Pam: 0:53

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

Kim: 0:59

And I'm Kim.

Pam: 1:00

And you found a place where Math is not about memorizing. Whoops. Yeah, it is. Wait. Oh, I'm gosh. I'm like, "...not about memorizing." I'm like,"Wait, do I mean that? What do I mean?" Okay.

Kim: 1:12

It's not.

Pam: 1:13

I was thinking about the fact that you were laughing right before we started.

Kim: 1:16

I know, I'm sorry.

Pam: 1:17

And when you said, "And I'm Kim," I'm like, "Oh, that was really super serious." Okay. And you found a place where math is... I don't even know anymore.

Kim: 1:26

It's not about memorizing.

Pam: 1:27

It's not about memorizing and mimicking, waiting to be told or shown what to do. But it's about making sense of problems, noticing patterns, and reasoning using mathematical relationships. That's what it is. Yes, we can mentor mathematicians as...no! That's not the one I want. I'm just going to skip that line.

Kim: 1:47

Okay.

Pam: 1:47

Not only are algorithms not particularly helpful in teaching mathematics, but rotely repeating steps actually keep students from being the mathematicians they can be. Alright, we're keeping this one because I want you to know, we re record that intro every time, and we've tweaked it lately, and I forgot and didn't have the correct one in here. And we were laughing right before we started, and I was having a hard time hanging on to it. And, ya'll, welcome to the podcast. Hey, Kim, let's kick this one off. What are we talking about?

Kim: 2:13

Okay. Alright. So, we absolutely love hearing from listeners about what they're interested in, right? It's super fun for us to hear.

Pam: 2:21

Yeah, and you can tell us if you like it when we totally mess up the intro too. You can let us know that.

Kim: 2:27

We want to know what you want to hear us chat about. So, not too long ago, I asked people in the Math is Figure-Out-Able, teacher Facebook group. It's a Facebook group that we have that lots of people are in. You should join it. And we asked what they were thinking about, and we got some really amazing responses.

Pam: 2:45

Yeah, thank you, everybody. We appreciate that.

Kim: 2:47

Yeah, we can't chat about everything all at once, but for the next several weeks, we thought we would answer some of the questions that people in the group requested.

Pam: 2:56

So, let's start with Sarah. Is it Gorecki? I'm hoping. Oh, wait. Sarah Gregywestrich, in the Math is Figure-Out-Able teacher group said, "Talk about questioning techniques for focusing rather than funneling." Well, Sarah, thanks for listening to the podcast and/or reading the NCTM... Oh, now I can't remember the name of it. It's the one where it has the essential teaching practices in it. It'll come to me in a minute. Because in both of those places, in our podcast and in that book, we talk about patterns of questioning. And there's two patterns of questioning that we can focus on. One of them is a focusing pattern of questioning, and one of them is a funneling pattern of questioning. And we've mentioned it once before in an episode, but we thought we dive in a little bit today and do more with that. Like, let's, because Sarah asked, let's talk a little bit more about these patterns of questioning, and so I just want to start by saying it's not about a focusing question or a funneling question, it's about a pattern of questioning. So, a question could appear in a focusing pattern of questioning, and that same exact question could appear in a funneling pattern of questioning because it's the pattern, it's what's happening in the whole interaction that's either more helping students focus on the relationships, and the math, and what they know, and how they can use them to solve problems. Or it's more of a funnel that you are kind of like helping the kids sort of funnel down the drain of like a sequence of steps or things to do. And they end up at the end of the funnel with the answer, but if you remove the funnel, then the kids got nothing. What wasn't happening is the student was using their own reasoning. They were using your reasoning, your funnel.

Both Pam and Kim: 4:51

Yeah.

Pam: 4:51

And so, Sarah's great. Like, let's parse that out maybe a little bit more. So, Kim, I said to you, "Hey, when we do this episode, I think it would be really cool if we do some kind of like role playing scenario kinds of things. And you pushed back on that. Can you say more about that?

Kim: 5:10

Yeah. So, it's really difficult. We're going to be in some like imagined situations, right? And like you just said, a particular question could fit into a funneling situation or a focusing situation. So, you know, we're kind of imagining a situation, and we don't know exactly what a kid would say. And so, so much of it depends on what a kid says and how you respond. So, yeah. (unclear).

Pam: 5:37

I mean, we talk about our mantra, know your content, know your kids, right?

Kim: 5:42

Yeah.

Pam: 5:42

So, if I know the content, I kind of have the the big ideas, model strategies. I have this real sense of what's next and what comes before, and all the connections that need to be made and the different ways they're related. And I know the kid because I'm talking to him, and I'm hearing them, and I'm asking them questions that help focus on what that student knows, help focus on the relationship that student owns. If I'm thinking about if I own those two things. I know the content. I know the kid. Then, the questions I asked will be hugely dependent on that kid. I have to know the content to know what kind of questions to ask. But then, based on how that student responds, based on interactions I've had with them before, the same kind of... This is what you told me before. The same kind of question that I could. In fact, can you say more about your kids?

Kim: 6:36

Oh, I don't know what I said about him. Remind me.

Pam: 6:38

So, you said something about.

Kim: 6:39

Oh, oh, oh. Yeah. So, I said. Sorry. So, I may be talking with Luke, and I...

Pam: 6:44

Your older.

Kim: 6:45

My older, right. And pick a kid. It doesn't matter. I might be saying something to one of my kids, and I might know what he knows about a particular situation, and I might throw out a question or two, and he might go, "Oh, yeah, yeah, yeah. Okay, I'm good." And I might throw out the same question or two to the other kid, and they might stare at me kind of blankly, so that's not helpful to them. It's not helpful for me to just say the same question one or two. And what I was just thinking about was, in a funneling pattern, this is where you might hear a teacher use the same series or sequence of questions, no matter what kid in their class they're talking to. And I don't know that we've ever said that. I don't know if we've ever verbalized that. But it might be that you use the same questions, all the time, over and over again no matter what kid you're talking to. Where in a focusing pattern, it should very much depend on the student.

Pam: 7:49

Oh, that's so interesting because as you said that, I'm picturing. I told a little bit of this story before. We were videoing in a classroom. It was a high school classroom, and this teacher was well liked, well respected. I think he was the senior... What do you call it when you're? Like, the advisor and helping the kids play in the prom. And, you know, all that senior kind of stuff. The kids obviously liked him. When I got into the classroom, he walked in a little bit after me, and he. They were talking about how he just had a pickup basketball game with the kids at lunch. And it was super. I was like, "Oh, I love teachers like this because they really like kids and the kids relate." You know, and it was a great relationship. But then, I watched him walk around during class. And if he walked up to a kid that was stuck, he would go,"Okay, so what's the this? Yep. Now, what's the that? And now what do you do next? And now you need to this." And so, he was asking questions, but when he got to the next kid who was stuck, he would say the exact same sequence: "What's the this? What's the that? Now, what's the first step? Now, you've identified the numbers, now what's the next step? What's the next step?" That would be a good ping to ask yourself, as you are helping students, do you tend to use the same sequence of questions?

Kim: 9:05

Yeah.

Pam: 9:05

That reminds me, Kim, of times where people have said,"Hey, we kind of want like a list of the best questions to ask."

Kim: 9:12

Yeah.

Pam: 9:13

And we've said, "I mean, that is a helpful thing. Sorry, I was totally just unplugging my headphones, and I was trying to figure out why I was hearing crackling in my.

Kim: 9:25

We are such a mess today.

Pam: 9:26

Today's a mess. Alright, I'm going to stop playing with the plug of my headphones. Where was I. Oh, yeah. People ask. Yeah, they asked for this like list.

Kim: 9:37

Yeah.

Pam: 9:37

Well, and you and I've always kind of been a little uncomfortable with that because there are good questions. We can give you a list of decent questions to ask.

Kim: 9:47

Sure.

Pam: 9:47

I think the reason that we get kind of pausey and hesitant is, it's you don't ask the same question, at the same time to every student.

Kim: 9:55

Right.

Pam: 9:55

And really you don't ask the same sequence of questions. That's probably the most important part of it.

Kim: 10:01

Yes.

Pam: 10:01

That sequence of questions is going to depend on the student.

Kim: 10:05

Yeah.

Pam: 10:05

Cool. So, I can also say, there might be a time where you're interacting with a student, and they're just kind of being obstinate.

Kim: 10:13

Right.

Pam: 10:14

Where they're going to wait you out until you tell them what to do. And in that case, we might as teachers... That might be the time where we get the most like, "Oh, let me just tell you what to do." You know like, when the kid's like, "I don't know. I don't know."

Kim: 10:29

Yep, yep.

Pam: 10:31

"Just tell me what to do." So, we also might want to kind of parse out when you're dealing with a kid who's just trying to wait you out until you just use a funneling pattern of questioning. And maybe we could talk about like, Kim, how you could. In fact, Kim, how would you handle that?

Kim: 10:48

I mean, so much of it is dependent on the relationship with a student right? That's kind of the first thing is, you know, how do we get to this place where they're so focused on the answer? Have I done something to indicate that I'm focused on the answer? You know, what's their background in mathematics?

Pam: 11:05

I mean, it might be the beginning of the year where they come to you, and they've all kind of had that as their background.

Kim: 11:12

Yeah. Well, it could be. You know, it has happened. You know, it's on me, and so I have to really think about what do I know about the student and try to enter into a place where they have access to something, right? I think kids, when they're seemingly obstinate, when they're like, I'm just going to say something. Most of the time it comes from they're trying to regurgitate something they think you want, or they're trying to check out a little bit because we haven't accessed what they know. And that's kind of the whole point of questioning to me is, let me get to where you are, that you know something about this. And instead of like, shove you along, let me dig into a conversation with you, and guide you, and partner with you, and have a conversation with you, so that we can make connections together.

Pam: 12:06

Yeah, so know your content, know your kids. You're sort of thinking everything you know about that student, and then you're using that to enter into the conversation.

Kim: 12:14

Yeah, for sure.

Pam: 12:16

Okay, so let's maybe try. We're going to try to kind of not really roleplay but kind of describe some situations.

Kim: 12:23

Yeah.

Pam: 12:23

Let's see if we can kind of parse out what would it look like to have a focusing pattern of questioning? What would it look like to have a funneling pattern of questioning? But we're also going to be super clear, listeners, that this is hard for us because we kind of were talking before, and as I try to do it, I just instinctively start "focusing". Like, it's hard for me to imagine funneling. I almost have to think of what I've seen. So, we'll do our best. Kim, you can call me out if you're like, "No, no. You're focusing not funneling." Alright, so let's say that you're sitting down with a second grade student, and there's a word problem. Could you envision a teacher saying? So, student's like. You know, teacher says, "Hey, you know..." I don't know. "Are you stuck?" Or whatever. The kid says. "I need help." In some way, the teacher's kind of entering in to help the student.

Kim: 13:11

Yep.

Pam: 13:11

Could you envision a teacher saying, "Okay, so it's a word problem."

Kim: 13:16

Yep.

Pam: 13:17

"Look at our poster over here. We've got our CUBES, our steps, or (unclear) poster on the on the wall." That was a joke, unintentionally. "Okay, what is the first thing you're supposed to do?" Yeah. And then look at the poster, right? And the kid says, Oh, I'm supposed to find the keywords." "Okay, go underline the key words. What's the second thing we're supposed to do?" "I'm supposed to identify the numbers." And so, the teacher is literally saying,"What's the first thing?" But, you know, pointing at the. With good intention, trying to get the kids to use the resource that they've already laid out. Whatever. And as I sort of like,"What's the next thing? Okay, do it. What's the next thing? Okay, do it." I would suggest that's a funneling pattern of questioning. I'm funneling the kids through this sequence of predetermined steps that someone else has thought about. And, again, it's with the well intentioned of if maybe we think if I do that enough with a kid, then they'll do that process on their own.

Kim: 14:11

Yes.

Pam: 14:12

We would suggest, that doesn't typically work very well.

Kim: 14:16

Right.

Pam: 14:16

So, what could it look like to help a student focus on that second grade problem, word problem?

Kim: 14:23

Yeah.

Pam: 14:24

So, Kim, you walk up to that second grade kid. What are some things that might happen?

Kim: 14:27

Well, so I had to write down some numbers because, you know, also that will depend. So, I just wrote second grade, 18 plus 39. So, I might sit down next to a student, and the first thing I'm going to say is, "Have you had a chance to read the problem? Okay, cool. We got that." So, I might say, "Tell me what you're thinking right now. And a student might say... They could say, "I'm not thinking about anything." But they might say, "Oh, this is about cars." Or whatever. Pick a thing. Like, Okay.

Pam: 14:57

Pokemon.

Kim: 14:57

Yeah, Pokemon. Good. So I might say, "What's the problem about?" And they might say, "Oh, well, there's like one friend has 18 Pokemon, and the other friend has 39 Pokemon." And I might say, "Oh, that's interesting. What's going to happen with this problem?" Like,"What do you know?" And they're like, "Well, there's two kids, and they have Pokemon." They might repeat, right? And I might say, "Do you think that there's going to be more Pokemon? Or do you think there might be less Pokemon? How do you know?" And they might say something about that. And I might say, "Oh, those are some interesting numbers. Tell me about those numbers." "Well, it's 18 and 39." Like, "Oh, those are interesting numbers. I wonder if there's anything near those numbers that might be useful?" And the kid might say, "Well, 18 is like kind of close to 20." Like, "Oh, interesting." So, it's a... I'm going to suggest something, and I'm going to take what you say back to me, and that's going to guide me to the next thing. If they say, "I don't know anything about what they're near." I'm like, "Okay, so you've said that you think the number's going to be..." When it's asking me about how many do they have together, you might say, "I think it's going to be more than the two separated, the 18 and the 39." And I might say, "Tell me why you think so?" "Well, because I think I'm supposed to add the 18 and 39." And once they understand what the situation of the problem is, then I can get into like a strategy they might use and have a conversation about strategy, right? So, the first thing about a word problem is, "Does it make sense to you? Do you know what we're even being asked?' And we're visualizing it. We're describing it. We're trying to understand what's happening.

Pam: 16:35

You're like diving in. You're diving in, and like really what's going on in this problem? Let's be really clear what's happening.

Kim: 16:41

Yeah.

Pam: 16:41

What the problem's all about.

Kim: 16:42

And then, I can have a conversation about, "Okay, so you think you're going to add these numbers. Tell me what you know." And so, I might say something like, "You said that 18 was really close to 20. How can that help you?" "Well, I think I can... If I add 39, then I can add 20. Oh, do you know 39 and 20?" Yes or no. "Okay."

Pam: 17:06

At each of these junctures, you're pausing before.

Kim: 17:09

Yep.

Pam: 17:10

And if they're saying something, you're not asking that next more particular question, right?

Kim: 17:14

Right, right.

Pam: 17:15

Yeah, I just wanted to. You're...

Kim: 17:16

Yes.

Pam: 17:17

Yeah, keep going.

Kim: 17:18

Well, I was going to say, it's really a conversation, you know. It reminds me of when you want to know something about, like, somebody's telling a story, and they say something, you're going to ask a deeper question, a more detailed question, so that you can really understand it more. And so, it's a back and forth conversation, not a series of questions that I'm asking because I need them to know, "Okay, now I'm going to ask you the next specified thing, and the next specified thing." Whatever they say, I'm thinking about, "What's the next thing I can ask, or think about, or help them visualize, so that then they know whether or not that's helpful to them?"

Pam: 17:58

Yeah, and maybe I'll say, what's the next thing you can ask to help them focus on whether that's going to be helpful to them or not? Right?

Both Pam and Kim: 18:06

Yeah.

Pam: 18:06

You're literally helping them focus by asking a focusing pattern of questioning. Kim, I want to highlight two things. I was writing quickly while you were talking. So, a couple of things that I want to highlight is that you started... So, the kid needs help. I feel like we've established in some way, the kid's raise their hand, or you've gone over there. You see they're. Whatever. Kid needs help. And the very first thing you said was, "What are you thinking about?" The very first thing you didn't say was, "Tell me what's happening in the problem." Or, "Tell me what you're going to do in the problem." Or, "Show your thinking on the paper." Or...

Kim: 18:43

"What operation are you going to do?"

Pam: 18:45

Yeah. What you said was this very open, "What are you thinking about?" Because that might have been enough, right there, that you wouldn't have asked any of the other questions you just asked. Because in that moment, they might have said,"Well, I'm thinking..." I don't remember the numbers. 39 and 18 or something. Whatever numbers you made up.

Kim: 19:00

Yep.

Pam: 19:01

"I'm thinking about 39 Pokemon and 18 Pokemon, and I was trying to decide if I was going to add 40 to 18 or if I was getting add 20 to 39." And then, you walk away, right? So, what I'm suggesting is, is that very first question, you're gathering information. Like,"What are you thinking about?" in this kind of general way? And then, you went on to ask more specific questions because you're assuming that when you ask that, the kid didn't exhibit a lot of understanding or something of what was happening. So, then, you're going to continue this pattern of focusing. I'm helping the student focus on stuff.

Kim: 19:43

Well, and so sometimes the if I say, "What are you thinking?" You know, a very common response might be, "I don't know what to do." And so, then, the next thing I might say is, "Tell me what you do know," so that I'm not assuming knowledge, and I'm not telling them what they should have known. I'm giving them an opportunity to share with me what do they already have under their belt about this particular problem.

Pam: 20:09

Yeah. Okay, and so I want to point out one other thing that you said. If I can read my writing. You said, "What do you think..." Once you got to sort of where you'd kind of identified what was. You know, the kids like, "Yeah, I know what's happening in the problem. And, it's these numbers. And it's more or less." Or whatever. Then you said, "What do you think about those numbers?" I just want to highlight that question. Because "What do you think about those numbers?" is exactly like that "What are you thinking about?" question. That we've established what's happening in the problem, and you know that these are the numbers that are important, and you know it's going to be more than those. And then, you just said, "So, what are you thinking about those numbers?" That's brilliant because, again, you're helping the student ask themselves, "What am I thinking about those numbers?" What does the student know? What's pinging for them? It's not you forcing something on them, it's you helping them focus on what they know.

Kim: 20:58

Well, and it could be that a kid might say something like,"I know 10 and 30 is 40." And instantly I'm like, "Oh, you're thinking split by place value." Or they might say, "Well, 39 is close to 40." I'm like, "Oh, you might want to do a little Over strategy." Or whatever. Whatever they say, I'm like racking my brain for strategies

Pam: 21:13

Yeah. that they might be thinking about, that then I can help think about that strategy aloud with them. Which doesn't look like you saying, "Okay, so then right now, you should... Okay, do the Over strategy."

Kim: 21:29

"Write 18. Now, make a jump of 40. Now, go back 1. Good job." Walk away. (unclear).

Pam: 21:35

That would be a funneling pattern right there. Yeah. Like,"Okay, then do these things." Instead, you're helping them focus on what they know. "Oh, so you're thinking about 40? Well, how could 40 help you with this 39 and 18. Oh, okay." Yeah, yeah. I love it. That was a super good example. Let me give you another example. Let's get a little older. So, let's say that a student is finding the volume of a rectangular prism.

Kim: 22:00

Yeah.

Pam: 22:01

Let's see, a funneling pattern could look like. "Okay, so it says you're finding volume. Get out your..." And we're in the state of Texas, so they have a formula sheet.

Kim: 22:11

The STAAR, yeah.

Pam: 22:12

Yeah. And so, "Take out your formula sheet for your high stakes test. Find volume. Okay, so what do you do? What..." See, now I'm trying to. I'm getting more focusing. Let me see if I can funnel. "There's the formula, so where's..."

Kim: 22:31

"What are the numbers?"

Pam: 22:33

Yeah, I was like. What would it be? Base times height times length or something? Length, width, height. "So, what is 'L'? Ok, go find it. What's'W'. Go, find it. What's 'H'? Go, find it. Okay, now multiply them together." Like, that would be kind of. I'm asking questions. "What's 'L'? What's'H'?" But they're just like plucking numbers, right? And they're plugging them in a formula, and they're not thinking about. Like, I've already even identified for them. "It's volume, get your chart out." Like, "Look at your formula." So, that could be kind of maybe a funneling pattern of questions. What would focusing look like?

Kim: 23:08

So, similar to the second grade problem. I might say,"Hey, tell me about this prism." So, they might say something like, "Well, I know it's 3 long and 2 tall and..." Whatever, pick a number. And I might say,"Can you picture that?" Like,"Can you picture what that would look like?" We might sketch it. We might not. I might say, "Hey, what's going on with the base? Tell me about the base." We might say, "Well, it's this wide and this long." "Oh, that's interesting. That's the base? Okay, cool." And then, "What else do we know?" They might say, "Well, it's whatever tall." I'm like, "Oh, okay. So the base you said was... blah, blah, blah. And how tall? Oh, okay. So, I'm picturing the base..." And I'm using hand motions at the time, and I'm helping them visualize what's going on. And I'm like, "I'm picturing some layers. Can you picture those layers? Okay, cool." So, tell me about the base again. Ah, so the bass is... blah, blah, blah. And then it's got..." I'm with my hand motions, thinking about some height, the layers of the height. And I might say, "What are we supposed to figure out?""The area." "Wonder how the base can help me find the area?"

Pam: 24:22

Oh, you mean volume, I think. Yeah.

Kim: 24:24

Oh, whatever. Volume.

Pam: 24:27

We had the area of the base.

Kim: 24:29

The area of the base.

Pam: 24:30

And you're trying to find volume. Whatever, Pam.

Kim: 24:32

"I wonder how the area of the base might help me..."

Pam: 24:37

I love it.

Kim: 24:37

With the total volume, right. So, there's a little bit of wondering aloud and a little bit of like asking them to be involved in the wondering with me and chiming in with what they know.

Pam: 24:47

Yeah. I love it. I wonder if even maybe... Earlier, I loved how you were envisioning. I wonder if I might have said something like, "So, volume. What is that? Is that like we're wrapping the box? Is that like we're filling the box? Like, what's happening? What does volume mean?" I might want to try to get it that, and then I might ask a little bit of a higher level question like, Well, once we've established, you know like, we're refilling it with these unit cubes. "Like, we could count all those unit cubes. But in class, we've developed more efficient ways of finding those. Like, tell me about that. Do you remember any of those? Like, are you? What are you thinking about? What's a more efficient way that we've kind of messed with?" And I might be able to refer back to the Rich Task that we did.

Kim: 25:32

"Do you remember when we did... blank?" Yes.

Pam: 25:33

Yeah. Or the Problem String that we did. And I might be like, "Remember when Roger was like, 'Well, if I just found the base...'?" And then, I pause, right? Like, Do you remember when Roger was talking about,'If I can just find the area of the base...'?" Pause. Or,"Remember when..." Pick another."...when Amaya was talking about, you know like, 'Well, if I know the number of layers I've got...' How was that? Do you remember? Was that helpful?" Like, I'm trying to ping on experiences that the students had.

Kim: 25:57

Yep.

Pam: 25:57

But I'm just saying just a little bit, right? We're just throwing out just enough for them to go, "Are these things..." And then, we're watching. You know, like, "What do they mean to you?" And then they just like, "Oh, yeah. I could count the number of layers." "Why? How does that help you if you have the number of layers?" Like, "Do we have that number here? How does that?" "Well, because if I had the base, then I could count how many of those." Again, like sort of helping them focus on experiences they've had and things we've developed in class, not a series of questions, you know, where they're just sort of looking at that formula chart, and we're asking them questions, so they could plug stuff in.

Kim: 26:34

Yeah.

Pam: 26:34

Hopefully that kind of helps a little bit. Yeah?

Kim: 26:36

Yeah. So, both of the examples that we just gave the second grade and the fifth grade might make it seem like funneling is like point to a resource. (unclear).

Pam: 26:44

Oh, yeah.

Kim: 26:44

We talked about the formula chart.

Pam: 26:48

The high stakes test formula chart. Mmhmm.

Kim: 26:49

But it's not that. It's not that, you know, you go to a resource, and that's funneling. Funneling can be questioning.

Pam: 26:55

(unclear) point to a list, right? It's just pointing to a list, and then following it. It could be that, but it's not only that.

Kim: 27:00

Yeah.

Pam: 27:00

Yeah, I agree. Okay. Agreed. Yeah.

Kim: 27:03

It's about leading them in such a way that they can answer your questions, but they're removed enough that they aren't in the conversation. They aren't cognitively involved in what's going on, and they cannot, at that point, go back and do it themselves. They can't think about it themselves and(unclear) funneling.

Pam: 27:23

Yes, exactly. They might be able to repeat your funnel, but what they're not doing is reasoning through that funnel, right? Like, because as a student if a teacher would funnel, had a pattern of questioning of funneling me, I would say to that teacher, "Do that, again. Funnel me again." Funnel me again, until I memorize their funnel, and then I was able to successfully repeat the funnel. So, we're also not suggesting that right? That's a funnel. It's not about memorizing. It's not about thinking about someone else's thinking. It's about what pings for the student, and helping them focus on the major relationships and what they can do with those relationships. Again, we're pulling back on experiences we've had. It's not like... I think about an Ed psych class I had where we talked about history of Ed, and there was a whole philosophy of Ed that you just let the kid wander through the garden, whatever they're interested in, then you kind of let them pursue that. It's not that. It's not like we're letting kids ramble, wander aimlessly at all. You have to know the content and know the kids. Know your content, know your kids. Knowing the content, I'm asking questions that help the student focus on what they know, relationships they're building, how they can use those relationships and connections for them to reason through to the answer. So, maybe let's give one other quick example. I kind of felt like we've done some young ones. Can we do kind of an older one?

Kim: 28:46

Sure.

Pam: 28:47

So, if we're finding the slope of a line. So, maybe I've given students two points, and I've said, "Find the slope of the line." So, if I was looking at a funneling pattern of questioning, it might be something like, "Which of those points do you want to be x1, y1? Okay, that one? Okay, good. Alright, so what's the formula? Okay, so where's y2? Plug it in. Where's y1? Plug it in. Where's x2? Where's x1? Okay, subtract. Subtract. Now, divide." Like, I'm saying, "Where's that? What's that?" And I might even at that point when they plug them all in, I might go, "Okay, what do you do next? Okay, what do you do next?" I'm asking questions, but it's this funneling. Now, you might be like, "Well, Pam, that is how you find the slope of a line." What would it be like to reason about finding the slope of a line between two points? Well, I might say to a kid, "Can you picture these two points? So, what do you know already? Like, once you can picture them, is there something you know? Is the slope..." And if they don't say anything at that point, then I might go like, "Is it increasing? Decreasing?" And if they don't say anything, I might go like, "Is the line going up? Is the line going down?" And I might draw on an experience that we would have had using a motion detector as time is happening."Is the line between those two points going up or is it going down? Increasing or decreasing. So, then, "You know that the slope is positive or negative. Okay, cool. Great." Like, I might start there, and then I might talk about. "What do you know about slope?" Like, when we've talked about rate in here, what's happening between these two points?" And then, I might draw on an experience we've had. So, if this was a frozen yogurt experience. If this was like I go to a frozen yogurt shop, and the more yogurt I put in the cup, the more I pay. So, as x is increasing...the x being the number of ounces of yogurt...then the cost is increasing. Then, I might go"Oh, so, this match is kind of a frozen yogurt. The more yogurt we buy, the more it's increasing. So, what's happening? What are these numbers represent? And can you reason through that?" Again, I'm not spending a ton of time regurgitating the frozen yogurt scenario. We've spent time in that scenario enough that I'm going to look at that kid, and I'm going to go, "Does that help this student focus that these values... In fact, I can even back up and say, "Which of the scenarios we've been diving into do these two points remind you of?" And if it's a lot of decimals, because frozen yogurt cost $0.30 an ounce, then they might go, "Oh, yeah, it's more like frozen yogurt." If it's a lot of bigger numbers... I'm trying to think of. Like, Driving in Texas is another example. Then, they might go,"Oh, yeah. It's like miles per hour because those are sort of..." Or kilometers per hour."Those are bigger numbers." So, we're going to draw on like,"Which of the major scenarios that we've been investigating does this ping for you?" And then, I'm helping that student focus on, "Well, what did we do there? How did we use the relationships there? Oh, can you use those relationships here?" So, hopefully, that's a little bit of an older example of helping students focus, not funnel. Yeah?

Kim: 31:41

Yeah. I think it's a different mindset, right? I think in general, it's a different mindset. Are you tapping on your thinking and asking a bunch of questions to get them to think about what you're thinking about? Or are you entering in a conversation to understand what they're thinking about and trying to draw it out?

Pam: 31:57

Nicely said. Thanks for tuning in, ya'll, and teaching more and more Real Math. To find out more about the Math is Figure-Out-Able movement, visit mathisfigureoutable.com. Let's keep spreading the word that Math is Figure-Out-Able!