Pam Harris  00:01

Hey fellow mathematicians, you're listening 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 you found a place where math is not about memorizing and mimicking, waiting to be told or shown what to do. But it's about making sense of problems, noticing patterns and reasoning using mathematical relationships. We can mentor mathematicians as we co-create meaning together. Not only are algorithms not particularly helpful in teaching mathematics, but rotely repeating steps actually keep students and teachers from being the mathematicians they can be.

Kim Montague  00:39

So if you are new to Real Math, like what we'd like to call Real Math, or your students are new to Real Math, you may have been listening to the podcast a while or maybe you've participated in a webinar, but you're not really sure how to get started. What are the first steps? How do you get kids involved? We've got some tips for you today. So the first thing that we want to mention is that we feel like it is crucial to build a strong mathematical community. So what do we mean by that? We mean that it needs to be a safe space for students who may be sharing their own thinking for the first time. And you have to be intentional about creating that space. It doesn't just happen overnight. We also think that you want to build community by showing curiosity and actually mean it. We think that it's important that you are vulnerable with your own thinking, and respect different thinking. We also think that we need to teach students how to disagree, or have alternate approaches, because that's going to happen when you actually honor thinking in your classroom. And we also think that it's incredibly important that you institute wait time for your students, because not everyone's going to come to some sort of thinking at the exact same time.

Pam Harris  02:00

In fact, that's probably one of the things lately, I've been noticing, I don't know, maybe more than in the past. Maybe I've gotten better at it or something's happening. The groups of students I've been working with lately, specifically with wait time, I'm looking at the student, I've asked the question the students are thinking and someone dives in to save the student. 

Kim Montague  02:20

Oh, yeah. 

Pam Harris  02:20

That's a moment where we can say, "Oh, actually, she doesn't need, he doesn't need to be saved. Yeah, he's got it. She's got it. Don't worry about it." If you allow students to dive in and save, that is sending the implicit message that you think that student needs to be saved.

Kim Montague  02:38

Yeah. 

Pam Harris  02:38

That student needs some help. That they don't have the wherewithal to think about it. That everything you just said about creating a safe space, and being intentional about it. And really being curious about how someone's thinking, all of that can be sent in the message when you can say, "Oh, this person, that person's got it, they've got it, like, give them time they can think." 

Kim Montague  03:00

And I think the respectful thing to do, I'm sorry for interrupting. 

Pam Harris  03:02

No you're good. 

Kim Montague  03:03

But the respectful thing to do is to teach very early on that you're going to ask, "Do you need time or help?" We've mentioned this before, that sometimes people need time. And sometimes they may ask for help. But we're going to put that on them. We're going to ask them, "Would you like help? Do you need some help in some way? Do you want us to help open up the thinking with you?"

Pam Harris  03:24

They get to ask for someone to save them if they need it. But until they ask they get some time. Absolutely. Yeah, nicely said, Cool. So it's going to be important as you begin with students, say you have a new group of students and you're thinking, "Alright, how can I like set up this to be the best situation possible?" Set intentional goals to build that safe community that Kim just talked about. So another thing that we're going to suggest, as you think about how can we serve really get more Real Math happening? May I wonder where you are on kind of a continuum, as you think about how much you want to do, I kind of think about teachers that are kind of on one side of the continuum that want to kind of dip your toes in. You're interested. You're, "I've been listening to podcasts." You're like, "This is interesting. I want to see how this is gonna go. I want to try some stuff." So you're kind of on one side of the continuum where you want, you're not on the other side. So if I'm looking at the other side of the continuum, you want to change everything you're like on a dime. You're going to turn and you'd like all of it. I could totally see and respect how we might have teachers that want to try some things. We might have teachers in the middle of the continuum that want to try more things. We might have teachers on the far side of the continuum that want to try all the things. Let's kind of walk through that continuum a little bit and what are, go ahead.

Kim Montague  04:51

Can I just jump in for a second because there is no right or wrong side of the continuum?

Pam Harris  04:54

Thank you. Yes. 

Kim Montague  04:56

Yeah. 

Pam Harris  04:56

We want to respect the fact that teachers are, in fact, I'm kind the crazy that's on the end of like, change everything. But there's some downsides to that, because I'm gonna make a lot of mistakes sooner. That's good for you all, because I'll tell you what they are. But there's downsides to both sides, everywhere. And so there's also upsides to everywhere. I've met a lot of people that will change just a few things very deliberately, and very thoughtfully, and they end up doing some things more deliberate and thoughtful than I might do, or someone that's a little further on the continuum. So it's not about being right or wrong. It's about where you are, if we're going to offer some things for you to consider. So maybe identify where you sort of think you are on that continuum of try a few things, try more things, try even more things, try all the things. Where are you there? And then let's give you some ways to think about that. Alright, so as you think about maybe trying a few things. So I'm going to be on that side of the continuum. You're like, "I'm, you know Pam, I'm tentatively interested, I want to kind of see how some of this would go." May I recommend that you carve out some time. That you not only find the time, make the time, but you also set it aside in students minds, in your mind. And what do I mean by that? I mean, maybe you're going to have, you're going to commit Fun Fridays, or Marvelous Mondays, or Watch out Wednesday, where you're going to take 15 minutes, and you're going to do a Problem String. I would recommend that the first thing that you try with students are some short, powerful Problem Strings. So what do I mean by carve out the time? Well, A: I do mean, make the time. Set it aside. Commit that you're going to take that time to do it. But also set it aside in your students' brains and in your brain, where you say to them, "Hey, during this time, it's gonna be a little different. During this time, I'm going to do some different things that you haven't seen other places. I'm going to maybe do some teacher (I wouldn't say teacher moves to students) but you might see me ask different questions. You might see me pause longer. I'm going to use this private signal, because we're not going to raise hands during this time." It gives you a chance to set aside set apart this time to be different than the rest of your time. That way, students don't expect, like if you say, "Hey, show me a thumbs up." And you do it during a Problem String, and then when you're doing sort of whatever you do normally during your class period, you're not going to have students going, "Well, why aren't we doing that then? Miss, what's wrong? What's, you know what, I thought we were doing this now." You can kind of get rid of some of our at least tone down some of the pushback the kids might have, because you're purposely saying, "During this time, we're going to do this thing." It's not going to permeate everything else yet. That can protect you a little bit from some of that, just kind of, I don't know how to categorize that, Kim, sort of that push back or that poking that kids might do?

Kim Montague  07:53

Yeah, what you might find greater success. And it's because you'll be able to be super consistent in those periods of time as it becomes a new habit for you.

Pam Harris  08:01

Yeah, so yeah, instead of trying to do it all the time, and you know, that's not going to work. And then you get down on yourself, and you're not as consistent as you want to be, just for 15 minutes, you're going to try to be as consistent as you can be. Try to implement during that time, a good Problem String facilitation. Then yeah, the chances for success is higher. So that idea of carving out some time, committing, I would recommend a Problem String a week. If you commit to a Problem String a week, you'll probably get a Problem String most weeks. There's gonna be some weeks where something happens, there's going to be an assembly or whatever. But if you can, you know, like, say to yourself, "I'm like, it's gonna be Wonderful Wednesday, where we do this." Whatever you want, you don't have to call it something but just so it's sort of set aside. That can be on that side of the continuum, you want to try something, my strong recommendation is a Problem String. Or I will also say I Have, You Need could also be a really nice beginning point. So that could be something that you do. I don't know that you need 15 minutes for that. So I Have, You Need could be the thing that you do when you have five minutes left in the class period. You have five minutes left before specials. You have five, you have this random sort of weird five minutes. And because you teach bell to bell, you know, you're like always teaching, there's always learning going on. When you have that random five minutes, that's where you could sort of dump in I Have, You Need. If you want to know more about I Have, You Need, we'll put the link to that in the show notes. So those would be some very beginning steps. Again, kind of carve out that time. This is what we do during that time. 

Kim Montague  09:33

Yeah.

Pam Harris  09:33

What if you want to try more things? Then I would recommend, again, that you carve out some time, but now carve out some time every day. So now say to yourself, "I'm going to find five minutes every day to play I Have, You Need." Now every time you say 'every day', let's be realistic. It's going to be three to four times a week because again, an assembly is going to happen, specials are going to go long, like something's going to, whatever's going to, you need more time for blank. But if you say every day, then it's going to happen four maybe three times a week, but four times a week, then you're going to play I Have, You Need. Play I Have, You Need and set aside 10 or 15 minutes to do a Problem String. So if you want to try more, the things to start with you might be like, "Pam, you said that for the people." Yeah, because the most important thing is to start with are Problem Strings. 

Kim Montague  10:21

Yeah. 

Pam Harris  10:21

And then also I Have, You Need is going to help you build relationships that can be, can become helpful in those Problem Strings. Now, once you get that settled, and you're like, "Okay, we've done Problem Strings four times this week." Then in that fifth day, then you could do one of the instructional routines that we really like. So you can go to the instructional routines page on the website and check out relational thinking. Checkout As Close As It Gets. You could do a Count Around. You could do, you could play one of our games. So you could try one of those things, because you've carved out that 10 or 15 minutes every day. Now you've got that time. So now you can begin to dabble with Which One Doesn't Belong and other kinds of instructional routines that can start to get student thinking going. Students start to see different kinds of reasoning. You get a chance to practice all that, as you try more things. 

Kim Montague  11:12

Yeah, absolutely. And this is probably for many listeners, the start of the school year or close to the start of the school year. And these are really great routines to start mathematical conversations, like we mentioned in building community. So these routines that are found on the website are short, they're about-

Pam Harris  11:30

 Focused. 

Kim Montague  11:31

Yeah, very focused. They're about getting kids talking and thinking about relationships and patterns. That also has to go along with something else that I wanted to mention, which is your students will start considering what you celebrate. A lot of your students if they have been in the realm of it's about answer getting and about one problem, one answer, this is the one way you do it, you have a really great impact on changing their thinking, based on what you celebrate. And Pam, you and I have talked about this before, about how did we get kids really talking? And I think you might have actually been the first one to point it out to me that what I celebrated in my classroom was was like, "Yeah, okay, we got the answer, or I'm not really interested in that quite yet. What I'm interested in is how you know, and like, what relationships did you use?" And I don't know that I'd ever really considered that. And I think you pointed out to me. But we all as teachers have that possibility in our classrooms, and as soon as we can help our kids recognize that oh, what he's interested, what she's interested is, what they're interested in is my thinking, And that's gonna help shift for your students what they want to share with you.

Pam Harris  12:46

That's what gets celebrated in this class. It's not the answer. It's not it's not just me doing a bunch of steps that I learned last year. I just did those. I got the answer. And the teacher just kind of like brushed over me, just kind of like, "Oh, okay. Oh, look at over there! Like, share that! That's, Whoa, you guys, look how interesting that is!" And students kind of naturally gravitate toward what's being celebrated in class. 

Kim Montague  13:08

Yeah. 

Pam Harris  13:09

It's absolutely very, very important. Yeah, nice.

Kim Montague  13:11

I want to mention one other thing that you didn't mention when you were listing out some of the cool routines, is that you intentionally put out problems every single week on Wednesday nights in MathStratChat. And that is a phenomenal way once you get kids on board with Problem Strings. And that's a routine that you do and they know what to do, and they love it. You can also introduce MathStratChat to kids, because it's a fantastic way to pull out different ways of thinking. Get them involved on you know, if they're older, and they're in social media, you can get them involved. You can go to the website, pull up a variety of problems that we have on instructional routine hub, and just pick a problem and have kids share their thinking about the problem. And then look, it's linked to what others around the world have done to solve that problem. It's a fantastic way to get kids thinking.

Pam Harris  13:59

And some teachers are starting to use those problems with their students, and then post on social media, some of the strategies that students are using, and getting feedback from other people. And then you can show that to your students. You know, "Look, check out what people around the world are saying about how you all solve this problem." It's totally, it's a great way to get your students involved. Absolutely. 

Kim Montague  14:17

Yeah, yeah. 

Pam Harris  14:18

Also, you might be on the far end of the continuum, where you want to try all the things. You want to organize your, like literally what you teach every day to build more and more Real Math, you don't want to do the same ole, same ole that you've been doing. And you're like, "Pam, I want to reorganize all the things." So if I could give you a vision about how to start thinking about that. The way that I look, say if I were to come into your class, and I was going to teach a two week unit, I was gonna be your long term sub, I would look at what did you want to accomplish in that unit, that unit of study, that sort of thing that you're about to do? And I would focus around a few Rich Tasks that really helps students grapple with the ideas, really invite students into scenarios and contexts that invite the mathematizing, invite students to really grapple with the relationships that are happening, invite them to consider what's actually happening so that the math is realizable, to use a word from Cathy Fosnot. And so I'm going to consider those big Rich Tasks. And then I'm going to think to myself, "How can I get those ideas percolating?" I think about the first rich task, how can I get those ideas bubbling up in class that need to be happening, so that we get really good rich conversations during this Rich Task. So students have an entry point into the search task, like even to the point where I might say, Ooh, this multiplication problem is going to come up. I know, it's a most missed multiplication problem. I might do a Problem String before that Rich Task with that multiplication problem to just get those, that sort of happening in class, because thinking about the relationships. And then it's kind of fun, when the Rich Task happens, it's almost as if the kids had the idea themselves. They're like, "Hey, like, I know that. Like I've dealt with that recently. I don't even remember when, but," and then they're able to, because that's now sort of pinging for them, the relationships are hot in their brain, then they can kind of use them. And now things happen in the rich tasks, because those ideas were kind of bubbling up beforehand. Then in that Rich Task, we grapple, and the kids are really thinking and reasoning and making sense of what's going on. We have a class Congress, where we bring those ideas together, we might compare what's happening, or we might think about some of the pitfalls or the tracks, people took that were down a rabbit hole. And why didn't that work. And we're going to have this really great conversation about the things that were happening in the Rich Task. And then I might ask myself, "Based on what just happened, what's something that we could kind of cinch? What's something that we could bring to some closure from, because we had lots of different really cool things happening in the Rich Task? What's something that we kind of use a Problem String to cinch?" And then I'll do that Problem String. I'll sort of do a Problem String that will help get that idea, bring it more to abstraction more to closure. I might follow that within the next day with another Problem String that continues to cinch that idea for a different Problem String that cinches a different idea that came up in that problems in that Rich Task. Then we move on to the next Rich Task. And I think to myself, "What Problem Strings could I do to get those ideas percolating and bubbling up in class that need to be happening for the second Rich Task to sort of be successful in class?" And then we do those Problem Strings into that Rich Task, etc. And then I think about as I have those Rich Tasks, kind of those are the main, those main Rich Tasks, and I'm going to develop the concepts really what's happening in that unit of study. Then I think, "Okay, these are the Problem Strings that are kind of coming in and out of them, and what other routines might I bring up that can support this thinking?" I might also then consider, what are some of those instructional routines and Problem Strings that I can be having often this kind of off track that will keep the ideas and other concepts and things that we've been grappling with before that, that could kind of be keeping those going, (clears throat) sorry. Or be leading towards things that I know are coming up in the next unit of study? What are some things that I could get happening now in this kind of off track, that could be getting ideas, we could be working on them. So here's an example in high school, where I could be using our factor puzzles to help students start to think about what numbers do I multiply to get that product that I would add to get that sum. And I start thinking about having missing numbers. And students are doing all of that work just with numeracy before we ever get to factoring quadratics. So whatever it is, what can we get sort of happening, I could be doing Problem Strings and routines in that kind of off track, to get them sort of ready for the next unit of study. Now y'all, that's a lot to think about. But we're not suggesting everybody do that. We're suggesting those of you who want to, there's a way for you to kind of think about a vision of how your curriculum could kind of be structured.

Kim Montague  19:08

And again, anywhere on the continuum is a great way to get started. 

Pam Harris  19:12

Absolutely.

Kim Montague  19:14

Another thing that you can do very soon is that you may have heard that we do Challenges a couple of times a year. In fact, we have a Challenge coming up this next week. We're super excited about it. It's for everybody. Pam, what's a Challenge and what does it look like to participate?

Pam Harris  19:31

Absolutely. So we call it the You Can Change Math Class Challenge. Y'all, you might be familiar with challenges that are out there. Challenge: get healthy in 30 Days. Challenge: eat more health more nutritionally, in two weeks. Or challenge: learn how to blank in two days. There are all sorts of challenges out there that are different lengths and that help you do different things. What's common about a challenge is that we all start with a common goal. And then you learn, whatever, whoever's giving the challenge, teaches you during the challenge. And then you come out better you know the things. Because in a challenge, you not only learn, but you're given tasks to do right away to implement what you're learning in the challenge, get quick wins. And then with all that momentum that you built up, go right into using whatever it is that you learned in the challenge. So our challenge is the You Can Change Math Class Challenge is all about helping you as a teacher, change your class to teach more and more Real Math. So we choose a focus. By the way, the challenges are all different. We'll tell you ever if there's sort of a repeat. We haven't had that so far. The challenges are different, where we focus on an area of teaching Real Math. And then we dive in and we teach more and more. What are the things that you can do as a teacher to teach more and more Real Math. And we do Problem Strings. We do Rich Tasks. We do routines. We talk about strategies, whatever it is that it's the focus. But more than the podcast, in the podcast, we can only be verbal, and we kind of give you this 20,000 foot view of all the things. In the challenges, we get more in an on the ground, like how do we make this work, because then we give you assignments for quick wins, where you can gain momentum and really get excited about teaching more and more Real Math.

Kim Montague  21:20

Absolutely, you can register now for our next You Can cChange Math Class Challenge at mathisFigureOutAble.com/change.

Pam Harris  21:30

So everybody register for our upcoming challenge at mathisFigureOutAble.com/change. Love to see you there live on Zoom. It's a blast. I always have a really good time doing those. So thank you for tuning in and teaching more and more Real Math. To find out more about the Math is Figure-Out-Able movement. Visit math is Figure-Out-Able.com. Let's keep spreading the word that math is Figure-Out-Able.