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Math, the Great (Potential) Equalizer

How current practices in math education around tracking and teaching can be dismantled to achieve the promise of equity in math classrooms

Math has a problem when it comes to equitable learning.

Inequitable math instruction is a result of tracking, according to Kentaro Iwasaki, Ed.L.D.'21, a former math teacher who led new math standards in California and now works with school districts nationwide to overhaul their math programs. Tracking in math contributes to segregation, with Black and brown students often placed in lower-track classes compared to their white and Asian counterparts, he says.

“When we go into classes or schools, almost every high school is tracked. With the doors closed and just looking through the window of a classroom, if you just look inside, you can pretty much tell what is a high track class and what's a low track class just based on the student demographics. And that's really unacceptable in our education system today, and particularly this is problematic in math.”

The negative impact of tracking carries over into students' self-concept, classroom dynamics, and overall educational experiences.

As a math teacher, he dismantled an honors math program at Mission High School in San Francisco. Still, this change resulted in increased AP enrollment and passing rates for all students, challenging the notion that tracking is necessary for academic success.

“Math is being used as a vehicle to maintain segregation in our education system and that it's more comfortable for parents, particularly parents with social, cultural, political capital, to argue for segregation under the guise of mathematics and saying, ‘Well, my student is at this level, so therefore should be in this class,’ and really kept away from Black and brown students,” Iwasaki says. “No parent is going to outright say that, but in my work with parent communities and listening in and attending school board and school committee meetings, that very much is the underlying conversation and that is what district leaders, district systems, really need to confront.”

In this episode, we touch upon the concept of complex instruction, the value of de-tracking math, and how like-minded educators can forge a new identity for math in schools.



JILL ANDERSON: I am Jill Anderson. This is the Harvard EdCast.

If you look around the country, Black, brown and low-income students do not have the same access to math learning. Kentaro Iwasaki says math is a vehicle to maintain segregation in education and one he wants to dismantle. He's a former math teacher who led statewide math initiatives in California. Today, he works with districts nationwide on making math more collaborative and just. How students are tracked in math can impact everything from the quality of their teacher to classroom dynamics and graduation rates. He told me there are ways to get beyond some of these roadblocks, but it's often controversial and political for schools to do so. I wanted to hear more about how math has become so problematic. First, I asked Kentaro whether math is the greatest equalizer in education.

Kentaro Iwasaki
Kentaro Iwasaki

KENTARO IWASAKI: I certainly see math as "problem content area" that we really need to address. Bob Moses, the founder of The Algebra Project, talks about math as the civil rights issue in our education system today, and particularly just the impact on Black and brown communities. When we go into classes or schools, almost every high school is tracked. With the doors closed and just looking through the window of a classroom, if you just look inside, you can pretty much tell what is a high track class and what's a low track class just based on the student demographics. And that's really unacceptable in our education system today, and particularly this is problematic in math. I and my colleagues experience, and educators experience and districts, I think, rightfully focus in on math, particularly I would say in the middle and high school years. Many of the districts I work with in ninth grade, a ninth grader can get placed into any of one of five math classes or five levels of math.

And then even within those courses, often there's the high track and the low track, so that really impacts both a student's self-concept and how much they believe they can perform in math. It impacts every aspect of a school schedule as well. So within the scheduling system, as soon as math gets tracked, and particularly what we're seeing is that white and Asian students are predominantly put into the higher-track classes. Black and brown students are predominantly put into the lower-track classes. That impacts the whole scheduling of a school day. And so you, in essence, maintain segregation in our school system because of math.

And even with some of the districts, when I dig into their data, like one of the districts I've gotten to work with in Massachusetts, which I really appreciate them taking a deep dive into their data around equity, but they looked at students who are getting an A or B, an eighth grade math and algebra, and they were seeing that 60 to 70% of Asian students were getting recommended for geometry, the higher-track class, and 16 or 17% of black students who are getting an A or B were placed into geometry or a higher-track math class. So there's this huge disparity. And the placement guidelines for math, for most districts I've worked with, I would argue, have huge bias within them. They're primarily teacher recommendations, and often there are categories like organization or hardworking, and that's very much a cultural definition and very much there's just huge opportunity for bias in that. So just a lot of the district systems and structures certainly lend themselves to inequity in math.

JILL ANDERSON: Rand released a survey of teachers and principals recently highlighting some of the inequitable access to math learning happening around the country. This isn't news to you. You've been working on this for decades. I want to know what it actually means for those students, those Black, brown, low income students who aren't getting that access to math learning, or maybe they're not being pushed or they're just caught in the system that's keeping them down. What happens to them?

KENTARO IWASAKI: Genie Oaks has research on the experience of students in tracked classrooms and very much if you go into classrooms today, that very much is the case. So the lower tracked math classes, honestly, I feel bad for the students in them. They experienced very low-level tasks. A lot of teacher directed instruction, often worksheets, rote problem solving, few opportunities for collaboration. It feels very stagnant in the class. And then you go to a higher-level math class and there's conversation, collaboration, interesting questions. The teachers often are more dynamic, using more instructional approaches and strategies that foster engagement. And so you really see the disparity in student experience. And of course, student experience is going to lead to student outcomes, and that very much is shown in the data. So a lot of the work I get to do with teachers is really examining their own practice, and particularly around an instructional approach called complex instruction that really examines status and power dynamics in a classroom around race and gender and socioeconomic status, language, and just how status shows up in a classroom and how that gets in the way of student learning and engagement.

And once teachers can recognize that and recognize how they themselves are causing some of the status issues within a classroom and implement strategies to combat and mitigate those status issues, students really engage much more fully and learn at much greater rates. That's a lot of the work I get to take up with districts is both examining their policies, their structures, but then really getting to the practice of how teachers are going about the work of instruction in mathematics.

JILL ANDERSON: Is that how you can begin to change this on the ground? Is it through that complex instruction, which I'd love to talk more about that, but is it based in instruction?

KENTARO IWASAKI: Yeah, I think that's the million-dollar question in education. Certainly, I am an advocate of looking at policies, structures, and practices within a district system. So I feel very privileged. Right now, I'm working with Cambridge in Massachusetts really closely, and I think they as a district are really examining their policies, structures, and practices. So at a policy level, they're moving forward with a policy of all eighth graders taking Algebra 1 by 2025, so that's a very ambitious policy. And then they're also examining their structures. Within the system, where is tracking happening and what are the results of the track? There's a famous quote that every system is designed to achieve the results it does, so what are the outcomes of the tracking within the system and what is that causing? What they're seeing in their data is over a quarter of the students are Black in Cambridge, but one ninth of Black students are ending up at AP Math.

And so they are examining their own district structures around that and asking the question, how are we responsible for this? So I really appreciate that at a structural level for them to ask those questions. Also, examining their curriculum, the professional learning. And then I'm also brought in then to look at the teacher practice, which is around creating more discourse in the classroom, more equitable participation structures among students to get students really engaging and talking about math. Certainly, the more engagement students have within a math class impacts their learning. They'll learn more the more engaged they are, so a lot of the work I get to do at the teacher practice level is around that.

JILL ANDERSON: I want to talk about tracking because you need to help me understand where this is going wrong, because from an outsider perspective, someone who's not in the classroom, it seems like it would almost make sense. If a kid can't do a certain amount or a certain level of math, then they wouldn't be able to progress to a higher level. That makes sense, at least in theory. But in this case, it sounds like it doesn't work. It's just creating more inequities.

KENTARO IWASAKI: Right. Absolutely.

JILL ANDERSON: How is this happening?

KENTARO IWASAKI: I think the way you describe math as this sequential building block process, that's the way our American system has imposed mathematics upon students. But really, I come out of San Francisco Unified and I'm really grateful for those years, but San Francisco Unified talks about math as more of a web rather than a ladder. So math is very much interwoven connection among ideas, and the new California Math Framework really emphasizes these big ideas in mathematics. So when we look internationally at other countries and how they approach teaching math, it much more is in this web fashion where ideas are connected to each other. And it's really our American approach, our US approach to mathematics, that creates the sequencing and really creates barriers and gatekeepers around what a student needs to know before they can progress.

So a really common example is the fractions, decimals, and percents you need to know before you can engage in algebra, but that's really a false idea. You can engage in the larger ideas of algebra and the beauty of algebra and geometry without complete mastery of the procedures around fractions, decimals, and percents, of really being able to know down to the minutia of all the processes and procedures of that. You can still engage in the larger ideas. They reinforce each other. So if you learn algebra and incorporate fractions, decimals, percents, it's going to build on each other. So very much our American system in mathematics is one that holds up barriers and gatekeepers. And I would argue that right now the debate of mathematics in our country in multiple media sources, the Wall Street Journal, Boston Globe, San Francisco Chronicle, the New York Times, as they look at math, the math conversation, the math wars, it's not about math.

I contend that math is being used as a vehicle to maintain segregation in our education system and that it's more comfortable for parents, particularly parents with social, cultural, political capital, to argue for segregation under the guise of mathematics and saying, "Well, my student is at this level, so therefore should be in this class," and really kept away from Black and brown students. No parent is going to outright say that, but in my work with parent communities and listening in and attending school board and school committee meetings, that very much is the underlying conversation and that is what district leaders, district systems, really need to confront. And it's a very challenging time politically, but math really fits into this larger political discussion that our country is facing, communities are facing. Math is certainly at the center of much of it in schools.

JILL ANDERSON: You've done the work of dismantling an honors math program, and when I read about that, I could only begin to imagine how challenging it must be to do something like that in a school district. What was that like to come out and say, "We're going to do away with the honors math program?"

KENTARO IWASAKI: My years at Mission High School in San Francisco Unified, I was there 13 years and I often say everything I learned about education, I learned at Mission High. We were the first high school to disband our honors program and to make all of our math courses heterogeneous and essentially just get rid of the leveling. And what we saw was really a 400% increase in AP enrollment. So we went from one AP math class, which was predominantly white and Asian students, to ultimately our AP math classes being much more representative of the school community, and also increased passing rates among all students, so white and Asian students and Black and Latinx students. And whereas in prior years, there have been very few Black and Latinx students in our AP math courses, we were seeing that Black and brown students were in our AP math courses and succeeding.

There are so many components of that, both a change in pedagogy and curriculum and parent outreach and community involvement, but also just a real belief system among the staff of really believing our students are able to do this when the messaging for their whole education career has been that they are incapable in mathematics, that they are failures. So to really change that mindset, both in the educators but in the students. And I mostly get to work with teachers and leaders now, but that mindset shift really needs to happen among the educators first, and then that mindset shift getting communicated to students, both in the practices, in the structures, in the policies around mathematics so that students can experience something different in mathematics and then ultimately achieve different outcomes.

I'm really excited that the work at Mission High, the model scaled to San Francisco Unified, that in 2014, the school board adopted Math Pathways that got rid of tracking. Right now, unfortunately, San Francisco Unified is needing to retract that. So they are with change in the times, change in leadership, at this point, San Francisco Unified is re-instituting tracking within the district. But I do feel very fortunate that I was able to be at Mission High that I got to lead this work in the high school and then ultimately see that expand in the district. And then to see this work now, the Math Pathways work, make its way into the California Math Frameworks, just as the California Math Framework talks about different approaches or different math pathways that are possible for students, but to really put out these ideas that de-tracking is possible and is beneficial for all students. That message I think is both controversial and very much not accepted widely in our communities.

JILL ANDERSON: Do you have any idea around the country how many districts or states or schools are not doing the tracking?

KENTARO IWASAKI: I've found very few, and honestly, very few who want to unfortunately, or they may want to, but the political climate does not allow the leadership to move forward with it. Certainly, some charter school networks have had more freedom to get rid of tracking, but within large district systems, it's very uncommon. And within school systems, it's very uncommon. The defacto is much more maintaining tracking within mathematics, and it's just very odd to me.

Mathematics is so different from every other content area. So in ninth grade in English, you take English 9, or ninth grade English, and whatever science or social studies class in ninth grade, and there may be an honors and there may be a non-honors course in those content areas. But within math that you can take often one of four or five choices. It's very unique to mathematics and it's very unfortunate just how we're approaching this in our country.

JILL ANDERSON: Is it possible to have equitable math if you have tracking? Is there a way to do this?

KENTARO IWASAKI: I would argue that there's only equity up to a certain amount with tracking, to a certain level. I think to achieve equitable outcomes and experiences for students, we need to abolish tracking. That said, particularly I would say the tracking of honors and non-honors courses within one class like Algebra 1. But I believe that districts and school systems are working very hard to make their courses as equitable as possible. I would just argue that once there's tracking in a system, the outcomes are very limited. The messaging to students is it's one of sorting them. There's this movement in education, colonizing mindsets and education and sorting students, and categorizing them and assigning them value. And really that's what we're doing, and we're imposing this colonized mindset onto students, so then students believe the labels we place on them, that they are a non-honors student.

JILL ANDERSON: They're not good at math. You're either not good in math or you're good in math, and it just splits you into these different groups.

KENTARO IWASAKI: I've worked with districts lately that I've just asked, "Well, instead of the district or the teachers imposing their view on the students, what if the students and their families choose the level? If you're going to maintain levels within your math courses, what if the students and families make that decision themselves?" Because as soon as a teacher with all their power bestows upon a student a label, the student really internalizes that, and really that sets their trajectory or that it limits how much they're going to be able to believe that they can perform in math. Different district systems are taking this up or at least discussing this idea, even when district systems say parents can override whatever recommendation teachers make, just asking parents or students to do that I think is inequitable.

But also, just furthermore, any of the labeling that we as a school system do to students is so detrimental to them, I would say both for the honors designation and the non-honors designation. There's research from Joe Bowler about high-achieving students or honors students are given the message of their high performance, there's an immense amount of pressure they feel. Feel also like they can't ask questions or show that they don't know. And then some of her research has shown that as they progress in mathematics into higher and higher levels, they begin to actually pull away from taking courses at higher and higher levels. So I think all of this labeling we do is really detrimental to all students, and particularly, though, Black and brown students.

JILL ANDERSON: I want to hear a little bit more about complex instruction. What is complex instruction? Is this something that a teacher can do on their own, or do you need the whole school on board?

KENTARO IWASAKI: Complex instruction is an instructional approach and instructional pedagogical methodology, and it's based in cooperative learning, and it really examines status and power in classrooms within groups. So the complex instruction model uses small groups and some of the traditional components of cooperative learning roles and norms. But one of the distinctions is that as students have roles, the roles actually hold some of the social norms that we want within a classroom to maintain more of the equity and the equitable participation structures.

There are open-ended tasks so students can access them from multiple entry points. And a huge component is having teachers call out academic mathematical competencies and strengths that students display, as well as social emotional strengths around communication and collaboration. So really fostering a sense of belonging within the class, of changing student identity or their sense of themselves as math learners, and really engaging in productive struggle and discourse.

And one other component that I really love around complex instruction is it's a model that can be used with adults. So with one of the districts I've gotten to work with, at the end of the training week, just as we began to examine status and power dynamics within the adult system within the school or the district, one of the teachers raised that 80% of their department's AP math teachers are white male, and 80% of the Algebra 1 teachers are white female. And so she was calling out the status issues within the adults and within the educators themselves. And so very much my advisor at Harvard, Jal Mehta, whom I love, he talked about system symmetry. So if we're seeing inequitable structures among the adults in the system, how much more is that going to get replicated among students?

So with the educators or with the teachers, I often just say, we have 50 minutes a day with our students and we're in charge of what kind of experience they're going to have, what kind of social structure we set up. And wouldn't it be amazing if we actually set up in our classrooms a social structure that is one that we want, that is not mirrored in our society? What students experience outside of our classroom is so much of the inequity, but what if we can cast a vision, actualize a vision in our classrooms of more equitable participation, equitable outcomes and experiences for our students, really mindful of Black and brown students, their experiences in our classroom, and ensuring that they and all students are succeeding in mathematics

JILL ANDERSON: Kentaro, what if you're a math teacher and you're listening to this and you feel like you're trapped in the system? Because after our conversation, I'm thinking, just like the students, a lot of the teachers are trapped in that same tracking and they cannot change it. What can you do?

KENTARO IWASAKI: So I'll share my personal story at Mission High. When I started there in 1998, I really felt like I could not unfortunately collaborate with any of the math teachers who were there. They very much were much more traditional than I was wanting and seeing I needed. And really, I found a small group of math teachers outside of Mission High. And then eventually, slowly, year after year, one math teacher would join that I felt like I could collaborate with. And then we hired on a couple more and more, and then finally it really changed the dynamics. So I would really encourage math teachers out, there are like-minded teachers, educators, communities that you can join. Certainly reach out to me and I'm happy to see what kind of network I might be able to provide. This is a really tough journey alone.

I often say I think teaching is the hardest job I've had, even sometimes harder than parenting. And I very much want to both esteem and encourage all educators and all teachers in this work. It's such difficult work, so let's not do it alone. Let's find like-minded colleagues in this work and develop those and really share in struggles and share in encouragement and share ideas and strategies with each other.

JILL ANDERSON: Kentaro Iwasaki is the founder of Concentric Math. I'm Jill Anderson. This is the Harvard EdCast, produced by the Harvard Graduate School of Education. Thanks for listening.


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