Are We Breaking Down Barriers to Student Learning?

By Matthew Larson posted 01-17-2018 10:17


Sometimes, even with the best-made plans, the research indicates that some students are forced off the path to mathematical success by structural or systemic barriers that exist in some schools (Jilk 2014). Two of these structural obstacles are student and teacher tracking. Student tracking is the placement of students into qualitatively different and in some cases dead-end mathematics course pathways. Student tracking is insidious because these dead-end pathways are not mathematically meaningful and do not prepare students for any continued study of mathematics.

NCTM officially reframed its equity statement to focus on Access, Equity, and Empowerment, to capture the additional and critical constructs of students’ mathematical identities, students’ sense of agency, and the teaching of mathematics for social justice. I outlined NCTM’s “Renewed Focus on Access, Equity, and Empowerment” in the September 2016 President’s Message. Traditionally NCTM has concerned itself with student access to high-quality mathematics curriculum and instruction. But moving forward, NCTM pledged more attention to what happens to students once they have access to rigorous mathematics courses.

At the San Antonio Annual Meeting, NCTM released Taking Action: Implementing Effective Mathematics Teaching Practices, a series of grade-band books.  Building on the effective teaching practices outlined in Principles to Actions, Taking Action connects each of the eight instructional practices to equity-based instructional practices in order to strengthen student learning and cultivate positive mathematical identities. In addition, NCTM released the first in a series of grade-band books titled Access and Equity: Promoting High-Quality Mathematics, that also address equity-based instructional practices in greater depth.

With NCTM’s increased emphasis on equity-based instructional practices, identity, and agency, I have been asked if this means that access to rigorous curriculum and high-quality instruction is no longer as great a concern. The answer is an unequivocal no. As mathematics educators we must simultaneously address the barriers too many students face to high-quality mathematics instruction as well as how students experience mathematics in the classroom.

Over the past year as I have discussed access, equity, and empowerment issues with teachers across the country, I have been struck by how often I receive push-back when I advocate opening up mathematics courses to students by eliminating traditional tracking practices that sentence some students to dead-end mathematics course pathways that fail to prepare them for the workplace, for participation in our democratic society, or for the continuation of their education. My anecdotal experience concerning the entrenchment of tracking in mathematics education is supported by the research.

Research indicates that students from marginalized groups continue to have less access to highly qualified mathematics teachers and less access to college preparatory pathways in mathematics (Nasir, 2016). A recent report by the OECD (2016) found that more than 70 percent of students attend schools where the principal reports that students are grouped by “ability” for mathematics instruction. I intentionally put ability in quotes because student placement in dead-end mathematics pathways continues to be done in some cases for a variety of non-academic reasons (Stiff and Johnson, 2011 in Strutchens and Quander). We have to be honest and confront harsh realities and break down the barriers that continue to persist in mathematics education.

Tracking is not just a secondary concern. Loveless (2013) reported that in 2011 nearly two-thirds of fourth grade teachers reported using “ability grouping” in math instruction. All too often this practice begins in the primary grades. For example, in some schools if there are three first-grade teachers in a school, at the end of kindergarten the students are “rank ordered” by achievement and divided into three groups; one first-grade teacher receives the highest third of students, one the middle third, and another the final third.

But the learning opportunities provided these students are hierarchically different. Rank ordering students as early as first grade potentially positions students to differences in instructional quality and exposure to rigorous curricula.  It is plausible that students in the privileged top third experience mathematics instruction that cultivates their mathematical identities, conceptual understanding, and critical problem solving and thinking skills. Students placed into the lowest third tend to focus on memorization of simple facts and procedures with little to no attention given to developing understanding.  These latter students develop the belief that mathematics is something they cannot do and become disaffected by their experience. And the replication of this experience year after year has devastating effects.

As Alfinio Flores and others have pointed out, these low expectations all too often become self-fulfilling prophecies. Once students are placed into a low track it is very difficult for them to leave it. The opportunity gap we create by tracking students into qualitatively different and dead-end course progressions puts students further and further behind in the curriculum and leads to what many people commonly refer to as the “achievement gap.” It is why I refer to the practice of tracking students into instructionally qualitatively different and dead-end course progressions as educide.

In recent years many schools, at least on paper, have done away with the traditional three-track sorting I described above. However, in some cases tracking now exists in new forms. For example, algebra course offerings may sort students into one- or two-year versions of the same course. Students in the two-year version are essentially denied an opportunity to learn as much mathematics as their peers placed in the one-year course.  A double-period version of an algebra course would lead to students having the opportunity to learn the same mathematics in one year.

In other new forms of tracking, some schools may label courses Algebra II or even Algebra, that are in no way rigorous enough to earn these course titles. Different groups of students are then tracked into these different versions of algebra (see Stein, Kaufman, Sherman, & Hillen, 2011).  Recent research indicates that students placed in less rigorous versions of Algebra have lower math attainment by the end of high school than those placed in more rigorous versions of algebra and this ultimately has an impact on students’ math aspirations and post-secondary education plans.

And sometimes mathematics teachers are tracked themselves– those with the most experience or perceived as most effective are assigned upper level mathematics courses while inexperienced teachers are assigned lower-level mathematics courses (Darling-Hammond, 2007). Similarly in elementary schools, the highest achieving students are assigned to the most experienced teachers and the most underserved to less experienced teachers.  We all have a professional and moral obligation to carefully examine whether our “teacher assignments and tracking practices are helping or hindering equity” (Lubienski, 2007).

Francis Su (2017), past president of the Mathematical Association of America, eloquently argued that “we have to recognize that even if people are just, even if they desire to be just, a society may not be just if its structures and practices are not also just.” The practice of tracking in mathematics education is not just. Therefore, as the authors of the OECD report Equations and Inequalities: Making Mathematics Accessible to All wrote, “mathematics education often reinforces, rather than moderates, inequalities in education” (p. 3).

Challenging longstanding practices, procedures, and policies is extremely difficult.  I encourage each and every one of us to commit ourselves individually and collectively to breaking down the barriers, such as tracking, that contribute to the thoroughly documented inequities in mathematics education. Only when we begin to discuss these barriers honestly and take action to tear them down will mathematics education become truly just.





01-18-2018 20:10

I am interested in how tracking undermines our ideals of community. In heterogeneous classrooms ALL students benefit from our differences, whether that be color, socioeconomic status or any other number of things. We all must learn to work together and learn from one another. This is community.

01-17-2018 16:02

Thank you so much for this very needed message Matt.  Tracking and ability grouping are shown by research to be unproductive practices that destroy students' identity as doers and life-long learners of mathematics. The numbers of students of color and second languages that end up in lower math tracks is a terrible social injustice that leads to unfulfilled dreams and wasted potential (Boaler, 2005).
This is an issue that challenges our deepest beliefs about what defines mathematics proficiency and something I have been thinking a lot about lately - meritocracy.  As educators we all have the responsibility to examine our beliefs about why we continue to track in mathematics when the research shows it to be counterproductive.  Do we have the courage to lead our schools and districts to change their current policies which tend to rely on the politics of social class and race?
With that in mind, I point to the courageous efforts taken by San Francisco Unified School district over the past three years to remove the barriers of math tracking and acceleration up through grade 11.  See the following page SFUSD Math for their course sequence and refer to their latest In the News story of success - Historic Shifts in Math Show Promise.  What other stories are out there for us?
However, with the above SFUSD data in mind, I believe that de-tracking alone cannot produce these results.  As Matt always emphasizes, a balance is needed in our approach that also requires high expectations for all students and instructional practices that promote a positive math identity across diverse groups of students. 
Happy New Year to all!