Pam  00:00

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

Kim  00:06

And I'm Kim. 

Pam  00:07

And you're in a place where math is not about memorizing and mimicking, where you're waiting to be told or shown what to do. But we believe it's about making sense of problems, noticing patterns, reasoning using mathematical relationships. Because we can mentor students to think and reason like mathematicians. Not only are algorithms not particularly helpful in teaching mathematics, but when we just have students rotely repeat steps, that can keep them from being the mathematicians they can be. 

Kim  00:35

Hello. 

Pam  00:36

Hey, Kim, what's up?

Kim  00:38

I feel like the last three weeks we've been talking about how busy we are.

Pam  00:42

Because we are jamming out those Problem String books! Whoo!

Kim  00:45

I know. And so many other things. Like, I'm loving it. I'm loving what we're doing. Okay, so I grabbed a review for us today, but I got to tell you.

Pam  00:51

Yeah.

Kim  00:53

Steven, the Wildcat Professor, WildcatProf. Thank you, for putting your name at the end because the name that... W116SCH? I want to know what that is. Or if it's just like autogenerated. Anyway.

Pam  01:11

Right, right, right, right. 

Kim  01:11

Steven says, "This is a must for elementary math teachers." I agree. "With experience as an administrator, coordinator, and now back in the classroom..." That's fun. "...this podcast has taught me more than I've ever learned in my college math methods course. Yes, one course. I love it. Well done, ladies."

Pam  01:30

Aww.

Kim  01:30

Well, thanks for that.

Pam  01:31

Thanks, WildcatProf. Thanks for that. Nice.

Kim  01:34

You know, sometimes I think back on my classes. And I actually don't think that my one math class was bad. Like, I think we had a great textbook, and we did some really cool things. Of course, not what's happening here. But I am a little jealous for your students. Your college students.

Pam  01:52

Yeah, I was going to say my Math Methods course is pretty good.

Kim  01:55

I mean, that's pretty fantastic. I'm so excited for those people who are leaving college with a kind of a new.

Pam  02:02

It is so much fun to go to conferences and have an adult come up to me and say, "I was in your university Math Methods course, and this is what I've done with it." And it's just amazing.

Kim  02:16

That's fun.

Pam  02:16

Yeah, it's really cool. Really cool.

Kim  02:18

Well, thanks Steven. (unclear). 

Pam  02:19

Yeah, cool. Hey, and, Kim, one of my favorite things about the university is that it's different than what I did for quite a while. For quite a while when my kids were certain age, I did a lot of travel. I did a lot one and done workshops, you know where I would just go, I would do the thing, and then I leave. I was super excited once I wrote the Building Powerful Numeracy books because then I could at least talk slower during that one and done (unclear) the book. I didn't feel like I had to give everything I ever knew in that one time.

Kim  02:46

Yeah.

Pam  02:47

You and I were writing together, and we were creating lessons and stuff. But I really loved it when I started teaching at the university because I began to be able to create longer relationships. 

Kim  02:56

Yeah. 

Pam  02:57

Oh, you know, I had a whole semester. And I could have students... I could see their growth. And, you know, like we created a relationship. I would have students walk me to my car at the end of class. You know, it was just... We'd continue to talk math, and teaching, and everything. And so, it's been really fun now to have that need also met in our Journey group. 

Kim  03:19

Yeah. Yeah, I don't mind, you know, going to a conference. But I'm not... That's not really my jam as much. I don't love a one and done type thing. And I think maybe that's why I love coaching because it's like a long term relationship, and I want to see what happens with these teachers and the coaches kind of implement change. And I'm super invested in that. And, you know, I love that you will go do national conferences, and I get to do stuff with Journey and JourneyLEADERs. It's just my favorite. Like, it's what I love. 

Pam  03:44

Yeah, it's nice. At one point, you and I did a coaching gig together. Yeah. There's a small independent school near us that wanted some professional learning and some coaching, and so the two of us, we co-presented together, and then you coached some of the teachers and I coached. You coached most of them, and I coached some of the teachers. And in that, it was interesting because part of what we did with that school was create. Well, we really grappled with creating a shared vision. 

Kim  04:27

Yeah. 

Pam  04:28

And we kind of wish in hindsight that we'd had a resource that we're going to share today to help co-create that. We wished that we had that. I think it would have been helpful. 

Kim  04:39

Yeah. 

Pam  04:40

So, last week, Kim, in the podcast, we talked about a Look For for Students, for student mathematics, that was created by New York City public schools by a very thoughtful group of people. And they created more than just that Look For's. I can't even remember what it's called. Look For's for Students. Is that what it is?

Kim  04:58

Mmhm.

Pam  04:58

They also created two other documents. One of which we'd like to talk about today. 

Kim  05:02

Yeah. 

Pam  05:03

So, (unclear).

Kim  05:04

So, we did student learning, and we talked about careful planning, and how it's really impactful. And even if it's just for one lesson on occasion, it can really help you create a habit of thinking and about important moves that you need to make. So, today, we're going to focus on the teacher version and get a little deeper on that because the original first one that we talked about was really teachers thinking about their students. And today is (unclear) 

Pam  05:31

(unclear). Yeah, to what extent students are doing things.

Kim  05:35

Yeah.

Pam  05:35

And today is more about... Did you say lesson design?

Kim  05:38

Yeah, it's about supporting conversations, maybe between coaches and teachers.

Pam  05:43

Ah, nice. So, it's definitely for teachers because it's supporting lesson design. But it could encourage a conversation between coaches and teachers. 

Both Pam and Kim  05:53

Yeah.

Pam  05:54

Nice. 

Kim  05:54

Which, could sometimes feel like it's from the coaches to the teachers. But I do love a good teacher who pushes on their coach and says, "Hey, this is what I want and need. And here's how you can support me."

Pam  05:55

Absolutely. 

Kim  05:55

Maybe I was that pushy teacher? It's not pushy. It's knowing what's helpful for you.

Pam  06:11

And advocating for yourself.

Kim  06:13

Yeah, absolutely.

Pam  06:13

Which is super, super important. 

Kim  06:15

Yeah. So, often, teachers will be interested in a model lesson, and they'll say like, "Hey, if I could just see what that might look like, then I'll be able to do the thing that you're suggesting." And there might be some value in that. I mean, sometimes we just want to see. It's easier to see than just like hear the words being talked about and like describe it. So, there's some value in that. But how many times have people seen you do a Problem String, they participate in a workshop or in a conference, and then when it comes time for them to turn around, they just (unclear) Because they're like, "Wait, that didn't go the way it went for you. Like, how did that happen? I don't know how to make that happen." And I think really, it's because they weren't aware of the kind of background planning, and the choices that you make, and the teacher moves that you make. It just feels like, you know, a list of problems. And "Surely, I can turn that around." But there's so much planning that goes into each of the things that we do, and if you're not aware, then you go give it a try, and you're like, "Oh, that did not happen like Pam did." 

Pam  07:25

Yeah, and when you say "so much planning", I don't want to give listeners the false impression that if you don't have a year and a half to plan for the next Problem String you do, then it's going to fail and be horrible. I mean, we do want you to dive in and try stuff. 

Kim  07:41

Mmhm.

Pam  07:42

I think maybe I would say yes, yes, so much planning, but that there are a few important things that really can help things get better. And so, one of the most important things that we do like in our Journey group is when we show a video of a Problem String with real kids not fake kids, that we then call out what made that go really well. We call out those few important things, and we discuss those and we make sure that that's sort of evident. We have that as part of the... Part of the experience isn't just watching. Part of the experience is the making those things visible.  I think the thing we're going to talk about today can help call those things out, can help you to say, "These are some of the things that you want to be thinking about to help make lessons snap, to help them really have mathing happening, not just memorizing and mimicking and..."

Kim  08:19

Yep. And I'm glad you mentioned that because never doing anything because you think you need to have it planned perfectly means nothing's going to ever happen. And so, you know, we learn by doing. And so, if you say, "Oh, you know, I saw that Problem String, and I'm going to go dive in. I'm going to do it," and it didn't go the way that you anticipated that it would go, then you're questioning why, and you're kind of trying to figure that out. And that is the learning opportunity. So, if you just sit back, and you don't do anything, and, you know, you're in analysis paralysis, then yeah. That's not helpful either.

Pam  09:12

Yeah, so teachers, I invite you to invest here today because this document that we're going to describe a little bit could help you plan and measure your current teaching up against a description of a possible.

Kim  09:26

Mmhm. 

Pam  09:27

And so, yeah, let's do some of that. So, if I can describe this document a little bit. It's called Look For's for Teacher Practice in Mathematics. And it has four sections. Go ahead.

Kim  09:38

Last week's Look For was really built to be a conversation between a teacher and themselves. It was really about what questions can you ask yourself about what your students are doing. And this one is meant to be a conversation between the teacher and the coach.

Pam  09:53

Or maybe a shoulder partner if you don't have a coach, but yeah, yes. So, those four sections are split up into... One of them is... Actually, let me read the first sentence. This classroom Look for tool can support conversations about the lesson design, teacher practices, and classroom culture for mathematics." So, there's kind of the setup, nice setup. Then, there's these four areas. One of them is "Tasks and Problems". One of them is "Mathematical Discourse". Third one is "Engage All Students in Productive Struggle About Mathematical Ideas". And the last one is "Assessment and Checking for Student Understanding". So, the first thing I want to say is, I appreciate the fact that the titles of those, they kind of used a buzzword, and then kind of use not buzzwords. Which I thought was helpful because they could have just for the last one said, "Assessment". But they mean, "and Checking for Student Understanding" because you could hear assessment and just think summative, you know like, the end of the course, or the end of the unit, or whatever. But they really want to talk about checking for student understanding. Another example is Tasks and Problems. I think sometimes we just say "Tasks", sometimes we just say "Problems". Let's talk about the stuff that's going on, you know the kind of activities kids are doing. Anyway, so those are the kinds of the four areas. In each of the areas, they have two columns. One column is indicators. And the other column are questions that are conversation starters. So, especially useful for a coach to say, "Hey, if I'm thinking about this particular category, and I'm looking at these indicators, I could start the conversation about this with these conversation starting questions. To do that, we're going to kind of do what we did last week, which is Kim and I both chose a favorite and instead of reading them all, we're going to kind of look at a favorite, and then kind of share how it's sort of built in these indicators and conversation starters. Yeah. Anything else, Kim, to overall before we talk about a favorite?

Kim  11:55

No. Maybe I zoned out. Sorry. The conversation starters, I think, is really important. Did you mention that? Like, I'm intrigued by the idea of conversation starters because it's not a judgment, and it's not like, you know...

Pam  12:13

Pass or fail.

Kim  12:14

Force something on the teachers. It really is, like, "Here's a good thing for you guys to have a conversation about to get a little deeper into what the indicator is.

Pam  12:25

And coaches, we would highly recommend that it's a conversation, it's not a "I'm shaming you by, you know, pointing out what you didn't do or did do or whatever." I think thoughtful adults can have conversations to get at the root of what they believe and they think, so that then it can transfer into their process, progress, pro... There's another word I want. Pro, pro, pro.

Kim  12:51

Yeah, I don't know. 

Pam  12:54

Transfer into what they do. 

Kim  12:56

Yeah. 

Pam  12:56

Okay.

Kim  12:57

I think in general in life, I like to listen a bunch. And I can tell when I'm super excited about something because I find myself talking more than less. And, you know, I really ask questions kind of in my life to hear what the other person's thinking. But I can tell in a conversation like this, I want to like dump knowledge, more than I...

Pam  13:21

You have a tendency to.

Kim  13:23

I do, I do, I do. Because I get excited when I'm having a conversation about something that, you know, I feel like I have some things to share. And so, you know, maybe a coaching thing is if you're talking more, and your teacher is talking less, what can you do to flip that? Because maybe they're processing while they're talking as well? Can I go first? Can I share one that I...

Pam  13:45

Yep, go ahead.

Kim  13:45

...that I found. Okay, so under the Assessment and Checking for Student Understanding that pings for me. Assessments, tough. I think we assess a lot. But I don't think all assessment is bad. What I think we assess a lot is like a paper and pencil, sit quiet at your desk, like do the things (unclear)analyze data. And there is room for...

Pam  14:07

There's a place (unclear)

Kim  14:07

...something like that. Yeah. But the one I love...

Pam  14:11

But maybe quit doing it so...

Kim  14:12

Oh, I mean.

Pam  14:13

Some of the schools our kids have gone to assess too often, too much. 

Kim  14:17

It's a lot. it's a lot. But I think assessment is crucial.

Pam  14:20

(unclear) in that way. I should have said assess in that way. 

Kim  14:23

way. I think assessment is crucial, and I think it should be often. But here's an assessment that I love that's an indicator. "In what ways does the teacher make in the moment decisions on how to respond to students with prompts that probe, scaffold, and extend?" Like, that is a true measure of a teacher assessing what's going on, assessing the conversation, assessing what students maybe know or don't know yet based on what they're hearing back from their kids. And this is like so important to me. I can remember being in a secondary classroom. And I was kind of helping to facilitate a student investigation, so that there could be a congress the next day. And the teacher called me over, and she was like, "Uh, like, I don't..." She's like, "Can you talk to them?" And I knelt down next to the kids, and I said something like, "Hey, will you tell me what you're thinking?" And she kind of stood back kind of eyeballing the class, but also listening. Which I think is really sharp on her part because it wasn't like, "I'm going to just... You deal with them. I'm going to walk away." She was really a student and a learner. And so, she called me over, and I knelt down, and I started talking to them. And, you know, I kind of picked into what they were doing and like nudged them, and off they went. And the first thing she said to me when I stood up was, "I don't know how to make that happen. Like, how did you even know what to ask them?" And I think it has everything to do with, you know, we talk about it over and over again, knowing your content, so that when you have conversations with students, you can very much do this making in the moment decisions about how to respond. In that

Pam  16:01

How to probe. How to scaffold. How to extend.

Kim  16:04

Mmhm.

Pam  16:04

Because you know the content, mmhm. 

Kim  16:06

Yeah, so...

Pam  16:07

Which is kind of you... I hear you saying, "Getting to know the kids."

Kim  16:11

Yeah.

Pam  16:11

You're there getting to know the kids. And then, as you're getting to know them, you're making those moment to moment decisions, because you know your content. Know your kids, know your content.  Yeah, you just stole the one I was going to share? 

Kim  16:20

Well, and also, we talked about this in a podcast episode. I don't know which one. But we talked about knowing your beliefs. It was very early on. Talking about cementing in yourself and in your teaching what you believe to be true about the way that you teach and about what you think about kids. Because it's not just like, "Do you know your mathematical content?" Do you believe kids can? Do you believe that it's worth the time? All the things that you know to be true for you as a teacher. And that's not for us to decide for you. But have you made those decisions and solidified those beliefs, so that you don't sway in the moment, so that you don't go, "Ugh, I got to change this right now for this thing." So, all of those in the moment decisions are based on your beliefs and about the content that you know. And I think that's worth having a conversation with people about. Like, can you make in the moment decisions? And then, what changes did you make in your lesson today? And what prompted those changes? Is one of the conversation starters. Oh, I'm sorry! (unclear).

Pam  16:25

That's okay. Well, so let me add on to that. Okay. The conversation starter. So, you read an indicator? "In what ways does the teacher make in the moment decisions on how to respond to students with prompts that probe, scaffold, and extend?" Yeah. And in the other column are a couple of conversation starters, one of which is, "What changes did you make in your lesson today?"

Kim  17:37

Yeah.

Pam  17:38

"What prompted these changes?" And what I thought about when I read those was the work of Deborah Ball at the University of Michigan recently where she talks about discretionary spaces. 

Kim  17:50

Yeah. 

Pam  17:50

And that the teacher has many discretionary spaces that are those in the moment decisions that you make. And I think that we add to that conversation is we need to have... How do I say this? We need to work with others to ferret out and uncover what is our underlying philosophy about teaching and learning? So, that then in those moment to moment decisions, we make them based on that. If we don't, like you were saying, if we don't know what we believe about teaching and learning, then we're probably going to make decisions based on our prior experience, the way that we were taught. Because that's kind of all we have to base it on. And so, one of the things we're trying to do in this podcast, and in our Journey, and in our online workshops, and all the work that we do is help people clearly see what their perspective was, so that then they can choose what perspective they want, and then make changes based on that. So, I think it's a brilliant conversation starter to say, "What changes did you make in your lesson today? And what prompted those changes? that as a way to say, "How were you assessing?" If you made a change, you were assessing. Something happened in your formative assessment to say, "Ooh, I need to shift here." And let's talk about that. Let's point it out. Let's discuss are you glad that you did that? You know, because it was based on blank, What would you want to do in the future? I think it's a great question for all of us to be able to think about as we improve our craft.

Both Pam and Kim  19:23

Yeah.

Pam  19:24

Absolutely.

Kim  19:24

And changes, you know, might be uncomfortable from time to time, but they're not bad. Like I think if we're not making changes along the way, then we're not really meeting the needs that arise as they come. So, you know, we might have a plan, and it might go pretty close to plan, but there will be some shucking and jiving that has to happen along the way. And you might have the same outcome that you hope to have, but.

Pam  19:49

But because you adapted to the students as you went, you were able to focus the lesson in the way that it could go. Not that it didn't matter what kids were doing. This is the worksheet at the end of the day, and I can pull out my entire quarter of worksheets that, you know like, when you print them off. Here they are. They're in this folder. That's not what we would call responsive teacher.

Kim  20:12

Yeah. For sure. Hey, I'm going to mention one more because I still think that there's time in the year to address this. Back in January in the teacher Facebook group. Which people should be in. Why are you not in the Facebook group, people? Join the Facebook group.

Both Pam and Kim  20:13

Yeah.

Pam  20:26

(unclear) The Math is Figure-Out-Able teacher Facebook group. It's a great place. Lots of good stuff going on.

Kim  20:30

Yeah. So, the question right below the one that I stole from you. And I'm really sorry about that. It says, "What might we try to surface student thinking, especially the thinking of students whose ideas we don't know much about yet?" And so, in January, I shared a prompt in that group that, that is a time for me to say like, "Who do I not know enough about yet?" And I literally would sit down mid-semester or whatever and make a make a list of who do I not know enough about yet personally, about their mathematical journey. And I would keep that index card or post-it note in my desk, so that when I opened it. I had a desk, for whatever reason. And I would pull it open, and I would see names. Like, specific names of kids that I would say, "I don't know enough about them yet." And, you know, sometimes the list was longer than maybe it should have been, but it was a reminder to me. So, if even at this time of the year, if there are kids whose thinking you don't know much about yet, it's not too late to make that be a goal.

Pam  21:35

Mmhm. Yeah, nice. Nice. Alright, my turn. I'm going to share one.

Kim  21:39

Okay. 

Pam  21:40

So, one of the things I really liked was in the section Engage All Students in Productive Struggle About Mathematical Ideas. And it's a conversation starter, so it's in the right column. And it said, "When students struggle, what do or what could you do..." So what do you do? Or what could you do? "...to maintain students opportunities to develop their own ideas and understandings?"  I thought that was a nice way. We've worked with a lot of teachers who... And I understand this. If you've never experienced real math teaching, like teaching real math, getting kids to really math, you could hear "productive struggle" as sort of your job is to kind of be a cheerleader. You know like, "Keep going! You can do it! Nope, not right yet! Guess again!" Versus, when students are struggling, what do you do? Or what could you do? And then, this is so important. Not to get them to get the answer right. Not so that you can move on, and they're satisfied. But what can you do to maintain students opportunities to develop? I really like that. Develop is so important. If we're developing, we're growing, and learning, and becoming. We're gaining capacity. We're getting stronger. All of those things are different than memorize the procedure differently, or you know, get the step right, or whatever. And I've been guilty of it, that in that moment to moment decision making when students are struggling. Teachers are struggling in PD, where I've had the inclination to go, "Yes." You know, just to answer their question. "No." You know or, "5." Whatever. Instead of maintaining the opportunities for them to develop. 

Kim  22:02

Yeah. Yeah. 

Pam  23:22

And I don't think that's trivial. It's so not trivial. I think, boy we can, as a professional group of learners, we could really help each other out there.

Kim  23:30

I think it matches what you say at the intro, that we're mentoring students. And I think it matches really well that we're mentoring students and teachers, so that they can develop. It's kind of our role. Yeah.

Pam  23:43

Yeah, cool. So, much of this discussion is about creating a shared vision. When we hand you these documents. This is a shared vision that the leaders in New York City public schools have created. We've also done some work, Kim and I, when we create this podcast. We've created a shared vision about what this podcast is done. We have continual implementation support group called Journey, in that we've created a shared vision of what it looks like to be successful on that journey. We call it a Success Map. Shared visions are so helpful and important. If you can find... Ya'll, if you can't find one we mentioned earlier, join our teacher Facebook group. If you can, join our Journey group where we are like-minded teachers and leaders, working together, helping each other build a shared vision. So helpful and important. 

Kim  23:44

Yeah. Hey, where can people find this teacher one? 

Pam  24:40

Yeah. So, again, crazy link. We're going to put the link in the show notes. So, if you've never gone to show notes before, just get into wherever you listen to podcasts and look down. They'll have a paragraph about the particular episode, and then there'll be a link in there, where you click on that link, and you can download it.

Kim  24:59

And while you're downloading, leave us a note.

Pam  25:01

Oh yeah. And then, give us a rating, gives us review. That would be fantastic. We'll probably also put a blog out somewhere around this time that will have all the links in there too. If you haven't checked out blogs yet, yeah, check out our blogs. And, ya'll, 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. And thank you for spreading the word that Math is Figure-Out-Able!