This is a paper I wrote in Fall 2020 for a class with Dr. Sheron Mark at the University of Louisville. The class focused on issues of power and culture in STEM education and STEM fields. Through this class, I learned to take a critical lens on policy, practices, and norms when I look at issues facing mathematics education.
Introduction
Mathematics education researchers and leaders continue to push for changes that will increase access to content and equity in learning opportunities for all students. Many have identified and criticized tracking as an inequitable system of labeling students at a young age and then setting them on an academic trajectory for their future. Mathematics is the most tracked subject in K-12 schooling (Loveless, 2013). According to the Loveless (2013), in the mid-1990s, tracking by ability grouping in fourth grade actually decreased before remaining constant for several years. But, from 2003 to 2011, tracking by ability grouping in mathematics among fourth graders increased dramatically from 42% to 61% trending toward 75% of students being placed in tracked mathematics classes. Tracked classes in mathematics education are built to separate students and continue to keep them apart throughout their schooling, often based on social classes (Boaler, 1997). But, as seen in examples like Railside school in California (Boaler, 2008), de-tracking can bring students back together and be more equitable. The academic impacts of tracking are often defined by achievement data and typically measured by standardized testing. Beyond these quantitative measures researchers also illuminate the problematic impacts of tracking on students’ beliefs about themselves and their academic identities. Questions discrediting the benefits of tracking have been well-researched but it is an enormous task to unravel what has been normal practice for decades.
In this paper, I question the perpetual implementation of tracking throughout our schools and inquire about the impacts of such a system on the mathematics identities of those students who have been disproportionally omitted from opportunities in their education, Black and Hispanic students. First, I will present a historical perspective on tracking and an overview of its impacts. Next, I will discuss the importance of focusing on identity as an element of the problematic results of tracking in mathematics. Finally, I will work through the systemic implications on mathematics identity develop for Black and Hispanic students if we continue practicing tracking in our mathematics classrooms and potential ways to de-track mathematics classrooms successfully.
Historical Developments and a Call for De-tracking
Tracking in mathematics education has become the norm but, in recent years, people have started to doubt the reasoning for continuing to group students by perceived ability. Recent research has shown that tracking deepens inequities in mathematics performance, interest, and opportunity. Mathematics education has gone through waves of reform over decades of attempting to reform policies and structures to be better for all students. Where we are now is a result of decisions made decades ago that produced structures that became the status quo. As discussed by Ellis and Berry (2005), the Progressive Education Association (PEA) movement of the 1920s produced a focus on differentiation in mathematics learning which resulted in the use of testing to prove certain students could actually do math. This adopted process created a system of providing basic mathematics to most students reserving higher-level mathematics for those who could perform on tests. Mathematics education became elitist and only for students, primarily white males, who had an apparent future in the subject. Tracking in mathematics became standard practice in the 1940s and still exists today in most schools.
Tracking systems place students in deficit positions in mathematics before they can even actualize their own mathematics abilities. Students backgrounds or perceived abilities largely determined their tracking position in mathematics leaving groups of students fixed at that level perpetually. In the late 1980s, ideas started to shift toward reforms that would benefit all students (National Council of Teachers of Mathematics [NCTM], 1989) calling for teaching that promoted students making connections between concepts to deepen understanding rather than formal direct teaching. These reforms helped reveal that not all students had equal access to mathematics and teaching practices needed to change in order to connect students culturally to mathematics and increase opportunities to make mathematics relevant to all students. However, tracking remained commonplace since standardized testing continued to be what most believed the best way to assess achievement. The results of those tests just reified students’ mathematics placements.
In the 1990s, groups such as the American Civil Liberties Union and the NAACP Legal Defense Fund denounced the use of tracking and some schools, particularly in Massachusetts and California, did adopt de-tracking policies but eventually many schools returned to tracking in mathematics (Loveless, 2013). Researchers further dismantled the idea that tracking was the most effective way to structure mathematics classes and that heterogeneous classes were beneficial to students (Boaler, 1997; Cohen et al., 1999). Students in heterogeneously grouped math classes performed better than students in homogeneously grouped, traditionally tracked classes in areas of understanding and applications. Students traditionally labeled as high-achieving did not falter because of de-tracking, they actually benefited and students in de-tracked classes reported more positive feelings about mathematics in terms of interest and motivation (Boaler, 1997). Similarly impactful, Boaler (2002) showed that students placed in the middle or lower-level mathematics classes were unmotivated and essentially gave up on their learning.
In the most recent decades, equity in and access to mathematics have become of utmost concern as researchers and educators have realized tracking in mathematics is a system which unequally gives power to some, rendering others powerless as it has for a century (Ellis, 2008). In Catalyzing Change (2020), NCTM makes a clear and commanding call for the de-tracking of mathematics classes citing significant research showing the gravity of the inequities created and perpetuated by homogeneous grouping.
“Tracking is the practice of placing students into qualitatively different course pathways or qualitatively different mathematical learning experiences. It reinforces the misguided notion that only some people are capable of achievement in mathematics” (Boaler, 2011).
De-tracking is not a process that can happen quickly since homogeneous grouping has been in place for decades. Teachers often push back against de-tracking because of the perception that it is too difficult to teach heterogenous math classes (Loveless, 2013). However, grouping structures need to be deconstructed in order to provide information on how those in mathematics education can better understand ways tracking impacts students beyond achievement data. A deeper conceptualization of the problem will bolster the argument to design more equitable structures in mathematics and attention to students’ identities as a form of evidence of learning (Gutiérrez, 2013).
Impact of Tracking Systems in Mathematics Education
Schools without tracking see higher achievement in mathematics than schools with tracking and a significant reason for such a difference is the improved achievement for students who would have been otherwise placed in lower ability groups (Boaler, 2011). When schools de-track math classes and teachers implement strategies for homogeneous groups, students from lower ability groups gain more support, see higher levels of achievement, and are more likely to continue taking higher-level math classes. Despite the research supporting dismantling tracking and the backing of national organizations due to the known detrimental effects tracking has on so many students, tracking remains prominent in many school districts (Boaler & Staples, 2008).
Burris et al. (2006) studied the effects of eliminating tracking in exchange for an “acceleration for all” approach. At a large, diverse high school in New York, the district decided to de-track in the early 1990s and continued this policy after they saw a dramatic shift in achievement and enrollment in higher-level mathematics courses. They changed to homogeneous grouping and provided “high-track” curricula for all. Burris et al. found that the students from de-tracked classes took more advanced classes, passed courses at significantly higher rates, and passed exams a year earlier than the average in the state of New York. Further, these researchers discovered a profound positive impact of de-tracking for Black and Hispanic students. In their study, all of the Black and Hispanic students (who were labeled high-achieving in their tracked courses) in their cohorts continued to complete trigonometry and enter pre-calculus as opposed to 69% when those students were in tracked classes. When they looked at socioeconomic status (SES), students with low-SES more than doubled in completing trigonometry and passing the state test. These findings were a direct challenge to systems of tracking in 2006, particularly for Black and Hispanic students, yet, tracking is still the norm in American mathematics education leaving Black and Hispanic students without equitable access to be successful in mathematics.
Within tracked systems, students not only suffer academically, but suffer effects on their self-belief and lives outside of school, even beyond school years. In 2005, Boaler reported on a longitudinal study after following students in schools that had traditional tracked classes and another school which had a much more delayed ability grouping policy. Boaler (2005) interviewed some of these students after they graduated and they described tracked classes as types of prisons impeding their abilities. Students reported their ambition being lost and their expectations of themselves lowered. Solely focusing on achievement, and the popularly discussed achievement gap, is not enough. Though mathematics research, education, and society has been focused on achievement gaps in testing, because testable outcomes are more concrete, sociocultural theories and cultural perspectives on learning enlighten people to the post-structural view of the complexities of learning (Gutiérrez, 2013). Identity construction in mathematics is one of those complex elements that plays a role in learning.
Mathematics Identity Development
Holland (1998) defines identity as “imaginings of self in worlds of action, as social products” and “conceptualized as they develop through social practice” (p. 5). For Holland, identity is a core element of sociocultural practice theory and how one sees themselves in their “figured world” (Holland, 1998, p. 52). Figured worlds exist within mathematics education when students are tracking in low-to-high levels as students build identities for themselves based on these structures. As discussed by Eisenhart and Allen (2020), students can develop an identity of being a good student based on taking challenging classes or considering themselves college bound. Gee (2000), another important theorist around identity development, discussed identities such that individuals can develop and maintain several identities and that identities are dynamic.
In terms of mathematics education, Boaler and Greeno (2000) detailed how mathematics education is its own socially and culturally constructed figured world through which students can develop their own mathematics identities. Considering the idea that students do not just learn mathematics content but they learn to see themselves within their own mathematics learning, students develop positive or negative identities based on the role they play as mathematics learners. Some students are believers and some are doubters in their own mathematics abilities (Boaler & Greeno, 2000, p. 192). Students can develop identities that overcome the obstacles they face in their figured world of mathematics learning and become successful mathematics students. Boaler and Green (2000) state that “careful study of mathematical learning environments could provide important understanding of the development of learning identities with significant agency” (p. 195). And, mathematics identities are often co-constructed with a students’ other identities like their race and gender, for example (Aguirre et al., 2013). A students’ mathematics identity cannot be described through achievement testing but testing is a popular form of judging students’ abilities. Systems of tracking create disparate mathematics learning environments for students in different tracks, also varying their connectivity to the content. Gee (2003) suggested that identity is dynamic in nature and “can change from moment to moment in the interaction, can change from context to context, and of course, can be ambiguous or unstable” (p. 99).
Racial and Ethnic Disparities
In 1989, Everybody Counts revealed a dramatic decline in overall engagement in mathematics among all American students but also a significant issue that Black and Hispanic students’ engagement was much lower. This document showcased tracking as a force creating disparities in opportunities for students based on race and ethnicity when stated that “differential opportunities to learn imposed by twelve years of multiple tracked classes produce vastly different evidence of mathematical power” (National Research Council, 1989, p. 21). The report goes further by stating that Black and Hispanic students will be left in an unending cycle of ‘mathematical poverty’ if structures and systems do not change (p. 21). And, whether one looks at the National Assessment of Academic Progress (NAEP) or the Third International Mathematics and Science Study (TIMSS), the evidence of racial and ethnic disparities in mathematics proficiency are clear for standardized testing (Schoenfeld, 2002). Even with an abundance of data over decades, structures continue to exacerbate differences in opportunities to learn and be successful in mathematics. Recently, Catalyzing Change (NCTM, 2020) detailed how Black and Latinx students, as well as those from low socioeconomic status, are more likely to be tracked in lower track mathematics courses or courses labeled as remedial. One might presume that students can move up in their assigned mathematics track but it is more likely the opposite. Actually, Catalyzing Change also discussed that analysis of student transcripts showed that students were more likely to move down in tracks than up. Educators have attempted to close achievement gaps and implement reforms to address mathematics inequities. But, reform efforts to provide equal access to learning mathematics have historically failed because they have been deficit focused or directed at helping America appear more competitive internationally in academics, not the learners themselves (Berry et al., 2014). Reform efforts and research have been historically focused on quantitative outcomes and ‘closing the achievement gap’ between racial groups (Lubienski & Bowen, 2000; Martin, 2019) thus devaluing individual learners’ experiences when they fall in demographic groups that also fall into achievement levels deemed inferior. Thus, reforms have attempted to repair students’ deficits rather than utilize students’ strengths or intersectional assets in order to narrow the gap. Most students still remain in inequitably tracked mathematics classrooms (77% of middle schools [McEwin & Greene, 2010]) where hierarchies of assumed abilities based on race and ethnicity are accepted. Mathematics education is not socio-culturally or socio-politically neutral. In Everybody Counts (1989), the National Research Council (NRC) warned the education world with their direct statement about racial and ethnic disparities in mathematics.
We are at risk of becoming a divided nation in which knowledge of mathematics supports a productive, technologically powerful elite while a dependent, semiliterate majority, disproportionately Hispanic and Black, find economic and political power beyond reach. Unless corrected, innumeracy and illiteracy will drive America apart. (p. 14)
For Black and Hispanic students who are more likely to be placed in lower tracks, their access to learning environments that enrich positive experiences is inequitable and they will more likely be objectified as students who struggle with mathematics. Most Black and Hispanic students will face barriers in developing productive mathematics identities within tracked mathematics systems.
Tracking is a policy and practice that educators and administrators have the ability to dismantle making students’ experiences more equitable for all. Inherent in tracking structures is a deficit view for groups of students that should be eliminated. However, the continual existence of tracking in mathematics is perpetuated by beliefs that some students are lacking; that some students have a cognitive deficit that existing educational structures can somehow fix (Civil, 2002, p. 136). The deficit views situated in tracking serve those who are tracked at the highest math levels and not all students. Though tracking is systemically implemented, some schools, like the one in New York (Burris et al., 2006), have taken on de-tracking successfully. In order to release mathematics education of the deficit views placed upon Black and Hispanic students, mathematics education must shift to heterogeneous, de-tracked classrooms. When teachers use constructive, culturally responsive, and collaborative methods in their mathematics classrooms, they can help shape students’ mathematics identities (Boaler, 2006). Specifically, Boaler (2006) not only de-tracked classes at an urban school in California but employed complex instruction (Cohen, 1994; Cohen & Lotan, 1997) consisting of seven equitable teaching practices: multidimensional classrooms, student roles, assigning competence, student responsibility, high expectations, effort over ability, and learning practices. Teachers received training on these practices in order to create more opportunities for success in their heterogeneous classrooms. When autonomy is afforded, educators can take the perspective of ‘conscientizacao’ to view their work as a means to look critically at mathematics education, the injustices that exist, and determine how to enact change for the purpose of educational and social justice (Freire et al., 2018). There is no disagreement that teaching pedagogies are more difficult when providing instruction for heterogeneous groups. However, de-tracking is more equitable and the difficulty level of implementation can be addressed instead of retaining it as an excuse for default homogeneous grouping. Existing tracking systems are inherently inequitable and oppressive.
Inequitable Educational Experiences and Opportunities
Spielhagen (2006) provides an example of how race or ethnicity plays a role in determine opportunities in mathematics. Spielhagen found that the odds of Black students enrolling in eight grade algebra was statistically significantly lower than the odds for other students. Further, in the same study, Black students comprised of 20% of the population but only 10% of the enrollment in eighth grade algebra (Spielhagen, 2006, p. 9). And, in 2013, 48% of eighth graders were taking algebra or a math course higher than algebra, up from 27% in 2000 (Loveless, 2003). Though this is an impressive jump, the upward trend in enrollment does not hold true for all student demographic groups. Black and Hispanic students are less likely to enroll in or achieve in algebra in the eighth grade (McCoy, 2005; Morton & Riegle-Crumb, 2019; Paul, 2005) leading to disproportionate access to high level mathematics courses in high school and into college. Tracking produces inequitable structures that can prohibit Black and Hispanic students from even attempting higher level mathematics course.
When Black and Hispanic students are disproportionally placed in lower mathematics tracks, it also means they are exposed to different learning experiences. Race and ethnicity are related to how students are tracked and their likelihood of continuing on to higher-level mathematics and also other science courses (Paul, 2005). Learning experiences in lower tracks are more rote and lack sociocultural considerations. Instead, the students in lower math tracks will be taught skills with practice and repetition, devoid of anything relevant to their lives (Civil, 2002). In lower tracks, there is an “exclusive focus on basic skills, low expectations, and the least qualified teachers” (Heubert & Robert M., 1999, p. 282). That is, Black and Hispanic students are twice as likely to have teachers who have three years or less experience teaching (Flores, 2007). If the argument is that students in the lowest track need the most help, this situation seems counterintuitive. The apparent deficit views for students in lower tracks strip them of more challenging mathematics and higher-level opportunities. Since Black and Hispanic students experience placement in lower classes more than other students, their learning experiences are therefore limited and inequitable.
Extensive research has been conducted to determine causes of the achievement gap between racial groups of students in mathematic but for decades, not much has changed as a result because this focus perpetuates the idea that student groups are different (Gutiérrez, 2008). Gutierrez states that “few studies using large-scale data sets move beyond issues of achievement to capture broader notions of mathematical identity and power” (2008, p. 360). Instead, Gutierrez calls for research to look at multiple identities of students, advancement of marginalized students without constant comparison to an idealized group, namely White students, based on achievement measures. In short, exploring mathematics identities matters to complement achievement research and understand the problem holistically. Yet, achievement testing is still the basis for judgement on who is learning and who is not, who is proficient and who is not. No Child Left Behind (NCLB) has left remnants of high emphasis on instruction aimed at test performance which is typically rote. And, for schools serving mostly Black and Hispanic students, to close the infamous achievement gap, the instructional focus remains on raising scores rather than high-quality mathematics instruction (Darling-Hammond et al., 2014).
Placement in a lower track becomes predictive of students’ mathematics achievement and futures when there are persistently low expectations and fewer opportunities to learn. Even when students showed greater mathematical ability but were placed in lower level classes, their achievement levels decreased as they succumbed to the expectations of that level (Stiff et al., 2011). Black and Hispanic students, through tracking, are overwhelmingly positioned to assume they are less capable in mathematics and once placed, their pathways are unlikely to change (Ellis, 2008). Immobility in mathematics tracking maintains racial disparities in mathematics education as inequities are reproduced from year to year, especially once students enter middle school (Morton & Riegle-Crumb, 2019).
The Influence of Tracking on Mathematics Identities
Minority students’ identities have the potential to stand at odds with the culture of schooling (Gilbert & Yerrick, 2001; Fordham, 1996; Fordham & Ogbu, 1986). Because science and math have an elite image, in these subjects, there is the potential to heighten students’ identity conflicts as they attempt to manage the tension between maintaining their identities and the identity of a math or science student. As language is invoked as a resource for signaling one’s identity (Gee, 2001), the math or science classroom have the potential to be seen as a politically charged space where classroom language and participation reflects membership into cultural domains.
Tracking sends messages to students about their abilities; that students in the higher tracks are capable and students in lower tracks are not. These messages are fixed and fuel the development of fixed mindsets in students which are often detrimental to their learning (Dweck, 2006). Mindsets are a component of students’ mathematics identities. Also, those students who identify as being successful at mathematics have a culturally and societally constructed form of power over those who do not see themselves as successful. Tracking produces and sustains this hierarchy of power. And, based on achievement data, success in mathematics is often defined by ‘whiteness’ since White students’ achievement data set where achievement gaps close. If Black and Hispanic students heavily tracked in lower mathematics classes look to success as being White, obtaining the test scores of White students, their identities as people and students are set against each other. If the dominant belief, displayed by tracking, is that Black and Hispanic students are less capable in mathematics, these students’ identities will be formed within this dominant discourse (Olitsky, 2015). As Olitsky discussed, marginalized students will need other ways to construct positive academic identities in order to overcome the identities to which they have been inequitably assigned.
Mathematics is seen as an elite subject. Students with positive mathematics identities, early on, are deemed more able and more intelligent. Tracking systems will reward students in the highest tracks and feed their positive mathematics identities while denigrating students in lower tracks to continue to believe they are incapable, thus feeding their negative identities. Tracking is a form of gatekeeping for and control over positive math identities reserved for only those deemed more intelligent, often based on testing (Gutiérrez, 2013). This structure prevents students’ in lower tracks, who are overwhelmingly Black and Hispanic, from more meaningful engagement in mathematics because, instead of seeing themselves as doers of mathematics, they are alienated and provided less opportunity to actualize their abilities in mathematics. Freire (2018) contends that this is an act of violence, regardless of the means. Without tracking structures which position students in a hierarchy of abilities and perpetuate prescribed identities for students, educators will be more able to employ flexibility and empathy toward students. There is an affective impact on students based on how they feel about their own mathematics abilities that will holistically impact their attitudes toward school outside of the mathematics classroom. Within heterogeneous groups, students can constantly shape and reshape their own mathematics identities instead of having their path be predetermined.
Moving Forward
The problematization of tracking in mathematics is clear and there is a need for widespread changes, particularly for Black and Hispanic students. Without changes at many institutional levels, these students will continue to manifest detrimental mathematics identities that will impact their education and opportunities as a whole. First, policies and practices must be anti-racist, not simply race neutral (Darling-Hammond, 2017; Reed & Oppong, 2005). In Closing the Opportunity Gap: A Call for Detracking Mathematics (2020), Leadership in Mathematics Education (NCMS) detailed many recommendations for moving toward more equitable classrooms by de-tracking. First, de-tracking policies need to be developed and adopted at all levels of K-12 education and the education community and beyond need to become more aware of the benefits of de-tracking. De-tracking is complex. Pre-service teachers and those in the classroom will need extensive training to examine biases and create and enact equitable teaching practices in heterogeneous classrooms. Through professional development, teachers will learn more about their impact on students’ mathematics identity development and be able to broaden their teaching goals to not only focus on content, but on the assets of each student. Educators need to move toward focusing on the strengths of each student and not their deficits. Also, curricular and pedagogical changes need to take place to promote accessibility to the content through multiple entry points within lessons and culturally responsive teaching practices and content.
Day to day, educators can affect Black and Hispanic students’ mathematics identities, as well as others, through the interactions with students and experiences they create in their classrooms. When students have more opportunities to engage, their ability to develop a positive mathematics identity with grow (Anderson et al., 2018). Finally, our Black and Hispanic students who have been marginalized through tracking need mentors and role models within mathematics education to help them understand that mathematics can be tool for empowerment and liberation (Martin, 2019). De-tracking is a part of teaching for social justice and is one part of a complex system of social, political, and cultural norms which all have to be addressed in order to achieve the goals of equity through de-tracking (Rubin & Noguera, 2004).
References
Aguirre, J., Mayfield-Ingram, K., Martin, D. B. (2013). The impact of identity in K-8 mathematics learning and teaching: Rethinking equity-based practices. National Council of Teachers of Mathematics.
Anderson, R. K., Boaler, J., & Dieckmann, J. A. (2018). Achieving elusive teacher change through challenging myths about learning: A blended approach. Education Sciences, 8(98). https://doi.org/10.3390/educsci8030098
Berry, R. Q., Ellis, M., & Hughes, S. (2014). Examining a history of failed reforms and recent stories of success: Mathematics education and Black learners of mathematics in the United States. Race, Ethnicity and Education, 17(4), 540-568. https://doi.org/10.1080/13613324.2013.818534
Boaler, J. (1997). Setting, social class and survival of the quickest. British Educational Research Journal, 23(5), 575. https://doi.org/10.1080/0141192970230503
Boaler, J., & Greeno, J. (2000). Multiple perspectives on mathematics teaching and learning. Ablex.
Boaler, J. (2002). Experiencing school mathematics traditional and reform approaches to teaching and their impact on student learning.(2nd ed.). Taylor and Francis.
Boaler, J. (2005). The ‘Psychological Prisons’ from which they never escaped: The role of ability grouping in reproducing social class inequalities. FORUM, 47( 2&3), 125-134.
Boaler, J. (2006). How a detracked mathematics approach promoted respect, responsibility, and high achievement. Theory Into Practice, 45(1), 40-46.
Boaler, J. (2008). Promoting 'Relational Equity' and high mathematics achievement through an innovative mixed-ability approach. British Educational Research Journal, 34(2), 167-194.
Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside school. Teachers College Record, 110(3), 608-645.
Boaler, J. (2011). Changing students’ lives through the de-tracking of urban mathematics classrooms. Journal of Urban Mathematics Education, 4(1), 7-14.
Burris, C. C., Heubert, J. P., & Levin, H. M. (2006). Accelerating mathematics achievement using heterogeneous grouping. American Educational Research Journal, 43(1), 137-154.
Civil, M. (2002). Culture and mathematics: A community approach. Journal of Intercultural Studies, 23(2), 133-148. https://doi.org/10.1080/07256860220151050A
Cohen, E. G. (1994). Restructuring the classroom: Conditions for productive small groups. Review of Educational Research, 64(1), 1–35. https://doi.org/10.3102/00346543064001001
Cohen, E. G. & Lotan, R.A. (1997). Working for equity in heterogeneous classrooms : sociological theory in practice. Teachers College Press.
Cohen, E. G., et al. (1999). Complex instruction: Equity in cooperative learning classrooms. Theory Into Practice, 38(2): 80-86.
Darling-Hammond, L. (2017). Teaching for social justice: Resources, relationships, and anti-racist practice. Multicultural Perspectives, 19(3), 133-138.
Dweck, C. S. (2006). Mindset: The new psychology of success (1st ed.). Random House.
Eisenhart, M., & Allen, C. D. (2020). Addressing underrepresentation of young women of color in engineering and computing through the lens of sociocultural theory. Cultural Studies of Science Education, 15(3), 793-824. http://doi.org/10.1007/s11422-020-09976-6
Ellis, M., & Berry, R. (2005). The paradigm shift in mathematics education: Explanations and
implications of reforming conceptions of teaching and learning. The Mathematics
Educator, 15(1), 7−17.
Ellis, M. (2008). Leaving no child behind yet allowing none too far ahead: Ensuring (In) equity in mathematics education through the science of measurement and instruction. Teachers College Record, 110(6), 1330-1356.
Fordham, S. & J. U. Ogbu (1986). Black students' school success: Coping with the burden of ‘acting white.' The Urban Review: Issues and Ideas in Public Education, 18(3): 176-206.
Fordham, S. (1996). Blacked out: Dilemmas of race, identity, and success at Capital High.
University of Chicago Press.
Flores, A. (2007). Examining disparities in mathematics education: Achievement gap or opportunity gap? High School Journal, 91(1), 29-42.
Freire, P., Ramos, M., Macedo, D., & Shor, I. (2018). Pedagogy of the oppressed (50th anniversary ed.). Bloomsbury Academic.
Gee, J. P. (2000). Identity as an analytic lens for research in education. Review of Research in Education, 25(99). https://doi.org/10.2307/1167322
Gilbert, A. & Yerrick, R. (2001). Same school, separate worlds: A sociocultural study of identity, resistance, and negotiation in a rural, lower track science classroom. Journal of Research in Science Teaching, 38(5), 574-598.
Gutiérrez, R. (2008). A 'Gap-Gazing' fetish in mathematics education? Problematizing research on the achievement gap. Journal for Research in Mathematics Education, 39(4), 357-364.
Gutiérrez, R. (2013). The sociopolitical turn in mathematics education. Journal for Research in Mathematics Education, 44(1), 37-68.
Darling-Hammond, L., Friedlaender, D., & Snyder, J. (2014) Student-centered schools: Closing the opportunity gap [policy brief]. Stanford Center for Opportunity Policy in Education, Stanford University. https://edpolicy.stanford.edu/sites/default/files/scope-pub-student-centered-policy.pdf
Heubert, J. P., & Robert M., H. (1999). High stakes: Testing for tracking, promotion, and graduation: National Academy Press.
Holland, D. C. (1998). Identity and agency in cultural worlds. Harvard University Press.
Leadership in Mathematics Education (NCSM). (2020). Closing the opportunity gap: A call for detracking mathematics [position paper]. https://www.mathedleadership.org/docs/resources/positionpapers/NCSMPositionPaper19.pdf
Loveless, T. (2003). The 2003 Brown Center report on American education: How well are American students learning? With special sections on homework, charter schools, and rural school achievement. Brown Center on Education Policy, Brookings Institution.
Loveless, T. (2013). The 2003 Brown Center report on American education: How well are American students learning? With special sections on homework, charter schools, and rural school achievement. Brown Center on Education Policy, Brookings Institution.
Lubienski, S., & Bowen, A. (2000). Who's counting? A survey of mathematics education research 1982-1998. Journal for Research in Mathematics Education, 31(5), 626-633.
Martin, D. B. (2019). Equity, inclusion, and antiblackness in mathematics education. Race Ethnicity and Education, 22(4), 459-478. https://doi.org/10.1080/13613324.2019.1592833
National Council of Teachers of Mathematics [NCTM] (2020). Catalyzing change in middle school mathematics: Initiating critical conversations. NCTM
McCoy, L. P. (2005). Effect of demographic and personal variables on achievement in eighth-grade algebra. The Journal of Educational Research, 98(3), 131-135. https://doi.org/10.3200/JOER.98.3.131-135
McEwin, C. K., & Greene, M. W. (2010). Results and recommendations from the 2009 National Surveys of Randomly Selected and Highly Successful Middle Level Schools. Middle School Journal (J3), 42(1), 49-63.
Morton, K., & Riegle-Crumb, C. (2019). Who gets in? Examining inequality in eighth-grade algebra. Journal for Research in Mathematics Education, 50(5), 529-554.
National Research Council. (1989) Everybody counts: A report to the nation on the future of mathematics education. National Academy Press.
Olitsky, S. (2015). Beyond "acting white": Affirming academic adentities by establishing symbolic boundaries through talk. Urban Education, 50(8), 961-988.
Paul, F. G. (2005). Grouping within algebra I: A structural sieve with powerful effects for low-income, minority, and immigrant students. Educational Policy, 19(2), 262-282.
Reed, J. & Oppong, N. (2005) Looking critically at teachers’ attention to equity in their Classrooms R. The Mathematics Educator, 1(2), 2–15.
Rubin, B. C., & Noguera, P. A. (2004). Tracking detracking: Sorting through the dilemmas and possibilities of detracking in practice. Equity and Excellence in Education, 37(1), 92-101.
Schoenfeld, A. H. (2002). Making mathematics work for all children: Issues of standards, testing, and equity. Educational Researcher, 31(1), 13-25.
Spielhagen, F. R. (2006). Closing the achievement gap in math: The long-term effects of eighth-grade algebra. Journal of Advanced Academics, 18(1), 34-59. https://doi.org/10.4219/jaa-2006-344
Stiff, L., Janet, L., Johnson, A., William, T., Karen, K., & Celia, R. (2011). Examining what we know for sure: Tracking in middle grades mathematics. National Council of Teachers of Mathematics.