Changing the Equation: How to Make Math Class More Meaningful

Hey, Michael.

Hey, Diane. How are you?

Well, I'm well. And I'm going to start with urgent priorities today. Do you have any recipes that use a lot of lemons?

Lemons. Okay.

After, after. And it's not because we're going to make lemonade out of lemons today. It's literally after years of drought with all the rain we've had, my lemon tree has gone insane. And I have now made curd and cakes and ice cream and ice cubes of juice, and I have run out of recipes, and I still have hundreds of lemons, so.

Well, it sounds like you're in California. It sounds like you've had rain. It sounds like I remember why I miss California. And I will tell you, the only other two I will add to your list is preserved lemons for salads. And then, of course, there's an alcohol that you could make as well. But we won't go there today. Instead, we could think about all the ratios and all that stuff that goes into making it just right. Because I know you've been wanting to talk about math and some of the things that you've been learning about how our school system thinks or perhaps doesn't think about math.

Yes.

In relation to work. So I'd love you to start to unpack that.

Well, great, because it's much better that I talk about this with you than turn to the drink, because math can make me feel like I want to do that sometimes. So I appreciate your willingness to have this conversation. And you know what, what is prompting it for me is, you know, you know, I. I have thought about math for many years from sort of a K12, you know, know, educator perspective. But now I'm coming at it from this new direction where we're really thinking about careers and post secondary and, you know, what's. What's getting me going on this topic is my observation of how important math is in careers and how that is really at odds with how people in K12, I think, think about it. And, and so let me just lay something out and see if it makes sense to you, which is my experience in K12 is there's a mindset there. And it's a mindset among students and parents and teachers and counselors and kind of everyone who is in the system that we really focus on math almost exclusively in how it relates to college and specifically, like, how do I do what I need to do in math? Because it's a, you know, key to college admissions, essentially. And so the, the big thinking that ends up happening, especially in high schools is, you know, if I can get all the way to calculus, it gets me a. It gives me a better chance of getting accepted to college and an elite college at that, maybe into the major that I want. Taking the most challenging. If I can't get to college, you know, taking the most challenging courses that I can in high school, relative to what's offer helps me get into college. You know, getting good enough grades in math helps in my GPA to get into college. You know, previously and maybe a little bit again now emerging, taking the SAT and the ACT and getting the best score I can helps me get into college. The point being, as you hear, it's all about getting into college. And as I think about my time in K12, we almost were never talking about, like, the value of the learning of the math. It was always this entry into college.

Yeah, I, it certainly matches up with my experience as well, Diane and, and I know it's playing out there in California. Let's go there in a moment. But I'll just add, Jeff Selingo has made the point to me recently that it's that, that all of what you just said is absolutely true. And it's a little bizarre that colleges care this much about math because, because most students, when they get to college, are going to take at most one math class. Now, if you're going to MIT or Caltech, maybe that's different. But for most of us, we get to college, you do your math requirement, if you have one, maybe you had Gen ed math, so you have to pass, you know, a test or something like that, and then most students are sort of done with it. DIANE so it's sort of bizarre how much the college and K12 system cares about it as an entry point into admission, as opposed to anything you're going to do with that track. But, but let's unpack what's going on in California.

Yeah, this is the other piece that just has me, you know, deeply into math right now, which is, I feel like California is always having a math war, but there is a renewed math war at the moment. It's, it's, you know, peaking right now over the last, you know, multiple years, about four years, California has been trying to, as a state, adopt a new math framework. And this framework has been very controversial and, you know, was first presented and everyone's in an upright, you know, outraged. And so they went back and they edited and revised. That's been going on for four years. Well, it just got, you know, approved at the state level. Still, people Very upset about it. But you know, I've been reading the coverage about it and the arguments around it and maybe I'll just give you a couple of quotes here that I think go directly to what we're talking about. You know, this is from the LA Times, you know, and the quote is another concern of people who don't like this math framework is that many top colleges still place an emphasis on whether applicants get to calculus and how well they do in that course. And so this is just a well known, well communicated expectation from colleges and universities. And what I would also say is from the most selective and elite because you and I both know there's a small number of those, there's a huge number of colleges that are non select. You don't need to take calculus to get into those colleges. So it's like this small number really driving the agenda for most people. And you know, the, on the, so that's on the one side you've got these people angry that, you know, because we're driving every kid to college, we're not actually focused on equity and like going at a slower pace and you know, more kids able to kind of learn together and things like that. And, and then the, the flip side of that is parents who are really frustrated and worried that their, their kids opportunities will be limited and held back. And this actually happened in California and in San Francisco where they decided they were not going to teach algebra in eighth grade because it wasn't fair and equitable. And so we're literally saying we're withholding learning from some kids in the name of. And I, on both sides, I'm like, oh my gosh, this. Michael, this is not third way thinking.

No, not at all. I mean it goes to the heart of, I think what frustrates both of us around these conversations is that clearly the answer to equity is not the opposite of excellence. And clearly having a system that drives off the expectation of calculus for all doesn't make a heck of a lot of sense. And I know you've been investigating about how does math even, you know, manifest itself into these careers. So I'd love you to tell what, what you've been finding in that because that may be the most interesting piece of the puzzle.

Yeah, and I think that my headline here is, and we're using, we're using data sets that lots of people use, so sort of the federal government data sets around labor and statistics and jobs and careers and things like that. And so as we just dig into this and really think about the usefulness of it. You know, my, my headline is, well, let me just share with you what we're discovering. So you know, There are approximately 923careers in the US and I say approximate. We do in these data sets believe there aren't careers that are represented in there. There are some. I will also tell you that I had no idea where careers. So it's fascinating. It's a little bit of a game. Like I, I challenge anyone to write down the number of careers you can think of. 923 is quite a lot.

There's no way I would get there.

Yeah, so, so you know, 235 of those 923 literally have math as an important skill for doing that job. And these are jobs where you're going to be doing math kind of on a daily basis, you know, doing calculations, using math in your actual work. And so just some examples of these types of careers. You're an actuary, you're a statistician, those probably seem pretty obvious. You're a sales manager, you're a personal finance advisor. And so I feel like those seem like, oh, but there's 235 careers that are using math kind of regularly. There's 573 careers inclusive of those 235 that also have math as like important knowledge you need for doing your job. And so you might not be doing calculations and stats every day, but like when you're a pharmacist and an economist and a wind energy engineer and a stone mason and a logistics engineer and an insurance underwriter and a farmer, you are literally, you need a grasp of and knowledge of math in order to effectively do your work and to be engaged in your career. And so I think that, and then the other thing I would just say about this is when I all These careers, these 573careers, when I look at them and stack rank them and money isn't everything, but making a family sustaining wage is really important. And the thing we aim for, you know, these careers are highly represented in the group that makes, you know, on average 75,000 or more a year. So in the sort of top end. So not only math, an important part of the majority of careers that are in the country in some way shape or form, but definitely overrepresented in those where you're going to make more money. And here's maybe the punchline. Very, very, very few of these careers require any use of calculus or quite frankly advanced algebra even. And so like most of them require just a strong grasp of real world Applications of math like statistics and fluency and basic math concepts and confidence that you actually understand these things and practical application of them. And so I just would say this is so contrary to my experience in K12, where almost no one is focused on math for career opportunities and success. Like, I don't think I ever had that conversation in K12.

No, that makes sense. It's interesting. It brings to mind when I wrote From Reopen to Reinvent, I joined the argument that many more people should be learning data, science and statistics rather than the algebra 2 into calculus path. And, and one of the arguments was Anthony Carnevale, who was then the director of the center on Education in the Workforce at Georgetown, had this stat in an article where just 11% of US jobs involved work that required understanding Algebra 2 concepts and only 6% regularly used those concepts. So a bare minority. But then you're pointing out these. That doesn't mean the careers don't have math at their heart. It's just not math. On this calculus track, if you will, that is a relic, we should add. Right. It's a relic of the sort of distinguishing between vocational education and the college track education, which in our mind is a boundary that, you know, should stop existing also. So that's an outgrowth of all this. So. So where do we go? I guess.

Yeah.

From here. If that's where. If that's, if that's the reality, where do we go?

Yeah, and I definitely want to get into some solutions. We never, of course, want to leave here without generating some, you know, paths forward, but it might be worsting for one more minute on like, what, what is underlying this problem because it's not just like K12 people running around and like, you know, purposely sabotaging math. I don't think that that's the objective, but I do think that our current design of our K12 system kind of, as we know, results in, in very few, let's call them mathematically literate, let alone fluent students. And you know, I was thinking about this because we talk about reading and we talk about literacy quite a bit. And as we both know, there's a, there's a Rene focus on the science of teaching reading and literacy. And, and I do think as a whole society feels very like convicted that everyone should be able to read and everyone should be literate. I, I'm not sure that that's how we think about math literacy, quite frankly. And so, you know, I think one of the things that you're just pointing to that's embedded in the system the K12 system we have is what if you have calculation as this destination and you just said it like there's one pathway, then there's like this sequence of courses that you take and really it's like every single person's on that same pathway and it's just how far you're going to get on it, in what period of time, you know, will you make it to algebra, will you make it to geometry, will you make it to algebra 2, to trigonometry, to. It's almost like this game of like, well, where is everyone going to fall out, if you will? And we don't, we're, we're not. This is all driven by this drive to four year college, college for all, which is a thing we've been talking about a lot. And so I just think it's worth us noting that only about 8% of high school students actually take calculus. So that is, that is the dropout rate, if you will, of math along this pathway. So I think one thing in the design we need to think about is this pathway concept. I think the second challenge is K12 is not really connected to employers and to employment. You know, we, again, college for all. That's our focus. That's what we thought we needed to be doing. And when you, when you're disconnected from the actual use and what people are doing, I think it's challenging. And then Michael, you know, there are very few teachers capable of teaching math. And I think this is something we're really going to have to grapple with. You know, I'm, when I'm going through these 923 careers, you know, you need to know a lot of math in order to teach math. And as we just showed, there's a lot of other careers where if you know math, you're going to be very competitive in those careers. They're very lucrative careers. They don't often require as much post high school education and credentialing. And so why would you choose to be a math teacher? And I will just say, you know, math teachers for a long time have been among the very hardest to hire. There are tons of math positions that go literally unfilled every year. And I just see this problem growing and not shrinking. And so I just think those are some of the elements of the system that we need to think about solutions for if we're going to do something different here.

No, that all makes sense. I'm just curious and you may not have a take on this if I'm putting you on the spot. But how would you think about defining what is math literacy? Right. As opposed to the completion of algebra 2, trigonometry pre CalCalc, if that's the old sequence. Right. How would you define that? And I guess. Or how would you think about creating a definition? Maybe that's the fairer question. And then the second part of it is I'm just sort of curious if you have a thought of does AI change any of that? We know, you know, a lot of these large language models don't do math particularly well today, but we also assume that that will change over time. So I'm just sort of curious how that enters into your thinking. Or no.

Yeah, this is such a good question. Well, the first one I love because you sort of are inviting me to think about a rubric and learning objectives, which, as you know, in my nerdy world is like a favorite pastime. So it's really fun. So the first logical place I think people go is, well, rather than this traditional sequence that most of us are familiar with, you know, sort of this pre algebra, algebra, geometry, algebra 2, etc. You go with an integrated math sequence. And California, this is one thing that the state has tried to do in this framework is promote a more integrated approach, which conceptually I think is maybe in the right direction in that it does seem to be a little bit more grounded in real world applications. Like, very rarely are you getting these pure sort of subjects when you're using math in the real world. I think it breaks down in a couple of ways. One, I don't know that it is truly connected to real world application. And two, I think in the teaching of it, it's not how math teachers are trained. Unless your entire system is doing this. When kids are having to move, shift back and forth like, it's just a mess. Right. And it's not recognized by college, which is driving things. So I'm not sure integrated math gets us where we need to be. So how would I think about what it would mean to be math literate and math fluent? I do think there's. Well, I mean, one way we could start would just be to go look at what is the math that is being done in, in these careers and quite frankly in real life. I mean, I don't know about you, but being a human, you have to manage your budget and your finances and like all of the. So like, what are the real world uses of math, concepts of math, and.

Then pull back and define competencies around that. Yeah, interesting. Okay. Yeah, yeah. And I guess it'd Be super interesting if AI starts to in fact change some of these professions. As you know, I'm seeing white papers come across my computer screen saying we don't need to worry about computation anymore. And I suspect there's a point where that's true and there's a point where maybe it's not true that actually still learning these fundamental processes in the same way, you know, we do work about, you know, in phonemes and things like that are still building blocks to understanding how math is in fact functioning, even if the manipulation of equations or things like that become less important.

I had a really interesting conversation the other night with Irham, who was on our second episode of this season related to AI about this very topic. And there's a big generational gap between us. And so he's always a little surprised about what I did in the old days, you know, but so he was saying to me, you know, he's like, I am one of the few people where I literally use calculus in my job. So he, he is truly using calculus. And so he's very mathematically literate and fluent, obviously at high levels. And he was so. But he was advocating to me that what most people should be focusing on is statistics and data. Significantly more to your exact point and what you've been writing about and certainly what I agree with. And he was so surprised to hear my experience of, of doing research methods in college and statistics in college. He's like, wait a minute, you used a calculator? And you. He's like, why would you do that?

Yeah, why wouldn't you just type into Excel P. You know.

The actual comput piece is just far less important to him. It's the conceptual understanding and the application and usage. Because in his mind we have all of these tools that do that. He's like, technology does that so much better than humans. The likelihood that a human is going to make a mistake is very, very high. Like, why would we. It's inefficient for us to be doing that type of mathematical work. And in some ways it's what becomes the turn off to a lot of people, I would argue, you know, sure, 100.

I mean, when it becomes so about essentially formula manipulation as opposed to understanding the conceptual underlying what you're in fact doing. Right, right. It turns a lot of folks off. So that, so that all makes sense. So, so if, if we've identified the problem, we've started to define, you know, how we would think about literacy and fluency in this world, we can admit we haven't nailed that yet. But, but sort of putting some questions out there and suggesting maybe some of this might evolve. Where would from us can we go to solutions now? What would you start to paint?

Well, you know, I, I mean, I guess my first, my first suggestion would be, you know, I don't know many people in America who are super excited about the presidential campaign this year, so maybe we take that one out and we sub in a different campaign. And here would be my vote for the campaign of is that we just need to rethink the importance of being math literate in America and why it matters to each of us personally. You know, I had, I, I used to work this with this incredible math teacher, Megan Taylor. And she, she always tried to drive the point home. She's like, no one would go to a party and like casually say, like, yeah, I'm illiterate, I can't read and be fine with that. And yet all the time people in social settings are like, I'm terrible at math, I can't do math. And so this, this notion that we have gotten comfortable as a nation that most people are terrible and can't do math, like, we need a campaign in the other direction of the importance of math and, and the, the importance of us collectively being literate at it. And so yeah, and, and, and a changing expectation. I would, I would want you and I, as starters, to be as passionate about, you know, young people coming out math literate as we are them coming out, you know, reading, writing, literate. So that's my first nominate.

Love it. I, I, if we, if, if in future episodes we cover the what presidential candidates should be saying about elections, we'll have to strike this from the record. But I agree this would be a much more inspiring use of the next year of our national dialogue.

I suspect indeed the second one we've already touched on a little bit and we started to brainstorm there. But like, we need the math that's being taught to, we just need to shift the focus, I think, in K12 away from, you know, how are we getting how, how is this a screener for a small number of kids into elite colleges? And how's that driving the whole system into what is the math that is meaningful and useful and used in the real world and really organizing our instruction around that. And you know, again, we've talked about like, integrated math should be able to do this. Maybe it's the starting place, but it's falling short right now. It needs some more.

Yeah. And on this one, and this may bleed into where I think you'll probably go next. But one of the thoughts that I've had is for those individuals like your home, who, like calculus is going to be central to what they do. I want that pathway available, but I don't want it to be the expectation that that's the only option. And I don't want it to be seen as better or worse then. I just want it to be a choice that I've made because it speaks to me, because it aligns with things that I have learned about my passions and purpose and things of that nature. And it's a considered choice as opposed to something either done to me or an option that I don't even have completely.

And you're. We're. We're going back. I feel like we're going back to our roots of what we actually originally met over, which is it's personalization. I mean, and. And I think that, you know, this is. This is probably the. Going to be the most controversial. And I want to be really clear about what I'm saying and not saying here and the whole totality of it, but I. We need to totally rethink how we're teaching math from a needs outcome, but a practical perspective as well. Like, we have technology and AI is only going to help this. We have personalized math instruction options that are pretty darn good right now in the world that really, I would argue, can do a better job of personalizing instruction and creating a personal pathway for every single student to learn math from very young, all the way through high school than what almost every math classroom in America can do. And then you add in the fact that, like, you have to have this math classroom be as good as the next year and the next year and the next year, which is just unrealistic at this point. You know, we need to personalize math instruction. We need to use technology to do it. And that means it needs to look completely different than the way it does in school. And there are many implications to that, and we can take a minute to unpack those. But I'm guessing that you're aligned with me here on this.

100%. 100%. And I think it's interesting for people who hear this, they'll say, well, tracking does that. And in my mind it doesn't. Because while, like, the opposite of tracking, putting everyone in the same thing at the same pace is not an answer, and I would totally argue against that. Tracking is a very blunt instrument on this. And as we know, math is cumulative. Right? So there's a Certain number of power skills that translate, that are critical for learning what comes next and that branch you in different directions and so forth. And you just think about that individual and I'll just tell you a story. This happened a few years ago in Lexington, where I live, where I was talking with the father over coffee and he was just anguishing because his then 8th grade daughter was trying to decide would she take, you know, honors geometry or regular track geometry, something like that, in, in the ninth grade. And I was just thinking, what a terrible choice for a young person. She should just be taking math and she could move as fast or as slow as she needed to do along the skills. And then if, because like of the way our education system works, we needed to give it a name afterwards, we could at the end of the year look at what she had mastered and give it a name. But like, why were we forcing her to make this artificial choice that was either going to hold her back or create stress she couldn't handle and all these other things when like, the objective should just be learning the math. And to your point, we can do this in an, in a personalized way. And then for people who I think may be hearing us and saying, well, that sounds really individualistic. Well, great, because then I get to work in projects where I apply the math. I've worked and in a group with people. But I'm not like being held back on the conceptual understanding because my neighbor is ahead or behind me at any given point in time.

We're totally aligned, Michael. And I would even, I would just add even a little bit more. Like, let's describe what this could literally look like in a school so people could imagine it, which is, imagine a young person going to school starting from kindergarten all the way through college, and they are literally in, you know, a software, a math software, technology program, probably more than one over the time. You know, maybe it's a small cluster of them, but they are in that program continuously for their entire K12 education. It's adaptive, it's growing with them. There is no limit on the amount of math they can learn.

There's no, there's no five week review at the beginning of fall to see where you may have or may not remember.

You're just making progress. You're never sort of waiting on a class or like behind on a class or, and, and so they're doing that. Imagine, you know, whatever, an hour or two or three a day, whatever it needs. They're doing that work in the, in the school building. What can the adults be doing. So they're not isolated. Couple of things. One, there's a whole sort of coaching and mentoring component to supporting young people to stay in there and hang in there and reflect on what they're doing and making sure that they're growing and mon. Monitoring their progress and diagnosing what's happening if they're, you know, falling off and celebrating when they're advancing. So there's that role and component which is important, but it doesn't have to be done by a math teacher and a math expert. And the second piece is, and you said it, if schools are teaching the way they should be, which is they have projects that kids are engaged in where they are really heterogeneously grouped and they are real world and they're applying these concepts, you can have exactly what the California math framework is envisioning and what San Francisco wanted, which is all these kids working together using math concepts regardless of where they are in their development and applying the math, being in a social setting, all of those things. So that's the type of thing we're talking about. But what that requires is changes in policy, changes in the role of the teacher, changes in course offerings, changes in how the transcript reflects what kids are learning, which feels a little daunting.

Yeah, I mean, there's a lot of work on this, as you know and I know that the traditional system, it's like, I mean, Clay would always say this when he would describe this Michigan Manufacturing Corporation case study news. Like there were metaphorical grooves in the floor that meant that the welding station only visited the, you know, whatever station and would never go across the factory floor to see someone else over there. It was like they were just so well worn. And that's sort of where our system keeps getting stuck as well, I think. And you make sort of a change to any one of these. Right. Like, we're, we're both pretty excited, I think, about the team teaching work that Arizona State is starting to roll across the next education workforce stuff, but that's going to bump into something else. Or as we've talked about in this podcast before you change seat time requirements, the Carnegie, you know, work that, that we've had Tim on talking about, Tim Knowles talking about. Yeah, but then finance, then like how you do scheduling, how you, how you've credentialed teach. Like all these things ripple in very complicated ways. That it's never just one simple.

No. Well, and this is, this is your expertise now. But as we know, the big existing, existing incumbent system doesn't really disrupt itself because something is always getting in the way. And so I do think we have to wonder, are there other ways to getting to this outcome because it's so important. And I do think this is where the rise of ESAs or educational savings accounts gets interesting. And especially if you combine that with, you know, what I think is an emerging opportunity for alternative methods to validate skills and knowledge. And we had some of that conversation with Tim when he was here in Carnegie and what they're doing with ets, but especially in the world of math where we have plenty of valid assessments that are valid and reliable. Yeah. And so what happens when families just what happens if the, the campaign works and families are like, oh, I need to get, I want a good career and career and job and I need to know math. And the school's not giving me a pathway to understand and learn the math I need. So I'm going to unbundle and I'm going to use some resources to go get that somewhere else.

Yeah. So before we wrap up here and move on to what we're reading, this just throws me back to season one where we had this conversation of the haves and the have nots in the schools and in like a place like Palo Alto where all the kids had already taken the math class before they showed up for math, you know, in summer school or in their Russian school of math after school or whatever it was. Right. And my reflection is, well, okay, I mean that's not how I would choose to spend my kids time or my money. But let's say they did it. Could you just say like, yeah, you've passed an assessment that shows you have mastered these math concepts. Great. Why waste your time doing the exact same thing now? Unless you didn't really master it, in which case it's more about cementing it and we should be able to, you know, these assessments can measure that as well. And I think you're right. You know, the ESAs, it's, it's funny how we both have come sort of around to this view that it, I think it creates a really important set of alternatives that aren't just schools to rethinking a lot of these structures. And you mentioned transcripts and grading and things like that that get very complicated. But when you get out of that world and you find other ways to validate and other ways to offer, it changes a lot of the questions that you ask in some pretty fresh, exciting ways that I think become more intuitive when they're not asked from the perspective of a parent. Or student in the system itself. Wow, that was a lot. All right, so let's, let's get out of there. And besides thinking about math and researching all the math that will be used in careers. Are you reading, listening to, watching anything outside of math? Because I don't know if you know this. We actually have someone on social media now who has created a Google Doc, apparently with all the recommendations we've given over the, you know, five seasons. So we.

Oh, my.

No pressure, but.

Oh, my God. Anything good tracking to make sure I'm not repeating. Well, I, I think I may have mentioned this, Michael, but, you know, Rhett is in his last semester at Minerva. He's in London. So I'm gonna head to visit him soon. And we're, we're actually gonna go up to Scotland and I'm. I'm super interested in Scotland because there's, you know, it was the, the heart of the. There's so many interesting things there. It was one of the most like, literate countries at one point in time. Small, poor, yet highly literate. An enlightenment. They're really amazing thinkers. So I've just been immersing myself in Scottish history and reading and I've sort of moved over to the, the fiction part of it now. So one of their most famous authors is Ian Rankin, and he has this famous detective and all the novels take place in Scotland. And so I'm actually reading his kind of memoir, which is super fascinating right now.

Wow.

Yeah. How about you?

That'll be an interesting trip. What about me? I was thinking about this beforehand. I have, like, not finished a book in a while, but I've just been continuing to geek out on tennis, which I think I said last time on the two minute Tennis. And so I am now completely hooked on. Andy Roddick has a new podcast called Served. I'm completely hooked on that. And then there's this like new rules of tennis, sort of money ball tennis sort of thing called fuzzy yellow balls. And I've been reading a video book and as you know, I don't irony since we're video recording this. I don't love watching videos generally to learn. I prefer to read. But I finally, like, I subscribed to it several months ago and then was like, oh, it's videos and put it aside. And then I have been obsessively going through this new singles rulebook. It helped me in my match the other day and it's been, it's been awesome. But I feel like I'm unlearning literally everything I thought was true about how you play tennis over the last few months, so it's been really cool.

You're a great model for what we should probably be doing in education.

There you go. There you go.

Sam.