cover it all. We can still have those same issues of students, zone out with midway through. I think we're on the same page there.
But you had mentioned too like the social distancing thing seems to be on your mind, obviously, I'm hearing a little bit about, maybe what that flow of that lesson might look like. I'm wondering, in your mind now, and this, I'm sure may change a billion times. We're talking about those sleepless nights, I had one last night where your brain just doesn't stop working. I'm sure you're going to have many of those leading up to September when we get going.
But in your mind now, can you walk us through, what would be your plan so far? And it can be general, like you can get as specific as you'd like, but no pressure here, but in your mind, what are you visualizing happening? And then even feel free to share maybe some of the parts where in your vision, you're like, I'm visualizing this, but I'm seeing a problem with that because of X, Y or Z.

Carmen Sinatra: Well, I have zero intention of trying to lecture the whole time. I think that would kill me. It's boring and I don't think that, like you guys said, it's not going to help them, they're not going to retain and it's not going to be engaging.
So what I would like and what I'm trying to wrap my brain around is somehow to keep the similar structures to what I was doing before, which is a lot of the idea of doing some kind of sparking curiosity, something at the beginning. It doesn't seem like I would be able to still show a video, short little video and then say, what do you notice? What do you wonder? That doesn't seem to be an issue. I think that could be fine.
But then once we get into the part where I say, okay, in your groups, get up to the whiteboards and start to try to work this through. I'm walking around and I'm slowly giving them some more information. The only thing I can think of is, is it still possible to do this? Can every kid have their own little whiteboard?
Or if there's going to be 15 of them, we are going to have more space. Can I still do a group of three, where they're standing a little farther apart, but they've got to then be able to articulate themselves well to talk to each other? Everybody has their own marker, can we do that? I really hope we're not going to be told that we can't, but I don't know if that's going to happen.

Kyle Pearce: I couldn't help but hear your voice when you said, okay, everybody up and work together at the whiteboard, just not that close together. Everything's going to be like a but or a not that close or not that much.

Carmen Sinatra: I've seen it in classes, they stand close to each other. And are we still going to be able to do that? Perhaps. I don't know.
And then after that, I'm envisioning that we would have some work time to consolidate some ideas, and then perhaps go into another activity. Because if you got two and a half hours, I'd like to break it up. So that's where I'm going with it.

Jon Orr: I think it's a reasonable plan to still plan that you're going to do two lessons or two ideas or two... Otherwise, you mentioned before that you probably couldn't come close to covering what you needed to cover or uncovering, like we say from our friend, Al Overwijk, uncovering the curriculum in that certain way.
So my plan also Carmen is to do two of our lessons, or have a lesson flow into the next. I think that is going to be... I'm excited for that part, that I'm going to have two and a half hours, and I know that there's a scheduled break in there, that they're going to leave the room. I don't know if they're going outside. I don't even know what that looks like yet for us. But I know there's a scheduled break in there.

Kyle Pearce: A scheduled a break to keep sitting in that one spot?

Jon Orr: It might be. Yeah, I'm excited to have that two and a half hours to see what we can do in that time, because I know it's often times that we're like, I wish I just had some more time as a teacher to keep going with where we're going, instead of cutting us off and saying, okay, now we're going to go home. We'll pick this up again tomorrow.
Especially if we're starting the class off with an investigation or an inquiry question or a three act math problem. We've often said that people don't think that's enough time to get into that kind of stuff. And I think it can be especially, if you're now going to be doing that, but also it allows, if we plan that right, the way that Kyle and I have done, for many of our lessons and shared on our tasks page for academy members, is that we can uncover many different curriculum standards in one of these lessons. Then we can branch off and go in different places.
So I'm really excited for the 2.5 hours.

Carmen Sinatra: I actually am too.

Jon Orr: Yeah, I'm with you though, on what it's going to look like for just social distancing. Like for us on our end, your area has forced the smaller class sizes and in my area, we have not. So in my area, I'm going to have a normal class size in my classroom already.
So when you're thinking about how do I keep my 15 kids apart, I'm going to have 30. Or 25, or possibly less, because they have the option to stay at home. But they have to make that choice before they come to school, like they have to make that choice now.
I'm wondering, well, if we're already 30 in the room, we're all sitting next to each other, like with our masks on, what's the difference between us going to the whiteboard to do that work? As long as we're all holding our own pens, we're not sharing resources. I'm not sure, because I haven't been told one way or the other, whether that's allowed or not.
But I think I'm going to go with as long as we're all safe, and we have our masks on, and we're using the board, but not sharing things back and forth, then I think that can be a reasonable expectation that we're still sharing that whiteboard.

Carmen Sinatra: I think so. To me, I feel like that sounds reasonable. And the other thing that's actually good is the fact that I don't have classes in the afternoon. I know that there's some schools, I'm not sure how yours is, Jon, exactly, but who do morning and afternoon.
So if you had kids working on whiteboards or markers, I would assume that they'd need to be all cleaned and sanitized before the next group comes in.

Jon Orr: That group of markers has to go in a box and then, or my plan with that has been the same for the last couple years anyways, everyone has their own marker, it goes in a baggie. The plan a couple years ago was that kids would treat them better, if it was theirs, instead of a communal marker. So that'll be the plan for us moving forward. But they can't share them. So we have to double the amount of markers.

Kyle Pearce: I'm listening in too, and just myself being in a different position currently, recently removed from the classroom to do this more of a consulting role, and trying to, I guess search, we always talk about those silver linings. That 15 or whatever the half number is, if you have a 34 person class and you have 17 on a day, I'm thinking about some of the benefits that I'm hearing is that opportunity.
And if let's say you're using that two and a half hours to have these inquiry experiences that flow from one and to the other, and building on it, and allowing you to maybe think about that two and a half hours as more of one block of learning. I know we're not going to ramble off for two and a half hours. But how I can make that first lesson connect to the second, maybe in between having this consolidation, obviously, like the teacher led consolidation, using student work that we talked about a lot here on the show.
But then also giving students an opportunity to have a little bit of alone independent journal time. I'm picturing in the class, like every student, probably, I don't know about you, I know Jon in particular, when we're in a large group, let's say for example, when we went to Richmond Hill to present for your school district a couple years ago in the summertime, if he's around people and having to engage in conversation all day, by the end of the day, he's exhausted. I'm feeling exhausted. But he's like, you can see it in his eyes.

Carmen Sinatra: Don't talk to me anymore.

Kyle Pearce: Two and half hours for us, I think something for us to consider in this two and a half hour block is also how can we do what we wanted to do before? But then also respecting the fact that, hey, everyone's going to need a little bit of downtime as well. And that might mean, all right, let's take 20 minutes and putting up a consolidation prompt. And if that's something new, that's new for me, it's only in the past couple years that I was introduced to this idea of the consolidation prompt, where we're asking a very specific, very intentional question to students to journal about.
And it can be a math question. But really the important part is to really try to figure out who heard what, and to give students that opportunity to work independently as well. I think when people listen to us, whether it's live in a presentation, in our online workshop, or here on the podcast, I think people assume that everything, like every moment of our math lesson is going to be kids up engaging and collaborating together the entire time.
And some days, in a regular class, that did happen. But also trying to be intentional about giving students that independent time is going to be really important here. I'm also picturing too, a silver lining of your 15 is, thinking about how much more reasonable it might seem to do a little bit more of that small group instruction.
Now, again, social distancing measures would have to obviously be in place, as you mentioned. I know Jon had already said that, if you've got your masks on and everyone's using their own resources, being able to try to maybe have a section of the class where you can work on specific challenges students might be having. These are positives I'm seeing. Again, trying to pull it all together might still be a little bit high level right now or a little abstract.
But take us a little deeper here, how are you thinking now based on what we've discussed so far? Is there anything I guess more specific that we can dive into? How are you feeling with your plan and how you might move forward with it? So we can try to figure out how we can wrap things up here before the conversation ends today.

Carmen Sinatra: I'm liking what I'm hearing. A lot of the ideas that I have been running around in my mind, but just talking it through is helping me sort it out. I like the idea of perhaps an area for small group instruction. Although again, I'm thinking about the fact that I'm not sure if they're going to be saying, okay, this child has to sit in this seat only.
But again, if I only have 15, I could theoretically set up my classroom, so that perhaps in a corner, there's an area for small group instruction and nobody sits there until they have to, I guess. I'm not really sure. Because I'll have to figure out how movement around the class is going to work.
I like the idea of giving them some independent journal time. I haven't heard exactly about this consolidation prompt, although I get it. I may want some clarification on that. And actually, I'm doing nine applied and advanced functions.
So the advanced functions likely is going to be pretty, well, it's currently my list says it's 30 kids, so that'll be 15 and 15. But my nine applied, the max it can be is 22. I'm like, cut that in half, that'll be 11. So there's things I can do with 11 kids, for sure. So some variety.
I think another idea that popped into my mind too is, I would like to take a little bit of time in maybe the first class. I don't know, your suggestion, maybe the second one, where I teach them, especially the first group, teach them how to do some of the online stuff. I don't know if that's going to work.
I'm just thinking about how sometimes with your online structure, it helps if you say, hey, this is what we're going to be... when we get online, it's going to look like this.

Jon Orr: I think that's part of every plan, that we have to set that up initially, in case, you're going to be online anyway. But even for us, who are not online, where you're in class every day, we have to set that up also, just in case we have to move online. We're ready for it and we're used to it.
I think throwing in things in class to do online is, a short thing to do online is not a bad idea. Maybe that's where the consolidation prompt comes in to your plan. And the consolidation prompt, just to clarify there for you is, Kyle and I used to spend so much of our lesson sparking curiosity. And then we've moved into feeling sense making, what are we doing to help make connections in concepts with kids? And what are the moves that we have to make there, the igniting our moves?
But there was a lot of times that we would get to the end of a lesson and we were like, we just did this react math problem and kids did this great work. But there was this, where did this note show up? Or how do we formally tie this together with the big picture of things?
I used to leave that off, I was really good at it when I was a traditional teacher, because you do it up front. You say, this is what we're going to do. This is where it fits, and then you go into it. But when we did some switching, we almost forgot about that. I think that's super important still, to tie it with a big bow at the end.
And that can happen in the middle of a lesson. It can happen at the end of the lesson. It can happen at the beginning of the next lesson, but I think that tying up has to come. Now, either it has to be carefully choreographed from the teacher. So it could be when you're using your five practices for orchestrating productive mathematical discussions. Let's say you're in your sequencing and the connecting stage where you're getting kids to share their strategies strategically, and then you're trying to tie that together with where that fits.
But sometimes that can't happen, just based on what you're seeing in the room and you need to formally say, this is what our learning goal here was today, everyone. These are the expectations moving forward. Sometimes I throw this word out here that's stuck around in education, these look fors, like a success criteria. Like this is what we're looking for in the future.
And I think that's great places to happen at the end of the lesson, to take the form of a note. Kyle's suggested it takes the form of a journal, like how to you see, or what did you learn here today? And how does that connect with what we learned yesterday? What are you still looking for to learn or there's lots of little prompts along the way. So it's just a general naming of, we do need to tie this up.
So that could be done on the online portion. But it also needs to happen in that two and a half hour block too, that we're going to be doing.

Carmen Sinatra: I'm actually just thinking, like normally, what I have done in the past is, when kids have their solutions up on the boards, I'll go around and pick ones, and I'll say don't erase that part. Keep that on. And then at the end, I will have them gather all in a big group around me. And then we walk around and say, look at this one, this is a good one.
And kids will be taking pictures of it. I'm thinking, well, I can't have them necessarily all gathering in a nice tight group. But there still can be me taking pictures, perhaps uploading it onto their Google Classroom. There can be ways of getting around that social distancing aspect.

Kyle Pearce: And Carmen, if you're interested in trying to get some specific example or examples of consolidation prompts, you can actually see some on our academy task pages. And some people who have listened to some of our past podcasts and our webinars would know that all the tasks in the academy, you can actually access the tasks and utilize them, even if you're not an academy member. The one part that you don't see is, you don't see the teacher guide.
So you can sign up for, we have a 30 day free membership. So people can dive in there and have a look around, and take what they can in the 30 days or stick around. But one task that just went up and just to give you an idea, and I'm going to try to paint a picture for those who are thinking about what this year might look like for them. And especially if they have long blocks, like both you and Jon have, long blocks to work with different groups or different sized groups of students.
But thinking about how lessons can build on one another and our units that we've been creating inside the academy are typically multi-day, sometimes four days, sometimes six days. And even looking at it, not necessarily because you need to use all of our units, but to look at them as a framework or a structure. We utilize the three part framework as we build these out, but then each day builds on the previous.
So if you're in this two and a half hour block, or maybe you're in a three hour block, or who knows what other listeners might be up against, you might have this opportunity to build out. Our most recent unit is the scavenger hunt task or unit. And it's a four day unit. And it's actually a data management unit, actually, it's all about the mean.
And early in the unit, it's all about this party. Kids, they all collected candy in a scavenger hunt and then they realize that the six friends all have different candy amounts. And as the days go on, they're first estimating like, oh, Jon has, it appears he has like two thirds as much as Kyle and really gets them estimating using fractions. So this multiplicative comparison.
And then by day three, the process basically shifts and it says, okay, well, one of the friends says, like, it's not fair that Jon has two thirds of what Kyle has. How could we redistribute this to make it fair? And essentially, through investigation, this task brings out the idea of average or mean. And we put them through the process where we try to get them to try to figure out what to do.
And ultimately at the end, they realize, oh, well, if we just put it all back in the middle and then fair share it, we'll be good, everyone will have the same amount, it'll be fair again. So this idea of the average or the mean pops out, and the consolidation prompt at the end of day three, there's two of them, but the first one sounds like this.
So just to give you like an idea of what that sounds like, it says, the process of redistributing the candy equally amongst all six friends is the same as determining the mean for a dataset. Using the values below, explain how this statement is true. Use visual models and context to support your justification. The values are 12, 17, 22, 16 and 18.
So even I'm picturing while this is more of like a unit generally created for a younger grade level, where students first encounter the mean, that prompt could still be valid in a grade 12 data management class, where we do work with means of the central tendencies.

Carmen Sinatra: Statistical analysis.

Kyle Pearce: So you could then extend it and say, well, which measure of central tendency would you rather have with these values?
So, the consolidation prompt is this opportunity for a student to take this, what they might have done collaboratively and then be able to go and think independently on it. And then you could be walking around the room at a distance and looking over the shoulders to try to figure out, and a colleague of mine, Yvette Lehman, she always says to figure out who heard what. That is a really important thing for us to be doing.
But then again, like I said, giving the students that opportunity to consolidate what they're doing and then write, even if it's in that same two and a half hour block, I could then continue into day four, which starts with a number talk. It builds on the concepts of the previous day.
So by looking at this, we'll call it like a holistic view of how we run our course, that might be a way where it doesn't feel like day one lesson, day two lesson, where they're like disjointed. But rather that it's like one big lesson that just keeps going, and it just feels like a bit of a process that students are coming along this journey with you.
I'm going to argue that even in two and a half hour blocks, you might have this four day unit, might take you two face-to-face sessions to get through. But in a student's mind, they're not going to feel like it was four lessons, they're going to feel like it was one big, giant lesson that was all connected.

Carmen Sinatra: Which is what you want. You want them to feel like things are all connected.

Kyle Pearce: Exactly, exactly. So we'll put that link in the show notes. We'll share it with you as well here today, because this won't go live today, obviously, but for those who are listening, we will share the link to the scavenger hunt task. But you'll also see the other tasks and the other units that are there.
We're actually really, really gearing up to continue building out those units inside the academy, and actually trying to build out our writing team. So those people who are listening, and especially folks who are fans of the format of the context for learning by Cathy Fasano, we really leverage a similar philosophy to how we build these units out.
So anyone who's listening, definitely get in touch with us, because we really want to create more and more of these units so that we can keep everything connected. So hopefully, those ideas might be helpful as you're heading into this uncertain year, with these super long face-to-face sessions.

Jon Orr: I'm wondering two things. One, I'll ask you first and the other one, I'll ask you after you answer this one. As we wrap up here, Carmen, what would you say is your one big takeaway from this conversation?

Carmen Sinatra: I think the idea of, let's be positive about this, see the silver lining. How can we make this even better? Having all those connections done at once, I don't want to say at once, but having an opportunity to do a longer block, I think it can really work. I'm really looking forward to that part.
I'm feeling more confident that I can still manage to do some group work within the confines of social distancing. I'm feeling more confident about that. And still also being able to have them, even by using some, taking pictures, putting them up on Google Classroom, to still get their engagement in there. I think that's going to be really important to keep up, because that's one thing that was really difficult with the online portion the last time.
So that's what I'm thinking about. I'm thinking, oh, my gosh, look at the time. And there's so many other things I wanted to ask.

Jon Orr: That's actually a great lead into my next question that I said I was going to ask you. We'd love to have you back and keep chatting about this, especially after we've started the school year. I know people are all listening and we're like, this is what could happen. But it would be great to come back and go, this is what we're in. This is what we're dealing with right now. This is the thing I was worried about before, but I didn't have to worry about that. It's really this one over here.
So we'd love to have you back relatively soon. So we'll connect, if you would like that, just to see how things are going, the start of the school year, and share that back with the community.

Carmen Sinatra: Yeah, absolutely. That sounds fantastic.

Kyle Pearce: Yeah, that's fantastic. Usually we say, hey, we'll check in nine to 12 months, but I feel like with this particular episode, already in my mind, my wheels are turning, like I said, I had one of those sleepless nights where the wheels kept turning, they're turning now. We're definitely going to try to squeeze this episode in much sooner, because it is what we feel very relevant, very relevant for so many people.
And who knows? I think it was slotted to go in somewhere in the new year is where we're recording out to right now. So we're going to slide that in. I think, like Jon said, bringing you back sooner would be great, even if it's a couple weeks into the school year. Because I'm sure you'll still feel like your wheels are spinning in the mud a little bit, and a lot of other people are going to feel the same way.
I think to be able to get those other questions out, those new challenges that you're going to experience along the way. And also, I think to selfishly help us as well, because for Jon and myself, we're learning from these conversations as well. So if that's okay with you, we'll try to get another date in the calendar and we'll do a check in and, hey, either there's going to be more struggles or deeper struggles to work on, or you'll have it all figured out and we'll just share all those successes.
But I have a funny feeling it might be more of the first than the second-

Carmen Sinatra: Probably.

Kyle Pearce: This is going to be a long journey for all of us. We just want to thank you so much for spending the time, it's an early morning for us. But we're so happy to have had the opportunity to chat here with you, and to share some of your wonders right now with the Math Moment Maker community.

Carmen Sinatra: Great. Well, thanks so much for having me. I really appreciate talking to me before the school starts. It has been very helpful. I do have still lots of questions, but I think feeling a little more confident about how I can put this all together and hopefully keep my team rolling too, with what we've been doing. And not feeling like we have to just throw our hands up and go, okay, I guess I should just like teach up at the front again.

Jon Orr: It's just too easy to fall back into that.

Carmen Sinatra: It is, it is.

Jon Orr: When I think about them, I guess it would be easy, but I think everyone would be miserable, even the teacher.

Kyle Pearce: I was just going to say on paper, it's easy, but to actually do it-

Carmen Sinatra: You can't go back.

Kyle Pearce: Would be just very hard.

Carmen Sinatra: And thanks so much for all the work that you guys are doing and bringing all of this to the community. I think it's fantastic. I didn't ask you anything about the first day, because I didn't feel like I needed to, because I listened to, I think it was episode 90. I don't know, there was a couple of other ones and they're just fantastic to listen to.

Jon Orr: Well, thanks so much for saying that. We appreciate you saying that. We appreciate you in the community.

Carmen Sinatra: Lots of appreciation. That's good.

Kyle Pearce: Awesome. Well, you have a fantastic day there, Carmen. And as we mentioned, we will be in touch to get you set up with another time slot, so we can chat again real soon.

Carmen Sinatra: Okay. Thank you.

Kyle Pearce: Have a great day. We'll talk to you soon.

Carmen Sinatra: You too.

Kyle Pearce: As always, 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 must reflect on what we've learned. An excellent way to ensure this learning sticks is to reflect and create yourself a plan to take action on something that you've learned here today.

Jon Orr: Yeah, great way to hold yourself accountable is to write it down or share it with someone, your partner, a colleague, a friend, maybe it's somebody that you go walking with after dinner every evening. But please share with someone and you can also share with us by tagging us at Make Math Moments on all social media platforms. And you can get into our free private Facebook group, Math Moment Makers K through 12.

Kyle Pearce: Awesome. And before we go, again, if you are listening the day this episode went live, we've got a webinar tonight, as well as later this week. So definitely get yourself signed up on how to start the school year off right during the COVID-19 pandemic. So go ahead, get on over there. Makemathmoments.com/webinar, it's free and a replay is going to be coming out for you to view afterwards. So get on over there and get yourself signed up.

Jon Orr: All right, are you interested in joining us for an upcoming Math Mentoring Moment episode, just like this one that we shared with you here today? You can apply over at makemathmoments.com/mentor. That's makemathmoments.com/mentor, and maybe we'll be chatting with you soon.

Kyle Pearce: Awesome, and make sure you smash that subscribe button on your favorite podcast platforms. Show notes and links to resources, including full transcripts available on the web, even with a Audible reader. And finally, downloadable transcripts available at makemathmoments.com/episode92. That's makemathmoments.com/episode92. Well, until next time, I'm Kyle Pearce...

Jon Orr: I'm Jon Orr.

Kyle Pearce: High fives for us. And...

Jon Orr: A big high five to you.