Initiating Critical Conversations on the Discontinuation of Tracking
The tracking of students for instruction in mathematics is a long-standing practice of schooling that segregates students of different backgrounds into separate experiences on pathways leading to different outcomes. The fact that the effects of tracking are consistent and predictable reflect the reality that this practice is built in to the structure of mathematics education. Students segregated into low-track mathematics are routinely exposed to instruction focused primarily on rote skills and procedures that do not stretch their higher order thinking and that give limited attention to developing their conceptual understanding. Students segregated into high-track mathematics typically experience mathematics that cultivates their mathematics identities, conceptual understanding, and critical problem-solving and thinking skills (NCTM, 2018). Tracking is a structural barrier with a large impact on the experiences of students and teachers in mathematics.
As a student and teacher of mathematics in urban and suburban schools in the United States, I have personally experienced and borne witness to the inequitable outcomes in mathematics learning. Tracking prevents students access to a high-quality mathematics curriculum, to effective teaching and learning, to high expectations, and to the necessary supports needed to maximize their learning potential. It is time to recognize and identify tracking as a systemic form of segregation. Tracking leads to the distribution of students in ways that are correlated with the inequities based on race, ethnicity, language status, and socioeconomic status found in our broader society. And it is time to begin the courageous work needed to intentionally and systematically remove the perniciousness of tracking and its associated curricular and instructional practices as we move toward creating pathways for success in mathematics for each and every student.
Catalyzing Change in High School Mathematics: Initiating Critical Conversations recommends that high school mathematics discontinue the practice of tracking teachers as well as the practice of tracking students into qualitatively different or dead-end course pathways (NCTM, 2018; p. 15). While Catalyzing Change focuses on high school mathematics, tracking has equally significant implications for early childhood, elementary, and middle grades mathematics. There is a compelling body of research dating back nearly 40 years documenting the consistently inequitable impacts of tracking and the role it plays in perpetuating and exacerbating biases and inequities found in American society. Given the body of research and the negative effects of tracking, we must wonder why many schools continue to engage in tracking. Schools and educators are not immune to the tendency to continue doing things the way they have always been done. If a teacher was tracked in mathematics as a student and teaches in a tracked mathematics situation, the idea of detracking is likely to be foreign.
The discontinuation of tracking is often characterized as an attempt to group students heterogeneously as a means of ensuring that each and every student, regardless of race, ethnicity, language status, socioeconomic status, or academic ability, has access to high-quality instruction, curriculum, teachers, and material resources. Detracking requires far more than simply rearranging instructional group patterns. It requires:
Below are actions teachers, schools, and districts can begin doing to move towards detracking:
As stated earlier, detracking is more than simply grouping students heterogeneously. Detracking is a deep commitment and an investment in people, curricula, and time to reach the goal of supporting and engaging each and every student in learning mathematics and increasing their opportunities. Teachers and leaders must be committed to the actions above when working towards the discontinuation of tracking.
Because tracking is insidious (NCTM, 2018), I encourage you to use the steps outlined above and in Catalyzing Change to begin discussions and take action to intentionally and systematically dismantle the structural barrier of tracking. Please share your successes and challenges on MyNCTM.org
Robert Q. Berry, III
I am tired of reading articles that are loaded with false or questionable assumptions, and this article is a good example of it. Without analyzing this article sentence by sentence, the assumption that is planted is that if you are in favor of tracking, you are opposed to equity (whatever that is supposed to mean in practice), you are a hide-bound reactionary, and you are probably a closet racist, whose sole purpose in life is to allow white people to keep their vaunted privilege. There is also another planted assumption, which is that the fact that tracking generally puts whites (and Asians, who one assumes have somehow become honorary white people) in the top tier means that there is a deliberate move afoot to keep others down. It is about time someone spoke plainly about all this, and I guess I am going to be the one.
I don't dispute the fact that tracking does leave whites and Asians generally ahead of others, but the assumption that this is pernicious is generally stated without any proof of bad intent, and there never seems to be an analysis as to why this is happening. I am no expert in this field (I am a mathematician who taught mainly at community colleges my whole career (no K through 12 at all), but I dealt with disadvantaged students my entire 34-year career, and I feel able to make some relevant comments.
First, there is no question that white people as a whole have a leg up for a variety of reasons (some of which include the fact that others have been held back by racism and other ills), but the obvious solution for this is to stop discriminating against people on the basis of race, and while we are not there yet (and, given human nature, never will be), the legal suppression of people on the basis of color and other irrelevant factors ended a while ago, starting with Brown vs. Board of Education.
The fact that white families generally ensure better education for their own children, by sending them to better schools and helping them in ways other families cannot, will lead to their kids tracking higher than other kids, but that doesn't mean tracking should end; it means that the other kids need more help. How they can get this if they are put into classes too difficult for them makes no sense to me. Kids from deprived backgrounds don't need education that is the same as others; they need more resources, and they need different resources. Putting everyone in the same room and expecting something good to happen is simply wishful thinking, and it isn't fair to any of them. What happens is that the slower kids will get pushed too fast and drop out, while the faster kids will get bored and as a result may also drop out. This kind of equity of failure may make some people feel better, but it is not worthy of serious consideration. I might also add that the assumption that the faster kids will take care of the slower ones is not only not realistic, it isn't fair to the faster kids, who have somehow been drafted by the Equality Police to take care of others instead of being allowed to thrive to the best of their abilities.
There is more to it than this, however. I attended a private school and excelled at mathematics, but I discovered that many of my fellow students, from the most privileged backgrounds imaginable, simply couldn't do math with any real proficiency past arithmetic. Some of them emerged bloody from elementary algebra, some from plane geometry, and others from college algebra and trig. (In 1959, when I graduated from high school, there were no calculus classes at that level.) When I taught calculus from about 1969 until I retired in 2002, only about one-third of my students managed to make it through Calculus I, although the influx of foreign students at various times (and especially from China right after the Cultural Revolution ended) would skew those statistics up. This didn't seem to have anything to do with race: most white people can't do calculus either (and there were many other reasons, like family problems, shift changes and so on). There seems to be an assumption that given the right circumstances, everyone can do mathematics. That is baloney, and it is poisoned baloney at that, since it leads to programs that are doomed to fail ab initio. The fact that there have been tons of programs trying for decades to remedy all this to little effect should be a clue that we are on the wrong path.
It seems to me, the first thing we need to recognize is that no matter what we do, kids not being in families that are able to give them the enriched sort of environment necessary (to some extent, anyway) to allow the flourishing of high intellectual pursuits may be damaged to the point of being unable to catch up. No one likes to admit defeat, and I am in favor of helping these kids as much as possible, but some consideration has to be given to recognizing that some children will ALWAYS be left behind. (I knew the no-child-left-behind movement was doomed the moment I heard its name.) If we have unrealistic expectations, we will have outcomes which are, by definition, and almost by pre-arrangement, unacceptable.
Second, we should recognize that while we should be sure our tracking methods are flexible enough to recognize that some people come to understanding later than others, the idea of grouping people with their intellectual peers makes sense for those who track higher and those who track lower. The higher can thrive in a richer environment, while the lower can receive the extra help they need to succeed to the fullest extent of their abilities and willingness to work.
Third, we need to get over the idea that elitism is a bad thing. If it isn't bad in basketball, why should it be bad in mathematics or other intellectual pursuits? The fact is, education is INHERENTLY elitist. If we had no tracking in basketball, we would have basketball games no one wants to watch, and the same is true if we do not allow good students to flourish so that mediocre students can feel better about themselves. Make the best effort we can to make sure that those born with the inherent ability to triumph in intellectual pursuits are tracked where they should be, and then let things sort themselves.
John C. Wenger
Emeritus Professor of Mathematics
Harold Washington College
I couldn’t agree more. Being retired now for 13 years, but keeping a hand in mathematics education by volunteering in urban schools for the past 7 years, I can see the detriment of tracking. I have 5 years of teaching in a urban high school and 36 years of teaching deaf college students as well as serving on my local school board for 28 years. Let’s get rid of tackling for good and replace it with intelligent placement by responsible professionals.
It is refreshing to see NCTM tackle this long standing problem. We have to ask ourselves, who, if anyone, does tracking benefit? Who does it do disservice to, and compare the results.
Thank you Robert for your contributions to this year's TODOS Conference.
I agree totally. I am a MAth Coach in Maine and have witness the reemrging of this practice in Middle Schools and now trickling down to the Intermediate Schools with little push back from District Leaders.
I am pleased that the conversation on detracking is moving forward. Note that detracking efforts must have supports for teachers and students. Effective target intervention should focus on content that is connected with and promotes the grade-level curriculum and should not simply be a review of low-level procedural skills. Some education researchers have recommended this type of additional instructional time, with students receiving tailored instruction during one period to support success in their core mathematics course. Double-period versions of a course do not represent lower-level versions of a course. Double-period versions of a course do not constitute tracking if the double-period version of the course has the same instructional objectives and expectations and uses the same core instructional materials and assessments.
Regarding acceleration, there are distinctions between tracking and acceleration and NCTM’s position statement, Providing Opportunities for Students with Exceptional Mathematical Promise (NCTM, 2016) makes clear thatacceleration is appropriate if a student has demonstrated deep understanding of grade-level or course-level mathematics. The statement emphasizes that “care must be taken to ensure that opportunities are available to each and every prepared student and no critical concepts are rushed or skipped.” If the demographics of students accelerated in mathematics in a school or district are not reflective of the school’s or district’s racial, linguistic, cultural, and economic diversities, then analysis and evaluation are necessary to determine why not, and actions should be taken to remove whatever bias and barriers leading to this inequitable outcome (NCTM, 2018).
This raise so many issues! I am looking forward to continuing the conversation. This also brings up the pressure to finish calculus before high school. How can we send the message that we want students to understand math deeply and not just at surface level to check a box? Frommy experience the professors would like students to have great problem solving skills and calculus is not always the answer, but do the admissions offices know this?
As I read the article, I also think of our special education students sitting in general education classes who need a little support, but are not given the time to think deeply about the mathematics.
I am very interested in continuing this conversation!
This is not a new idea or educational movement. I look forward to exploring what is fresh in what I expect to be a thoughtful document.
Right on x 2! Echoing Dr. Karen Fuson.
I have taught in a destreamed classroom setting - a grade nine class where students ranged from the grade 4 level through to kids who were gifted and two grades ahead. What ended up happening is our applied classes with a lower class cap were combined with academic classes with a higher cap and we taught at the higher cap level. Basically we taught more kids with more needs. We were expected to gap fill while teaching to catch the lower kids up and enrich the higher ones - I would be exhausted every day - when the weak were frustrated they would act out - when the gifted were bord they would act out - I would be running between both extremes and a classroom management nightmare. Plus, not all math concepts have lessons that can be developed with multiple entry points for all levels.
I want to echo the comments from Valerie. I am deeply troubled by the throwaway line "...detracking is more than simply grouping students heterogeneously." While motivated by good intentions to support and engage each student and to avoid the kind of tracking that has perpetuated inequities based on race, ethnicity, language status, and socioeconomic status, Pres. Berry seems to want to take us back to the outdated ideas of Slavin (1990) pushing heterogeneous grouping, and then going beyond that to insure individual differentiation of instruction to reach each and every child. How? That's a tall order, beyond the capabilities of most teachers working with 30 students at a time.
The real losers in a rush to heterogenous-plus are the students at the upper end of the spectrum. The National Association for Gifted Children addresses these concerns in its Policy Paper on Grouping (https://www.nagc.org/resources-publications/gifted-education-practices/grouping). Too often, mathematically gifted children grouped heterogeneously in the classroom are expected to "teach" the other kids, but instead end up bored. They need cluster grouping with their peers (let's call it what it is - homogenous grouping), acceleration, curriculum compacting, and separate pull-out programs. And all the recent research supports this approach.
So, do you advocate putting new high school students who test at the 4th, 5th, 6th grade level into high school prealgebra and algebra classes, along with allowing the mainstreaming of behavior-disorder students and special ed students without sufficient aids into general math classes? Our program is a full-time math teacher short of what is needed for any significant interventions. We are evaluated on how a WHOLE class does on a standardized by our state. We are reprimanded if there is a downward trend in test scores over a year or two, or if we give too many F's to those who refuse to participate and do no work. If state evaluations change and hiring freezes discontinued, we can do more of what you speak to in the article. All great ideas in theory, but the government is not cooperating. I sound bitter, I know, but after 43 years of denial from the state on what is best for math education, I am frustrated.
Right on!!! Let's do it. Thanks for tackling this issue. Karen
I also struggle with the de-tracking of students. As a child, I moved between the lowest two tracked groups in math. This was primarily, because I didn't have the same level of support at home as the other students in my upper-middle class school. When I learned about the self-fulfilling prophecy in college, I agreed whole heartedly. While I grew into a confident student, many of the peers that were in those elementary classes with me never moved out of that lower tier. Fast forward to about 10 years later in my career, and I noticed some differences in my own child that encouraged me to get licensed in gifted education. I now teach the math portion of the gifted pull out program in the elementary school where I teach. I tier the instruction in my classroom and see a wide range of readiness in my students, which I only serve the students identified as gifted. They also participate in general education math that is not tracked and it feels as if many of them are just going through the motions. I agree that we should hold all students to high standards. All students should be given access to grade level rigorous and in depth work, however some students need more than that in order to connect with and develop a love of mathematics. It seems without tracking and with the existing pressures put on all students meeting minimum standards the needs of highly advanced students could be overlooked.
"This school has seen improvements in the social, emotional, and academic outcomes of students and in teacher morale and efficacy."
I'm confused by this sentence. Maybe this was originally a speech at a particular school?
I find the whole tracking issue very confusing because my experience as a teacher and parent doesn't always line up with what I would otherwise believe from research and my own beliefs about math education. The main problem I've seen with not tracking is that some kids (like my older son) get bored with math and feel like it's all tedious emphasis on review of stuff they already know and "showing your work" for problems they can too easily solve in their heads. ("They want me to lie about how I solved it," he used to tell me with great annoyance.) On the other hand, I have to admit that tracking didn't solve that problem: he didn't take Calculus because he was so bored with PreCalculus and couldn't face the homework.
I feel like as teachers we need more support at how to build in teaching and learning of previous years' standards without boring and exasperating kids who already know them (and who sometimes make that clear to other students, which is intimidating), and how to provide tasks that are not only low floor but also high ceiling -- truly involving and difficult for kids who need more of a stretch.
For what it's worth, my lower-tracked son has experienced richer classrooom math than my higher tracked son, whose teachers tended to be older and more direct-instruction and drill-oriented. In my district, at least, less experienced teachers end up teaching the lower tracks because classes are assigned by seniority, and they are generally less tradition-bound. However, they also have less institutional support (more reassignments, more burdensome evaluations, worse classrooms, etc.).
These observations are all generalities and are subject to my own biases, though. I will continue to research this, especially if my opinion ends up mattering to what my district or school does (not the case yet, but I live in hope).
In light of this research, how do we handle 8th grade Algebra? Most students going into STEM fields must have Calculus on their HS transcripts. 8th grade is where most of the tracking begins.
Robert Kaplinsky offers the following thoughts.
Assuming that you need to have AP Calculus AB in high school at all, then you might wonder how students get to AP Calculus AB if they take Math 6 in 6th grade, Math 7 in 7th Grade, Math 8 in 8th Grade, Algebra I or Integrated I in 9th grade, Geometry or Integrated II in 10th grade, and Algebra II or Integrated III in 11th grade. How do they take Pre-Calculus and AP Calculus AB in a year?
A couple of things to consider:
So, my suggestion is to combine Pre-Calculus and AP Calculus AB into a single course. Again, if the choice is between making 6th and 7th graders decide whether they want to be on the path to AP Calculus AB or delaying that decision until 11th grade, I’ll take delaying that decision.