On Tracking in Middle School Mathematics

By Sandra Kingan, Associate Professor, Brooklyn College and the Graduate Center, CUNY @profkingan

Sandra Kingan

To develop learning that can lead to mathematical power for all California students, the framework has much to correct; the subject and community of mathematics has a history of exclusion and filtering, rather than inclusion and welcoming. There persists a mentality that some people are “bad in math” (or otherwise do not belong), and this mentality pervades many sources and at many levels.

This powerful statement opens the proposed new Mathematics Framework for California Public Schools: Kindergarten Through Grade Twelve expected to go before the State Board of Education in November.

Tracking is the practice of assigning students to more or less advanced courses in a subject. The draft Framework proposes to remove some of the tracking done in mathematics in the sixth, seventh, and eighth grades. I support the draft Framework’s stance on tracking.

The current approach to tracking is based on the premise that the only way to challenge high-achieving mathematics students is to accelerate the pace of content learning—the race to abstraction and formality. The draft Framework upends this notion. It provides the following paragraph as justification

As early as preschool and kindergarten, research and policy documents use deficit-oriented labels to describe Black and Latinx and low-income children’s mathematical learning and position them as already behind their white and middle-class peers (NCSM & TODOS, 2016). These signifiers exacerbate and are exacerbated by acceleration programs that stratify mathematics pathways for students as early as sixth grade.

Yes, this is sadly very true. In fact, children of all races and genders are suffering on account of tracking. Last year I wrote a blog post on how children are suffering on account of mathematics no matter what their parents’ privilege. It seems to me that the document would be more impactful if de-tracking is presented as helping all children, especially since the children who make it past the placement exams and get into advanced courses are not necessarily enjoying mathematics. The pressure to succeed is enormous. College admission officers say that students should take the highest level math course offered by their high school to get into a good college. This amplifies the need to take Calculus by twelfth grade.

Tracking closes doors for students, not just in mathematics, but also in the sciences, and it does this based on a child’s capability at the age of ten to thirteen. Students in sixth grade take a math exam and, depending on their score, take Algebra I or regular seventh grade math. Students in Algebra I typically go on to Geometry in eighth grade. The rest take a placement test in seventh grade and again, depending on their score, take Algebra I in eighth grade or regular eighth grade math. Students who don’t take Algebra I by eighth grade lose the opportunity to take Calculus in twelfth grade. This is because they have to do Algebra I in ninth grade, Geometry in tenth, Algebra II in eleventh and Precalculus in twelfth. This is the basic secondary school mathematics structure heading to Calculus, though there are variations on this theme. It makes no sense to make decisions on a child’s future capability and potential in mathematics at such a young age, and yet this is precisely what tracking does. As the draft Framework notes:

Students internalize these messages to such a degree that undoing a self-identity that is “bad at math” to one that “loves math” is rare. Before students have opportunities to excel in mathematics, many often self-select out of mathematics because they see no relevance for their learning, and no longer recognize the inherent value or purpose in learning mathematics. The fixed mindset about mathematics ability reflected in these beliefs helps to explain the exclusionary role that mathematics plays in students’ opportunities, and leads to widespread inequities in the discipline of mathematics.

These statements accurately capture the problems with tracking.

So why is the draft Framework presenting de-tracking as an accommodation for kids who aren’t particularly interested in mathematics and conflating de-tracking with race? There appears to be a considerable amount of unconscious stereotyping going on. Race and gender and a massive overhaul of the existing system are emphasized to a very large extent, and unnecessarily so because the proposed changes for de-tracking are quite moderate. It would help if that moderation came across more clearly and was presented as helping all middle school students. For example, the document proposes the following approaches to filling in gaps in student understanding.

This is all good sense. Pacing guides and creating prerequisite courses for the prerequisite courses are ineffective educational practices. It would simplify matters if there weren’t three prerequisites in high school before Calculus: Algebra I, II, and Precalculus. Surely algebra and trigonometry can be spread out over just two years giving all students the opportunity to reach Calculus in high school.

The trouble with mathematics is that the subject and the stewards of the subject are perceived as cold toward the suffering of students and unwilling to make any changes. But the opposite of making no change should not be making every possible change and conflating all sorts of issues. A new draft is imminent; perhaps some of these issues will be pulled apart and made to stand on their own.

Sandra Kingan is an Associate Professor of Mathematics at Brooklyn College and the Graduate Center of the City University of New York. She loves mathematics and loves to communicate how wonderful mathematics is to everyone willing to listen to her.