am  0:01  
Hey, fellow mathers! Welcome to the podcast where Math is Figure-Out-Able! I'm Pam Harris, a former mimicker turned mather.

Kim  0:11  
And I'm Kim Montague, a reasoner who now knows how to share her thinking with others. At Math is Figure-Out-Able, we are on a mission to improve math teaching.

Pam  0:20  
We know that algorithms are amazing human achievements, but they are not good teaching tools because mimicking step-by-step procedures actually traps students into using less sophisticated reasoning than the problems are intended to develop.

Kim  0:33  
In this podcast, we help you teach mathing, building relationships with your students, and grappling with mathematical relationships.

Pam  0:40  
We

Pam  0:41  
invite you to join us to make math more figure-out-able. Hey, Kim.

Kim  0:46  
Hey, how's it going? 

Pam  0:47  
Whoo, fast and furious. And fun.

Pam  0:51  
Good time today. 

Kim  0:52  
Yeah. So, today, we want to share something very exciting. You know, we're always up to creating new things, new helps for teachers. And today we want to share about a recent endeavor that we've been working on. This is a relatively small ask for teachers that makes some really good impact. So, we're going to unpack that a little bit today.

Pam  1:15  
Yeah. You know, when I dove into research, one of the first things that I ran into, very fortuitous was Cathy Fosnot and her Young Mathematicians at Work material.

Kim  1:25  
Yeah.

Pam  1:25  
Then after when I would see people try to implement rich tasks, or routines, or investigations,

Kim  1:34  
Mmhm. 

Pam  1:34  
Problem Strings, try to get discourse in class, reasoning, build conceptual understanding. All of those things. I could see little misses that made a big impact because of the lens through which I was viewing everything. It was so, so important. With little shifts, teachers could harness the power of the tasks, the routines, the listening, the talking, student strategies, and help move the mathematics forward for more students. So, we're super excited to announce a new mini workshop. 

Kim  2:10  
Yeah,

Kim  2:11  
so we now have two mini workshops, each focused on different grade bands. We call them Transforming Teaching K-5: Small Shifts, Big Impact. And the brand new, Transforming Teaching 6-12: Small Shifts, Big Impact.

Pam  2:27  
So, both grade bands now have a specific workshop all about the small shifts to make a big impact. Here's the overall structure. We've got four lessons. The first lesson, What About Strategies? Second lesson, What are the Major Strategies? Third lesson, all about our favorite routine, Problem Strings. And the fourth lesson hits the frequently asked questions and misconceptions that we see everywhere as we travel around. Let's dive in and get more specific about each workshop. So, Kim.

Kim  3:01  
Yeah? 

Pam  3:01  
Tell us what they have in common, and we'll highlight some differences. 

Kim  3:04  
Yeah, so

Kim  3:05  
you said that the first lesson is about strategies, so What are Strategies? In the K-5 workshop, we have the difference between strategies and algorithms, and why strategies are so important to students' mathematical development. We also talk about the differences between strategies and models, and why models are so important in facilitating learning. And also we have how building numerical relationships naturally leads to using strategies.

Pam  3:34  
We really focus on all those things in the K-5. And in the 6-12, there's just a few differences because we need to bring in a little bit more of the development of mathematical reasoning, so we can talk about functional reasoning and proportional reasoning. We also bring in formulas, and equations, and functions with different models than we've used in the K-5. We've got to bring in some different models that are popular and that are necessary to use at 6-12. And then also the important ideas of how do we build functional relationships? Alright, how about that second lesson? 

Kim  4:07  
Yeah,

Kim  4:07  
so second lesson is about the major strategies that we would expect to see in K-5, the major strategies for each operation. And they're listed in order from the least sophisticated to the most sophisticated. So, sometimes we get people asking. You'll find that there. And we also have the major models that we use to make student thinking visible and take-up-able for the other students

Kim  4:30  
in the class. 

Pam  4:30  
Very nice. And importantly, it's just a small set of those major strategies and major models. And so, in the K-5, we're focusing on those mostly with numeracy and operation. And in the 6-12, we're focusing on those major models and strategies for solving proportions and also using the numerical relationships into solving those more middle school problems. We also explore functions through the lens of sense making without step-by-step procedure, but really how can kids reason about parent functions and transformations and make that fit with modeling and all of that secondary content.

Kim  5:07  
The third lesson is all about our favorite routine, Problem Strings, but we actually snuck in a second one. So, in this lesson, we talk about the difference between Problem Strings and Problem Talks, so that you can maximize the power of each. These routines focus on the relationship and strategy development. And we unpack the Most Important Numeracy Strategies ebook, which have some sample Problem String lessons that you can take back to your classroom.

Pam  5:34  
Wonderful. And in that K-5 where we really focus on a lot of teachers having done Number Talks or Problem Talks, the difference between them, we have more teachers in the secondary that we help them differentiate between Thin Slicing and Problem Strings and how to harness the power of both. We'll also give you a download with sample Problem Strings and a really nice definition description of what the routine of Problem Strings, what that routine is.

Kim  5:59  
Yeah. The fourth lesson is a really exciting lesson because this is where teachers have asked over the years a lot of frequently asked questions and some misconceptions. We unpack their answers to questions that teachers ask when they are shifting from teaching algorithms to teaching math that is figureoutable. We unpack some common mistakes, maybe, some misconceptions surrounding teaching strategies and models.

Pam  6:24  
Y'all, we kind of consider this as,  as we work with teachers, what are the things that as you dive in to make math more figure-out-able, they're just the typical things that if we can help you from the beginning know these little shifts to make, then as you dive in, you're going to have the more impact, a bigger impact, and it's going to work better and more smoothly. If you're a listener who's heard us talk about other ways to get involved, and you've thought, "Whew, too much time, effort, bandwidth," whatever, this is your opportunity to have a bite-off-able chunk. If you're a leader who's looking for small chunks to work with your teachers, this is your opportunity to take away the most important things for you to consider, for teachers to consider, that are small shifts that can make a big impact.

Kim  7:16  
Okay, so let's slow down for just a second. You said, if you're a listener, if you're a leader, so if I'm a teacher wanting to take this workshop, say more about that.

Pam  7:26  
Yeah, so if I'm a K-5 teacher, when you're diving in, you're thinking a lot about, "Oh, okay, there's this small set of major strategies. Which of these do I own? Which of them are new? Which ones can I then go and listen for in my students?" Then in that second module, you're really thinking about what is the difference between a strategy and a model? And we're giving you lots of practice. So, we're giving you some posters that we see in teachers' classrooms, and things we've heard teachers say, and helping you kind of parse out the difference between those. And then we give you Problem Strings to try. And you actually can do them sort of with us in the workshop, and then you can go try them with your students. And, again, all that listening for how are students really thinking about problems? And sort of grow in your, "Okay, I'm starting to recognize the major strategies. I'm using the major models." And then you can read those frequently asked questions and really get a good sense for really the answers to your questions because you probably have many of them. And then in those misconceptions, maybe like, "Oh, wait. Is that what people meant when they said, 'Represent student thinking?' It isn't about memorizing a sequence of steps with a manipulative. It's about helping kids really gain these relationships but not towards the end of mimicking steps of an algorithm." So, lots of sort of misconceptions we kind of iron out in that section. Yeah, go

Pam  8:50  
ahead. 

Kim  8:51  
Yeah. So, it feels to me like, you know, we have some people who say, "I found the podcast, and I just binge listen." This is a way to see what you hear. So, we talk about a lot of these ideas on the podcast in snippets and kind of here and there. This workshop feels like a really small ask, financially and time wise, that you can see some of this stuff in practice. And, like you said, get some questions answered that people put in the teacher Facebook group. Or they, you know, send an email, and we say, "Go to that group." So, yeah, it's a nice place for them to get kind of a cohesive look at what we're talking about here. 

Pam  9:26  
Yeah,

Pam  9:27  
and if you're not in our Math is Figure-Out-Able Teacher Facebook group, we highly invite you to join that. That's a great place for you to get more feedback and more ideas or kind of hear what lots of people around the world, how they're diving in to make math more figure-out-able.

Kim  9:39  
And we've had that one for a while, but now we have a new one that we're super excited about.

Pam  9:46  
A new workshop, yeah. And that new mini workshop for 6-12 teachers, we realize that we need to help 6-12 teachers also make the differentiation between formulas, and strategies, and algorithms.

Kim  9:58  
Yep. 

Pam  9:59  
And how those are different than models like the box method and how that that can kind of muddy the water. And how we can help secondary teachers get more clarity around how can you reason to solve proportions? And what is the major set of strategies for really reasoning proportionally? There's a great statistic Susan Lehman cites that she thinks 90% of adults aren't reasoning proportionally. Ah! So what that says is that they need deliberate experiences. And often in especially middle school, we just say cross, multiply, and divide, but we haven't given students experiences to know when to do that, versus all the other sort of things they might do when they see two rational things maybe equal each other, or times each other, divide. You know, whatever the operation is in between. And so, we really help the 6-12 reason proportionally. But then also some high school strategies. So, we even dive into a radian measure Problem String, so that high school teachers can get an idea of what we've been talking about at the elementary level, but really with high school content. Not numeracy into high school content, but actual secondary content, how we can make math more figure-out-able there.

Kim  11:14  
Yeah, and I think this is really unique because giving people a snippet to help them see what we're talking about at a 6-12 level is really rare, so I'm excited about this because I feel like we finally have something for everyone in a small bite. You know, we've always had full length workshops. But a small bite to give your teachers, if you're leaders, to give your teachers something to look at, something to hear about these major... I almost said "issues", these major pieces, is super important. You want to talk about leaders, what leaders can do with these two workshops?

Pam  11:50  
Yeah, thanks. So, if you're a leader and you work with teachers, we have full length workshops. And just for comparison sake, those are 18 hours.

Kim  11:59  
Yeah.

Pam  11:59  
They're meant to be sort of a full year experience when you leaders work with teachers. These mini workshops are two-hour experiences, and so it's really an opportunity for teachers to learn the small shifts. And really it's sort of the first small shifts. What are the first things that we can help teachers recognize, so that they can implement, that have the potential to make a huge impact. 

Kim  12:22  
Yeah. 

Pam  12:23  
So, just some small shifts. Leaders, we know that as we try to work with teachers that asking teachers to... In fact, I was given some really strong advice to never say, "Change". I'm doing air quotes here. To not say, "Teachers, we need to change things." But instead, "How can we shift things?" And I know that might sound semantics. But just human nature wise, often it can be easier to think about shifting something we currently do, rather than a wholesale change. And so, what are these small shifts that can make a big impact? Leaders, this can help you know what those are. 

Kim  12:55  
Yeah.

Pam  12:56  
And then it also gives you an opportunity to grab your teachers and enroll them in the workshop and do it with them, and in that, like you said, a small bite-off-able chunk.

Kim  13:04  
I'm glad you said "shift" because I think a lot of the shift happens in your own mind, like your view. Like a little shifting your view. Which doesn't mean run in the next day and just like completely change...

Pam  13:17  
Change everything.

Kim  13:18  
...up your entire class. It's like this is a great way to say, "Let me like maybe think a little harder about what people are saying, so that, you know, maybe I can consider it in a new way, K-12.

Pam  13:32  
Yeah. And when you say a little harder, it's not like we're saying people aren't already thinking hard. We're suggesting that we can shed some light on a way... Yeah, a way to think that sort of help translate. I think there's a lot of good people out there that are suggesting things that, given our background and our experience, we might be like, "I don't even... Like, talk about what in math class." Ooh. Well, we could give you some ideas of why people are pushing discourse, and better wait time, and better questioning if we can make a small shifts. Yeah, go ahead.

Kim  14:05  
And I think sharing with 6-12 what they've probably heard about in K-5 for a while is bridging the gap maybe a little bit to help secondary teachers understand what's been going on and having that conversation, K-12, in a district or in a school, you know in a system, is really going to shed some light across the grade bands and to give them common language to say, "This is what I understand from what I've seen."

Pam  14:34  
You know, and you just reminded me. I've talked to several leaders lately that are in a K-12 position.

Kim  14:40  
Right. 

Pam  14:40  
But their expertise is K-5, or their expertise... You just talked to one yesterday, the expertise is 6-12. And the sort of feeling tone is like, "I don't know what they're doing down there." Or, "I don't know how to talk to them up there."

Kim  14:50  
Right. Yep.

Pam  14:51  
Leaders, this could be a really nice way for you to get a handle on what are the major sort of small shifts that we can make and have that conversation, K-12. So, it could be nice way to sort of support you in maybe the area that has not yet been your expertise. 

Kim  15:07  
Yeah. Yep. 

Pam  15:08  
Cool. To sign up, to register, go to mathisfigureoutable.com/mini-hub. That's mathisfigureoutable.com/mini-hub.

Pam  15:20  
So, we invite you to dive into the version of our Transforming Teaching: Small Shifts, Big Impact in the grade band that's best for you, either K-5 or 6-12, and learn all about small shifts to make math more figure-out-able. Y'all, 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 mathisfigureoutable.com. Let's keep spreading the word that Math is Figure-Out-Able.

Transcribed by https://otter.ai