Ep 211: Making Progress - Building Your Numeracy

What does a landscape look like for teachers trying to develop their skills to facilitate real math? In this episode Pam and Kim discuss one stage of the Success Map. 
Talking Points: 

• Teachers, like students, are in different places in their journey in teaching real math.
• Designing the Success Map was not trivial
• Building your own Numeracy - a starting point
• The Success Map journey is cyclical
• What are the major milestones in develping numeracy?
  • Solving problems using relationships
  • Understanding models versus strategies
  • Owning partners of 10, 100, 1000, and 1
  • Describing mathematical relationships correctly
• Developing Mathematical Reasoning free online workshop is a great place to begin

Check out the free Developing Mathematical Reasoning workshop at mathisfigureoutable.com/freeworkshop 

Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC 

Transcript

Pam  00:00

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

Kim  00:09

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  00:18

We know that algorithms are amazing historic achievements, but they are 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. Ha! I made it. I'm so proud.

Kim  00:35

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

Pam  00:43

And we invite you to join us to make math more figure-out-able. With the longest sentences and intro ever

Kim  00:50

Listen, when you stopped, I was actually thinking in my head, "Oh, man. Like, I haven't laughed like halfway through," but then you made me laugh.

Pam  00:59

Well, good. There you go. Hey, so Kim.  I have been doing some presentations. I've been doing some in person and some virtual. And (unclear) 

Kim  01:02

Everywhere. Yeah. 

Pam  01:03

A lot of places. Yeah. You and I were talking about some things that's happened. I've been in Ohio, and Austin, and Fort Worth, Texas. I've done some virtuals with Singapore, and Australia, and Canada. All around the US. Yeah, it's actually funny. Where was the place? New... New Dublin. It was New Dublin. And I was like, "Man, I'm talking to Ireland!" No, it was like New Dublin, New Jersey. New Dublin, Connecticut. Which, sorry, New Dublin. You guys were fantastic, and I thoroughly enjoyed meeting you. But it was just kind of funny.

Kim  01:39

That's when you know, you have a good team because you get to like show up and you're like, "Who are we talking to today?"

Pam  01:44

Yeah, who's here? Yeah, it was fun. Anyway, it was totally cool. So, it really struck me. I was in Ohio a lot. Go, Ohio. You guys are on fire! And it really struck me that in some ways we work with people, quote, unquote, "all over the map". And I just kind of, you know, mentioned a bunch of places all over the world. But also all over the map in kind of their mathematics education journey. 

Kim  02:08

Yeah. 

Pam  02:10

Particularly, I'm thinking about a specific workshop that I was doing in Ohio. And there were people there. I mean, everybody was fantastic. I had a really good time. There were people there, who were brand new, had never heard of Math is Figure-Out-Able, had never met me. And when I gave them a problem to solve in the middle of a Problem String, they were either doing a you know, just... Well, of course, what you do is you would line these up, and you would do an algorithm. Or they were really trying hard. You know like, there was a lot of effort to like, "Wait, don't do that? Okay." And they were diving in, trying to use what they know to solve problems. And then also there were... This was a specific time in Ohio. There was one of our Journey members who's taken several workshops, who was there in the audience, who has a lot of numeracy and has been doing Problem Strings in her classroom, and has been asking lots of questions in Journey. And then there was everyone in between. You know like, there were these people who were beginning, and there were people who were kind of advanced and expert. And then people who had tried some things. And people who were working on their teacher moves. There was just this vast difference of experience levels. And when I was talking with the leaders who had asked me there. So, I would say there were two leaders that brought me, and one of them was there the first day, and then she was also there the second day. So, I do two... How do I say this? I was there for two days. One day was with high school teachers and one day was middle school teachers. And the one leader was there both days, and the other leader was just there the second day. And so, I was aware that I was repeating several things from day to day because there's several things that I typically do an introductory workshop that are kind of the same. And that the leader who's been with us for a while he's done lots of things, who has a lot of experience was there, you know, both days. And I said something to her the second day. I said, "You know, I hope you're not too bored." And she goes, "Oh, no. Oh, no. I'm learning a lot." And I was reminded of how we at Math is Figure-Out-Able envision working with teachers who are kind of quote unquote "all over the map" in their mathematical journeys, in their experience level. So, today, Kim and I thought we would pull back the curtain a little bit about how we work with teachers who are all over the map in experience levels in the same room at the same time. How do we differentiate learning for teachers as we are Mathematics educators, right? 

Kim  03:08

Right.  Yeah.

Pam  04:55

Yeah. So, we do that in our online workshops, our asynchronous online workshops. We do that in live workshops. As we work with leaders. We do it in our Journey program. Like, in all of these ways, we work with teachers who have varying levels of experience. And today, let's pull back the map... Pull back the map. Pull back the curtain on what we think about differentiating for teachers. 

Kim  05:23

Yeah.

Pam  05:24

Yeah, cool. So, Kim, one of the things that we think about is that as teachers are in... Right now, for some reason I'm back in Ohio. Actually, I may go to the Texas thing that I did recently. So, I was in a workshop in Texas, and we had several people in the room. We had a Journey member. We had a team member. So, Martha was there. Martha's on our team. And then we had people, you know like, brand new. And so, as I started particular Problem String or a task that we did that day, I was very well aware that there will be people in the room who had never sort of thought about solving that problem in any other way than the way that their third grade teacher told them. You know like they were just used to, and that was kind of in their minds was the definition of math. They were going to do that. But I also had people in the room who had done some Problem Strings before, and they were using a strategy. And as I would walk around and look at what they were doing, I would ask questions like, you know like, "What other strategies are there?" There were also people in the room that I was like, "Hey, when people are verbalizing their strategies, how would you represent their thinking? Or maybe, "Pay attention to how I'm representing their thinking." And then I was also aware that one of the things as I was walking around, our Journey member was like, "Oh, I saw that teacher move you just did." Like, she was really focused on the teacher moves that I was making. And at the same time, then our team member said, "Oh, yeah. And I bet you're going to go here next." Like, she was thinking about like sort of the sequence of the day, and like how I was going to kind of advance the math from there. In big ways, participants were able to all dive into the same Problem String, wherever they were and with that experience level and gain more. Either more mathematics. Learn more mathematics for teaching, Learn more mathematics teacher moves. Or really think hard and learn more about sequencing math and advancing the math, moving it forward. So, that's kind of an overview of what we at Math is Figure-Out-Able call our Success Map. Like, how do we help teachers get more success? How can we help them build? Make progress? How can we help them make progress? Well, depending on where they are kind of in this map, then we can help them sort of progress forward. 

Kim  07:46

Yeah. And when we sat down to start talking about this Success Map, we beat it out for a really long time. 

Pam  07:53

Yeah, yeah, this is not trivial.

Kim  07:55

(unclear) work, right, to say what are the major things that we want people to experience? And what are the major kind of... I don't know if I want to say stages, but kind of, you know, where do people progress? And like what are some important things that we need to consider as we create content and as we work with leaders and teachers? How do we acknowledge that there's a journey that people go through and it would be unfair to expect people to all be in the same place? Just like we wouldn't expect them to be at the same place in our classrooms, we want to acknowledge and raise up the idea that people are in different places. But they're all really important places to be and how do we help people progress on their journey? So, acknowledging it, first of all, and kind of identifying what those are. What we've declared that they might be. And how do you know where you are with some different markers or some milestones?

Pam  08:51

Yeah, and honoring that people are in those different places, so that we offer something to everybody when they (unclear).

Kim  08:58

Yeah.

Pam  08:58

Yeah, it's interesting. Oh, go ahead. 

Kim  09:00

No, I was going to say and like you said, sometimes it might be slightly different. But sometimes it's just helping people frame what they're looking for or what they're doing within the content that we share. Because like you said, a Problem String, one of the things that's brilliant about it is that everybody can be engaging in a Problem String with a slightly different lens. And so, we're really helping people to understand what their lens is and how to view the things that they're looking at, so that everyone is growing in an experience.

Pam  09:31

Mmhm. Yeah, what I was going to say is I was just filling out a conference proposal form, a speaker proposal form for a conference. And as I was doing that, one of the things that I had to mark was, was it a beginning session, an intermediate session, or an advance session. I remember thinking, "Ah, yes. All the above. How do I..." And I couldn't. I had to choose. I had to choose one of them. I don't know. I'm sort of curious. What do you think I chose? If you had to guess.

Kim  09:59

Yeah, I don't know. 

Pam  10:03

See! Like, (unclear).

Kim  10:04

Are you going to do a Problem String? 

Pam  10:05

Oh, yeah. Yeah. And I was going to talk about the trap of the traditional algorithms and how we can avoid those traps. That was kind of the main.

Kim  10:12

Oh, I have no idea. What did you pick? 

Pam  10:14

I picked intermediate. 

Kim  10:16

Okay. 

Pam  10:16

I thought that way maybe. Maybe the beginners who, you know, really want to know more would still come and maybe the advanced people would be like, "Oh, no, but this is interesting, so I'll lower myself to go to intermediate. I don't know.

Kim  10:19

Yeah. 

Pam  10:32

I don't think about that. 

Kim  10:32

Yeah, yeah.

Pam  10:34

Yeah. 

Kim  10:34

And you know what? I'm going to poke on just second because you said "lower myself". And I don't think you meant it like less than.

Pam  10:41

No, no.

Kim  10:42

But if you're going to call something intermediate or advanced, I think you're kind of like. Those are weird words. Anyway.

Pam  10:48

They are.

Kim  10:49

But what I really appreciate. And, you know, I'm really proud that we took the time to beat this out for as long as we did. (unclear).

Pam  10:56

Oh, my gosh, and when you say "beat". Like there was blood, I think, a little. Tears. Tears, maybe. A little bit.

Kim  11:02

We leave and come back. Because I think that the kind of the places that we landed on are so important, and so... Like, they're so crucial to understand deeply. And it's not that like one place is better than the other. Like, we're excited for people wherever they are on their journey. But there are some things that we would say, in this moment of your journey, we want you to really focus on this one particular thing. So, that's what we're going to do, right? We're going to lay out over the next couple of weeks. Frustration.

Pam  11:03

Few episodes. 

Kim  11:18

What we think those stages are, so that people can kind of know what to focus on, where they are. So, should we dive in? (unclear).

Pam  11:46

Let's dive in. Let's dive into the first one. Yep.

Kim  11:48

So, the first stage. Can we call them stages? The first... 

Pam  11:52

Sure.

Kim  11:52

Place. The first whatever.

Pam  11:54

You might find yourself. 

Kim  11:56

Yes. So, you might find that you are building your numeracy. And that kind of like the starting point for us is we believe that you joining the Math is Figure-Out-Able movement might be in a place where you are building your numeracy. Or if you're a leader... 

Pam  12:15

Where you're deciding math is actually figure-out-able. What does that mean? Alright, let me dive in and start figuring out math. Yeah, sorry.  Yeah, real quick. And it might be that you are diving into a particular part of math being figure-out-able.

Kim  12:21

Yeah. No, that's okay. And you might be a leader who's working with other people who are diving into math being figure-out-able. And we are thrilled that you're in that place. It's a time of a major perspective shift, right? It's a time... You know, when people come to a workshop, they're like, "Wait, what?!" And, you know, their heads are spinning. But it's a very important shift about mathematics. And it can feel unsettling, but it's often exciting and freeing for the first time ever. You know, when I look at our message boards and in the Facebook group, people are just like, "I have never thought this way before." And they're diving in and they're excited because maybe for the first time ever, math makes sense. And they're like, "I don't know what it used to be. Why was that hard? But I'm seeing it for the first time ever in the way that it is very real." So, we've highlighted some major milestones. Go ahead (unclear). Yeah, mmhm.

Pam  13:13

So, you might be like, "Well, I've always thought about, you know, addition, subtraction, multiplication, division. Those were... Oh, but middle school math? But wait, proportions are figure-out-able? Like, wait, high school math is... What?! It's all figure-out-able. 

Kim  13:36

Yeah.

Pam  13:36

Yeah. 

Kim  13:37

I'm glad you said that because it's not just like all math, right? And sometimes... We'll get to the point where we talking about this later. But you might be really working on multiplication. And you might progress through some places on your journey about multiplication. But then you got to cycle back and be like, "Wait, now, my kids have gotten older. I got to do more work to support them in high school. So, yeah. (unclear).

Pam  14:02

So, we actually see this as a cyclical process. 

Kim  14:05

Yeah. 

Pam  14:05

And so, you might be in this place where you're like, "Whoa, this particular area of mathematics is figure-out-able?! Bam, I'm diving in, and I'm figuring it out." Yeah, that's a great place to be. So, those major milestones you mentioned. (unclear).

Kim  14:16

Yeah. Okay, so one major milestone is that you are solving problems using relationships. So, no longer with a rote memorized algorithm, with lots of non transparent steps, but you are diving in and solving problems using what you know. 

Pam  14:32

Yep.

Kim  14:33

Another major milestone is that you are describing the difference between models and strategies. Which we know people conflate all the time. And there's lots of...

Pam  14:44

Super confusing. 

Kim  14:45

Yeah, work out there about trying to figure out the difference between the two and which is more important. We also believe that a major milestone at this stage is owning your partners of 10 100, 1,000, 1. So, we've got some... You know, we got some routines about that.

Pam  15:02

Mmhm. 

Kim  15:03

And we also know that a major milestone at this place is describing mathematical relationships correctly.

Pam  15:09

What do you mean by that, Kim?

Kim  15:11

So, you know, there's a lot of maybe lazy or incorrect language about mathematics. So, this is clarifying what you mean. This is maybe owning some properties and making sense of mathematics for the first time ever.

Pam  15:27

So, it could be if you were diving into this stage, making fractions figure-out-able, it might be that when you see the fraction three-fourths that you know that that's three 1/4s, and you don't say it's 3 "over" 4.

Kim  15:39

Right.

Pam  15:39

That would be describing mathematical relationships correctly. 

Kim  15:42

Right. 

Pam  15:42

Yeah, cool. 

Kim  15:43

So, this stage is all about building mathematics.

Pam  15:47

Your own.

Kim  15:47

In a reasonable, sensemaking way. Right. So, if you're a leader who's working with teachers at this stage, we would like to encourage you to encourage them and grow alongside them. Have teachers grow alongside their students, and you grow alongside them. Your teachers can be thinking aloud and looking towards numbers, rather than diving into algorithms. This is not a stage where you have to know everything before you can do anything with students. But you're encouraging them, and they're encouraging their students. And as a leader, we would expect that you would provide teachers opportunities for them to talk to each other to hear what others are doing so they can learn together.

Pam  15:49

Yeah.  Yeah, totally. Yep. I love it. And sometimes, we describe this stage as we can tell light bulbs are going off. 

Kim  16:35

Oh, yeah. 

Pam  16:38

We hear people say, "Man, I have a fresh perspective on math! I'm excited! I'm feeling energized and inspired!" And it's really this kind of like. It's almost like this area of mathematics is sort of new and, "Whoa, like I can? I can! It's almost like you want us to use what we know to solve the problem." 

Kim  16:56

Yeah, we were on a trip not too long ago, my husband and I. Just a quick thing. And I was looking at the message boards on the car ride on the way home, and I read several comments to him. And I said, "This is like super exciting to me," because I was just reading comment after comment from people taking workshops, who were like, "I never knew math was like this before." And he was just like, wowed by like people are saying that. And I was like, "Yeah, there's more than you realize."

Pam  17:23

So fulfilling. Yeah, cool. Alright, so some things that you could do if you find yourself thinking, "Yeah, I'm really thinking hard about this area of math," or, "I want to dive into this particular area of math and really figure it out," then you might play I Have, You Need to earn to... Earn? Earn? What's the word I'm looking for? Learn? Own. Learn and own at the same time. Learn and own at the same time. The partners have 10, 100, and 1000. So, play I have you need. You might join in MathStratChat on Wednesday evenings and check out how people from around the world are solving the problems,. Check out our short podcast episodes where we talk about those. Solve problems using what you know. When you find a problem, stop yourself from instantly lining up the numbers or whatever the typical steps are that you would solve that problem, kind of take a breath and think to yourself what do I know about this problem? What do I know about what's happening here? And can I reason using what I know? You might also double numbers. Just, you know like, when you're walking down the street, or driving in the car, or going on the subway. Wherever you are, you might just like throw out a number, and just double it. Just play with doubles. Play with halves. Mathy people sort of own doubles and halves. And take our Developing Mathematical Reasoning free online workshop. It is a fantastic opportunity. In fact, Kim. Where was I? I don't know, One of the trips that I just took. Somebody pulled me aside during break. You know, kind of one of those times where I'm like headed to the bathroom, and they're like, "Can I see a question?" I'm like, "In a minute." No, they were very polite. And they said, "Hey, you're free workshop. How long is it going to be free? And I was like, "What do you mean?" And they're like, "Well, it's free. You know like, are you going to turn it into a paid workshop at some point?" And I smiled, and I was like, "I don't know. So, take it now. Like, maybe." We've talked a little bit about how long we're going to keep it free. For now, it is free. I'm saying that on a podcast, so I don't know when you're listening to it. Check it out. See if it's still free. You can sign up for that free Math is Figure-Out-Able workshop. It's called Developing Mathematical Reasoning at mathisfigureoutable.com/freeworkshop. Ha! That makes sense, doesn't it? So, mathisfigureoutable.com/freeworkshop. And that would be a great place for you to build some of your own mathematics. Hey, I'm going to throw one in there too. We also have on Facebook the free... Oh, yeah. 

Kim  19:03

I wanted to say "free" too. So, the teacher math is Figure-Out-Able teacher Facebook Group is a great place to join because there's a lot of other people there who are building their numeracy. And sometimes I'll throw out a problem. Or somebody else will say, "Hey, I ran across this. How would you solve it?" And so, there's a lot of great chatter there as well for other people building their numeracy. 

Pam  19:59

Alright, So if you find yourself in this stage with a particular kind of mathematics, we invite you to dive in and make that area figure-out-able. Ya'll, thanks for tuning in, teaching more and more real math. To find out more about the Math is Figure-Out-Able movement, visit mathisfigureoutable.com. And check out next week's episode for the next stage. Let's keep spreading the word that Math is Figure-Out-Able!