Pam  00:01

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

Kim  00:07

And I'm Kim. 

Pam  00:08

And you found a place where math is not about memorizing and mimicking, where you're 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 students to think and reason like mathematicians. Not only are algorithms not particularly helpful in teaching mathematics. You're like nodding along. But rotely repeating steps actually keeps students from being the mathematicians they can be. Do you do that when we normally record?

Kim  00:36

I know. I was going to say, should we just tell everybody right now that we are not in the same room when we record. Is that a thing? 

Pam  00:42

Normally we're not, but today we are.

Kim  00:43

Today we are.

Pam  00:43

So, today, we can see each other, and it's actually a little bit disconcerting because it's like. 

Kim  00:46

Because we are at NCTM today. It's super, super exciting. 

Pam  00:49

Woo-hoo! NCTM!  NCTM International in Washington, DC. And it has been fantastic. 

Kim  00:54

Yeah, it's been super fun. Except for I'm tired.

Pam  00:56

Yeah, well because you don't sleep. 

Kim  00:58

It's been fun. Pam just finished her session. It was fantastic. Super fun. Always great. 

Pam  01:04

We have been doing so many things. And the kind of finale today was to do a session. Yeah, it was great. We had a full room. Cathy Fosnot showed up, which was unbelievable. I'm super honored that she would come. And I had a brief conversation with her at the end, and she was grateful that I acknowledged her. Which is sort of important, right? It's actually really important to you. 

Kim  01:23

Yeah, it drives me a little bit batty when people don't acknowledge each other's work, so. (unclear)

Pam  01:30

(unclear) Well, I'm trying. I have not always. I'm trying to do better job. 

Kim  01:32

It's fantastic. 

Pam  01:33

You help me with that. 

Kim  01:34

Great.

Pam  01:34

It's nice. 

Kim  01:35

Okay, well, it's weird to see your face, while we're talking, but I enjoy being with you. 

Pam  01:38

And we're Kind of like hovering over this microphone, and that's equally disconcerting. Speaking of disconcerting things. So, you lost your glasses yesterday. 

Kim  01:46

Ya'll, so I have old eyes now, and I... 

Pam  01:50

Even though you're not old. 

Kim  01:51

I mean, I'm getting there.

Pam  01:52

Because you're younger than me, so you can't be old. 

Kim  01:54

Oh, okay, maybe. 

Pam  01:54

That's not a thing. 

Kim  01:55

Well, so I do have contacts, and they're multifocal contacts. You would not think this is a problem, but I am wearing readers as well. If you see me in person, and I'm on my computer, I'm obviously wearing readers. And, yesterday... I don't know. Like at the end of the day, I was like, "Pam, I can't find my readers." And (unclear).

Pam  02:11

So, we looked, right? You looked through all your stuff. All the things. 

Kim  02:12

We looked everywhere. Looked through my stuff. We went to dinner. Our friend Danica took us to CVS, so I could buy some some good readers.

Pam  02:19

Like, we had to go out of the way to find a cute little drugstore to find readers. 

Kim  02:22

Very expensive readers. (unclear).

Pam  02:23

Very expensive. Holy cow, expensive. Who had Christmas stuff up? What is that? 

Kim  02:27

It's October. 

Pam  02:28

It's October.

Kim  02:29

Anywho. 

Pam  02:30

Okay, so...

Kim  02:30

November? I don't even know what month this is yet.

Pam  02:32

No, it's October. Oh, this is going to drop in November. 

Kim  02:35

Anyway.

Pam  02:35

it's October 31 today.

Kim  02:37

No. No it's not.

Pam  02:37

People are wearing Halloween stuff. It is. I don't know where I am.

Kim  02:41

Anywho. (unclear).

Pam  02:42

What is today? Oh, my gosh.  Why do I think today is Halloween? 

Kim  02:46

Okay.  I don't know. It's not.

Pam  02:48

I thought today was Halloween. I don't know. 

Kim  02:50

The point is, we got back to the hotel, and we started unpacking your stuff, and I look over at Pam, and Pam is holding my old readers in her hand. 

Pam  02:59

Kim, why were your readers in my bag? 

Kim  03:01

I have no idea.

Pam  03:02

I want to know. So, now, you have a very expensive but cute looking. 

Kim  03:05

I mean, they're just... Yeah. 

Pam  03:06

Wait, are those the ones you bought last night? 

Kim  03:07

Yeah, they are. Anywho. And also speaking of losing things.

Pam  03:11

I thought your other ones were cuter. 

Kim  03:13

Well, I have them both now.

Pam  03:14

Whoa!

Kim  03:15

This morning. 

Pam  03:16

Oh, gosh. So, we're sitting at breakfast this morning with another Kim. Which that was a fun breakfast. Thanks, Kim. Other Kim. And I couldn't find my morning meds. I'm older than you are, and so I take drugs... Meds. Meds in the morning. I say drugs, and my kids get mad. They're like, "Mom, don't say drugs! Say meds!"

Kim  03:34

Oh, this... I went to a session. I'm going to skip ahead for just a second, and then I'll come back to your story. 

Pam  03:38

(unclear). You just almost poked me with that pencil. 

Kim  03:40

It's sharp. 

Pam  03:40

It is a sharp. Oh, my gosh. 

Kim  03:41

I'll tell you why it's sharp in just second. Oh, so many stories. So many stories.

Pam  03:44

All the stories. 

Kim  03:44

But I went to a session... Oh, forgive me. Speaking of who needs to credit who. 

Pam  03:48

Credit. Credit. Credit. Credit. Do it. Do it. Do it. Do it. 

Kim  03:51

Liesl. Liesl. 

Pam  03:52

Liesl! I know her last name.

Kim  03:54

I can't say her last name. 

Pam  03:55

Yeah, yeah, yeah.

Kim  03:55

Anyway.

Pam  03:56

It will come to me. Liesl. 

Kim  03:57

She had a fantastic session, and she said...

Pam  04:01

McConchie? 

Kim  04:01

Yes. Yes.

Pam  04:02

Liesl McConchie. Liesl, you did a great job. Even though I wasn't there. Kim was impressed, which is hard to do. 

Kim  04:06

(unclear). It was fantastic. 

Pam  04:08

Okay.

Kim  04:08

And she said, "I want you to be a drug dealer for your kids. Deal out that dopamine because they need that every day, and you can be their biggest supporter." And I just love that. So, you can say "drugs" if you want. 

Pam  04:18

Okay. It's because Liesl does, and we like you. At least what you did yesterday. What was I going to say? Oh my meds. 

Kim  04:25

You lost your meds. 

Pam  04:25

So, this morning. So, I have this backpack. And I'm actually kind of excited that it's fraying a little bit because I've had it forever. And it's been... You know, I like to buy quality because then it lasts. But sometimes things last longer than you wish they would. I've been wanting a new backpack for a while, and it's fraying just enough that I was like, "Sweet! I can get a new one!" But the good part about the fact that I've had it for a while is I know where everything is. It has so many pockets. I love pockets because I can just put things where they belong. People are probably like, "Is this the Math is Figure-Out-Able podcast?" We're getting there. We'll do a little bit of math in just a minute.

Kim  04:56

We're tired.

Pam  04:57

We are tired. So, I couldn't find my meds. And I look through everything. And you guys were like, "Do you want to dump everything out on the table?" I was like, "No, don't dump. Don't dump on the table because I don't even know what all is in my backpack." But it's like a container, so I would have... You know, it's big enough. Anyway. So, I finally gave up, and I'm like,(unclear) go to the room and get tomorrow's meds. Well, no. Go to my suitcase because we already checked out. It's a mess. And so, I reach into the pocket of my jacket. And oh, there they are. So, that was a moment where we're like, "We're tired." 

Kim  05:23

Yeah. Loosing things.

Pam  05:25

Because this is when Kim and Pam go to a conference together. We just talk all the time about all the things we're learning. And we still haven't... I don't even think we started the list of things we brought to talk about. Have we? 

Kim  05:34

No. No work from back home has been done. Sorry team. 

Pam  05:38

Yet. 

Kim  05:38

Sorry. 

Pam  05:38

Yet. 

Kim  05:39

Sorry about that teammates. 

Pam  05:39

Yeah. Hey, why is your pencil sharpened? 

Kim  05:41

Oh, because I was getting ready the morning it was time to leave, and my husband said, "Is there anything I can do to help you?" And I said, "No, I've got it covered." And then I said, "Oh, wait. Wait, wait, wait. I need pencils, and I need a lot of them, and they have to be sharp, so will you please go sharpen like a dozen pencils for me?" And he said, "Do you want a..." No, stop with the pen.

Pam  06:00

I'm holding a pen. 

Kim  06:01

He said, "Do you..." Oh, okay. Hang on. He said, "Do you want a pencil sharpener?" And I said yes. And he went out to a shop and he got me a wood sharp pencil, but it doesn't have a cap. And I was like, "Am I supposed to like sharpen the frayings or the shavings on the table?" 

Pam  06:14

Like, on the seat in the conference room that you're in?

Kim  06:16

He was like, "Go to a trash can, man. What's wrong with you?" Do you know that (unclear).

Pam  06:20

Has he ever been to a conference center where you're sitting in the middle of 400 people?

Kim  06:24

Probably not. 

Pam  06:24

In the middle of a row? Did you just like fling the shavings at everyone? 

Kim  06:28

I actually didn't use it because I brought enough really sharp pencils. 

Pam  06:31

You brought multiple pencils. 

Kim  06:32

Like a dozen.

Pam  06:33

You brought multiple pencils and the pencil sharpener.

Kim  06:35

I did. But we're still going to NCSM, and they're starting to get dull, so I'll definitely need to do that. 

Pam  06:40

So, you'll probably do that in the room, and then you'll have million (unclear). 

Kim  06:42

In the trash can. Do you know that in your presentation twice you said?

Pam  06:46

Oh, what did I say?

Kim  06:47

"Pick up your pencil and..." 

Pam  06:47

I said pick up your pencil not your pen?! 

Kim  06:50

Twice. And I smiled so big because I thought you were doing it on purpose to poke at me. But... 

Pam  06:55

Let's pretend I was. 

Kim  06:56

You did not. Okay, should we talk about what actually we're talking about today? 

Pam  07:00

Okay, so we went to dinner. We decided that this podcast was going to be what happened here. And we have some amazing, fun, cool things to talk about. Mathy. So, if you've haven't been paying attention, come back. Here we go. So, we went to dinner with some friends of ours, and... Maybe even newish friends. And we had a great time at dinner.

Kim  07:20

Yeah.

Pam  07:20

And Susan Smith had a great story. So, she's one of our...

Kim  07:25

(unclear) Yeah, one of our Journey members.

Pam  07:25

She's one of our Journey members, and so we've gotten to know her a little bit. She's actually a little new. And she was like on fire when she started. She's like, "I'm a fourth grade teacher. But let me tell you, I've done all the things!" And it was like kind of... Not quite, but almost one of those people that you're like, "Okay, breathe." But in all the right ways.

Kim  07:41

All the best ways.

Pam  07:42

All the best ways. Yes. We thoroughly enjoy Susan. So much that we had dinner with her. 

Kim  07:45

Yeah, absolutely. 

Pam  07:46

And her friend Jennifer. And it was delightful, right? 

Kim  07:48

Yeah. 

Pam  07:48

I think the other Kim was there as well. 

Kim  07:50

Yeah, mmhm.

Pam  07:50

Yep. Anyway, so at dinner Susan says, "Ya'll..." I don't know if she says "ya'll"

Kim  07:51

"I got to tell you this story!" 

Pam  07:55

Yeah. Does she say "ya'll"?

Kim  07:57

No, probably not. 

Pam  07:57

Anyway, she said, "Hey, I have this story..." So, she's starting the school year. She teaches fourth grade. And she's been building her numeracy. And she said, "So, at the beginning of the year..."

Kim  08:07

First day.

Pam  08:07

She said, "I just made up this random multiplication problem." And I think it was 49 times 84. 

Kim  08:12

Yep. 

Pam  08:12

And she said, "It was totally random. I just threw numbers on the board." She goes, "You, students. We are going to be able to do this by the end of the year." 

Kim  08:18

I think she said October.

Pam  08:20

Oh, maybe by October.

Kim  08:21

Yeah. Whatever. Fourth grade. (unclear)

Pam  08:21

Fourth grade. Fourth grade. "We are going to do this in fourth grade." The kids were like all wide eyed. They're like, "Oh, really?!" And she's like, "Oh, yeah. Oh, yeah." Becuse she's an excellent teacher. So, she's getting them excited. She's giving them something to look forward to. Blah, blah, blah. Time goes on, right? They're doing beginning double digit multiplication. They're thinking about smart partial products, I think.

Kim  08:38

Mmhm.

Pam  08:39

And one day... Do I have this right? One day one of the students said, "I think we could do that. I think we can solve that problem."

Kim  08:44

(unclear) And she was like, "Yeah, let's do it. Go for it."

Pam  08:45

"Bam! Let's go." And so, I think she said most of the kids were like splitting by place value. That's kind of what they've been doing. They're, you know, they're going on. And then, if I remember the story right, Susan says she looked at the board, and she goes,"Oh!" Like, "I picked numbers that I can actually think about." (unclear).

Kim  08:56

Well, I don't know, that (unclear). But she realized that there was a strategy that she could do that wasn't. Like, she saw the numbers, and she had an inkling of an idea, and it just hit her.

Pam  09:09

Rather than splitting by place value. 

Kim  09:10

Yeah, yeah, yeah. 

Pam  09:10

She's like, "Whoa! Whoa! Woah! I can do something cool with those numbers!" 

Kim  09:13

Yeah. 

Pam  09:14

And I think they were dealing with like... So, it was 49. 

Kim  09:17

Yeah. 

Pam  09:17

So, she's like, "If we can get to 50..." 

Kim  09:19

Yeah. 

Pam  09:19

"...then it's just a little Over." And she was thinking about Over, and Over was in her head." If it's 49 times something. If we get to 50 of them, it's just going to be backup one." So, then, I think they did that. I think students kind of worked on it. 

Kim  09:30

And it was kind of tough for them because they did 50 of them. 

Pam  09:32

I think they did 100. 

Kim  09:34

No, I don't think so. I think they did fifty 80s, and that took some work. And then, 50 times 4 was nice because that was 200. But then, another kid said, "Oh, we could have done one hundred 84s, fifty 84s to get to forty-nine 84s." And so, they're really excited. And then... 

Pam  09:54

Now, they have to do the subtraction, right? 

Kim  09:55

Yeah, yeah, yeah.

Pam  09:55

Yeah, so they have to do the subtraction because they have fifty 84s.

Kim  09:58

Mmhm.

Pam  09:59

They have 1 too many 84s because they only need forty-nine 84s. So, they're going to subtract 84. 

Kim  10:04

Yeah. 

Pam  10:04

And then, in that moment, I think a kid said, "We could do, I Have, You Need!" 

Kim  10:08

Yeah. 

Pam  10:09

And Susan's eyes, again, bug and was like, "We could do I Have, You Need!" And it's all there and all the excitement. And she was like, "I realize! Like, it's all fitting together! And all the things!" And yeah, it was a super cool story. I think part of what I liked about that was how Susan's world opened up. 

Kim  10:24

Yeah, absolutely. Yeah. When she put that problem up, she didn't have any inkling of like a type of problem or what she was looking for. Or a rich problem that was going to...

Pam  10:33

(unclear) She just threw up a random problem. 

Kim  10:34

Yeah. And a few months later, as Susan began to develop more strategies, and as she was more thoughtful about number, and she had had more experience, then she was able to look at a problem and go, "Oh, I see what I could do with that!" 

Pam  10:47

Yeah, which is our goal, right? Our goal is, we all can build from where we are. We all own some relationships. We can build from there, and now we own more relationships. I can't tell you how many times I'll do... I just did my session here at NCTM. It was fabulous. In the back of my head, I often have this inkling. And then, people will say it often. Where I... How do I say this? I do a Problem String with adults for adults. And they will then say, "Yeah, yeah, yeah. But my kids, they can't enter that problem. They don't have access to that beginning problem." To which I will say, "Right. Like, I knew who my audience was here. Know your content, know your kids. Know your content, know your audience. I knew I was going to have a group of adults, so I chose numbers that I was pretty sure every adult would have access to. But yet the string itself would challenge learners just enough. So, I chose those numbers on purpose." "Well, what do you do if my kids can't do that? My kids can't do that thing." Then, not this Problem String.

Kim  10:49

Yeah.  Yeah.

Pam  11:44

Then, you need to get to know your kids. That could be a problem talk. You interact with them around, you know, everything. Get to know them a little bit. And then, you have an inkling where you can start with them. "Oh, you know, that. Let's build on those things." And even if not everyone in the room owns maybe that first relationship in the first problem, make it visible. Now, they all have that to build from, and then you know, "Okay, we need to continue to build those kinds of things."

Kim  12:13

Yeah, and I don't think you're suggesting that that first experience that you do with people is enough that now they're going to own all the relationships and all strategies, right?

Pam  12:20

Yep. Yeah, and I can't tell you how many times I'll see a problem now, where I come at it differently than I did before. 

Kim  12:21

So, the more and more. So, I think what was fantastic about Susan is that she had been involved over the course of months with her students in developing more numeracy. And I know she's super active in Journey and super active with doing MathStratChat. So, she had developed over the months, and then saw the richness of the problem that could be done.  Yeah.

Pam  12:31

And it might be the thing I was playing with yesterday.

Kim  12:52

Oh, absolutely. 

Pam  12:53

In fact. Kim, do you remember? Totally off script here. Because there's no script, right? Do you remember when I was writing Lessons & Activities? I sent you some of the multiplication problems. And you gave me some feedback. 

Kim  13:05

Yeah. 

Pam  13:06

And then, I sent you some of the division Problem Strings. And you said, "Pam, you're playing around with the same relationships. There are other relationships." And I said, "It's all I can see right now." 

Kim  13:19

Oh, yeah. Yeah. 

Pam  13:20

And in that time... The reason it came up is we're about to have some MathStratChats that come out.

Kim  13:24

Yeah. 

Pam  13:25

Where I realized after I had written them, that I'm now playing with the same numbers differently. So, at that time, I was playing around with 22, and 33, and 44. In that, I was like, "Hey, once you find 2 times something, you can scale that to find 20 times that thing. Now, you have the 2 and the 20. You got 22 of those things." Same thing with like, 33. Once you scale up and find 3 of those things, you can then scale that times 10 to get 30 of those things. You can add them to get 33 of those things. And I was so excited about that relationship that I was pulling it out in lots of the Problem Strings I was writing. And you were like, "We got that, Pam."

Kim  14:03

It's time to do some other stuff. 

Pam  14:04

And I had to say to you, "Like, what else?" And I'm so glad that you did because then we were able to put other relationships in the book that maybe I owned a little bit less at the time, that I own more now. And so, coming up, ya'll, there will be some MathStratChat problems. I'll be honest with you. It's not for a couple of months because we write those in advance. But in a couple of months, there will be some problems with 22s, and 33s, and 44s, and I'm not going for those strategies. So, you can do what I just said in those problems. Look for that. But there's also some other things I'm playing with that I hope come out when people are also solving those MathStratChat problems. Yeah. Cool. Okay. So, Kim, we wanted this episode to be some things that we are thinking about here at NCTM, that we're learning about here. One of them was that great conversation we have with Susan at dinner. Another thing that I wanted to bring up. I came out early to NCTM. We did not fly out together, even though we live near each other. We are flying home together. 

Kim  14:58

Yeah.

Pam  14:59

I think I'm driving you home that night. 

Kim  15:00

Yeah, that would be great. I appreciate the ride. 

Pam  15:02

Absolutely. Absolutely. You don't live as close to me anymore, which is not very nice. 

Kim  15:07

I know. Sorry. 

Pam  15:07

You moved away from me. Thanks. Anyway. So I came out early. I'm so honored that I was asked to speak at the CPAM Conference. Which, now I'm going to remember what it stands for. What does the C stands for? Congress? Oh, hang on a minute. Hey, do you guys actually remember what the C stands for? We're sitting by some friends here that wanted to listen to us record. The "C" of CPAM? Congress? Is it committee? Committee for Presidential Award Winners in Mathematics. Of Mathematics. Okay, so in the United States, there are Presidential Award Winners for Mathematics. And, you know, that's an amazing award. And super cool. And so, there's this committee that pulls together a pre-conference workshop for them. And this year, they asked me to do that presentation in that pre-conference workshop. I'm so honored that they did. It was amazing to meet all the Presidential Award winners. Fantastic people. Several of them have been retired. Few of them were brand new. It was great when they introduced themselves. They introduced with their name, and then the year that they won the Presidential Award. I thought that was really cool. 

Kim  16:14

Yeah. 

Pam  16:14

Anyway, I was super honored to be there. While we were there, one of the participants. They could invite guests. And one of the guests, actually. Jennifer was telling me afterwards, an "aha" that she had. And I thought I'd share this "aha" because I thought it was great. So, often, when we talk about developing mathematical reasoning, we'll have the graphic, and I'll talk about kids go from counting strategies, to additive reasoning, to multiplicative reasoning, to proportional reasoning, to functional reasoning. And I'll talk about the trap of algorithms, and how if you do an algorithm to solve any one of those, kids could be using reasoning in the level before. So, they could look like they're using multiplicative reasoning in the long. But doing the long multiplication algorithm, they could actually be using additive reasoning to do skip counting for all those multiplication facts. And she said, "Well, yeah. As I was thinking about the multiplication algorithm, absolutely. Kids could be doing skip counting to do the multiplication facts in that algorithm." But she realized she has lots of students who... Or maybe it's not her students. But she has seen... What's a good word. Not an accommodation because I don't to make it sound like it's a Special Ed thing. But yeah.

Kim  17:22

Teachers want to offer.  There's no way that we can build students reasoning, if we're also giving them something that is focused solely on getting answers, 

Pam  17:24

Help to students who are struggling with multiplication facts. And one of those helps that they often offer is a multiplication table. And she said, The "aha" she had in that moment was, "Oh, now we're taking them even out of additive reasoning." Now, we're saying to them, "Don't even think about these multiplication facts at all. Just go over and up on the multiplication table till you find that fact. Write that down." And then when they get... So, now, they've written all the multiplication facts down in the two rows, or whatever, with the magic zero. And she said, "And now when they do the addition, then they're counting on their fingers." So, in reality, the only reasoning students were doing was retrieving from rote memory. I'm not calling that reasoning. But they were retrieving from rote memory. And then, they are adding on their fingers using counting strategies. But they look like they're reasoning multiplicatively. Ooh, say that, again. 

Kim  18:17

There's no way that we can expect kids and help them build reasoning, if all we're doing is giving them support that focus solely on getting answers

Pam  18:25

Ways to get answers. 

Kim  18:26

Yeah.

Pam  18:26

That don't at the same time build reasoning. 

Kim  18:28

And if we're handing kids a multiplication chart, so that they can get an answer, whether we're doing it out of kindness or because we have to or whatever, they're focused on getting an answer to a problem. And they're not getting any work or support in building their reasoning.

Pam  18:43

It's not helping their brain think more sophisticatedly. Would you say that's also true for like handing them a calculator? If the reason you're handing it to them is to get an answer?

Kim  18:55

To get a quick answer. 

Both Pam and Kim  18:56

Yeah. 

Kim  18:56

Yeah. And I think that sometimes what happens is, we think this is a problem that kids aren't going to be able to do with some reasoning. And the more... Just like Susan have happened to her over more and more experiences. As her brain has grown, she's able to recognize that more and more problems are figure-out-able. More and more problems are able to be reasoned through. And I think in the beginning of work that we do on ourselves... We have a small subset of problems that we think, "Oh, for this number, I could do reasoning."

Pam  19:04

Totally.

Kim  19:07

"For these small..." But the more and more experience you have, and the more and more that you work at building your reasoning, that widens up, right? And now, you and I have done some work with each other, and with ourselves, and with our communities that we talk math with that the types of problems, the amount of problems is actually quite large.

Pam  19:51

Yeah. Hey, Kim, can I admit a fail? 

Kim  19:52

Sure. 

Pam  19:53

So, another thing that I did while I was here. I came that day early, and since I was here... We have a Journey member. Her name is Adina. Adina. Shout out to Adina! Who invited me to come to her school to work with her teachers that morning. 

Kim  20:05

Yeah.

Pam  20:05

And it worked out. I was able to train up to Baltimore, spend an hour and a half with her teachers, and then make it back down for the CPAM. Oh! Oh, we forgot to tell the funny part about CPAM. So, Jennifer was a guest of one of the award winners. And when she was invited to come as a guest, the person had said... The award winner had said, "Hey..." I think it was Kim. You're like, "You can come as my guest to CPAM." And Jennifer was like, "I want to see Pam!" So.

Kim  20:31

But it turns out, she got to.

Pam  20:32

That's not what CPAM stands for. But it was kind of funny that she didn't really know that. Hey, Brendon! Across the hall. We're really at NCTM where people are walking around. And there was Brendan (unclear), I think on Twitter. Hey, Brendon! Anyway, so CPAM does not stand for seeing Pam Harris. But in that moment, it did. Okay, anyway, my fail. So, I went to work with third grade through middle school teachers at this school. They were delightful. It was a delightful group. And as I was working with them, one of the teachers walked in a little bit late. And I'm actually not sure she's a teacher. Administrator? I don't know. One of the participants.  Walked in a little bit late. I don't think I told you about this, right?

Kim  21:07

No, I don't think so. Yeah.

Pam  21:07

Yeah, Kim's like, "I don't know what you're going to say."

Kim  21:09

I don't know what you're going to say. 

Pam  21:11

So, she walked in a little bit late. And I had already talked. We had already done a Problem String. We've done some work. We had talked about Developing Mathematical Reasoning. I talked about the graphic a little bit. And she said, "Okay, right. But you just did problems with 99." Because I had said, "You know, can we reason about 38 times 99?" Well, we got ninety-nine 38s. We can think about a hundred 38s. We had done 99 plus 38. She goes, "You just gave us numbers that are super reason-about-able. Like, what about other numbers?" And she then threw out a problem. And it was something... It was actually not bad. Sometimes people give you problems where they'll say, "You know, like, 75 times..." "I got that." You know like, they'll often throw a problem out to me that I have a really nice strategy for. So, it actually takes some thinking, some numeracy to come up with a problem that the best I can do is partial products. 

Kim  22:01

Yeah. Like place value. Yeah. 

Pam  22:01

And there are a few of those. Like place value partial products. 

Kim  22:03

Yeah.

Pam  22:03

There's a few of them. 

Kim  22:04

Right. 

Pam  22:05

And as I say that, maybe because I don't own enough relationships yet. But using my major strategies, you're probably going to partial product something like 37 times 78. 

Kim  22:19

78. I was going to say maybe 72.

Pam  22:21

Maybe. Oh, I don't know.

Kim  22:22

It's really close to 75, though. 

Pam  22:24

Yeah. And 72 is so close to 75.

Kim  22:26

Yeah.

Pam  22:26

But 37 is also close to 36. 

Kim  22:28

Yeah.

Pam  22:29

So, if I can do 36...

Kim  22:30

We should spend some time coming up with what are the worst three. 

Pam  22:32

What are the worst problems. Because 36 times 72, I bet we can do some stuff with factoring. 

Kim  22:36

Maybe the listeners can send us what are the worst three?

Pam  22:38

What are the worst problems that you would have to...

Kim  22:40

There you go, Susan Smith. You can geek out on the worst three problems. 

Pam  22:43

Okay. Alright. So, yeah. She gave a fairly decent problem. And in that moment. Here's my fail. She kind of boldly was like, "So, you know like, are you saying that we don't need algorithms at all?" And in that moment, I looked at my watch. I knew I had to quickly run to the train station, grab the train down to DC. I didn't want to be late for the CPAM... 

Kim  23:05

Yeah.

Pam  23:06

...workshop. All the things. And so, in that moment, I thought, "What can I do here? I cannot answer her well." 

Kim  23:10

Yeah. 

Pam  23:11

And so, I said, "No, we do not need algorithms." And then, I moved on. I'm going to say that's a fail because what I wish I would have done is say back to her, "What are you thinking?" 

Kim  23:23

Yeah. 

Pam  23:24

"After what you've just seen and what we've just done."

Kim  23:27

Yeah. 

Pam  23:27

"What are you thinking?" Because as soon as I say no... 

Kim  23:31

Yep.

Pam  23:32

...she now has the option to take what I say, and maybe go further. But I've now like... I don't do that with students. 

Kim  23:39

Right. 

Pam  23:39

Like, we have the neutral response. 

Kim  23:41

Right.

Pam  23:41

I did not walk the walk that I profess. So, I'm going to call it right now, so that I won't do it again. But by giving a non-neutral response, like saying, "Nope. Nope. Here it is," I would suggest that the chances are high I stopped her thinking. The chances are high that she... I'm not going to say for sure. I don't know. Like I'll be super curious to know, you know, what happens from here on out. I don't know if I'll ever talk to her again.

Kim  24:08

Right.

Pam  24:08

How might you have? I don't know if you have a different take on?

Kim  24:11

Yeah, I think that happens in classrooms too, right? Time. Time is always a factor, and we have to... It's interesting to me because this is something that you feel strongly about. And we all can get tripped up, right? Like we all can go, "Oh, that doesn't match with what I believe. Because we don't believe in telling people. We believe in having a conversation and asking them what they think, and then helping people have an experience that then allows them to open their minds to something different, something that they didn't grow up with maybe, something that is a possibility. But you know what? It actually makes me think of a coaching session. 

Pam  24:50

Oh, okay.

Kim  24:52

You and I... Yeah, we talked about this a little bit. You and I were in a coaching session. 

Pam  24:56

Well, we have been going to coaching sessions because...

Kim  24:59

Oh, yeah. 

Pam  25:00

...we're trying to build our JourneyLEADER program.

Kim  25:03

Yeah.

Pam  25:03

Listeners, I don't know if you're familiar with it.

Kim  25:05

Yeah.

Pam  25:05

But we work with teachers in workshops and in Journey. But we also have leader support. 

Kim  25:09

Yeah. 

Pam  25:10

And we are loving working with coaches and district leaders and service center leaders to help them really think about working with adults and moving systems forward. 

Kim  25:19

Yeah. 

Pam  25:20

So, one of the things we did at NCTM was actually go to a few coaching sessions, leadership kind of... Hey, there's (unclear). 

Kim  25:24

Yeah. 

Pam  25:25

And also, that's why we're going to NCSM, right?

Kim  25:28

Yeah. Well, and also it's been really difficult because NCTM is huge, right? Big Conference, lots of sessions.

Pam  25:33

How do you choose? 

Kim  25:34

Well, and also we believe very strongly in shared experiences. So, if we want to create something together, we want to have an opportunity where we both attended a session, we've thought back and forth about the session. And we're not trying to describe, "Hey, I went to this one. This is what the highlights what you should know." So we're...

Pam  25:52

Let me dump on you what I just learned. Instead, we believe in shared experiences. So, we've actually tried to attend...

Kim  25:57

It's been a compromise.

Pam  25:58

...many of them together. Yeah.

Kim  25:59

Yeah.

Pam  25:59

Yeah.

Kim  26:00

Anyway, so we were in this coaching session. And, you know, it was all about like questioning students and kind of anticipating the challenges that students might have in the midst of solving problems. And I think I leaned over to you and I said, "But what about the teachers that don't have the content knowledge to be able to anticipate struggles that students might have?"

Pam  26:19

Yeah, because they were kind of suggesting, "Coaches, here is a..." What did they say? A specific? Deep and specific? 

Kim  26:25

Yeah.

Pam  26:25

Something. 

Kim  26:25

Deep and specific (unclear).

Pam  26:26

"Deep and specific conversation to have with your teachers." And in the suggestions they were giving all assumed that the teachers already owned the math content, right? 

Kim  26:36

Yeah. 

Pam  26:37

And so, you leaned over and said, "We can't have this conversation if the teachers are stuck in rote memorizing?"

Kim  26:45

Right.

Pam  26:45

Right? 

Kim  26:45

Right, right. 

Pam  26:46

Yeah. So, at that point, then I started thinking about, "Okay, so..." I'm looking at you because I'm like, "Is that where I go (unclear)?"

Kim  26:53

Yeah, sure. Yeah, yeah, yeah. Yeah. 

Pam  26:54

I wasn't sure if I was interrupting you. What if the leaders don't? Because we said, and the leader of the session said, "Yeah, like coaches, leaders. We need to work with teachers to help them build their content, so that then we can have these conversations with them."

Kim  27:11

Absolutely. 

Pam  27:12

And that's when you and I looked at each other, and I said, "And we need to help leaders...." Because just because you're a leader. And I'm not trying to diss anybody at all. I don't own everything yet.

Kim  27:23

Right.

Pam  27:23

Like, we're all on a Journey to gain content knowledge, so that then we can have these conversations kind of at all the levels. 

Kim  27:31

Yeah.

Pam  27:32

We all need more content understanding. Which... Oh, man. I forgot to say that my session today! One of the things I meant to say in my session today is, "There's a lot of good people out there talking about the 'how' of teaching." 

Kim  27:44

Yeah. 

Pam  27:45

And I think, uniquely, we bring also the "what". 

Kim  27:48

Yeah.

Pam  27:49

Where we can help teachers think about content. And teachers and leaders really think about the math, the mathing, in a deep, consistent way, so that then we can have conversations about the pedagogy. 

Kim  28:03

Right.

Pam  28:03

And move the pedagogy forward.

Kim  28:04

Well, and it tied to actually today with... We talked to this nice guy, Jacob, after your session. And he asked a couple of questions. And the last question he asked me was, "Hey, I get opportunities to do work with these teachers. I'm this director of..." You know, whatever. And he said, "What would be the first thing that you did with teachers? If you were in charge of like moving a district forward, what would be the first thing you did?" And I said, "You've got to do math with your teachers." Like in Pam's session... Uniquely, in all of the sessions that I've been to, it was the only session where we actually did math. And I find that interesting at a math conference. But...

Pam  28:39

You brought that up a couple times.

Kim  28:40

I did a few times because, you know, I'm a learner, and I want to do math.

Pam  28:43

Do some math! 

Kim  28:43

I'm trying to find sessions where I can like actually dig into some higher math. And maybe I just missed them. They might have been here. But the response to Jacob was, "You got to do math with your teachers, and you got to do math with your leaders, so that they have the content knowledge underneath them, so that they can ask the good questions, and so they can anticipate students thinking and how to connect relationships between grade levels."

Pam  29:06

So, one of the things we do in our Journey... 

Kim  29:09

Yeah.

Pam  29:10

...is we provide a space where teachers can sort of safely risk.

Kim  29:16

Yeah.

Pam  29:17

"I don't know how to do that thing."

Kim  29:18

Yeah. 

Pam  29:18

"Teach me this thing."

Kim  29:19

Yeah.

Pam  29:20

And we do it. And we don't tell.

Kim  29:22

No.

Pam  29:22

We do strings, and we do...

Kim  29:23

We do some live math stuff. 

Pam  29:24

We do some live math.

Kim  29:25

Yep.

Pam  29:25

And lots of experiences where leaders and teachers get a chance to build their math. They're mathing. Their content knowledge. So, that then... Well, "then". And? And we can have conversations about pedagogy at the same time. And we can have conversations about pedagogy because we're actually doing the math the way we're suggesting they do the math, right? 

Kim  29:46

Yeah.

Pam  29:46

We're teaching. Doing the math teaching the way we suggest they do the math teaching.

Kim  29:49

And the people in Journey or in JourneyLEADER get an opportunity to have a shared experience that you and I are having together here today. We're having shared experience, and we'll take away from this for the next couple of months or whatever, "Hey, remember when? And what can we use that for?" And, you know, sometimes teachers are on an island. They're the ones who are trying to lead the tide in their campus, and they don't have a lot of people to share experiences with. And so, I think that's what's really beneficial in Journey because they get to have conversations with other people who are also like minded.

Pam  30:20

Yeah. And if you're listening to this, and you're like, "Geez, sure wish my administration was paying for me to go to NCTM." We do, too. Like, we wish that we could have hung with you here, and that you had a chance to learn stuff. We will bring everything we can to you in the podcast. But you might check out the other things that we offer for support for places that we can all learn more math and pedagogy. The "what" and the "how"

Kim  30:41

Should we sign off?

Pam  30:42

(unclear) it has been super fun to be here at NCTM with you.

Kim  30:44

Yeah, thanks for having me come. 

Pam  30:45

Hey, everybody, Math is Figure-Out-Able. And I have an ending to this that I got to pull up on my laptop now because I can't even... I don't remember it. And here I go. Ready? Thank you for tuning in and teaching more 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! Say hi everybody!

Participants  31:10

Hi!