[00:00:02.000] - Pam
Hey, fellow math-ers! Welcome to the podcast where Math is Figure-Out-Able. I'm Pam Harris, a former mimicker turned math-er.

[00:00:11.520] - Kim
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.

[00:00:19.440] - Pam
We know that algorithms are amazing historic achievements, but they are terrible teaching tools because mimicking step-by-step procedures actually traps students into using less sophisticated reasoning than the problems are intended to develop. Then they never develop the more sophisticated reasoning.

[00:00:35.820] - Kim
In this podcast, we help you teach math-ing, building relationships with your students, and grappling with mathematical relationships.

[00:00:42.300] - Pam
We're so glad you're here with us to make math more figure-out-able. Hey, Kim, so you know I just recorded the audiobook for Developing Mathematical Reasoning: Avoiding the Trap of Algorithms, which is a bestseller for Corwin.

[00:00:57.420] - Kim
Very nice.

[00:00:57.900] - Pam
May or may not have just won an award that I'm not supposed to mention yet.

[00:01:01.490] - Kim
Very exciting.

[00:01:04.130] - Pam
But do you know one of the things when I was recording the audiobook? The audiobook recorder editor... Producer. That's what he was called. The producer said to me, "You have to pronounce every word. You can't swallow words like you do when you're talking. You have to actually pronounce like the ends of words." And he was kind of doing this as like an intro, you know, whatever thing. I was just noticing as we were... Because am I right? You read the intro? I read the intro.

[00:01:29.550] - Kim
Yes, always.

[00:01:30.270] - Pam
I don't have it memorized. I was just noticing you do that well. Like you enunciate. You don't... Words don't drop off. You don't swallow words.

[00:01:38.030] - Kim
Well, thank you. That's hilarious because I feel like I get to the end of one of the sentences, and I mumble them all together.

[00:01:45.470] - Pam
[mimicks mumbling]. Well, not today. Today, you did not.

[00:01:47.310] - Kim
Great.

[00:01:48.030] - Pam
Today it was on top of my mind because I was thinking about, while I was reading. It was like, "Okay, remember, don't leave..." It was interesting. There were several times they had me re-record a sentence because not... Every word wasn't.... And part of the reason he said to do that is... What? Did I just stop the sentence in the middle? No?

[00:02:05.290] - Kim
I was going to say. Did he say you have to finish a sentence before you can move on to the next? Because everyone who ever does work on captions of yours says, "Pam, I don't know where the sentences start and end." And I go, "Welcome. I know."

[00:02:21.930] - Pam
That's true.

[00:02:22.570] - Kim
We both do it.

[00:02:23.560] - Pam
You said it right when I just only said half a sentence and didn't finish it. That's fantastic. I don't remember where I was going.

[00:02:29.640] - Kim
Oh, sorry.

[00:02:30.440] - Pam
What was I going to say? Something about how he said you have to... Oh! Because if you don't enunciate every word at regular speed, when they turn up and listen to the audiobook at like 1.5 speed, they won't hear everything. It doesn't...

[00:02:44.920] - Kim
Oh.

[00:02:45.160] - Pam
Whatever. That interesting? And to which I was like, "Are you sure they're going to 1.5 me?"

[00:02:50.750] - Kim
Oh, my gosh.

[00:02:51.870] - Pam
I read kind of fast.

[00:02:53.550] - Kim
Well, and I'm used to hearing you. So, like I know a lot of what you're... Not everything you're going to say. But, you know, I kind of sometimes know where you're going, or I... So, I can listen to you on double speed, which is fast.

[00:03:07.310] - Pam
Wow, wow.

[00:03:08.750] - Kim
But I don't... Maybe other people can, but I think it's because I can pick through a few words. But my kids or my husband will be in here and they're like, "What are you listening to?"

[00:03:22.750] - Pam
That's hilarious. Okay. On the other, on just personal note, I was listening to a novel audiobook and realized I really like the narrator. I think the way she does it is brilliant. And I was like, "I wonder what she actually sounds like." Cause I was listening at just at 1.25. Not even that fast. Just 1.25. I slowed it down to 1, and I was like, "Oh, that's painful."

[00:03:42.110] - Kim
Yes.

[00:03:42.590] - Pam
That sounds... After you've... Right? After you've kind of gotten used to a two-thirds of the book at one speed.

[00:03:47.710] - Kim
Yes.

[00:03:48.030] - Pam
You cannot slow it down.

[00:03:50.570] - Pam and Kim
It's bad. Oh, Gosh.

[00:03:53.690] - Pam
Okay, so I'm not alone in that. Alright, Pam—Kim. Recently, I was... Podcast, podcast. Recently, I was asked to do... I was working with a school, and I had this... I don't want to say unique opportunity, but I don't do it as often as I used to. And I love doing this kind of thing. Where I got the opportunity to teach students. And so they said, "Here is where this..." I have several classes and, "Here's where this class is. These are the things they've been studying. This is what they're about to learn. And we would like to see a Rich Task and a Problem String in each one of these classes." And I gulped. Like, I took a deep breath, and I was like, "You want a Rich Task and a Problem String?" And I... That is... That is really... That's asking a lot for a few reasons that I'd like to talk about today.

[00:04:43.670] - Kim
Okay.

[00:04:43.750] - Pam
So, one thing that made this extremely difficult is that I don't know the students. So, as I'm planning, I asked several questions about, "Wait, I know you said you did this unit, but tell me more about that. What was in..." You know like, have kids done this or that? And how successful was it? And, you know, a little bit more details. But what I cannot ask are questions like it's hard to ask. Let me say it that way. It's hard to ask who genuinely needs just a little bit more time, and so I should be keeping my eye on that person as I pace the class. Versus who's actually kind of messing around. And if I can help focus them, they don't actually need more time. Once they're focused, they're good, and so they're not a good way for me to judge whether it's time to move on. Like, that's kind of stuff I think you feel out.

[00:05:35.090] - Kim
Right.

[00:05:35.250] - Pam
Like, that's me. Those are things I'm looking for. I don't even know if I asked you my specific questions about how I judge timing, if you would even, if those are things you look for in the same way that I look. You know what I mean? It's kind of personal.

[00:05:48.070] - Kim
Yeah.

[00:05:48.470] - Pam
So, I don't know. I don't know the students. And so, I'm thinking about, you know, what can I get in and how long will this Rich Task take? I don't know the kids. That's super...yeah. That's one thing that made it difficult.

[00:06:01.910] - Kim
Well, and did you say this was several classes in one day?

[00:06:06.630] - Pam
Yes.

[00:06:07.910] - Kim
Which is... It's intense work. And so...

[00:06:12.180] - Pam
Yeah, yeah, it was like four different age groups. And not in order.

[00:06:17.940] - Kim
Which is a thing for you. Yeah, so rich tasks...

[00:06:21.220] - Pam
You're saying it's not a thing for you?

[00:06:23.060] - Kim
Um, I don't...

[00:06:23.940] - Pam
Very first time I ever did that, I had so much respect for like the PE teacher, and the music teacher, and anybody who ever had to take... Like, I would say that third or fourth group, I would like, "Talk to me. I need to feel how old you are right now. Like, just say words."

[00:06:35.700] - Kim
Well, but when you taught. When you were teaching high school, you taught different sections. Does it matter? You didn't do Algebra 1 first period and geometry second period and Algebra 3.

[00:06:43.840] - Pam
No, but then I knew the kids. So, I guess that, yeah, so I guess I don't feel for PE teachers when they know the kids.

[00:06:51.680] - Kim
I feel for them in general.

[00:06:54.720] - Pam
I think it's mostly when you don't know the kids.

[00:06:57.600] - Kim
Yes. Yes.

[00:06:58.640] - Pam
And then you have these different ages coming at you in different orders. You can't just think, "Well, these guys are going to be a little further along than the last period. Nope." You know like, does that make sense?

[00:07:08.000] - Kim
It makes sense. Yeah.

[00:07:08.960] - Pam
Yeah. And you often say, very important, that we should... Let's see if you can finish my sentence. What are our two mandates that we?

[00:07:17.680] - Kim
Oh, know your content, know your kids.

[00:07:19.760] - Pam
Yeah.

[00:07:20.800] - Kim
And that is always true. But man, I think in a Rich Task, that is an example of a type of lesson where I think if you don't know your content, know your kids, it is almost impossible.

[00:07:36.440] - Pam
So hard to do.

[00:07:36.920] - Kim
To get what you want to get. Yeah, it is.

[00:07:40.920] - Pam
To make it be a meaningful, useful, moving the math forward.

[00:07:45.000] - Kim
Yeah.

[00:07:46.120] - Pam
It's harder to do. Yeah. Okay, so Kim. What are some helpful things when we say know your content, know your kids? And maybe specifically thinking about Rich Tasks.

[00:07:55.720] - Kim
Okay.

[00:07:56.040] - Pam
What are some things that are helpful to know about kids? When we say know your kids, what are some things we're looking at?

[00:08:01.850] - Kim
Yeah. So, I think it's really important that you know what opportunities that those particular students have had with whatever prior knowledge that you're going to be calling on. So, you know, in a Rich Task, you're not... You know, it's going to be connected to something that you've done or somebody has done, and so you got to know a little bit about those opportunities that they've had. I would want to know who tends to engage.

[00:08:30.810] - Pam
Oh, before you go on, can I just real quick?

[00:08:32.890] - Kim
Yeah.

[00:08:33.130] - Pam
An example of what you just said is I was going to do a lesson that kind of extended area. And the teacher had said, "We've already done area." And I said, "Tell me more about that. Like, they know the formula, and they've plugged in numbers. Have they used an area model to represent their own strategies?" Like, those are like far on a continuum for me. Like, you can't just tell me, "We've done area." I need to know what that means to you and looks like. That's just one example.

[00:08:59.840] - Kim
Yeah, that's a great example. We have some nice video of a third grade class with a fraction Rich Task. And the teacher had said to me, we have quote, "done fractions."

[00:09:08.640] - Pam
Oh, yeah. I remember that, yeah.

[00:09:10.160] - Kim
And we went in an entirely different direction and got some great stuff from the kids, but.

[00:09:17.840] - Pam
Well, you say that. It wasn't entirely different. You just, you slowed way down. Nah, slow down is not the way to say it.

[00:09:23.600] - Kim
Our end goal was... If the end goal was to get the students moving forward, we had to make some adjustments. But it was because I had never talked to these kids before.

[00:09:34.970] - Pam
Yeah, yeah.

[00:09:35.610] - Kim
And so.

[00:09:35.930] - Pam
Yes, and the teacher said we're done with fractions this year, so you made some assumptions, which... Yeah. Yeah, exactly that. Alright, what were you? You got another one.

[00:09:42.810] - Kim
So, it's also about kids. I think I would want to know who tends to engage or not engage right away. For a whole host of reasons. But who are the kids that  tend to dive in? And then maybe who's quieter and needs their voice to be elevated because, you know, quiet doesn't necessarily mean anything about your mathematical inclinations or what you know. So, I think those are important kind of things I need to know about the children. I also think it's really important to know about what's students' general relationship with math has been. You know, before, in this class. You know, who are the kids in the class who tend to shy away because they say things like, "I don't like math, I'm not good at math." It's just extra information.

[00:10:32.780] - Pam
Mmhm.

[00:10:32.860] - Kim
You know, are there kids who have found minimal success in the past or who have maybe found a lot of success in the past?

[00:10:40.540] - Pam
Yeah, can I give a quick example of that one?

[00:10:42.540] - Kim
Yeah.

[00:10:43.580] - Pam
Several years ago, I did a model lesson at a high school, and they didn't tell me that the class I was working in was a class of kids who had all failed several years in a row, and they had a lot of behavioral issues in the class. They just didn't mention that. So, like when I say "behavioral", like these are kids that were in a separate class with a behavioral person who worked with them consistently. And so, you know, I started the lesson off and we actually were doing pretty good, but I still don't know exactly what I... Something I did would have been helpful to have shared with me. I did something that set a kid off and he started throwing stuff. And so, you know, that his person was there, and they stood him up and walked him out in the hall. And I was like, that might've been helpful to know. Like, it might've... When you don't know... Well, so I think the list that you're giving here are things we're encouraging teachers to find out about their students, right? Most people aren't going to be us where we dive into a class we don't know because we're filming for our teacher coaching program or our leader coaching program. Most of them are getting to know their students, and we're sort of suggesting these are some things that we consider when we're planning a Rich Task, and if we know these things, that Rich Task will go better. Would you agree that that's kind of the list we are talking about.

[00:12:00.280] - Kim
Yeah, I think it's just these are the kinds of things that you want to know about your students in general, but particularly to have in mind when you're doing something as... I almost said "heavy". It's not heavy. It's not...

[00:12:12.470] - Pam
Meaty?

[00:12:12.950] - Kim
But yeah. But like there's so much to a Rich Task, and like this careful, considerate weaving that happens during a Rich Task that knowing your students makes that possible.

[00:12:28.070] - Pam
Mmhm, mmhm.

[00:12:28.150] - Kim
I am always interested to be thinking about my students too who are always seeking for extra challenge. Not that I'm not going to give everybody extra challenge, but there are some students who drink it like they're dehydrated, like want extra challenge, like more, give me more, give me more. So, you know, thinking about those kids as I'm planning is really going to help them be fed as well.

[00:12:57.000] - Pam
And that could be something, teachers, you could ask for help. If you have a coach that says, "What do you want to work on?" Oh, man. I would love for you to co-plan with me just to help me think about ways in this Rich Task to challenge in the Rich Task, not give them something else to do, not to give them something completely unrelated, but in this task, what's a way to keep them challenged? That's really good and work that I think happens better when we do it together.

[00:13:23.220] - Kim
Yeah, for sure.

[00:13:23.860] - Pam
Alright, keep going.

[00:13:25.380] - Kim
I think we also tend to want to think about who wants to find one and only one way to think about a problem. Like, that's their mindset currently, that that's something that they, for whatever reason, that they like to find one and only way. I think, you know, and also just in general like as human beings in our classroom. Like, what's going on in their life? Like, these are just really big kid-centered things that I think the more that we know about our students as we're planning for a Rich Task and as we're maneuvering through the Rich Task, we'll get more from them. We'll get more out of the lesson. And those are... I mean, just knowing your kids to the level that we're talking about can take some time.

[00:14:13.470] - Pam
Yeah. One of the things that I would do at the beginning of my year as a high school teacher is only one, but I would say, "Listen, everybody's going to have a bad day. When you're having a bad day, let me know. Like, just say something. Walk in, give me, write me. Just somehow let me know, not today. And I'll let you have a bad day. Now, I'm not going to let you have a bad year. Like, we're going to do some learning, whatever. But like, you know, Kim, I did have students that would let me know. But for the most part, I think there was just them knowing that that was like in my worldview to say. They could just walk in my room and just relax. Like, you could just see them breathe. There was something so... I don't know. I felt just really strongly that they knew that I knew that about them and that I wanted to give them the opportunity to, you know, save face when they needed to or cry when they just broken up with whoever. You know, whatever. I mean, I taught high school.
Anyway, so that was one way that I considered what's going on in their life.

[00:15:14.930] - Kim
I mean, yeah, because no matter how much you may even love math or love the class, you know, when real things were happening in your real life, it's going to be more important than what you're learning that day.

[00:15:28.930] - Pam
Absolutely. Yeah. People are important. Okay, cool. So, also, when I was thinking about this request. And I had a great time doing it. But it also made me... It reminded me that when I travel around, I talk to a lot of teachers. Teachers in our coaching group, leaders in our coaching group will often say things like, "Okay, help me with Rich Tasks." Like, teachers will say, "I want to do Rich Tasks." Or leaders will say, "We're going to have all of our teachers this year. They're going to do Rich Tasks." And I will often say, "Um, you tell me more about what you've done to get to the point where you're kind of commanding this Rich Task thing," because I think they're difficult. And you've said that already. We've said that in the podcast today. So, Kim, what makes a Rich Task harder than other? Like, than a Problem String, or even a Number Talk, or other instructional routines, or games? What makes a Rich Task difficult?

[00:16:26.100] - Kim
I mean, they're definitely difficult. They're not not doable, but they're definitely difficult as a way to get started with the kind of work we're talking about. And that has everything to do with the content and the pedagogy that is needed. Besides...

[00:16:43.610] - Pam
Neither of which we probably experienced when we were students, right?

[00:16:48.730] - Kim
Yeah. Oh, I was not engaged in any Rich Tasks for sure.

[00:16:51.610] - Pam
Yeah. And so, we don't have a lot of our own experience to draw from. I think that's one reason. Sorry for interrupting.

[00:16:59.610] - Kim
Well, I mean, you know, in general, the first part of it is, you know, is your classroom set up for that kind of lesson? You know, you have to set up expectations. You have to make sure everybody knows what their role is. And so, that's not terrible. But, you know, it is a thing. If you don't set up your expectations in the way that you are engaging in Rich Tasks. And then, you know, you'll learn real fast that you didn't set the expectations.

[00:17:29.060] - Pam
Yeah, and I think it's one maybe place or time where teachers are trying hard, but because we don't have a lot of experience to rely on, and maybe we're not even sure how to set up those expectations, kids can feel like it's... Golly help me. Less structured. Like, they don't know their role. They're not comfortable. They're like, "Wait, I don't even know what I'm supposed to be doing here. What are we supposed to be doing?" We're not suggesting that, right? We're suggesting kids should always know their role. They should always be comfortable, confident in what...Their task at hand. Now, how to do the task and what the relationships are, that we want to dive in and grapple with. But not like where to be, and who to be talking to, and how to accomplish it, and what's legal to be using, and...

[00:18:15.270] - Kim
Yeah.

[00:18:15.670] - Pam
And yeah.

[00:18:16.600] - Kim
Well, and that doesn't mean shy away from doing them. Like, it sounds like we're saying like, "These are terrible. Don't do it. It's so hard." But just know that there's a lot to consider. One of the things that I think makes Rich Tasks more challenging, like more to consider, is that you, as a teacher, have your eyes everywhere at the same time. At least I do. So, you know, I'm... And not that I'm not for other kinds of lessons, but not to this degree. So, I'm, as a teacher, and I'm circulating, and I'm listening, I'm watching every single board as students are writing. I'm like glancing. How far did you get? And where are you at? And what's the next thing you wrote and how are you recording it? And like I'm kind of taking in all that information at the same time to know where am I going next. Which group am I talking to next? Where am I... Like, so your eyes are everywhere Yeah.

[00:19:13.940] - Pam
Yeah, yeah, yeah.

[00:19:14.960] - Kim
You're also, um, listening in on multiple conversations at the same time. So, my home base might be the center of the room, and I'm listening in to all the different boards to hear like snippets of conversation and, you know, who's talking and who's not talking. And, you know like, what kinds of mathematical conversations are happening or not happening. So, it's this all on, which is why when you said it was multiple grade levels in the same day, I thought, "That's tiring." You know, it is because you're on for that portion of time just taking in everything with all of your senses and constantly like spinning your head to go like, "What am I going to talk about? Where am I going to go next?" It's also I think important to know what to say when as a teacher and when to be quiet and wait. So, if you approach a group, sometimes the best move you can make is shut your mouth and just...

[00:20:12.730] - Pam
Listen.

[00:20:13.130] - Kim
Listen. Listen to what's happening. And, you know, we are so helpful, and we want to dive in, and like direct the show. And so, knowing what to say when or not is important.

[00:20:26.170] - Pam
Nice.

[00:20:26.570] - Kim
It's also... Man, it is so important to think about what content is horizontal and vertical to the goals that you're headed towards.

[00:20:38.280] - Pam
Just to be clear, I don't think you mean here vertical whiteboards versus sitting at desks.

[00:20:43.320] - Kim
No, I mean... Yes, thank you. I mean, if I'm in a 3rd grade classroom working on this particular portion of fractions, I need to be thinking about what do they know ahead of... You know, they've come with. Where is it going, so that I don't let students...

[00:21:01.980] - Pam
Sorry, and that's vertical, right? What's the content before? What's the content after? That's kind of the vertical look of it. Mmhm.

[00:21:07.420] - Kim
Yeah, but also the horizontal look is like what are some things connected to multiplication that they might be thinking about with fractions? What are some they might be thinking about with like Doubling and Halving numbers that has to do with fractions? So, kind of spanning in your mind where everything is connected in a mathematical landscape is happening kind of as you're watching all these things occur.

[00:21:31.780] - Pam
Yeah, yeah.

[00:21:33.620] - Kim
Maybe one of the most important things to consider, for me, is knowing how to nudge but not ramrod the conversation to meet a goal that may be not right right now. So, we mentioned that third grade classroom. I don't think our goals at the end of the year necessarily change. That's based on the standards that we're given where we live. But the goals can shift a bit based on where students are. And sometimes we make assumptions about where our kids are that we assume wrong or we don't have all the information, and then we learn things as these Rich Tasks are happening. So, we make like a little bit of a lateral shift to have like a maybe a mini-congress or a some sort of thing that occurs so that we can get back on track. And so, rather than me ramrod the conversation to be what I want it to be or what it was supposed to be, we're always listening to the students and asking like the next question that could move things forward.

[00:22:38.020] - Pam
Nice, nice. Yeah.

[00:22:39.860] - Kim
Yeah.

[00:22:40.100] - Pam
I like it. I like it. Okay, so, teachers, leaders, if you found it challenging to do Rich Tasks, don't be too hard on yourself because it is hard. Those are, like we just said, we don't have that past experience to lean back on and go, "Well, this is what it felt like when I was a student. I'm going to act like Teacher So-and-So. Or I'm going to..." We just don't have as many of those experiences to fall back on.

[00:23:07.660] - Kim
Yeah.

[00:23:08.220] - Pam
But they are worth... Well, so maybe I'll say this. So, maybe don't have them as the first thing. Like, try Problem Strings first. Get good at Problem Strings, and then dip your toe into Rich Tasks. I think that would be our recommendation.

[00:23:23.180] - Kim
Yeah.

[00:23:23.580] - Pam
For one reason. If you try Rich Tasks first and go, "This is too hard," and throw it out, you may never come back to Problem Strings. So.

[00:23:31.660] - Kim
Or back to Rich Tasks, you know.

[00:23:33.580] - Pam
Or even back to Rich Tasks, yeah. Or just teaching Math is Figure-Out-Able. Like, we don't want you to try something. You're like, "Okay, alright, Math is Figure-Out-Able. I'm going to try to teach it that way." And you jump into the deep end. Like, we would have some suggestions about helping that be. And one of those things is, get better at content. Know your content. And like we talked about today, knowing your kids.

[00:23:54.300] - Kim
Yeah.

[00:23:55.100] - Pam
Nice. Don't think that you have to do Rich Tasks or nothing. There are some other things that you could start with. Like, I just mentioned Problem Strings. Even MathStratChat. Just one of the things that Kim started with was she just went back to her class and started talking about how do you guys think about problems like this? This is how I think about it. And just start listening to people. Asking people at random in your community how they think about different things. It might surprise you. Playing I Have, You Need. Several podcast episodes on that. Some things that you could try. It doesn't have to be all or nothing. You just heard us kind of talk about how difficult a Rich Task can be.

[00:24:29.100] - Pam
We're just honoring the fact that when you do one well, it's quite an accomplishment.

[00:24:35.020] - Kim
It is.

[00:24:35.500] - Pam
And we would love to support you in that. Alright, y'all, thanks for turning in and teaching more and more real math. Did I just say turning in or tuning in?

[00:24:44.020] - Kim
You did. I was just going to let it go.

[00:24:44.260] - Pam
Good heavens. Wow. Thank you for... Okay. Thank you for tuning in and teaching more... Craig, don't cut that part though. And teaching more and more real math. To find out more about the Math is Figure-Out-Able movement, visit mathisfigureoutable.com. Y'all, thanks for listening to the podcast. Keep spreading the word that Math is Figure-Out-Able.