A Thought Experiment on Tracking

Lots of talk on tracking in the math world right now, and I’ve enjoyed following along with the comments on this recent NCTM President’s Message from Robert Berry and this blog post by Michael Pershan, as well as the conversation on Twitter (for instance, here).

In the comments linked above, many people make an argument along the lines of, “but what about the gifted/smart/advanced students?” Tracking is the status quo, and these are the students who many perceive would be affected by a change. They argue that ending tracking will reduce opportunity for a certain group of students, labeled as more able than others. They argue that these students will be less challenged, will love math less, and will struggle to be engaged in the typical heterogeneous class. For more detail, check out the comments and conversation in the links above — there are many compelling arguments, from the perspectives of educators, parents, and former students.

Here’s a thought experiment. What if, instead of a world where tracking is the norm and NCTM is advocating to end it, we imagine a world where there is no tracking, and someone is advocating to institute grouping students into classes by perceived ability? What might people say if heterogeneous classes were the status quo, and we argued to change that?

Here’s an argument I might make:

What about the students who won’t be selected for a higher track? They’ll be pushed into low-level classes taught by less qualified teachers, they’ll interpret tracking as a message that they are less “smart” (likely based on standardized tests), and they’ll be segregated based on those messages, undermining community as entire classes come to believe they’re not mathematically capable. Given the way that academic ability is currently assessed, tracking will create a system of de facto segregation based on race and class, exacerbating differential access to the type of education that young people need to be full citizens in their country. And as tracking spreads, opportunity will be hoarded by families who know how to manipulate the system and buy advantages for their children, whether through private tutoring or pressure on their schools. All of this will limit the mathematical trajectories of many students, often before they’ve hit puberty.

In this alternate world, where tracking is a change to the status quo, what would you advocate for to better support all students?

12 thoughts on “A Thought Experiment on Tracking

  1. Michael Pershan

    What if, instead of a world where tracking is the norm and NCTM is advocating to end it, we imagine a world where there is no tracking

    This is really interesting!

    It seems to me that in imagining a world with no tracking, you’re making a lot of assumptions about how that world would look. I think those assumptions might be useful to make seeing as we know two things from our world:

    (1) As Danny Martin and many others point out, in the past, policies and structures that organizations like NCTM have argued are equitable have been co-opted in support of the status quo.

    (2) As Rochelle Gutierrez (1996, 2012) and many others have pointed out, there are plenty of detracked schools that remain highly inequitable and entangled in racism.

    So in thinking through your scenario maybe a little bit more literally and seriously than I should, what sort of reality are you imagining in a detracked world?

    {And so that I’m not misunderstood by someone reading these comments who haven’t read my posts, I am not a blanket defender of tracking. But I think there are tough questions to ask about NCTM’s position that tracking = evil and always racist, and I’m a fan of Guterrez’s writing in those 1996 and 2012 pieces.)

      1. dkane47 Post author

        This is interesting. I think I agree with you that tracking is not the most important structural thing we can change in schools. If someone made the mistake of putting me in charge, I don’t think it would be at the top of my list, in part because of the political issues of fighting with parents. But I find that whole line of reasoning to be a bit of a non-sequitur. Maybe tracking isn’t the most important thing, but it’s a thing, and we’re talking about it. Whether or not we should be focusing on tracking, or NCTM should be focusing on tracking, etc, I think it’s still useful to take a principled stand, especially if that principled stand reflects larger issues in math education.

        Here’s my answer to your question — I don’t think we have to imagine a magical world where there’s no tracking and we serve every kid perfectly. Our schools now are far from perfect, and I can imagine heterogeneous schools where certain students often feel confused, where teachers gravitate toward in-class ability grouping to cope with large differences in prior preparation, where classroom management is challenging with so many different needs. I’d love to be optimistic that that environment would help more teachers push themselves to grow and better serve all students, but it wouldn’t be pretty. There are lots of inequities there. But I see those inequities as less likely to persist (i.e. start in elementary/early middle school and play out that way for the next 6-10 years), and less likely to reinforce existing inequities in our country at large (I’m thinking largely race, class, and families’ ability to manipulate the system/buy extra education resources). That flexibility is huge in my opinion; it reduces systematic bias that compounds over years.

        I recognize that what I’m arguing isn’t captured in the research you have shared. I’m curious if you see that as an area the research hasn’t explored fully, or if my perspective is contradicted by the research.

        1. Michael Pershan

          I just want to clarify one thing about what I see as my take.

          It’s not me saying, “tracking shouldn’t be high on your list of structural changes to school.”

          Instead it’s me saying, “there is not a single answer as to whether tracking should be high on your list of structural changes to school, as whether it reinforces inequities and reduces flexibility depends on other variables”

          It’s also me saying, “research suggests to me that tracked schools that have really positive departmental cultures and math programs for the lower track students can reduce inequality; research also suggests that detracked schools that have negative departmental cultures and math programs for the lower track students are as bad as anything*. so we shouldn’t demonize tracking itself and instead focus on helping schools meet the particular challenges they face, however they’re organized.”

          So my issue isn’t with us taking a principled stand on tracking, it’s in taking a single yes/no one-variable NATIONAL stand on tracking. I don’t believe research (or experience, or my conversations with other educators) supports the idea that tracking is always harmful in the ways you say they are. And there are lots of potential areas of harm that are specific to detracked schools that we aren’t talking about, because of the single yes/no one-variable focus on a national policy on tracking/detracking.

          I think that’s something that we should move away from — best practices, worst practices, single-variable explanations. Frankly, NCTM (like most people in edu) like those sorts of things — manipulatives good, and later we’ll get Deborah Ball telling us “it depends”; textbook reform, and later we’ll get David Cohen telling us it doesn’t work to just change your list of books.

          So that’s what I’m saying — that “yes/no” is the wrong sort of position to take on either tracking or detracking.

          1. Michael Pershan

            * Here are some tough questions that I don’t know the answer too, from the perspective of “tracking needs to be eliminated”:

            What about acceleration? NCTM says that it’s a big fan of ‘appropriate acceleration.’ What would that look like, utopianly? What do we think that would likely look like in practice?
            What about special resources that are currently directed towards supporting students who are having a hard time in classes? Should we eliminate special education teachers and programs? Is that part of this discussion too?
            System-wide, would insisting on eliminating class-level tracking result in more school-level tracking? Would it be better to have magnet schools or high track classes?
            Right now there is a pathway to the highest levels of mathematics achievement post k-12 for under-served populations through assessment, identification of high-achievement, and then access to resources through tracking and placement in things like gifted programs. How would these students be impacted, relative to their high-SES peers, from initiatives that eliminate tracking?

            These are important questions to me that nobody in math education seems to be interested in tackling because we overly focus on one-variable changes. Catalyzing Change has a few things to say about this, but not much.

          2. dkane47 Post author

            This reminds me of some things I’ve read about feedback — that feedback works well when it’s part of a larger system. I.e. when we try to isolate best practices for feedback we’re actually selling it short because feedback is connected to so many other things, and the research on feedback is full of examples where “this worked here but not there.” So you’re arguing that tracking is one piece of a larger system, and looking at it out of that context may lead to unhelpful decisions? I think I can get on board with that.

            The one place I would push is to think about the dynamics of race and class within a school, and make sure that that is a major consideration and that tracking doesn’t get separated from the goal of an education that creates opportunity for every student.

          3. Michael Pershan

            Total agreement, and I’m totally on board with what you’re saying about feedback. (I’ve written a few things making something very similar to that argument for feedback in particular.)

            And I do completely agree that there needs to be an racial and class equity lens when thinking about anything close to these issues.

  2. TracingWoodgrains

    I like your thought experiment, but what if we take it further? Why stop at age? Let’s create a fully heterogeneous learning environment, where 17-year-olds and 5-year-olds are in the same classrooms, taught by the same teachers, learning the same subjects. We can implement low-floor, high-ceiling problems, differentiated instruction strategies, and cooperative learning tools to make sure that every student is challenged and engaged. What do the 5 year olds think when we tell them that 17 year old students are more capable, and the 5 year olds are stuck learning addition while the 17 year olds explore trigonometry and calculus? What would it look like in a world where that was the norm, and we tried to move from that to age grouping? What is unique about age as compared to any other tool that could be used to make grouping more homogeneous that makes it appropriate where other measures are not?

    1. G.W.

      Interesting extension you pose…I’m not really sure we currently do track math courses by age so much as by perceived ability level, particularly after elementary school. Where I teach, only about half of the students are taking “grade level” math. About 45% are accelerated at least one year, and about 5% are “behind” by one year. In our Algebra 2 Honors class, it is not uncommon to have four different grade levels of students in the same classroom (8th – 11th). In the regular Algebra 2 class, each class has 3 different grade levels (10th – 12th).

      But this did get me thinking, in terms of the core academic classes, this diversity of ages seems to be much more prevalent in math classes than in any of the other core subjects (science, English, Social Studies). So what makes math instruction (with regards to acceleration/tracking) in the U.S. different than English or History instruction? I do see honors/AP vs. regular English and History classes but I see very minimal (if any) acceleration of students in the humanities as compared to acceleration in math courses. What makes the timetable for leaning mathematics so much more variable than for the other subjects?

      Do the humanities teachers wrestle with the same questions about having honors vs. not having honors in their classes? They don’t have to worry about acceleration as a variable? So what is it that opponents of tracking have an issue with? Is it the acceleration, the honors/regular/remedial classes, or both?

    2. dkane47 Post author

      Thought-provoking. My first reaction is that age doesn’t exacerbate historical educational inequities, but I see your point. At the same time, I think eliminating age-graded classes creates inefficiencies in ways that our current system does not. Not to say our current system works well, just that it’s designed to serve average students and, more or less by definition, most students are near the average. It’s for those outside that middle part of the distribution, however we measure that, where things get hard.

      1. TracingWoodgrains

        One of my most memorable experiences while I was a substitute teacher came in a fourth grade classroom, when the teacher had left me division worksheets and some time to fill. A few of the kids in the class zoomed through it the moment they got it, then came to me bored asking what was next, while a handful just sat there, looking at the papers as if they’d never seen a division problem before in their lives. I did my best to help, but in the meantime, there were twenty-some other kids who needed attention, and I could only spend so much time trying to reteach division to the small child who kept repeating that they just didn’t get it. I walked away feeling a deep sense of inefficiency and helplessness–kids on so many different levels I wanted to help, with no way to alleviate the boredom of the one group or the frustration of the other. What could be done for them? Certainly, from my role as a substitute, not much of anything. All I could do was ask the faster ones to read quietly, quiet the disruptive ones, help the slower ones, and ignore the quiet ones.

        I share that vignette to underscore that I’m not sure how different the inefficiencies are with same-aged heterogeneously grouped children and different-aged ones: in both cases, scenarios like that occur day to day and have no good answers as they come up. Equality is important, and protecting and advancing historically disadvantaged groups is vital, but with all that I just have to wonder if there is a way to protect students outside the middle of the distribution in both ends. They both need help, and past a certain point of heterogeneity there is only so much a teacher can do to help either or both of them. Focus on the average is a necessary feature of classes to keep them running, but it’s the students at the edges who are already most vulnerable to discouragement, social isolation, and frustration–even before teachers run into the reality of simply not having time to help them all.

        1. dkane47 Post author

          I see your point, and I think stories like this are part of why tracking has endured. But I’ve taught classes that are one of three tracks, and the disparity you’re describing seems just as large and insurmountable. Tracking is a tempting solution, and I think it can serve some students in some situations. But I think it’s a stopgap solution that doesn’t address larger issues, and it creates issues of its own, in particular around racial bias. Difference will never go away, and I think the fundamental logic of tracking is to try to minimize difference when what we need is to develop pedagogies that capitalize on it.


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