Pam Harris  00:01

Hey fellow mathematicians. Welcome to the podcast where math is Figure-Out-Able. I'm Pam. 

Kim Montague  00:08

And I'm Kim. 

Pam Harris  00:09

And we answer the question, if not algorithms, then what in the world are you doing in mathematics?

Kim Montague  00:17

Okay, Pam, let's set the stage. We are in the middle of a three part series and our top three ways to start the school year. Last week, we talked about helping students feel seen, acknowledged, and valued by learning and using their names. Next week, we're going to talk about the importance of having your beliefs about teaching and learning solidified, so that everything that you do fits.

Pam Harris  00:39

So today as part two in our three part series, we're going to talk about building a community of learners. So important.

Kim Montague  00:48

Yeah, I don't know that building community is a brand new idea for a lot of teachers. But I do think that what we're going to hear this year in particular is that teachers are going to have to work extra hard and really maybe don't even know how to build community in this remote setting that we have. To be clear, we don't necessarily mean a bunch of cute getting to know you activities. It's much more about creating a space where individuals feel like they can be heard and their voice is meaningful and valuable in the conversation.

Pam Harris  01:18

Yeah, so let's think about the Math Practice Standards for just a second. We want learners to be doing, building, conjecturing, critiquing the reasoning of others, formulating arguments. All of those mathy things can happen more effectively, in a community of trust. So we want to build community early so that when we're expecting students to be justifying, critiquing that they can do it from a place of support, a place where they know that their thinking is valued. They need to be in a space where they're treating each other with respect so that we could challenge each other. In other words, we need to get to know each other so that we can work together well.

Kim Montague  01:57

Yeah, I think that this week, we should focus a little bit on building community remotely, because that's going to be a reality for a lot of people. I'll share a little bit personally. I have two boys, elementary and middle school, and they ended the year for the last couple months remotely, right?

Pam Harris  02:15

 Pandemic hit. Here we go.

Kim Montague  02:16

Yeah. And so my husband is also in school. And he had a different experience. So he's doing school remotely right now. And we've been doing a lot of conversation, a lot of discussion. And we've realized that his situation was supposed to be in person. It went to online only. And what that looks like for him is sitting in front of his computer, watching a lot of videos, taking a lot of notes, doing a lot of tests online. He doesn't know anybody in his classes. He doesn't have much communication with his professors. And so we've just had a lot of conversation about if there was a place for him to pause and participate, he'd feel more like a member of the community rather than just sitting there solo taking some notes.

Pam Harris  03:03

And he'd rather do that, right? 

Kim Montague  03:05

Right.

Pam Harris  03:05

He'd rather have some sense of community with the people that he's learning from. 

Kim Montague  03:09

Sure.

Pam Harris  03:10

He definitely anticipated that when signing up for in person, school. And then, of course, what we don't want to do is put any kind of blame or shame on teachers. This is a crazy unprecedented pandemic. We do wonder if we could think about some things that maybe we could help set the stage for this next year, where again, there's still lots of unknowns as the pandemic continues, but maybe we can share some insight that we've had. We've actually been moving towards the online space for a couple of years. So it was interesting timing for us as the pandemic hit that we were actually able to pivot fairly seamlessly into the online space to do a lot of our work remotely. I'd like to tell you a little bit about our online workshops. So you might know that we have some online workshops for math teaching available on the web, and I really pushed back on the idea of creating online workshops initially. I really had to think hard about how to do asynchronous online workshops. Because I feel so strongly that the best learning happens in relationship, that learning really is better in a relationship between teacher, student, student and teacher and students and students. So, after thinking really hard about it, doing a lot of research and a lot of thinking and a lot of talking with colleagues. We put some things in place that might be helpful and give you some ideas. So I'll tell you a little bit about some things that we put in place in our online workshops. First, we decided that instead of me being a talking head, just talking to the computer and telling you about things, instead, we would do a live workshop with teachers and film that and then take that film and cut it up and put it in to the online forum. So that might not be a possibility for you. But that was one of the things that we thought about that because now participants can, because we cut it up in such a way that we'll launch the problem. And then the video stops. And we give participants an opportunity for them to solve the problem. Maybe talk to other people about how they solved the problem before they then click to the next video, to see how in the live presentation, the live workshop, how other people responded. And then they can watch me in that live presentation, if it was live, they can watch me model people's thinking, make it visible, and they can kind of compare what they did to what they can see. So that was one thing that we put in place. Another thing that we did and we do in our online workshops is we'll ask, it's not just a bunch of video that you watch, but we will ask questions after the video. So you watch parts of the video, and then we'll ask a question. But we'll ask the question in what they call an accordion so that you can see the question but you have to click on that before a kind of suggested response falls out. Now that might not sound like a big idea, but it's just a little bit of an attempt to say whoa, like think about this question, give it your - before you just see a possible response that comes after that. Just a little bit of a way of helping it be a bit more interactive,

Kim Montague  06:15

Right. And we're not claiming to be experts in all things remote teaching. So let's just share a couple of tips about remote instructions with things that we are especially good at: Problem Strings and Rich Tasks. So Pam, give us some tips about doing Problem Strings remotely,

Pam Harris  06:31

Right. Because we're not experts on all things but we have done the Problem Strings and Risk Tasks remotely. And so alright, a few tips on Problem Strings. And if you're new to Problem Strings, you can head over to mathisFigureOutAble.com and check out our blogs about Problem Strings. Problem Strings are an instructional routine. It happens to be my favorite instructional routine. We love them and they work really well to help students develop mathematically. So what can a Problem String look like remotely? So if you can get 15 minutes, I think a Problem String is a great choice. Whether you're live on zoom with students, or if you're recording it ahead of time, I think it could be a decent alternative to do. So here's some possibilities. Let's say that you do have students live on the computer like in a zoom atmosphere. So you can do a Problem String where you launch the problem and ask students to solve it, I would suggest that you have students with blank paper and markers. Now the markers because then when they write, it's a little bit darker and so that as they write their thinking, and then hold it up to the camera, now you can see it a little bit easier because it's a blank paper with that marker. So that's a suggestion. I also suggest that you wait a little longer than you might think. We did a lot of online professional learning this summer. And one of the things that we all struggled with a little bit was waiting long enough. You'd see one or two people look up and we're kind of in this weird online atmosphere and so we're almost like panicking a little bit. Like, Oh, we don't want to make anybody bored. As soon as we saw a couple people look up then we're like, "Oh, hey, people are done. I'll call on you." But in reality, a couple of people looked up, right? So we suggest that you actually still use a thumbs up private signal, so that when students look up, they give you a thumbs up signal, then that helped me go, "Oh, okay, just because a couple of thumbs are up, I need to make sure that I've got most thumbs up." So we still use that thumbs up private response signal. You might have to have students hold it a little bit higher. Sometimes the thumb gets a little hidden below the camera. So again, you're looking kind of for this signal to say, "I've had a chance to answer the question. I'm ready to respond." And then you can call on students whose thumbs are up. Now, typically in a Problem String - ideally, if we're in an in person situation, I get to walk around while students are solving. I get to look over shoulders or interview students individually, I get to kind of ask them how they're thinking and then I know who to call on. That is one of the biggest pitfalls or downfalls to the remote thing like in a zoom, because I can't look over students' shoulders. So instead, I have to be prepared to ask questions like, "Hey, did anybody use the problem before to help them solve the problem?" Or, "Did anybody use the 10 to help them think about this?" So I need to be thinking about the kinds of strategies I'm expecting students to use, and then ask questions toward those strategies. So I'm wondering, and then you might be in a situation where you've anticipated a strategy that you kind of need to show up in the first problem in order for it to work well in the rest of the Problem String. And you might say, "Hey, did anybody use the 15 to help you?" Nothing. Like if nobody looks like they've got it, you have a couple choices at this point. One choice might be for you to say, "Could you? Could anybody use the 15?" or the problem before or whatever way that you could sort of nudge to wonder if students used that relationship? And then if somebody grabs it, it's within their zone of proximal development, then you can have that student share how they did it, and then the Problem String will work. Another thing to know is if nobody uses that one, then it's probably not the best choice of Problem String. And you might want to back up and adjust the Problem String or move on to the next task and then rethink what might be the best string to do at that point. So if you're in a live situation like a zoom, you can still absolutely use Problem Strings. Now, if you're recording that, so that maybe some students are on live with you, we still think that's a fabulous way. That kind of mimics what we do in our online workshops. You do the Problem String with the students who show up live, record that session, and then you can have students who weren't able to be on live watch that. So that's another alternative. You might have the situation where you have to record your sessions. Or maybe I shouldn't say sessions, but you have to record what you're going to do with students ahead of time because maybe you have students who don't have bandwidth to be in a zoom call, or maybe they don't have the data capability to do that. Hopefully we're getting to places where students are having enough internet access so that you can do more live things with them. But let's say that your district has said, "You must record your teaching with students, and then students can watch it whenever they have the ability." We still think Problem Strings are a fine thing to do. In that case, if you're recording a Problem String and it's just you talking to your computer, then you can do things like, "Okay, guys, here's the first problem. I'm gonna launch the first problem, here it is. Now go ahead and pause the video and solve that problem. And then after you've solved the problem, then go ahead and hit play again. And we'll share some strategies that we usually see students use." And then pause a little bit and say, "No, really, really pause the video, everybody pause, like, please pause the video. It'll go much better if you've actually solved the problem before. Okay, okay. I have anticipated that you have paused the video. Here are some strategies that we typically see students at your grade level using to solve this problem." And then you kind of talk through and model, represent student thinking using some sort of visual model. Now to do that while you're recording, my favorite way is to plug in my iPad, or a tablet into your computer and then share that screen. If you're using zoom, you have a great capability to share an iPad plugged into your computer, it's pretty easy to do. If you want more information on that, we'll put a link in the show notes to how to do that. That's on the blog. We talked about how to plug that iPad in, and then you can sort of write on it live and share that screen. But some low tech alternatives, you could just have a whiteboard that you hold up and just hold it up in front of your camera and you can write on it. Even lower tech, you can have a blank piece of paper and a marker. You can write on that. That's my least favorite. Um, it works fine until you need to erase. Some Problem Strings are better if you represent student thinking and then you actually want to erase some of the marks to kind of keep things clean enough that students can use what has been done before in the Problem String without maybe all of the marks on there. So that's my least favorite way to do it. But some Problem Strings work just fine that way. So there's some alternatives for you to use Problem Strings, strings or series of problems that are constructed in certain orders to help students create relationships. To use those Problem Strings, whether you are live with students or whether you're live with some students recording or whether you need to record and then just let students watch those recordings on their own time. Alright, so that's a little bit about how to do Problem Strings. Kim, what about Rich Tasks? Tell us what you're thinking that teachers - how can they use Rich Tasks in an online environment?

Kim Montague  13:32

Right. So a Rich Task to us is, is a little bit of an investigation where you'd launch a problem or scenario. Give kids time to work on the problem either in pairs or groups. You circulate, have conversation with kids and then come back together often to have some sort of congress or debrief where students share their thinking and their work to further move the entire class forward. So I think even - 

Pam Harris  13:57

Love em, those are some favorites!

Kim Montague  13:59

Yep. So even with a Rich Task, I think there's some ways to involve students and have some options remotely. If it were me, I think I would be really careful about which times I thought it was important to have kids right in front of me. And I don't think that that's necessarily every single piece of it. So I think that it's possible to pre-record the launch of the investigation where I tell the story, show pictures or the objects, give students a real sense of what's happening, and then set them off to work. I think that can be done asynchronously in some situations. Kids just watch a video of me having that conversation. Then I think I would schedule some 10 to 15 minute time with small groups on zoom. Then we can have a conversation. I can answer some questions. I can get a sense of what the kids are doing and pose questions along the way. I can even leave them continuing the work and ask them to submit their work by holding it up to the camera while I take a picture or they can take a picture and email it to me. We could put it all in a shared Google Doc, some way to submit the finished work to the entire group. That way, I have a chance to view all the student's work ahead of time and carefully choose which pieces of work to share the next day. Right? In a Rich Task it's not every person share. I'm specifically choosing work that we're going to talk about the next day.

Pam Harris  15:31

That moves the math forward.

Kim Montague  15:33

Right. Even if I were in a classroom, I often try to schedule that congress or that conversation the next day so that I have time to really evaluate the pieces of work. So that's going to be really no different than in this remote setting. So they could submit the work and whichever way works for us. I pull up the work the second day, and then whoever can join, right? As many kids that can join in that congress, I pull up the work and I'd have students share their thinking. And then really importantly, there'd be an opportunity for students to comment on each other's work to ask questions to respond. The Rich Task may take two days, but I really feel like it's going to be based on meaningful discussion like if we were together. If you were a kid who cannot participate in that conversation, there might be a way for them to submit questions to each other to continue the conversation further. Students can still feel like they're in a community of learners and sharing ideas rather than watching a single video and doing all their work alone.

Pam Harris  16:40

Which is so important to building that community, that math community where we are working and learning together because we want communities of learners where the learning happens as we work together, talk together, they build shared understanding. Okay, so that wraps up part two of our three part series on our top three ways to start the school year. Today, we talked about how we could use important lesson types even if we're teaching remotely to build a community of learners. Last week we talked about helping students feel seen, acknowledged, and valued by learning and using their names. Next week, we'll end our three part series by talking about the importance of having your beliefs about teaching and learning solidified so that everything you do and say fit together.

Kim Montague  17:27

If you want to hear more from Pam, check out her blog on the website mathisFigureOutAble.com. As always, join us on Wednesdays on your favorite social media for MathStratChat. And if you like the podcast and give us a review, that would be outstanding.

Pam Harris  17:43

So if you're interested to learn more math, and you want to help students develop as mathematicians then the Math is Figure-Out-Able Podcast is for you. Because math is Figure-Out-Able!