High School Mathematics Reimagined Revitalized and Relevant

In this episode of Room to Grow, Joanie and Curtis speak with leaders of the National Council of Teachers of Mathematics (NCTM) about their recent publication, High School Mathematics Reimagined, Revitalized and Relevant.  Latrenda Knighten, NCTM President and Kevin Dykema, NCTM Past-President share a great overview of how rethinking how and what we teach in high school math can be improved so that more students leave high school prepared. This preparation involves not only knowing more mathematics, but believing in their capability as math learners and in their preparation for whatever path they have chosen for themselves after graduating.

The new “three Rs” of high school math build on NCTM’s previous high school publication, Catalyzing Change in High School Mathematics: Initiating Critical Conversations from 2018, and give practical examples and suggestions to engage students in mathematical and statistical modeling, make connections across major concepts, and using mathematical and statistical processes as a frame for student thinking. 

We encourage you to explore the resources below, referenced in this episode:

o   You can find NCTM’s webpage dedicated to supporting the book HERE

o   NCTM’s webinar about the book was recorded and is available to all HERE

o   More information about the Launch Years Pathways work out of the Charles A. Dana Center at the University of Texas at Austin can be found HERE

o   Guidelines for Assessment and Instruction in Statistics Education (GAISE) reports can be found HERE

Did you enjoy this episode of Room to Grow? Please leave a review and share the episode with others. Share your feedback, comments, and suggestions for future episode topics by emailing roomtogrowmath@gmail.com . Be sure to connect with your hosts on Twitter and Instagram: @JoanieFun and @cbmathguy. 

Transcript

00:00:00:00 - 00:00:22:03

Latrinda

I was really shocked that there was this disconnect with model and modeling. When I think about the modeling process and we look at those things that we are putting for, those are the things that we do every single day that are those real life simulations. 

00:00:24:03 - 00:00:22:03

Curtis

Today, Joanie and I had the opportunity to talk with the current and past presidents of NCTM about their new publication.

00:00:30:08 - 00:00:48:03

Unknown

High School Mathematics Reimagined, revitalized and relevant. We learned about their vision for a shift in the high school math classroom, with relevant, dynamic approaches that prepare all students for the futures they envision. We are really excited to share this content with you, so let's get growing! 

00:00:50:03 - 00:00:48:03

Curtis

Well, Joanie, I am really excited for today's podcast and recording the Room to Grow podcast yet again here.

00:00:57:03 - 00:01:24:15

Unknown

And today we have a couple of guests with us, which I'm really excited to chat with, and I'm looking forward to hearing from them about this, this work that they've done. The book is titled High School Mathematics Reimagined, Revitalized and Relevant, and we are joined by the current president of NCTM and the past president, the most recent past president of NCTM.

And Joni, why don't you introduce our guests or give them an opportunity to do so? 

00:01:24:15 - 00:01:53:15

Joanie

Absolutely. Well, I am so excited to host these two. Curt, these are definitely VIP guests in the world of math education. You know, and we couldn't be more honored to host the two of you here just a few weeks after the release of the new book. So, quick, quick intros, I think because, folks are going to know you from, you know, you kind of are visible as the leaders of NTM, but, let's start with La trend tonight. And just give us a little quick background on yourself. 

00:01:53:15 - 00:02:14:15

Latrinda

Hi, I'm Latrinda Knighton, and I think that, a little bit over two weeks in as president of NCTM. 

And so just a little bit about me, recently retired from my school district after 32 years where I worked as a teacher, math coach, math supervisor. And so that's me in a nutshell. 

00:02:15:15 - 00:02:34:09

Joanie

Well, welcome Latrinda and congratulations on the role. I know we're going to learn great things from you in your presidency. And we're excited to welcome back to Room to Grow. The now past president of NTM, Kevin Ma. So just for our folks that maybe didn't hear you on our podcast a couple of years ago, Kevin, give us a quick intro of yourself as well. 

00:02:34:09 - 00:03:03:01

Kevin

Yeah. Thanks, Joanie and Curtis for having me back. So I'm Kevin Becker, the current past president of NCTM. I've been looking forward to supporting lecture and I in this upcoming year, my day job.

I've been an eighth grade mathematics teacher in Southwest Michigan. Now I'm doing a little bit of district level support, which is really going to be code for lunchroom supervision, and I'm reduced to sub. I am well aware of that and looking forward to to doing some work back in the district. And so excited to be with you guys here today to talk some more about high school mathematics.

00:03:04:03 - 00:03:44:06

Joanie

Yeah, we are really excited about this. And I think you both know that Curtis and I are both former high school math teachers, and certainly a lot of the stories of our experiences teaching high school math and our and our challenges that we faced and the things that we wished had been different, have occupied a lot of our room to grow episodes. So, we're really excited not only for this episode, but also for this book and the content that it holds and the influence that it will hopefully have over making some real, much needed change in high school math. So, maybe one of you can kind of started on, a little bit of background, like, how did this book come to be, you know, who was involved in it and why now? Why, why did this become the time that this book needed to be published?

00:03:48:06 - 00:05:39:05

Kevin

I'll jump in with this one because I was more involved with the start of it and the trend was with that. So it was a it's a collaborative effort between NCTM, NCSM and ASSM. ASSM is the Association of State Supervisors of Mathematics, the set of presidents before me for all three of the organizations got together and said, what's the next big thing that needs to happen in mathematics education?

And the tools that we really need to keep pushing at that high school level, because there's still work to be done at the high school level. There's work to be done everywhere. But we know that the, the students needs aren't being currently met by what's done in many high school settings, not all high school settings. There are some high schools that are rocking it, but there are a lot of high school classes that unfortunately look very similar to the high school class.

And I was, I don't even want to figure out how many years ago at this point in, in time. So the three organizations formed a writing team, and that writing team got to work and looked at all of the past work that had been done in the math education field and said, we're not throwing it all away.

Catalyzing change is still catalyzing change. Those four key recommendations are still valid. The eight effective teaching practices, while they're ten years old for principals to action are still available. But what's this next step? What do we need to do to continue to provide tools for the mathematics education field to really change the trajectory for students? For far too long, students leave high school saying, I'm not good at math or I'm good at math, but I took as much math as they could in high school, so don't ever have to take another math class in the future. And we recognize that we need to have a different student experience. So in this book, we really take the, the student and put it at the center. What are what are those things that we need to reimagine or revitalize, make relevant. So the student has a different experience than what many of us may have had as high school students.

00:05:39:10 - 00:06:12:07

Curtis

I love that, I love that that's the, the goal of this student centered nature of the work that you guys have pulled out, pulled on and pulled together inside of this book. And the things that you guys have talked about, I really connected to that concept. I can't tell you how many times I've heard I took everything I needed to so I never have to take another math class. And, and just that thinking and and your desire and your passion for changing that mindset and trying to help us have the tools and realize we have the tools to change that mindset is really exciting.

00:06:13:07 - 00:06:12:07

Joanie

 I agree, and I would just add that it's we certainly don't like the attitude of like, let's get math out of the way. But I think about and again, we all have people in our lives and our experiences who math has been a gatekeeper for them. My husband is one. My husband was like, I don't feel like I can be successful in math. And, you know, changed his major in college because of math. And, you know, so certainly the implications are high when, we think about the current state and the things that are not working.

00:06:43:03 - 00:07:18:18

Unknown

So the timing of this, I think it's been needed for a long time, and I'm thrilled that it's finally out there so that the three R's within the title reimagine and revitalized and relevant give us a great structure for our conversation today. And I think, as I've heard the two of you talk about the book in the past couple of weeks since the release, you always start the conversation actually with the third hour of relevant. So, Latrinda can you give us a little bit of framing around why we start talking with relevant and what does that mean in terms of how the book spells out what relevant high school mathematics actually is.

00:07:19:18 - 00:09:06:22

Latrinda

Thanks, Joanie. When I think about those three hours and I think about the state, and I'm glad Curt mentioned the idea of the student-centered maths. I feel, as you know, experience educator that that's where I want to start. Because when I think about the relevance, I'm thinking about children, students thinking, why does this matter to me? How does it connect to what I'm going to do in my future, what I might want to do in my future has it connect to my lived experiences. How does it make sense? And I also think that the relevance is what's going to get students engaged.

So I like the idea of going to the relevant first, because I'm thinking about the student, because at the end of the day, that's why we do what we do. So we're thinking, how are we going to get the student to truly engage in mathematics? And when I to talking about just the student who says math is not for me, you know, how do we get the students who are quote unquote good at math?

They just go through it like, you know, this is just a process. I'm going through the assembly line. I do this and this and this, and I'm not really active or engaged in this, but I know if I just do this part, you know, Miss Jones is going to give me an A and I'm going to make it through. And I can check this off the list. How do we get them excited? How do they see that this makes sense, that this is something that connects to every single thing that you'll do in your life, but how do they, you know, see that? So, so I think that's why a lot of us start with the relevance, because we see that as this is why we do this. This is why we're starting here.

00:09:06:22 - 00:09:11:06

Joanie

for sure. Every high school teacher has dealt with that. When am I ever going to use this question? 

00:09:11:06 - 00:10:03:06

Kevin

Yeah, and when I think of the relevance, you know what I think I've changed as a classroom teacher so often I say, oh, I don't have any control over that. That's the district level. That's the state level.

That's a structural thing. But the relevance is a piece that I think directly applies to classroom teachers. I need to do a better job of helping my students to see the relevance of what I'm doing. I can find spots that I can increase, the amount of mathematical modeling that I may have used, the amount of statistical modeling that I'm used. I don't need to wait for a new set of state standards to do that. I don't need to wait for assessments to change. To do that, I can help my students relevance. I need to be doing more of that. So I think that's one of the reasons I like to start out with that relevance piece, because I think that speaks directly to the classroom teacher. Some of the other stuff, it's a little bit more structural, and some of the teachers are like, oh, that's out of my control. I can't do it. I give myself a free pass. I can't give myself a free pass on the relevance. 

00:10:03:06 - 00:10:57:06

Curtis

 I think that's such a huge thing. And, and Latrinda you said something that really excites me.

How do we get them excited? How do we get them curious? How do we get them connected? Because we know, we know, the research shows it that connected students engage, students retain more. It is just a fact, right? I remember the things I'm interested in. And so how do we get them thinking in this way? Hey, this is really matters to me. How do we find things that matter to me? I watched the the webinar from, earlier this week when we're recording this and I saw or I heard you talk about, you know, the problems where Susie's buying 59 watermelons or whatever, at the rate. And it's like, nobody buys those 59 watermelons. Let's think about ways that we can maybe figure out how do we get this planted in their world so that it becomes more relevant for them?

I love that.

00:10:57:06 - 00:11:06:06

Music break

End of segment 1

00:11:06:14 - 00:12:02:14

Joanie

So, I would I, would pull out one of the key ideas from the relevance section in this book is this idea of mathematical and statistical modeling. And that's not that's not a word, not a new phrase that we've, you know, never heard of before in math education. And I even think back to when the Common Core State standards were released and, you know, model with mathematics as one of the mathematical practices that came alongside the content standards. And I think there's some misconception about what it means to model with mathematics. I know my teachers were like, oh, yeah, we're, you know, drawing a square for X and little tiny cubes for, constants on the board. So we're modeling with mathematics and that kind of that's a form of modeling, I suppose a representation, but that misses the mark a little bit. So can we unpack a little bit what's meant by mathematical and statistical modeling? What does that look like in a reimagined high school classroom? 

00:12:02:14 - 00:12:02:14

Latrinda

You know, I think is really it's a little bit funny to me when you mentioned that, because I spent the bulk of my teaching career working with elementary and some middle school, I when I transitioned to a district position I was really shocked that there was this disconnect with model and modeling. And so when I think about the modeling process and we look at those things that we are putting forth, those are the things that we do every single day that are those real life simulations. So when you think about how does this, metric that decides that follows me on social media or follows my email and knows what my purchases are on a regular basis, that is a model that is being used by an algorithm that tells what I'm going to do next, or what I'm going to purchase, or it knows my habits or things like that. Those are just some examples are how we connect it to things that happen in everyday life. How do I use that to actually ask questions, to pose those investigations and actually try to find answers about those things? And so I think that was the biggest disconnect for me when I saw that there was that misunderstanding. And then when I saw that modeling was supposed to take such a huge active component of the secondary classroom and that our students were not having that, I think when I, you know, we have a lot of rich resources, it's kind and said we're not reinventing anything that actually talk about modeling tasks. How do you take an application or task and turn it into a modeling task? And so when I would go in and I would visit with teachers and they weren't seeing that, I'm saying this is what's going to get your students excited because this is going to connect the mathematics that they're doing to something that's real, that's tangible, that makes sense. And so they will actually have it. It will stick because it makes sense. They can actually connect with that. So I think that's one like vision I think of it I see it that way. That's a way for our students as well as our educators to see, how do I make this real? How do I make this come alive for my students?

00:14:32:12 - 00:16:45:01

Kevin

Yeah. And and so it's helping our students recognize when you make an assumption that's going to affect the outcome. And changing some of the assumptions that you make may change some of the outcomes. And that's part of that modeling and helping students recognize that people who are who are looking at mathematics and statistics for a living or that's part of their job, they're having to make some assumptions about things, and it's based on those assumptions that can drastically change the and the outcomes. This past summer, I went to the joint statistical meetings. So it's all been I mean, it's a lot of PhD level people who are there, they're sharing their research. And I was there talk about the state of K12 data science. But I went through a couple of sessions, and one of the sessions that I went to was one about sports, and it was just fascinating to sit in there and to listen to people with PhDs say, oh, here's my assumption that I made and all the questions that people were asking were about the assumptions. What do you mean? If you change this assumption, what happens if we don't do that? I don't say we. I don't do that enough for my classroom. The classroom conversations we have are about, oh, did anybody do it a different way? They weren't talking about different ways. They were talking about they were really trying to to hone in on,  all right you made this assumption. Are you sure that's the right assumption to make? What if you change that and we need to do more of that? I think so many of our students leave the K-12 system thinking that mathematics is all about doing a worksheet. Yeah. Nobody in the real world, in the outside of the K-12 space, they're not doing worksheets. No. Somebody makes you mathematics who is a mathematician as part of the title. They're not sitting down and doing a worksheet. The statisticians aren't sitting down doing worksheets. But yet that's what we do in the K-12 space. And this modeling, you know, we're trying to talk about it's not new . Joanie, you talk about it's not a new game report. The games report. We know a lot about what the mathematical modeling should look like, what statistical modeling should look like. We just need to continue to amplify those resources and share, as educators, those different resources that are out there so that we can start to to find additional spots where we can put those in. And it's so exciting to think about what's going to be coming out in the next few years and coming from other places.

What examples are going to be shared among the broader mathematics education community? So we put actions to our words.

00:16:45:01 - 00:16:45:01

Curtis

 I love that example of the fact that nobody in the real world is doing sets of worksheets one through 50, odds or whatever it is that we, you know, that we tend to to assign students when we think about this and that, that they have real problems they're trying to solve and they have real assumptions that they're making, in those situations. And thinking about, how do we bring those kinds of ideas down into our classrooms. I was watching a webinar earlier this week, where some folks were modeling the rate of change of, of, disease as it modeled going through a population. Right, and thinking about that exponential growth and kind of, helping students to intuit that from the data that they collect, right, to, to really think about.

Okay, so what is different about this? It's not the linear, you know, relationship that we've been studying this whole time. It doesn't have a constant. How do we change our model to kind of catch up with this one here? So that was, you know, these kinds of things, thinking about real scenarios that that apply is so important.

00:17:54:23 - 00:18:16:01

Joanie / Latrinda

You know, when I if I see oh sorry, go ahead Latrinda. If I may just add one thing. When I think about this, it also reminds me of providing students with those opportunities for inquiry. And so a lot of times we think that only resides like in the science classroom. And so this is that opportunity. That's how they get engaged. Because where you're talking about you're thinking about what could happen, those assumptions. And I'm not just basing it on just some rote problem. That's where they are curious and they really are using their critical thinking skills. And I think that's when they get excited about what they're doing. I mean, believe it or not and then I'll start getting excited about this.I mean, it's not a good thing. But when we had Covid and students were actively watching the reports, when you mentioned that, it made me think about it like kids were watching all the graphs, they were looking at the science and predicting the growth in my area and what's going on. Right. They were actually doing this. They were doing a lot of mathematics, and they were excited about that estimate. I mean, they were a little scared about what was happening, but there were some rich discussions we were having about that when we flipped the script and we talked about those things. Okay. So how do you apply that to the math that you're learning? That's one of the first times I actually saw some of the secondary students in my district that I had the opportunity to work with, get excited about math when we did that.

00:19:28:09 - 00:20:38:23

Curtis / Joanie

Right. Yeah. That's right. The ability to follow your natural curiosity. There's nothing more motivating than that for for a young person before you move on, I just I'm going to ask a question that I know doesn't have a good or easy answer, but I just would love your reflections on it. You know, when I was in the classroom and the years that I spent working with and supporting teachers that were in the classroom, no one would disagree that this is a great idea, that, you know, relevance is important in allowing students to, you know, have inquiry opportunities and follow their own curiosity is, is great for student motivation. In my experience, though, it's nerve wracking as a teacher because you don't necessarily know where the students are going to go and their natural exploration might lead to some mathematics that isn't part of my course, and that maybe I'm not prepared to guide them on. So what advice would you give for teachers that are feeling that hesitance to dive into mathematical and statistical modeling, just because it feels a little out of control and a little uncomfortable? How how can we start to reconcile that a little bit?

00:20:38:23 - 00:21:35:15

Kevin

 Be brave, be willing to take a risk. And I also think this is where artificial intelligence can be our friend at this point in time, when there's something that's not that's out of my comfort zone, I can go to ChatGPT or something else and say, hey, can you give me a quick explanation of whatever at a 10th grade level? Artificial intelligence sometimes will do good, I'm sure. Sometimes it may not do. Yeah, it's pretty good, but I think we can we can start to utilize some of those resources that are out there for it. And I think it's good for our kids, for our students to see, hey, we're taking a risk. We don't know everything about math. My eighth graders sometimes are surprised that they think I'm a math genius, and I like to think that I am fairly good at eighth grade math. But they'll ask things about things that have nothing to do with math, and I just don't know sometimes. And, it's have to be willing to say, I don't know. I've never thought about it that way before. And let me, let me keep thinking about it. 

00:21:35:15 - 00:23:18:05

Joanie / Latrinda

I love that one of the things I also think is it makes them, as Kevin pointed out, (inaudible), because kids should not be bad where the stage, on the stage we have all the answers and as adults we have to get past that too. We have to be willing to be a little bit more honorable and take the messy pieces. You know, it's not going to be very neat. So, you know, you're going to have some days things might be a little bit longer. They may go in some different areas, but embrace that when you're scared and said, be brave. Be willing to be vulnerable in this, a journey that you will take with your students and students to begin to feel a little bit more confident because they know it's okay if I have to tinker with this to find the answer, because we're doing this in class with Miss Layton as well. So we're all tinkering and learning together. And I think that's a very good example, especially in high school, that we need to provide for students, because I know I thought some of my teachers were supposed to be the geniuses because it's high school and it's high school math and, you know, it could be a little bit of a beating when you say, oh my God, they steered me down the wrong path. But, you know, they didn't come back the next day and say, oh, you know what? Let's have a do over. But it would have felt so much more comforting if that had been something that happened. You know, it's we all learn from our mistakes. So let's just dive in, work together and really, you know, take the messiness along with the neatness I think.

00:23:18:05 - 00:23:27:06

Music break

End of segment 2

00:23:27:07 - 00:24:26:12

Curtis

I love that I love that we're talking so much about, relevance. I think that really is such a foundational piece of this work and of this book. And, I love that that's kind of the place that we started here, because that really forces us into the student, centered thinking how we shift students to the foreground, how we shift them to the to sort of the center of our approach. Now, I want to I want to kind of maybe transition us just a little bit as we as we think about the revitalization of the high school math classroom. We've already touched a little bit on this, on this idea of, critical thinking and thinking about how do we get students interested in the statistical processes, maybe can, Kevin, can you dive a little bit deeper into the use of these, processes to, to critique the world around them and kind of how that how that maybe fits into your imagination of this, revitalization of teaching practices.

00:24:26:16 - 00:26:30:09

Kevin

Yeah. As we think about the revitalization, we're really talking about revitalizing that student experience. And we present a loving mathematical, statistical processes for those that are well versed with the the Common Core standards of math practice, people recognize how those eight standards of math practice are involved with those 11 mathematical political processes reworded, combined split, some new things added. But we've also taken those 11 practices, sorry, 11 processes, and we've clogged them together to four clusters. As a classroom teacher, I can't remember 11 different things, but I can remember four different things. And we're really all about those big clusters. And I think of sometimes those 11 processes, 11 mathematical physical processes that there's are just examples of those being four clusters. We need to be looking at what are we doing differently with our students? How are we getting our students to do that? Deep thinking a teacher should be mentally fatigued at the end of the math class, but we should not be the only ones who are mentally fatigued at the end of the math class. And I think so often we are. And so there are so many classrooms our students leave really not having to do a whole lot of thinking during that class. But when we revitalize that student experience, I'm really focusing on those 11 processes arranged or almost four clusters. I think our students will start to do some more of that work, and they'll start to see those connections. They'll start to say, this is what mathematics is. It's not just a series of of what appears to be to students to be random sets of procedures. We know they're not random sets of procedures, but so many students just see these random sets of procedures. Let's revitalize that student experience. Let's get them actively engaged. Let's get them developing some of those habits of a of a mathematical and statistical thinker. Let's get them explaining, reasoning, improving. Let's get them modeling and using those tools and representations. Let's get them to see, generalize and describe structure and we'll focus in on those. We're really focusing in on making mathematics that much more relevant for our students.

00:26:30:09 - 00:28:40:21

Joanie

 I love that I, I like that this, doesn't attempt to erase and rewrite the standards for mathematical practice, right? It's just intending to provide a little more structure and access to those standards. And I love, you know, I be very familiar with, SMP. I like the sort of new ones, you know, this there are 11 here now instead of eight. But they really I think they really tap into some of the things that help provide, a foundation for which students can use to engage with the content of the mathematics. And I just want to share and latch to I want your thinking on the mathematical and statistical processes, too, but I just want to share this really cool thing that one of my math coaches, when I worked in my district position, one of my math coaches said, you know this, that these math processes, these thinking processes are not about what they are about what we do all the time. But it's you don't really realize you're doing them until you don't know what to do. So she talked about it like in parallel to reading strategies. Like we teach kids reading strategies so they have something to do when they're stuck. And I just loved that analogy of like, these are ways to help kids frame how to think about mathematics. So when they're struggling with something, maybe they're struggling to see connections. Well, let's think about structure. What kind of underlying structures can I tap into? Or if they're, you know, feeling like they, they're stuck in the numerical mathematics, being able to zoom out into what's the context here? And how can I reason about, you know, the real world situation on which this problem is based. So, I just really liked that as an idea. As you know, strategies for when kids struggle. Because I think, as we've said before, when people struggle with mathematics, they just think, well, I'm not a math person. I'm not good at this. So, Latrinda, I just want to hear your comments on the organization of this or like the content of these, how do these complement the the high school content that teachers are teaching?

00:28:40:23 - 00:31:42:01

Latrinda

Thanks, Joanie. I especially appreciate the example you just gave from your math coach, because one of the things that I think about with these, they're intended to revitalize that experience for students. But I honestly believe that for a lot of teachers, this is going to revitalize their experience as a teacher, because sometimes we only do what we know or what we've been told. And so when something different, you know, I can say new, but something different is posed and we really go back and we're reflective. It's just like your coach observed, oh, you know, it's not something that we're actively making a list that we're doing, but we step back and we see that it's happening intuitively. And so I think knowing these 11 things that are clustered around these four topics.

So as an educator, I'm going to have those four topics in my head. I'm already familiar with many of these from the other Aids than this from mathematical practice, but these have just been enhanced to add maybe a couple extra pieces and then to make it more relevant to the high school experience. And the thing I like about this revitalizing what happens in math class, especially in high school, because now it doesn't matter what course I'm in, which pathway or trajectory I choose, I should be deeply engaged in these processes in every single math classroom.

And if students are engaged in these practices, we really are building a stronger, more confident maps student, I believe, because now I'm not just a passive person who just has to get as much content pushed in because you need to have this foundation and it's for the students who are making that requirement for however many courses they need to graduate from high school.

And for those who have already decided, what they call smart. So I'm going to take as many as I can. So when I go to college, I'm going to opt out of those first two years of math because I've taken these advanced coursework. So now you actually have given them something tangible that they're actively doing as they learn mathematics. And I really do believe that some of our teachers are going to see more of a purpose, more of our connection to what they're teaching, because we have the habits of mind, of what students should be doing as they learn. So now we're kind of giving them a focus to go with the content. And it's nothing different. We're asking you don't have new standards, the content is the content, but this is how you interact with it. And in most cases, you actually will engage with it now because you have something active to do. I believe.

00:31:42:01 - 00:31:51:15

Music break

End of segment 3

00:31:51:21 - 00:33:28:19

Curtis

I love the imagery of having something active to do, and the fact that we've added some tools to our toolbox now, right. We're thinking about these new tools or these, and giving access to, to these tools. And I also was thinking, as you mentioned, that, you know, we're, we're doing a lot of this and thinking about focusing on the student student centered things. And I agree with that. Shifted. But you made a comment Latrinda about, that as teachers start working this way and pulling these things in that they're also, potentially going to revitalize their own teaching experience. And I was reflecting on my teaching experience as a stats teacher. And one of the things that I loved more than anything else about the teaching of statistics is you get to play in everybody else's backyard. I mean, this is this is, you know, getting to kind of dip my toes into all of these different places and see how those things kind of benefit from the utility of the mathematics that that I'm teaching in my class right now. And, and seeing how, those concepts kind of interweave within, these other areas of study and utilize those to help my students make connections, in those classrooms.

So as we kind of maybe move into, this idea of re-imagined high school mathematics classrooms, maybe Latrinda can you expand a little bit on that idea of those crosscutting concepts and this idea of creating interesting pathways throughout our mathematics careers?

00:33:28:19 - 00:36:45:06

Latrinda

 One of the things I was so excited about when I came on board, like a year ago, to the board, not gotten a chance to have more of a preview of the inner workings of this book. You know, the other people who are anxiously waiting for the book to be released. And I was really excited when I saw the like, crosscutting concepts and I think for those people who dabble in the science world, you know, that they're crosscutting concepts in science. And that was one of the things I was most excited when we had updated standards in science, when we had that kind of idea of that unifying theme. And so when I think about this, the five crosscutting concepts, because I think, yes, someone mentioned earlier that maybe a teacher that's comfortable in his or her domain, algebra. I only teach algebra. I don't know what happens in geometry, so I'm just not going to dive into that world. I think this gives us an opportunity to help students see just that cohere science in what they're learning, because the cross-cutting concepts are a theme that are woven throughout every single math course that you participate in. And so now these are just actions, you know, patterns and generalizations that really will involve how things happen in the world. But now I see how this this look in this avenue and when I'm in this course, how does it look in the next one, I can start to make connections to what comment about patterns and generalizations. I may have different content. I'm using a word, but what are those commonalities? And I think when we start to do things like that, students are going to begin to make more sense about the work that they're doing. They're going to make connections, and then they're going to build, I think, a stronger foundation that they can actually keep adding pieces to. So those layers will actually be a little bit sturdier.

You know, I think about that. So, you know, sometimes those pieces are so fragile because they're tied to my memory, this fact or that fact that that formula. And sometimes they just don't make sense. They don't connect. So now we're really helping them with that sense, maybe. And I think showing them how it connects to so many different things I think that strengthens the idea of those interest driven pathways, because now I'm going to see how something that maybe I'm interested in, but I can really make connections to how math plays a role in it and how I can utilize what I know for something I may want to explore later or I'm thinking about. This is something I possibly want to do the rest of my life, or just to maybe take some other courses and look at it. And I think students will just be a lot more critical about the things that are presented to them, because now they're looking for, okay, how do I look for this thing in this? Has this make sense? And they're actually going to expect to be able to make those connections. And I think it's just going to solidify just their thinking and their foundations. I really do. 

00:36:45:06 - 00:38:52:04

Kevin

And I think that only for the students, I think for the teachers, they're going to see different connections. I know as I've started to dive into some of these and thinking about, all right, yeah, we're talking about for 912, but they're just as applicable for the k eight states.

So I think of, you know, the kind of like time eighth grade have I seen how patterns of generalizations. I mean, we'll go from the beginning of the year to the end of the year. Have I looked at the variability of change, the making and interpreting predictions, and I've started to see different connections than what I may have seen in the past. So, you know, we've talked about with those mathematical statistical processes, it's going to revitalize the teachers instruction. I think this is another one that's going to help to to really benefit the teacher as well. And we're really focusing on the student. But as a side benefit, it's going to it's going to help us do that. One of the things I want to build off the pathways with, with Latrinda, I one of the things that that I often note is our other content areas in high school have lots of options for 12th grade, and we just don't.

And I've shared in a slide in Chicago when we launched the book in my president's address, we talked about or I talked about the book. My wife happened to be sitting in the back of the room, and she is not a mathematics educator. She had stepped out of a meeting for work and saw part of my session. And then she we had to go back to, to work. But at night, she said, I had never really recognized that, that my language arts in my high school, we had 4 or 5 options. In science, we had 4 or 5 options and social studies, we had 2 or 3 options. In math, we had one option. We all took that same senior level math class, and that was eye opening for her. And I think that's a that's so true. We don't offer our students options based on what their interest is for that senior year at the time is now to do that. So our students want to continue to take math and they start to recognize math is relevant. Math is going to help me in my career, and not everybody needs to be taking a pre-calculus or calculus class. We need to be offering that style because many students do need that. But for many students, a class in quantitative reasoning and data science, statistics, and you name it is much more relevant and much more beneficial for them. 

00:38:52:04 - 00:41:16:19

Joanie

I really love how this section, this reimagined section of the book, gives us the content piece that we know the the relevance and the revitalized part give us. You know, modeling has to be forefront. And here, statistical and mathematical processes that undergird the thinking throughout all the coursework. But this section, those crosscutting concepts and that they concept of idea, the idea of interest driven pathways and alternatives to calculus for everyone, really hone in on the content challenges that high school has faced. And one of my favorite things about the crosscutting concepts, first of all, the connection to science is super cool because when those came out in the, next generation Science standards, I was like, oh, that's such a great way to help make those connections. And again, this was a common criticism of the, the Common Core standards there is this really nice and obvious coherence across the standards and K-8. And because the high school standards were not written to address a specific course or grade, and then states like Colorado, where I live, where it's, you know, local control, so we don't have our high school standards are just all clumped together. So using the cross-cutting concepts as a way to help focus on what are the big ideas of high school that all students should be engaging with, regardless of what course they're taking? Like, these are big mathematical ideas that are that are going to be built upon. They are the foundation of what students are learning in K-8. I love that you brought that up, Kevin. Like, these are not just specific to high school, right? This is the continuation of the K-8 standards. And how do we help students really see mathematics and I'm sort of, I'm sort of looking ahead to, you know, wrapping up our conversation. I don't want to go there quite yet, but thinking about, that, when we were talking about the mathematical and statistical practices, I was like, wouldn't the world be great if we asked people what is mathematics? That they responded with those things? It's about problem solving. It's a term like, and then if everyone could say, yeah, in high school math, I learned about, you know, functional relationships. And I learned about, change. I, I just think that there would be if the world would be a better place. Let's just.

00:41:16:19 - 00:41:16:19

Music break

End of segment 4

00:41:27:20 - 00:42:08:17

Joanie

So I, I want to add. And I'm hoping I'm not throwing too much of a loop on everybody here, but I want to add a fourth are, and the fourth are that I would love for you to, to talk about before we wrap up our resources. NCTM really nice job of not just saying, okay, here's this book.

Go ahead, world and figure it out. There's a web page will link to that web page in our show notes there. There's a ton of additional things that already exist that can help round out understanding and implementation of the ideas. It's in this new book. And then there's more work coming from NTM. So, Kevin, you want to start us off with some of those resources that are available or are on the horizon?

00:42:08:21 - 00:44:07:21

Kevin

Yeah. So on that landing page NCTM.org/hsreimagined, we have some resources there. We're going to continually add resources. There are some stories of states that have already done some great work around pathways and other things. And we're looking to add some stories there for our listeners today. If you're working in a school district, we would love to get some school district stories as well, so that we don't just give this impression that it's just state level work and school district level work as well. We've also taken the, you know, the catalyzing change and catalyze to give up on a central content. We've taken that essential content and matched up with these new cross-cutting concepts. We've provided sort of the answer key, but we've also provided a blank set so that you can make your own relationships with that, and you can have those conversations in a PLC, and you may see different connections than what our team that put the in the answer key, so to speak. To do that, we've looked at those 11 processes and around of those four clusters and said, hey, those are essential content. What I know which of those four cluster might be the best match for that recognize. And we can't do all 11 of those processes at all times. But some content lends itself more to to one of those four clusters. So we provide some resources there. There's a fantastic book club study on there. So if you're working in a in a small group, if you're a district leader or a department chair and you're saying, hey, I want my whole staff to go through and do this, you don't have to create the book, set it for you. We create it for you. And, you know, there's links to some other podcasts and it's webinars and there's lots of other things that we will continually looking at, new things that we can put on there to really help support the feel, because we recognize there's a lot of work to be done there. I'm confident that through the collective we that we can really impact and we can change high school mathematics to really focus in on that student and have students have better experiences. Latrinda, you want to share the new upcoming projects. I mean, you've been a lot more involved with that than I have.

00:44:07:21 - 00:47:48:14

Latrinda

 Sure. And I would just add that there are so many other links and references to existing NCTM series and resources you can use, like our modeling series. And so one of the things that came out of this is that disconnect that you mentioned, Joanie, that a lot of people felt when who work online courses, who were not on the course aides, but just the high K, it's there. There's coherence. Then high school was just here we are, we're there. You know, you got to learn math in high school. So here it is. And our students get there. And there's no connections whatsoever to what we're doing. So for our listeners and our members who are thinking, okay, we're reimagining high school, we're going to recharge and revitalize what happens there, but they are not left, you know, just to watch and observe the good things happening in high school, because we realize the power of making those connections across that entire K-12 spectrum. So in two years, we will have a new publication. And so we're building off the pre-K eight focal points, which is a document that was a precursor, you know, to anyone who was involvement with the Common Core standards of college and career readiness. The numbers, as some states label their standards these days. So we know that that looked at some key content areas for the pre-K, eight grade bands and actually how those can make that and those that coherence. So we'll do something similar to what we see in high school reimagined. But what's most important is we're going to take those crosscutting concepts, and we're going to look at them and see, based on the content that is grade level appropriate for your grade level, how do we address those cross-cutting concepts and build on them from pre-K through high school? So those people who are familiar with crosscutting concepts in science now, we will have that same type of mechanism for mathematics, where we see that we're constantly building and adding on to those pieces for students. So students have that coherence, they make sense of it. And also because modeling and statistical practices are important for all students as grade level appropriate, we will bring those processes to those grade levels as well.

So we'll have a new document that actually puts those pieces together so that people began to see that it's not one story here, one story here. And here's a different story that is a continuous story and that we're adding on to those pieces at each level, at each layer for students. And I think that's going to get our teachers talking more to each other to talk about what comes before the great level that I actually am assigned to teach, what are those foundational pieces that are happening?

And so how do I make those connections? So I think that's just that coherence that people have been asking for for a long time. I've heard math teachers ask for this, and some people do it on their own. As Kevin said, some districts, some schools do this well. Some schools have sister schools or the K-8 school in the local high school, and they do this well. So tell your stories. We want to know. But now we're going to just give a little assistance to those people. Maybe they'll have a mechanism for that and they'll have that guidance for that piece as well. 

00:47:48:14 - 00:48:09:13

Joanie

There's so much power in what you describe, because just as we as we've said throughout the whole conversation, none of this is new. We're just putting it together and making connections in ways that help people realize, you know, the intent always behind the standards and the hopes for how students learn and engage with mathematics. It's really exciting what's on the on the horizon.

00:48:09:13 - 00:49:56:11

Curtis

 I was just going to say the same thing. Like, it's super exciting to hear that being on the horizon.

Really looking forward to the next couple of years and seeing that, those processes realized for the broader audience, which is going to be really great. So I had one, comment I was just in listening to the to the whole of this conversation and thinking about how we we started with this idea of relevance and then working through the revitalization of our math classrooms and then the reimagination of the content and organizing these things. At the end, it was feeling like we were circling right back around to the relevance to our students. I just felt this cyclical approach beginning to happen in my own mind as I was thinking about these things, beginning with relevance, and then just kind of going through the cycle over and over again. And that was that was exciting to me. As I was thinking about how those, those resources and the way that we're going to be teaching in our classes will become more and more and more relevant to our students, it shift towards their interests, give them ideas and things that they can, that they can move on with and, and follow their passions. Because, like Joni, you said, like they're being led by your curiosity and your passions and your interests. There's no better way to to learn content than than by focusing on those things. And so I'm really excited about all of this. So, just in one final kind of question to wrap us up, at the end here, I want to ask both of you, maybe later to to start, what would it look like if the vision of this book, the vision presented in this book is actually realized in our classrooms, in our schools?

00:49:56:15 - 00:52:54:21

Latrinda

What would it look like? Well. The first thing I actually honestly believe that we're going to see students and teachers and those the caregivers at home, those students I think we will see like a difference in their attitude and their mindset and their thoughts about mathematics because it's going to grow. You know, the students feel relevant, the students feel more engaged.

You know, the parents don't have that struggle with, you know, oh, what's my kid going to do? And, you know, just like anything that's different are new. Parents are going to want to know, well, what does that mean? What does that look like? And to be completely honest, some of them are going to be a little bit more revitalized when they think about this is something I had to learn to do when I got into the real world. So now my child is actually applying those concepts in a classroom setting as they're learning it. So it's going to make sense and it's going to stick. And Abby will will here is that this will become a part of that vernacular. Like, you know, I've every time I hear an administrator say, I went to this classroom and I just didn't see that print, that's the struggle. I kind of giggle a bit because, you know, ten years ago no one said that and definitely not an administrator who's never taught math. And so I think we're going to hear, you know, these cross-cutting concepts being said, we're going to hear people look for those processes for mathematical modeling and statistics. And I think our students, once they get that first teacher who does this, they're going to expect this when they move to the next math course. Right? So, you know, students are going to drive some of what happens. Because now I've had a taste of this and I've had an opportunity to, you know, be more engaged to be more active, to have things that are contextual and make sense. And so a lot of times that can be the driving factor that makes sure that students get those pieces they need.

So I expect to see not just students who actively engaged teachers will be more purposeful about the work that they're doing, making connections. And at the end of the day, the post K-12 secondary community is going to feel a lot more confident about the students that we're sending to them, because now we're sending people who see relevance. I see connectedness make it work in multiple contextual situations. So they're going to have those desired skills that employers want. You know, for someone out in the workforce, I believe. 

00:52:54:21 - 00:54:21:22

Kevin

Oh, that's a tough answer. To follow with that. That was a, it was a great thing, a trend. But I'm a Pollyanna. Yeah. So to me, you know, in ten years, five years, how will we know that there was an impact? I think it's coming back to the student. I think if we have students who are leaving high school mathematics saying I am capable of learning mathematics, I see the reason why we're learning mathematics. And it's really about a positive mathematical identity that when we start to to hear loss in society of, oh, I'm not good at math, never be able to say, oh, me neither.

And for it to be celebrated when we see less of that, I'll know we've made an impact. And I know that high school mathematics have been changing so that students are leaving. Recognizing that math is understandable. There are connections between things. It's that memorize a bunch of stuff, plus bunch memorize a bunch of new stuff, flush them, and actually see those connections to those crosscutting concepts. We've had those interest driven pathways so that students are recognizing math is applicable to their own lives. They're recognizing mathematics is not all those concepts. It's those 11 mathematical statistical processes. So then we can truly change that. Student experience and truly have a society that that doesn't proudly say, I'm not good at mathematics. I know we've made an impact at that point in time.

00:54:21:23 - 00:54:48:20 

Joanie

Amazing. And I just want to wrap up by thanking you both for your leadership to get us to this point, to ensure that this book made it out into the world. And I'm excited for folks like Curtis and I and our listeners to do everything we can now to realize the vision that was held there in Latrinda I love that you said you expect this to happen. And, I want to not let you down. So thank you. Thank you both for the time today. 

00:54:48:20 - 00:54:51:06

Kevin / Latrinda

Thank you. Thank you guys.

00:54:56:03 - 00:55:17:10

Joanie

Well, that's it for this time. Be sure to check the show notes for the resources we mentioned and others you might want to explore. We would love to hear your feedback and your suggestions for future topics. And if you're enjoying learning with us, consider leaving a review to help others find us and share the podcast with a fellow math educator. See you next time!