S6-E10: Supercharge math fluency through problem-solving

Tune into this episode of Math Teacher Lounge, featuring math teaching and learning specialist and friend of the podcast, Fawn Nguyen. Listen as Nguyen dives into the unique and powerful relationship between math fluency and problem-solving, and learn about how problem-solving activities can be leveraged to engage all students and fuel math fluency development.

Learn why math fluency and problem-solving have a symbiotic relationship and how to create problem-solving activities that generate individual and peer learning opportunities, including examples from the California framework. Plus, hear tips for supporting  the relationship between problem-solving and math fluency that can implemented in the classroom, throughout the school building, and at home.

Transcript

Speaker 1: 0:00

People would just abruptly say to me, how does my student be able to engage in this problem if they don't know their facts? And I, I think out of all the things that I hear, that one breaks my heart because somehow we're equating computational and memorization with be able to think, be able to enjoy mathematics.

Speaker 2: 0:19

Hi, and welcome back to another episode of Math Teacher Lounge. I'm Bethany Lockhart Johnson .

Speaker 3: 0:24

And I'm Dan Meyer. Great to see you folks here. Hi, Bethany.

Speaker 2: 0:27

Hi. We are on episode 10 of this season, all about fluency. And you know, I gotta say, we started out this whole season talking about how you felt about fluency. I'm not ready to yet, Dan, to hear how far you've come, but I just wanna say that like the guest we have today, if no one else can convince you about the power of fluency, it , it's, it's this guest.

Speaker 3: 0:55

Yeah. I feel like me and this guest, and I will , uh, not be mysterious about it. It's Fawn Win fan favorite second time appearance that I, I feel like Fawn and I come from a bit of a similar tradition in that we like both appreciate problem solving, mathematical modeling, thinking that isn't often easily captured in like, let's just say a , a math drill worksheet. Um, so I, I feel like I, I we've recruited onto the show today, someone with whom like, I'll , I'll be on the same frequency with Fawn and I hope to learn a little about how Fawn sees fluency and problem solving and how they relate.

Speaker 2: 1:33

Well, that's exactly what I mean. Like, I feel like there's something about the way you both talk about math and problem solving that will just like finally be like , oh, I'll listen to you Fawn , not Bethany

Speaker 3: 1:47

<laugh> . Right, right. Not

Speaker 2: 1:48

Our other fantastic experts and thinker. Fawn got you

Speaker 3: 1:52

Fond though. Yeah, fond has that but

Speaker 2: 1:54

Fond though. Yeah. Yeah . We're both fans. And , um, hey, so before we dive in though, how are you doing, how is the world of fluency in your first graders lives?

Speaker 3: 2:04

Right, right. Thank you for asking. Um, we are , uh, coming up on end of the first semester and I would say my approach to fluency from day one, the day whatever we're at day 100 or so , um, has changed a lot over the course of this season. You know, through learning with experts here on the show, through learning with you, I find myself much more excited to inject elements into fluency, work with my kids that are gamey, that involve choice, that involve , um, you know , thinking about structures that try to help like properties of math emerge that aren't just like the numerical answers , um, you know, on the paper. And so I would say I'm , uh, you know, people are generally pretty math positive around here, still in kinder and first. So we'll take that for a win. People aren't freaked out by seeing numbers and we still have some conversations here and there that are, you know , kind of creative and fun. So I'm, I'm, I'm loving it. Thank you for your help with that.

Speaker 2: 2:55

Hey, I gotta say, I was hoping I'd get far more texts from you featuring, like, images of you all mid gameplay , but, but I understand you're so in it that you're not even thinking about I , you know what, I should share this magic fluency moment with Bethany . But yeah , I'm happy to hear, I'm happy to hear it's, it's going well.

Speaker 3: 3:14

Yeah, it has been careful with that. What , what you wish for there. 'cause I might just FaceTime you in and have you teach my kids on every afternoon or try to, anyway, <laugh> . So watch out with that

Speaker 2: 3:24

For having your children. I would be delighted too . I would be delighted too . So we're bringing back fa now . Fawn joined us season two of the show. Season two, Dan, season two. That's when we were on video.

Speaker 3: 3:37

Yes. We had characters in our drama that were still alive. Like there's some major plot points , um, that hadn't yet been revealed , uh, in our drama that is Math Teacher lounge. Back in season two, we were talking to Fawn about was it problem solving then? I wanna say it was problem solving. Yeah ,

Speaker 2: 3:52

Yeah, yeah , for sure. And it was, you know, we got such good feedback about it. Yeah.

Speaker 3: 3:56

So if you were not around in season two, or for some reason don't know about Fawn , lemme just tell you a bit about Fawn . Fawn is currently a specialist on the math teaching and learning team here at Amplify. Um , but in F's career, F's I , I think better known as, as a math teacher, and certainly like a, a capital M, capital T math teacher, a math teacher's teacher. Um, fawn loves the work , uh, as much or more than anyone I've ever met. Teachers will attend Fawn Sessions around the world and will just vibe with her immediately for lots of reasons. But I think a lot of it is just that she, she really gets the work and presents as someone who has done the work for a very long time, knows what kids are like, knows what math teaching is like, and , um, it's just very, I guess authentic is an overused word. I think Fawn is one of the most authentic math teacher types I know. Um, yeah. And Fawn has also done work as a math teacher coach in case that wasn't , uh, you know, super obvious from the intro there. So yeah, just really excited , um, to have Fawn back on the show and to help you folks and all of us learn about how fluency and problem solving , which I have had in my head as somewhat, you know, antagonistic as somewhat like unfriendly to one another to help us and especially me learn how they relate. So please welcome Fawn back on the show. Hey, fawn , good to see you again.

Speaker 1: 5:10

Hey. Hey, Dan. Hi Bethany . My god , I finally get to talk. Oh , <laugh>, my goodness. 20 minutes in

Speaker 3: 5:21

<laugh> . That's a great intro to Fawn. Yeah, fa vibe right there. Thank you, fawn . Alright , yeah , I'll go . We'll go shorter next time. Yeah. Good to see

Speaker 1: 5:27

You. Great to see you guys.

Speaker 2: 5:28

Welcome to the chant . Thank

Speaker 1: 5:30

You for having me. Yeah, it's always a pleasure.

Speaker 2: 5:33

So we have been asking all of our guests if there is an area of your life beyond mathematics where you're currently building fluency.

Speaker 1: 5:44

I know I heard some others. I've been listening. And , uh, it's baking, bake a baguette, not just any baking. I love to cook. I love to cook. And so on the stove top , I'm, I'm, I'm pretty good. But yeah, baking is another beast. And but Baguette and , uh, someone told me that that actually is the measure, the quantitative measure of , uh, the chef. Right. The one who really knows. And , uh, well, no wonder I've , I've been, yeah, it's tough. It's tough. It's too many moving parts, too many variables. And , um, I don't think I have the right water, I feel like, because I've tried everything. So it's baking a baguette.

Speaker 3: 6:24

We've had some chats about , uh, yeah. Making roast chicken with Jason Ziba and now a French baguettes with Fond Wynn . We , we have like a, a real, we can pivot to a different kind of podcast here, Bethany pretty easily, I think. Yeah. Yeah .

Speaker 1: 6:37

We , we have a channel for cooking.

Speaker 2: 6:39

I love hearing about what folks are working on. Yeah . And I think it just helps us broaden our definition of fluency. And I also think it helps us remember that we're all learning, it's all about learning, and we all have things that, you know, maybe we are fluent in our math facts, and so it could be hard to relate to the topic, but then when you remember, there's things that you're brand new at too, it can help kind of ground your work and your thinking and remind you what it's like to be a beginner. So we have so much we wanna talk to you about, but I have one more baguette question. What would you say, like, thinking about one of the first baguettes that you made, right? Right. And compared to like what you are putting on the table now, how has that process changed or how has that, like your thinking about the process changed?

Speaker 1: 7:31

Right . I definitely have improved. For example, I've got, you know, the , the proofing down. So yeah, there's definitely, I , I can, you know, I wish I did the before picture right . Graduate , because I'm definitely getting better. So now, like I mentioned, maybe it's just the water is that one part that's not quite perfect. But otherwise, yeah, I mean, you know, made leaps and bounds. So we , we get better at something we spent , um, a lot of time on.

Speaker 3: 7:57

Um, we are so excited to talk to you because one, you're fantastic, and two, you're an expert on problem solving. Uh , before we delve into the nitty gritty, I'm just curious at a high level, how does an enthusiast on problem solving think about fluency?

Speaker 1: 8:13

Well, first what , anytime I hear the word fluency , um, it always takes me to the context of what it means to be fluent in a , a language, because I'm an English learner, right? So to have flow, not stumbling, not being stuck. And I finally can make a claim like two days ago that I can speak English fluently. I mean , it's just right . So I'm, I'll always be an English learner. I feel like that. And , um, now sadly, however, I have to say I'm no longer, I was just in Vietnam last month and I am no longer fluent in Vietnamese. Right. 'cause I spent so much time I left when I was so early. I spent so much time , um, trying to learn English. Oh, wow . And now that I have it, yeah. So I , I can't say I'm, I'm fluent in Vietnamese anymore. You know what's weird though , uh, Bethany and Den is I woke up one morning and I wish I'd written down the date. I woke up one morning and realized my thoughts were in English, my thoughts in English, right? It's a language I'm trying to learn. I'm trying to learn. I'm, I wanna get this right. And then all of a sudden it's like, wow, I'm my thoughts in English. Oh, wow. So that's when I knew I'd switched over. It's weird. Right now, you know what remains completely intact, however, completely intact is my Times table is in Vietnamese, because I had learned that in Vietnamese, right? So , oh . So even though I've, you know, yeah, I , um, well maybe this had everything to do with it, which was, it was literally beaten into me. And I've shared this story hundreds of times, and you can ask any Vietnamese , uh, who went to Catholic school. So we would stand and , uh, so we'd all stand up with our palm face up like this one palm face up as , as we all stand. And the teacher would walk around with a stick to hit us and just point at us and say like, you know, seven times eight. And if the answer does not come promptly, you know, automatically, then we get hit. The problem is, well, it , it hurts a lot. But the problem is, what normally happens is one of us in the room, and it's like, who is gonna be is, you know, we're humans, right? We, we , we naturally just kind of pull back, so we flinch and pull back. If you pull your hand back and the teacher misses your hand, then you're gonna get twice. Then you get two . Yeah. So that happened a few times. So what we do is a lot of us do, is we take the other hand and we grab our wrist just to hold it in place and then look away. But then if we look away, we don't know if the teacher's pointing at us. So it's like, oh, so that's, that's traumatic, right? That, that is, that's how I learned the times table by just, it was literally beat into to us. Uh , yeah , I don't joke about that. That's just, yeah. So it is terrifying. I remember missing it a few times or, you know, I'm just taking my time just trying to figure out what it is. And it didn't come out fast enough for the teachers and then Yep . Got hit.

Speaker 2: 11:06

What an interesting, like, connection to fluency. Like the , the , you know, what an interesting connection to, to thinking about how you learn something and to thinking about how your relationship with math developed, right? Like , right.

Speaker 1: 11:21

Yeah. And so I , I don't know if that's why I'm, so, I'm literally scared. I mean, I freeze up anything. There's time when something is timed. Even games like Kahoot, which is very popular among teachers, right? Kahoot games when I'm playing a , a game , um, I don't know all those apps. And if there's a time factor, I I just lose it as I give up. I don't even try anymore. So that's how , um, yeah, I don't know if that ties back to being hit, but something, right. It's , it's pretty good evidence.

Speaker 2: 11:51

I would , I would say there's probably a

Speaker 1: 11:52

Link. Yeah . Right ? Yeah. Uh , alright , well, so I think math , um, back to the math fluency, it's , it's quite similar to language fluency, right? It's doing mathematics with a flow, not fast, I didn't say fast, but flow, it's like fluid. So it's having confidence in knowing efficient and accurate ways to compute. It's being flexible in one's thinking and applying strategies. And school math, I wanna say seems to tie fluency more to basic facts and computation. And this is evidenced , um, by the explicit language that I see in the grade level standards, right? I mean, I don't recall, I don't know if you , correct me if I'm wrong, but I don't recall seeing fluency standards in high school. So, which further sends a message that, hey, you're in high school now, you should have these procedures down, right? So it , it puts a stop to fluency to me that, that this seems, when it's not, it's not mentioned as often, you know, you should be fluent in high school and in upper grades. And I think that's just something, I don't want it to be that way. I don't want that to be the case. I think you can always learn new strategies and learn more efficient ones. So the , the intersection for problem solving that you brought up, I think, you know, the three words that we always use to describe fluency, right? It's , um, efficient. We want to be efficient with problem solving so we don't get bogged down in too many steps and lose track of our reasoning. And , uh, we certainly wanna be flexible in flexible in problem solving. Just like in fluency is knowing more than one strategy, knowing more than one approach. That way you can choose in order to pick the right one, we have to have more than one to choose from. And also we might use one strategy to problem solve and a different strategy to check the result. And then the third word we use to describe fluency that you can also describe problem solving is to be accurate, right? So of course we wanna be accurate during problem solving. Uh , we wanna do careful. That means careful recording, mindfully systematic in our recording and always double checking our work. I mean, all of those habits of mind or just , um, those quantitative qualitative measures apply if I take all the problem solving strategies or the common problem solving strategies and put it side by side with fluency strategies, right? If side by side they have quite similar, for example, or very powerful problem solving strategy is to do a simpler problem and fluency. That's what we're , we are doing when we are decomposing and breaking up numbers, right? To do a simpler problem. Another one is working backwards in problem solving . It's helpful to sometimes think about applicable to use working backwards. And that's inverse operations. You know, I, my ad in a subtraction problem, I'm adding, I'm moving forward, you know, all these inverse operations , um, make a table in problem solving. That's literally the organization of the Times table , right? And then this one I love, this is from , uh, Jocelyn Zucker. I , I love this strategy for problem solving. It's called wishful thinking, right? The problem's difficult, we're not quite sure. So we, we wish it were this part or we, we wish this constraint wasn't there. We wish this, we wish that, so that , um, we can control some stuff, make it easier. And that's just when we do in fluency, right? I for example, don't multiply by seven ever. I don't, I I , there actually, there are many, honestly, if you ask me to multiply a three digit or more , um, I stop at two. I stop at two. Uh , if I, I take a three digit number, multiply by. If I had to multiply by three, I will multiply by two and then add that whole , you want me multiply by four? I do double, double , right? I tell my students this , I don't multiply by five, I multiply by 10 and I divide by two. 'cause there's , there's just easier operations. So that's what I mean by wishful thinking is , um, we do a lot of rounding. If I had to multiply by eight and nine-tenths, eight and nine-tenths, okay, that's a little taxing on my brain. I'm gonna try multiplying by nine instead or by 10 and take away that kind of thing. So just a ton of strategies. And for me it's more, it's fun because I , you know, it , it , it's fun to play. Why not? Why not play with the numbers in that way,

Speaker 2: 16:19

The language that you're using to describe problem solving ? You talk about those elements of fun. I love the, I haven't heard you said Josh Zucker's wishful thinking. I hadn't heard that idea of, well, imagine it in another way, right? And I'm imagining the strategies that students are using to solve problems and using derived facts, using known facts to figure out facts that they don't know. And when I'm thinking about students in my class or when I'm thinking about games that they're playing, students are actively , like, I want them actively playing around with the numbers, right? And trying out, well, let's see, let's see if that works. Or how did you think about that in sharing their strategy and those conversations that are happening in fluency practice. I so see that connection to problem solving. Because in problem solving, I want my students to think about, well, what did you use to solve that? Or what do you understand about the problem? And how did you get that part? Or where did your thinking come from? And those conversations and that meaning making it, it, the playfulness with which you talk about problem solving, I think a hundred percent, it's so often missing from fluency practice. And so I love those links that you're building.

Speaker 3: 17:38

I think it often feels like that fluency is there to support problem solving is how it's often positioned where kids need to be drilled on their basic facts and had to have to , uh, have everything down to automaticity and then they can engage in some problem solving experiences. But like Bethany said, it's really nice to see the bidirectionality here where you can inject elements of problem solving into fluency. How they can support one another. If you had, you know, any kind of way other ideas to inject that energy of problem solving into fluency work, I'm sure we'd love to hear it.

Speaker 1: 18:14

Well, first, I, I wanna mention what you , you said earlier about , um, you know, that you have to be fluent in order to problem solve. And I unfortunately, I , I hear that a lot. And actually people would just abruptly say to me , um, how does my student be able to engage in this problem if they don't know their facts? Right ? And I, I think out of all the things that I hear, that one breaks my heart. It really breaks my heart because somehow we're equating computational and memorization with be able to think, be able to enjoy mathematics, right? And then the intersection between problem solving fluency is symbiotic. There's, you know, if I can think of it that way, right? One helps the other, it really, you don't need, it's not a prerequisite. And if anything , um, when you have a kid engaged in the problem, problem based , that, that engagement, right? We want kids to be interested in the problem, then that would just bring out, now they're interested, now they wanna spend time working on something. And then so it , it , you know, one should be playing off the other . And I remember , um, in Dr. Staley's podcast, I really appreciate hearing you say, Dan, about the binary, right? That when we say that the kids can do this or not do able to do something, and I think, you know, where's the progression when we say they can't do something that , that's just, that just makes, you know , me just wanna die because Yeah. Well , it , it's such a heavy label that you can't do something. I mean, I know we say that as adults often, but when we're, when we're labeling children that they can't do something and, and something such as fluency, which is, is supposedly take , um, this lifespan, right? This K through 12 at least. And again, I keep mentioning Dr. Staley just because I, that's the last episode I had listened to, and I so much appreciate everything he said. He mentioned the story and math as a story, and how is this vertical, how mathematics is more vertical. And then we have, we owe it to the children, we owe it to the kids that they get the time to process. And it just seems, yeah. It's like what? They can't be exposed to this interesting problem just because they don't have their number facts.

Speaker 3: 20:30

Yeah. My feeling is that when, when people say that students can't do a particular problem solving experience, it's often because of poor design of that experience, not because of any kind of limitation on the kids themselves, like students , right ? Right . Kids, people are all sense making mammals, like they look at things and make sense of them without even having to, in lots of ways. And when, you know, I've worked on some of the problems that, that you've produced for people. Mm-Hmm . <affirmative> , like, they're visual. They propose a question without even really needing to state it out loud, right ? For instance, they invite me to experiment and to, to push things around and see what happens next , um, to talk to people. These are all just like basic fundamental, you know, attributes of being alive and as a human. These are very, like, natural competencies. We're not talking about knowing, you know, the long division algorithm here, which is different of course. Um , so I'm just wondering, I guess like when we think about the , the kinds of drill sheets that people often produce and other kinds of fluency experiences that students could be having, that involved everything I just mentioned, that's in your problem solving work, you know, experimentation, visuals, et cetera, communication. Like what are ways that those attributes can be transferred onto fluency exercises? Have you seen any, have you produced any that you think capture elements of problem solving better than the fluency? Exercise Worksheets do.

Speaker 1: 21:55

I mean, right. There are really smart worksheets, really smart worksheets, and I, I don't get to see them often, but they're smart because they, they focus, they have the kids focused on, it's called variation I might be familiar with, right ? It's a term, right? It's variation, whereas it's not just a bunch of variety of problems, but it's just, it's smart practice because it's having kids honing onto one thing that's different, right? So those are wonderful. I mean, worksheets are not bad. Tests are not bad. It, it's what's on there, <laugh> , I always say , you know, right. It depends on the content and, and the context of it. But , um, yeah, I mean, you can turn a , a , um, a numerical test into problem solving. So I'm, I'm less of , um, you know, those non-routine. I used to be really love those non-routine tasks. But I think you can take anything from the textbook, from, from text and turn that into problem solving simply by when and how you introduce it, when, if you just do it earlier prior to teaching it, there you go. It becomes, right. So if I gave you a multiplication problem, solve it , it's a , it's an exercise for us. But if we gave a multiplication problem to a child who has not learned it, that's problem solving. So there's that, there's that basic, just, you know, the definite problem solving simply means, I don't quite know how to do this, but I understand multiplication, or I understand repeat addition . I understand something about it. Right? And, and , um, yeah, and, and you can put it in context, but it , it's just all around us. You don't have to search for, I think the degree to which , um, something becomes problem solving is simply how familiar we are with it. Whether we have a prescribed set of steps.

Speaker 3: 23:40

I'd love to push a little bit more on this right here, where, like, if I gave a , a calculus question to a third grader, like they, that would be earlier than they'd been taught it , obviously. And , um, so , but like, it , it wouldn't feel like a problem solving exper experience, I would imagine so much as an experience of , of frustration and futility, right ? So I think that there's like maybe something extra, I'd love to hear from you about what makes the experience a problem solving experience.

Speaker 1: 24:04

I'm gonna steal what Terrence Tao , uh, I heard him say once, and I love that he said just out of reach, just like , so it's right there, just right there, right? So for example, I've, I've been in elementary classroom where the teacher says they haven't learned , um, multiplication yet. So I thought, okay, that's perfect. That's what I'll do, right? That's , or they'll, they'll learn , um, about area in the spring, like perfect. That's then that's , I'll do, that's in the fall. Just , just , they're gonna get to it soon enough. But I just know they have, you know, have enough, have enough so that it becomes problem solving.

Speaker 2: 24:40

I, I think about in, you know, particularly like thinking about work with Megan , Frankie and cognitively guided instruction. Yeah . I I I've seen so many examples of students who, like, for instance, in conversation, not in like a specific rote assessment, but in conversation saying to a student, like I even my kindergarten student saying, you know , uh, you have three packs of gum and in each pack is four pieces. Like, how many pieces of gum do I have? Right? Mm-Hmm . <affirmative> . Yeah . And looking at the, I'm not expecting the student to use multiplication, right? But thinking about how does the students solve it and what are they using to solve that problem, right? Right. And so sometimes students are saying, well, I know four and four is eight, or they're , they're , you know, we have tools on the table. And so students are sometimes pulling out the tools, or, or another example that I do in my fluency work a problem. We have Dr. Garino on the , uh, podcast, and we had worked with my students on this problem where Dr. Garino has five bunnies in the hutch. Sometimes the bunnies are inside the hutch and sometimes the bunnies are outside of the hutch. What are all the different ways the bunnies can be, you know, she could come out right and see the bunnies, right? And there are ways that students could solve it that, I mean, there's, they could make up, you know, equations, all , all sorts of things. I'm sure there are very advanced mathematical, right ? You know, if that you could extend from five bunnies to a million bunnies, right? Like , and Bethany,

Speaker 1: 26:10

That's a kind of lesson that I lose sleep. I mean, I am so excited. I, I loosely yes . Can't wait because what , what you're saying, I can't wait to see their strategies. I mean, yes, I think that's, you know, my blog will will , you know, if, if anybody reads my blog, it's just those types of lessons that it's just, I can't wait to share this because it blows, it goes in a direction. I'm super proud. It's, you know, I don't want class to end kind of thing. You know, I've done, you know, Dan Dan's, the taco card brings to mind just penny pyramid. Just those things where, you know, I, I , you know, there's some calculus problems, but no, we can do what we can do, right? We can do, and they can take it as, as far as they can, but just so, so right there, it's, it's problem solving when it's just a little outreach.

Speaker 2: 26:54

But I give those examples too, because what I am, as you're talking about the link between problem solving and fluency, I'm feeling like, let's say I'm doing that problem in my class. What I think I hear you saying is then you're attending to the strategies that students are using or the meaning making that students are using. And are you saying that then that can be transferred to the way that they're building fluency? Or are you saying fluency is happening as they're

Speaker 1: 27:23

Both, I, I want to say both.

Speaker 2: 27:25

Yeah . Yeah. I'm , I'm imagining that the teacher that's listening to this and thinking about their fluency work is solved, right? They're, they're hoping to develop fluency in a way that will support problem solving. And I'm wondering, you know, I love hearing the way you think about those links.

Speaker 1: 27:42

Yeah. So for example, if by engaging that task, and with classmates, right? They're always doing these in groups. When they see, they're motivated by when the , the group's strategies is , oh, we're building this table. And they can hear, I mean, when , when we, especially when we randomly group kids, they will know who has what facts, right? And then when it , it's helping each other out, and they say, okay, you know, I'm, I'm, I'm doing this my way, I'm doing this my way. But somebody else next to them is like, oh, I'm doing this way. So hopefully, you know, they're seeing the efficiency, right? They're seeing , oh, that's more efficient. And that's where the number talks come in also is so powerful. The number talks. I think the most powerful thing about the number talks, which is mental math for me, when I say number talks, is the shared strategies, the share strategies is my favorite part. Not just , um, not just because, okay, I'm hearing different things, but the best part is they're saying, I just learned a new way. Bethany did it this way. Oh my gosh, I just learned it. And then the next time they name it after you, Bethany Mm-Hmm , <affirmative> . So I started Bethany's way, or I really like how Dan started the problem, and I started the same way. So it , it's, we have mathematicians , um, right, have names, and they're sitting right in front of us, all of them. And, and it's empowering. We talk about wanting to , um, empower the kids. How, how do they know that they have a place in mathematics? It's, it's only because they have a voice. And so the number talks not just in, in, in the fluency skills, but building those skills, build confidence, but also just the fact knowing that they have a voice is, is , um, one feeds off the other, right? When , when you're, you're this good, and then when you're told, yay , you know, you applauded, you, you , um, you , you respected for your thing, and that just, it just feeds on, its its own. And then now you wanna work more on that. So, so there's that balance. Whereas a worksheet doesn't do the same thing for you. It doesn't give you that feedback that other classmates can give feedback to . In addition to number talks, which I do as warmups , um, every other day, by the way, we do number talks every other day. And , um, you know, I , I want teachers, I always encourage teachers to always ask for estimates all the time. 'cause that builds number sense and play games. And I know you had , um, Jennifer on , um, the live session that was, that's fun, right? And , um, so play games , uh, strategic games like she had. Um, and then I want to also mention that numeracy routines, because numeracy is part of fluency that's important. I think fluency is, that's why fluency is such a bigger category for me. And , um, one of my favorite activities with fluency also is , um, different bases working other than Base 10 and James Tanton exploding dots come to mind when kids learn, you know, to work in base five, base three, all of a sudden they really pay attention, especially in the decals unit, right? And now, now we get to the decals and it's like, yeah, it's, it's on our Base 10 system. What if we were, you know, an alien dropped in and they only function in base seven, that kind of thing. So , um, and then , um, school-wide, nothing should happen in isolation, right ? I don't want math to just happen within the, the math classroom. We wanted that to , um, be far reaching as much as we can. So I was thinking, you know, I would love to have, you know, schools adopt where over the pa announcement that happens every morning that they maybe just end with a mental math problem. Just, just toss it out there and, and whatever class wants to pick it up, pick it up. But it has that, that school kind of theme that , um, community sense and , um, newsletters, home, newsletters home, encourage parents to play with mathematics with their kids. And , um, yeah, just school-wide things. And, you know, I, I would love to start a staff meeting with a number talk. Really just, just drop it everywhere, everywhere you can because , uh, once you promote something so that it , it's natural and , um, you know, it becomes embedded. And it's not, oh, I'm going to math. I only do this in a math class. It really should be borderless

Speaker 3: 31:56

Fa . That was , I really appreciate you adding those bo those , uh, agenda items for, you know, the fa Winn School of the Future at the <laugh> one at some point. <laugh>

Speaker 1: 32:04

Just a little bit more.

Speaker 2: 32:05

Well, I love that the way you're talking about those ideas, fawn, are , you're not talking about something that requires massive overhaul of like school systems or massive budget, reallocation, <laugh> . These are things that you could start incorporating. Um, and you know, I feel like the work that, and the , what I've heard you talk about, I've heard you talk about work like not only in the school, but at district levels. And, you know, we, here we're three math educators all based in California, and you know, California has a brand new math framework, which it's going beyond just fluency, but it places a greater emphasis on real world application, right? And so I'm curious what stands out to you in, in the new framework as you start to dive in

Speaker 1: 32:53

There? There are several things. One of the key things, and I really applaud the framework, is it's the most equity-based focused recommendations, right? And we are in a state, we have 6 million students in a state . So I'm glad equity is at the forefront. Also, the advocates for collaborative inquiry-based learning. And I think , um, back to the binary, I I, I'm hearing it around Twitter in terms of, you know, it's, it's direct instruction versus where it's, it's a blend. And so I'm glad to hear that. No, we're not saying it's one or the other, but it's, it's problem based . But that doesn't mean it's all just, you know, give a kid a problem and let 'em go at it. But it has directed instruction also. And , um, the push, because of the push for collaborative inquiry-based learning, and along with the equity-based, it just, it makes this very wonderful promise that we will support all students from diverse backgrounds, include English learners, like I am and neurodivergent learners to know that we all belong in a math class. Another thing that , um, the framework does is the big ideas, right? The , the big ideas is a big thing. And we have data science along with the fluency, but the data science and math content itself supports the equity based in a way that when the students can examine the important issues and address the inequities that they may see in their own communities. So that part is, is wonderful. I think what we all need now is , uh, what we've always needed is the teachers providing that support because , um, we, it took a bunch of years, right? Three, four years for that to get finalized, get approved, and , um, we need to focus on providing teachers with the support, not just in the pedagogy, but the, the math content to bring that framework to life.

Speaker 3: 34:48

Yeah. Right? The framework. I mean, it is just always so interesting when these documents come out, the common Core math framework and others like, like teaching is the single largest profession in the us . There's just so many teachers of so many different capacities, and from novice to veteran, from, you know , people who have math degrees and who don't, who are generalists and specialists and so on. And it really, it's a very lovely marker to put out there a flag on the ground is my feeling about it. And now I'm left to wonder, yeah . So how do we, how do we back those words up with deeds with, like you said, fawn , um, with , with, you know, the pedagogical support for teachers and what good is pedagogical support that teachers don't have useful materials to work with that bring out, right . From students, that invite from students. So it's exactly, the work is just beginning here is is what it seems. But I love how you highlighted what's so, so good, good about this document.

Speaker 1: 35:38

Thank you. And , um, this is something I read and I just want , um, and it sticks with me that I love. And , um, I don't know who said it, but , um, I love it. It says, it's not that students don't need math, it's that math needs students, right? All of them math needs students. 'cause we always say, you know, you need math to do this and that. I said , no, mathematics needs kids, needs humans. All of them

Speaker 3: 36:05

Shout out to, I think , uh, Rochelle Gutierrez has made that a part of her, her messaging about mathematics. I love that.

Speaker 1: 36:11

I could've guessed that <laugh> Yeah .

Speaker 3: 36:13

Matches, right? Uh , well th thank you so much for coming on the show and , and talk to us again about problem solving fan favorite, but also how to link that up with fluency and help the two of those nourish one another rather than being kinda these competing priorities in a class. It's been wonderful to chat, so thank you so much. Fun . Thank

Speaker 2: 36:28

You, fa

Speaker 1: 36:30

Thank you so much. Appreciate you guys always. Thank you. Thank you. Please see you in real life soon.

Speaker 3: 36:35

Soon enough.

Speaker 2: 36:38

Thanks so much for listening to our conversation with Von Nguyen specialist on the math teaching and learning team at Amplify.

Speaker 3: 36:45

If you folks are interested in delving deeper into the future of math in California, we're excited to announce that Bethany and I will both be a part of a brand new webinar series exploring just that beginning of February. You can catch the two of us hosting conversations as part of a free series all about math in California.

Speaker 2: 37:03

That's right. We'll be breaking down the new California Math framework in greater detail. We're talking about building equity and engagement in California's math classrooms. And we'll answer all the questions you've ever had <laugh> about authentic tasks and problem-based learning. Actually, Dan, we can't promise all , all of the questions will be answered, but we're gonna do our best. I think together. We can at least tackle a few of 'em , right, Dan? Yeah , let's

Speaker 3: 37:26

Do it.

Speaker 2: 37:27

For more information and to register for the webinars, go to amplify.com/ca. Math webinars, that's amplify.com/ca. Math webinars, all one word. And we're also gonna put a link into the show notes. And speaking of show notes, that's where you can find links to follow Fawn and watch her first appearance in the Math Teacher Lounge way back in season two. Next time on the show, we are wrapping up our fluency focus season. We're gonna be talking about what we've learned, what questions do we still have, and try to synthesize some of all these amazing thought leaders and what we've learned together. Find that episode and everything else we've done this season in the Math Teacher lounge, feed . Wherever you get podcasts, you could find more information on all of Amplify shows at our podcast hub. Go to amplify.com/hub.

Speaker 3: 38:24

Thanks for listening.

Speaker 2: 38:25

Bye.