Pam  00:01

Hey fellow Mathers, welcome to the podcast where math is figure outable. I'm Pam, a former mimicker turned Mather.

Kim  00:11

You just like took me back to I'm Pam, and I'm Kim, and I almost mess it up every time, but when you say your last name, I almost dove in.

Pam  00:21

And I'm Kim. Wait, no, you're Kim, and you're Kim.

Kim  00:24

I'm Kim, a reasoner who now knows how to share her thinking with others at Math is FigureOutAble we are on a mission to improve math teaching.

Pam  00:32

 We know that algorithms are amazing human achievements, but they're not good teaching tools, because mimicking step by step procedures can actually trap students into using less sophisticated reasoning than the problems are intended to develop.

Kim  00:47

In this podcast, we help you teach math-ing, building relationships with your students and grappling with mathematical relationships.

Pam  00:54

And we invite you to join us to make math more figure outable.

Kim  00:58

Hey there. 

Pam  00:59

All right. Yay. Good intro there. So do you want me to always say my say both? Like, that's what threw you off, right? Is that I said I'm Pam instead of I'm Pam Harris. 

Kim  01:09

Yeah. I mean, no, we you alternate, and then I just do what you do. So I don't know you've done that. It just for some reason I went straight back to old. It's been a while too. Okay. Anyway, I have a review for you today. 

Pam  01:21

Oh, I love reviews. 

Kim  01:22

Yeah, you do. This is from a while ago, but it's from math in Charleston, SC,  And it says Beth, (laughs) today's gonna be fun. Not Beth, best math podcast for teachers of all levels. And she says, he, she, I don't know. Oh, mama, she. Pam and Kim bring humor and realistic ideas to all math levels. I always take away a new idea and solidify existing math learning. I'm a veteran teacher, but new to math. I taught ELA for years, and needed a change. Teaching math and science for me is that change. I was never, quote, good at math, and with time, Pam and Kim have given me confidence to be able to let the numbers dictate how I solve problems. My own number sense has increased with this podcast, and I'm able to help kiddos at all levels. This is the podcast that all math teachers need to listen to.

Pam  02:08

Ah nice. South Carolina, okay.  Oh, nice. Thanks. Math in Charleston, SC, that's awesome. And oh,

Kim  02:22

It says math Not at my best today, I did mama, sorry if you're not a mama. 

Pam  02:32

And when, when you say, I was never, quote, good at math, and now you are. So how cool that is. Like, yeah, I mean, maybe you were never good at fake math, but bam, you're proving that you're good at real math. That's

Kim  02:42

Super. Also they said, "Let the numbers dictate how I solve problems."

Pam  02:47

That's what a real mathy person does. So you're proving yourself right there with your words that you are in a real mathy person. Yeah. Cool. You know, Kim, it's fun. I've been doing a lot of virtual sessions lately. 

Kim  03:00

You have been. 

Pam  03:02

Sort of more and more and more, I think, which is totally fun, right? I mean, people from around the world, I'm having a blast doing it, but it's always fun when we'll have a math experience. You know, one of the first things I'll do is to say, hey, dive in and feel like, feel with me what it looks like and feels like to math, the way mathy people math. We'll do some of that. And in the middle of it, I'll say, "Hey, hey, that problem you just solved. How do you solve that?" And people will just, like, their eyes get big in this like, and I like, "Sit up tall." And also, "You just mathed, the way mathy people math." But the fun part for me is, when I say, "Sit up tall," the number of people that actually do, like, physically, like, sit up tall. And I'm like, I mean, you don't, I didn't. I don't actually mean physically. So I mean it as a kind of, like, turn a phrase to say, 

Kim  03:45

Yeah. 

Pam  03:46

"Be proud of yourself," you know. But it's always fun for me. And I really appreciate the people who do it, because it gives me just a little giggle inside to go, like, "Look at you just sitting up tall." Because, like, how cool it is that they're actually mathing, like, math in Charleston, south SC is mathing, and it's, yeah, it's super fun. 

Kim  04:05

And they're improving their posture.

Pam  04:09

Sure enough! You made me bark out loud. Our poor editor is probably, "Whoa. Like, cut that. Sound down a little." Sorry, Craig. Okay. So Kim, today, we thought that we would talk a little bit about, we've had a lot of questions about sequencing tasks. And so we thought we'd mention some things that we think about when we think about sequencing tasks. And one of the things that we think about is like, what are we trying to get at in the next little while? What are the, what is the scope and sequence from our school, from our district, the standards from our state or province, or, you know, sort of the people that say, "Thou shalt teach this in thy grade level." So we're kind of thinking about lots of levels of things, but as we kind of drill that down to: So, what of that am I going to try to accomplish in, say, the next two or three weeks? And what is the kind of big conceptual stuff? What's the strategy? What's the model? Maybe, what are the couple of strategies, or the couple of models we might be playing between. Or maybe one model where, whatever it is like, what is the major, kind of, I'm really getting at multiplication and using the associative property. Or we're really trying to connect multiplication with area. Or, if I'm a younger grade teacher, we're really working on partners of 10. Or maybe we're actually working on adding 10 to anything, maybe, maybe adding 10 to make the teens. Or if I'm a middle grade teacher, maybe I'm really thinking about interest, or I'm thinking about percent. Or maybe if I'm a high school teacher, I'm really thinking about taking a specific kind of data and fitting a function to it, like, what is maybe, it's a particular kind of function. So if I'm kind of thinking about, you know, in general, like, this is the topic, the big thing that I'm trying to get across. Then we think about sequencing tasks. We think about not just like, okay, every day is going to be the same. Kind of, well, the way I was taught was, you know, the teacher stood up and said, "All right, everybody, here's the sample problem, and I'm gonna do it, and then we're gonna do it, and then y'all go do it." Instead of that kind of like, that's gonna be the thing that we do every day. We actually like to take different kinds of tasks and alternate them, sequence them, have them come up in a sequence. We're all about sequence, right? Everything's a progression. So we really think about that sequencing. And one of our favorite ways to sequence tasks is to think about those big, major things that we're trying to accomplish, and say, let's just choose two weeks. And in that two weeks, what are some big kind of, or eh, I don't have to say big. What are some messier? Well, maybe I'll just say this, what are tasks that aren't instructional routines? So they could be a big mitchie. Mitchie? Messy, rich. I was saying messy and rich at the same time. They could be a big, messy, rich task. They could be a tighter, not so messy, not so rich, but just a task where kids are kind of grappling with some things. They could even be a game. It could be some things that are getting ideas percolating, getting kids to mess around with things, getting kids to really dive into kind of that big thing. When I was creating sequences of tasks for high school courses, we created some videos that would kind of get kids into a scenario, kind of like, Hey, I'm diving in. I'm kind of feeling this scenario. Is one way to kind of feel the phenomena that would be, you know, one of these sort of non instructional routine tasks.  The reason I'm calling them non instructional routine tasks is because then we like to take instructional routines and alternate them. Think about, oh, could I do an instructional routine? If I think about this other, this non instructional routine, task of maybe a rich, messier task, how do I get into it? What are the ideas that need to be percolating and kind of happening, bubbling up in kids so that this task will work well. And often, maybe most often, that's a Problem String. We say, oh, let's do this Problem String so that we get those ideas percolating, get them sort of happening in class, and bam. Then now we can do this kind of richer, messier task that gets at those bigger ideas. And then we think to ourselves, how can I get out of that? Like, if it is a task where kids are grappling with those bigger concepts, those conceptual things that are happening, then we're going to admit that we didn't actually cinch something that was happening in there. We might have cinched it kind of but we don't like to cinch things all at once, right? We like to give kids multiple experiences. So what could be an instructional routine that we could follow that task with, that could help cinch one of those strategies, maybe, or make the model a little bit more clear, or even take one of the big ideas that was happening and kind of refine it. And often that is a Problem String, but it doesn't have to be right? It could be another instructional routine, like, As Close As It Gets, like, a Count Around, like, Relational Thinking. We've talked about slow reveal graphs. Like, there's lots of other instructional routines. I would say that by and large, we do Problem Strings most often, but we like to intersperse other instructional routines, including games. Would you agree? 

Kim  07:54

Yeah, yeah. Yeah.

Pam  07:54

I'm going to interrupt you for a second.  Yeah, please. 

Kim  07:56

When you, I'm going to back you up. 

Pam  08:00

Thank you. 

Kim  08:18

When you talked about a Problem String leading into or something leading into the task, that choice might be because you want to introduce a model that you think would be helpful for them to have used or seen in that rich task. You might lob out like a number sequence, or the types of numbers that you're going to be using in the rich task, or whatever the, you know, whatever. It might be that you, at my grade levels, it might be that we're going to be messing with quarters. And so I want to do something with something 25 in a Problem String. Or, you know, maybe I want to see where they are with decimals before I ask them to mess with them. So, it could be a number, it could be a model. It could be me feeling out like, what am I going to be able to elevate in the rich task? So there's a lot of things that you could do prior to kind of set the stage. And then on the other end of that, you know, you mentioned a couple of routines that we love for afterwards, and you mentioned cinching it. It's also might be a choice that you make to give kids a chance to have some fluency with the idea. You know, they, they're grappling with it. They, you maybe have a congress and you've had some conversation about it, but then they get to apply it in some way that isn't, you know, like you've mastered it. We can move on. They still get to mess with a little bit more afterwards.

Pam  11:07

Yeah, we can high dose pattern them so that that thing they were messing with now becomes a more well traveled path. It becomes like, something that they now do a bit. I'll just say that. A more well traveled path so that their brain is more inclined to go there again when these kinds of relationships happen. 

Kim  11:26

Yeah, and I think that that is sometimes what is missing. You know, people will say to us, "I did this thing, but I don't see my kids using it in the math work that we do." And we've, maybe we've talked somewhere in the podcast, but about helping direct their brain that way. And Problem Strings are a great opportunity to do that. 

Pam  11:47

In a very sort of natural kind of, instead of saying, "I'm telling you to do this, I'm telling you to think about that thing." We're gonna raise it and allow kids to go, "Hey. It feels like, it feels like, quarters are like showing up in my head". Or "It feels like, I feel like going over here." And, well, yeah, because, like, we're just high dose patterning you. Thanks, Brendan Scrivener for that. I talk about Problem Strings as high dose patterning so much more now that Brendan gave us that, that phrase. It's awesome.  So Kim, as we talk about Problem Strings to get into tasks, and Problem Strings to get out of tasks. One of the things that you and I and our team have been working on for a little while now is that we've been writing Problem String books. And I had written Problem Strings for middle and high school in my Building Powerful Numeracy for Middle and High School Students. I've written Problem Strings in Algebra Problem Strings and Advanced Algebra Problem Strings for High School. And we lately have been writing Problem Strings for elementary, right? We have our we'll have K5 books out. I'm not sure when people are listening to the podcast, but soon we'll have books for every grade level that can have Problem Strings. To do that work. Well, as we've been working on those, we've had a lot of teachers say to us, "Yeah, but what about those things in the middle? You know, you keep saying the Problem String helps you get into that task. It helps you get out of that task. What about those tasks?" Kim, I just took a deep breath.

Kim  12:16

Super cool.  We can finally share. We can share why everything takes little bit longer. 

Pam  13:18

Our lives are full of amazing, important things. And one of the things that our lives have been full with lately is that we have been working with hand2mind on an amazing product that is called Foundations for Strategies, Small Group Lessons. And I love that the tagline underneath it is, "cultivating mathematical reasoners through purposefully sequenced lessons." Y'all these are the tasks that you can put in between those Problem Strings to help develop the big ideas, models and strategies for addition and subtraction of single digit numbers and addition and subtraction of multi digit numbers, and we're not done yet. Multiplication and division of single digit numbers, and multiplication and division of multi digit numbers. We are so excited to tell you that this product is on its way. We're working on it, hot and heavy, it is going to be well, it has been announced, and we've just announced it here. It will be available for pre order on the hand2mind website. Um, it'll be in stock in early 2025, so we'll be talking to a lot of people about this in the upcoming time. But we're super, super excited about giving you some tasks to help cultivate mathematical reasoners. Whoa, yeah.

Kim  14:40

These are gonna be really fantastic. You know, sometimes people ask, you know, "I've got a Problem String. I'm really excited about that. I know what to do with problem strings, but what about the rest of my class time?"  And this is going to be super helpful for people to read. You know, they're easy to read. It's a two page lesson. And it's got some great, I hope that you'll hear the Math is FigureOutAble voice in those lessons, because you know the same language that you're going to get from here on the podcast and in Problem String books. They're just going to be really great to connect. 

Pam  14:52

Yeah, Exactly.  and some other things that you'll recognize as you look at these four, so there's four kits. Each of them has a book full of lessons, and then it comes with the necessarily, necessary manipulatives to help you do that. You'll see the the Developing Mathematical Reasoning is all over. Like, how do you get kids from counting strategies to Additive Thinking? How do you get it from Additive Thinking to Multiplicative Thinking? How do you get them to more sophisticated Additive Thinking in addition to subtraction and more sophisticated Multiplicative Thinking and multiplication and division? Yeah, totally help there. Yeah, go ahead. 

Kim  15:50

Yeah. You'll, you'll see the models that you're used to seeing here. I'm super excited about one of the books Pam wrote about building a number line, which is, you know, it's fantastic. It's, there's some really nice, rich groundwork lessons. And you're going to see all the models, right, younger grades. You're going to see some number racks and

Pam  16:12

Rekenrek, yeah. 

Kim  16:13

Number lines. 

Pam  16:14

Number lines. You're also going to see arrays and ratio tables for multiplication. So you'll see the models that we promote, like we actually use them. You're going to see the strategies. When we say that there are major relationships that lead to major strategies, and really there's only a small set of major strategies, bam. That is, like the product is literally called Foundational Math Strategies. And it is those foundational strategies that we help you really get started in students. And then we totally anticipate that you would book end them with the Problem Strings. Get into them with a Problem String, get out of them with a Problem String. Super. This is our answer to the question that we've been getting so often of like, "All right, Pam, we've been hearing that Problem Strings book end these tasks. Where are those tasks?" Well, y'all here we go.

Kim  17:06

You can see too, ways that we nudge students with questions that we would ask and the purposeful moves, the things that we would bring out. You know, and we don't always get to talk about those. So unpacking a little bit of that thinking is, is there too.

Pam  17:23

Yeah, absolutely. We you'll see some anchor charts in there. You'll also notice that we take kind of an interesting, what we would call a product approach to multiplication. It's kind of similar, we've talked a little bit on the podcast. Go listen to the Stick and Split episode where he takes a product approach in his game. We also take a bit of a product approach, where we ask students, "Hey, what are all of the factor pairs for, say, 12, or what are all the factor pairs for 24?" Then we do some really cool things, connecting that with area. We also talk about for younger learners, for addition subtraction, hey, if we're going to have vanilla and strawberry ice cream and we're gonna have 10 of them. How many vanilla might we have? How many strawberry might we have? And really, having kids kind of figure out all those different combinations to make 10. You'll notice the math is there, like, with the different meanings of subtraction are brought out. Where the different meanings of division are also, like, definitely, you know, we're messing with problem types and making sure that that's all in there.

Kim  18:23

Yeah. And you know what was most fun for me, I think, is some of our old favorites are in those books as well. It was a lot of fun. We got to put in some I Have, You Need work and Count Arounds, Hint Cards. We've sometimes called them Clue Cards, but Hint Cards are in there about gaining fluency with facts. There's also some really nice Card Sorts that you can have kids analyze strategy and really make sense of models and strategies in a new way. 

Pam  18:50

So if you hear a little excitement, you might also hear a little, we're so glad that it's almost done. Like we've been working for a while on. It's been quite a project, and we've brought in lots of what, lots of resources from our team to make this be a product that we're super proud of. And yeah, we're really excited to be able to offer this to everybody. We've been working really hard on it. Thanks Kim. Thanks Kim for putting your brain in and making it what it can be. And everybody out there, hopefully, even if you don't ever, you know, you're like, Pam, I'm not going to go buy that, just to hear kind of the things that we put into it. And the idea, you know, like when we just mentioned some of the things that you'll recognize in it, those are the kinds of things that we would recommend, that if you're creating your own sequence, that you stick in your own sequence. And so now you have those ideas there. 

Kim  18:50

Yeah. 

Pam  18:51

All right, everybody, thank you for tuning in and teaching more and more real math to find out more about the Math is FigureOutAble movement. Visit, mathisfigureoutable.com. Let's keep spreading the word that Math is Figure OutAble.