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Access to Mathematics: “A Possessive
Investment in Whiteness”1
DAN BATTEY
Rutgers University
New Brunswick, New Jersey, USA
ABSTRACT
While mathematics education gives access to elite universities, higher-paying jobs,
and the accumulation of wealth, it continues to be framed as a neutral curricular
domain. However, data continually show differential access provided to students
of color and their White peers through tracking, the availability of Advance
Placement courses, and counselor referrals. This article frames mathematics
education within a broader racial context to show how it functions along the
same dominant racial ideologies within society. I analyze national data sets in
the United States to calculate the wage-earning differential attributable to differences in mathematics coursework by ethnic/racial groups across three time
points: 1982, 1992, and 2004. This analysis projects advantages for Whites due
to differential access to mathematics that total in the hundreds of billions of
dollars. The article explores one way to see how color-blind ideology and whiteness produce material stratification through the institution of mathematics education. Drawing on the constructs of interest convergence and divergence, the
article ends with envisioning ways to enact a more race conscious mathematics
curriculum.
INTRODUCTION
The curriculum of mathematics has been used to sort students, give access
to college, and filter people into higher- and lower-wage work. Oftentimes
mathematics gets framed as neutral subject matter, devoid of culture,
feelings, and based on a system of meritocracy. However, this field of
mathematics education has a long history of giving access to students
differentially, particularly based on the ideological construction of race.
With this in mind, scholars are increasingly calling for systematic research
on everyday racialized experiences and the organizational structures that
shape access and opportunity in mathematics, rather than merely disaggregating data by race (see Diversity in Mathematics Education Center for
Learning and Teaching [DiME], 2007; Martin, 2009).
© 2013 by The Ontario Institute for Studies in Education of the University of Toronto
Curriculum Inquiry 43:3 (2013)
Published by Wiley Periodicals, Inc., 350 Main Street, Malden, MA 02148, USA, and 9600 Garsington Road,
Oxford OX4 2DQ, UK
doi: 10.1111/curi.12015
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Often, when achievement data are disaggregated by race, differences
are framed as a gap between White students on the one hand and Latino,
African American, and/or Native American students on the other, without
also researching how those differences were constructed or produced
(Gutiérrez, 2008). When referring to students of color, gaps are framed as
deficits, pathologizing the intelligence of students of color based on test
scores, intelligence, and ability; the same is not done when White students
have lower test scores. Instead, students are compared internationally
with Asian nations such as Singapore, Japan, China, and South Korea
(Fleischman, Hopstock, Pelczar, & Shelley, 2010) and the onus is placed
on teachers’ content knowledge (Martin, 2009). The mathematics curriculum is employed to spur economic action for the sake of global competitiveness rather than for racial justice in giving students of color more
access. The clear rejection of pathologizing White students’ mathematics
performance speaks to impoverished racial theorizing in mathematics
education research (Martin, 2009).
Instead of presenting disaggregated data as bereft of context, this study
attends to social, historical, and political context. This is because achievement outcomes are intertwined with mechanisms such as tracking and the
accessibility of Advance Placement (AP)2 courses. Mechanisms such as
tracking have historical and political roots in grouping students in lessrigorous coursework and continue today by stratifying access to content
racially (Oakes, 1985; Oakes, Joseph, & Muir, 2003). These educational
mechanisms serve to make the mathematics curriculum an institution
because it functions as a social structure that requires participation through
compulsory schooling, has specific social purposes, and establishes rules
governing individual behavior. The assumption in this article is that the
mathematics curriculum, as an institution, is not neutral, but functions
along the dominant racial ideologies in society. From this perspective, the
mathematics curriculum functions independently from individual opinion
that may be in opposition to the current racial ideology. While institutional
racism can be difficult to represent tangibly, many governmental programs
privilege Whites even though they purport to be race neutral. Lipsitz
(1998) calls this the “possessive investment in whiteness.” By this, Lipsitz
refers to the investment by Whites in racially stratifying distribution of
opportunity, education, and wealth. One way of exposing this is by examining advantages that racism affords Whites over minorities, while noting
the processes that allow advantages to take place. Perlo (1996) illustrates
this by analyzing the exploitation of people of color through cumulative
wage differentials for people of color as compared to Whites.3
Employing a similar framework, this article analyzes the wage-earning
differential related to stratified mathematics coursework by ethnic/racial
groups. While mathematics education is not the sole factor in income
differentials, it is related to differences in income. To calculate the wageearning differential, I use a statistic generated by Rose and Betts (2001) for
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DAN BATTEY
the income 10 years after high school associated with mathematics coursework. They use a regression analysis to examine the relationship between
math coursework, income, socioeconomic status (SES), and race. In their
research, they find the average income 10 years after graduation based on
differing mathematics coursework. They then use regression to see how
much of wage differentials can be accounted for by race, SES, and mathematics coursework. The analysis of Rose and Betts is not causal as regression merely establishes whether there is a relationship between predictor
and outcome variables. As was the case in the Rose and Betts study, the
relationship between race and income differentials reported in this article
is based on an examination of the association between the two constructs.
No causal claims are made.
This work extends the initial work of Rose and Betts by addressing two
limitations as well as extending their analysis across multiple time points.
First, the metrics they use for SES are confounded with race when one
considers material racism. While the present study is limited by national
data sets that confuse race and ethnicity, a more critical stance is taken to
defining these terms than in Rose and Betts (2001). Rose and Betts never
define what they mean by race or ethnicity and therefore run the risk of
reifying either biological or socially unchanging constructs. Because race is
a fictive social construction, there would be no reason for fictive racial
economic differences to arise based on biology or social definitions. Fictive
races would only produce economic differences if this fiction were given
meaning through the societal stratification of resources and opportunities.
Therefore, any differences that occur are a sign that racial stratification of
opportunity has occurred socially and historically. Second, Rose and Betts
underestimate the relationship between income and race by using a limited
statistic for dropouts. In addressing these limitations this article also
extends the literature by examining income differentials across three time
points (1982, 1992, and 2004) and projecting these differentials across a
work-life and generation. This allows for a calculation of the differences in
accumulated income as it relates to differential racial opportunities in
mathematics schooling. The income differential is therefore a correlation
between racial stratification and economic outcomes and serves as an
appropriate model to project investments related to the mathematics
curriculum.
One consequence of viewing the mathematics curriculum as a racially
stratified institution is that it makes racial justice more complex than
students taking more mathematics courses. From this perspective, when
students of color take more mathematics courses, we would expect the
system to adjust to either track students, raise the bar as far as what mathematics is expected, or change the requirements, minimizing the progress
of students. A good example of this is the “Algebra for All” movement in
California (DiME, 2007; Paul, 2003). While this movement was meant to
require all students to take algebra by eighth grade, multiple forms of
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algebra were created in urban schools that defeated this purpose. Urban
schools developed courses termed “2-year algebra,” “1-year double-dose
algebra,” and “algebra essentials” to remediate students deemed not ready
for a typical 1-year algebra course, while still satisfying the state mandate
(DiME, 2007). The school system responded by using the mathematics
curriculum to racially stratify access to college-level mathematics courses.
Therefore, from this perspective, the mathematics curriculum is a
complex social institution that makes such strategies as requiring the
same coursework for all students an unlikely solution for addressing racial
injustice.
In the following sections of the literature review, the article first looks
at work in mathematics education that conceptualizes race, structural
analyses, and whiteness. To situate this work, I discuss the construction of
an ideology of whiteness, which creates a historically contingent dominant
group (Whites) and those subjected to systemic racism. I then examine
the function of racial ideologies (both whiteness and color blindness),
integrating notions of material racism to show the very real consequences
of such constructions. The next section shows how color-blind policies in
housing, taxes, and education are connected to material benefits accrued
from being included in the racial group of “White” and to racial stratification. I end by describing how the investment of Whites in the mathematics curriculum was calculated in this article as a way to quantify the
reproduction of racial stratification. Therefore, this article serves as one
way to represent the mathematics curriculum as part of a broader system
of racism.
RACISM, STRUCTURES, AND WHITENESS IN
MATHEMATICS EDUCATION
As opposed to simply disaggregating data, without regard for mechanisms
associated with achievement differences, more recent work in mathematics
education is tending to issues of race and racialization and bringing critical
perspectives to racial experiences, structural issues, and the effects of colorblind ideologies on teachers. Some of this work focuses on the successful
mathematics experiences of African American students (Berry, 2005;
Martin, 2000, 2006a, 2006b; Moody, 2001; Stinson, 2008; Thompson &
Lewis, 2005); others have attended to using culture and/or parents as a
resource for Latino students (Anhalt, Allexsaht-Snider, & Civil, 2002; Civil
& Bernier, 2006; Gutstein, 2005, 2006). This research challenges the dominant narrative that treats the underachievement of students of color as a
given or related to their lack of concern for educational attainment.
Another area of work is structural analyses, which focuses on access and
opportunity for students of color in mathematics education. For example,
Oakes and colleagues draw attention to tracking, the lack of AP courses in
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urban schools, and teacher quality (Oakes, 1990; Oakes, Joseph, & Muir,
2003). Additionally, research has examined policy and court decisions such
as Hobson v. Hansen (1967) and People Who Care v. Rockford Board of Education
(1994) on tracking and what this meant for mathematics education (Tate
& Rousseau, 2002). Studies of successful mathematics departments and
schools for Latino and African American students have found that students
are supported in learning mathematics when they have access to a rigorous
curriculum coupled with the instructional support, active teacher commitment to students, commitment to a collective success, an empowering
department chair, and standards-based instruction (Gutiérrez, 1996, 1999,
2000). All of this work takes a structural perspective in analyzing the
influence of policies on the mathematics schooling of students of color. If
these researchers disaggregate test scores, they also analyze mechanisms
related to achievement differences. However, none of this work deconstructs the presence of color blindness in mathematics education.
Two studies begin to unpack the presence of color-blind ideologies in
mathematics education. Reed and Oppong (2005) highlight how a colorblind ideology served to shape one White teacher’s mathematics instruction. Even though the teacher considered issues of equity in terms of
gender and special needs, she still framed Latino and African American
students’ abilities using racial stereotypes and deficit narratives. In another
study, Brewley-Kennedy (2005) examined one mathematics teacher educator’s struggle to integrate equity concerns in a mathematics methods
course. While more comfortable discussing issues of equity with regard to
gender and special needs, she nonetheless shied away from race and class.
These case studies highlight the need for more research that represents the
mathematics curriculum as part of a larger system of racism. A major gap in
this literature is connecting the institutional analyses, discussed previously,
with work that places mathematics education within a broader system of
racial ideology. To begin this, I first look at research on the construction of
whiteness as a form of racial domination.
WHITENESS, COLOR-BLIND IDEOLOGIES, AND
MATERIAL RACISM
Lipsitz (1995) states that “a fictive identity of ‘whiteness’ appeared in law as
an abstraction, and it became actualized in everyday life” (p. 370). Much
like “Black” is a cultural construction based on perceived skin color and not
on biology, whiteness developed out of the reality of slavery and segregation, giving groups unequal access to citizenship, immigration, and property (Ladson-Billings & Tate, 1995). By giving Whites a privileged position
in relation to the “other,” European Americans united in a fictitious community or passive collective (Lewis, 2004). As a group, Whites are unified
by their actions around certain objects (passive collective); it is not a
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self-conscious choice to be a member of a group (identity). The concept of
a passive collective allows for the enactment of whiteness and institutional
racism, including unearned advantages, without the intentionality of
Whites. Therefore, all Whites experience race daily, living and working
within racial structures, though race and racism are not necessarily explicit
for them (Lewis, 2004).
Compounding the implicit nature of whiteness, it is a constantly shifting
boundary separating those who are entitled to certain privileges from those
subjugated for not being White. The boundaries of the social construction
of whiteness have constantly shifted over time (see Haney-Lopez, 2006).
Many ethnic groups have sought out equalization through citizenship
(Foley, 2002), but when African American citizens still had to sit at the back
of the bus and could not vote, assimilation became the goal for some. As
“not-yet-White,” ethnic immigrants strove to assimilate as a way to attain
whiteness (Roediger, 2002); “immigrants of color always attempt to distance themselves from dark identities (blackness) when they enter the
United States” (Bonilla-Silva, 2003, p. 271). Toni Morrison (1993) discussed the final step in assimilating into whiteness: “A hostile posture
toward resident blacks must be struck at the Americanizing door before
it will open” (p. 57). For many immigrant groups the path to whiteness
became not so much about losing one’s culture as becoming wedded to
the idea that Blacks were culturally and biologically inferior to Whites
(Morrison, 1993).
Recently, the ideology of whiteness has been supported by a color-blind
ideology, a form of maintaining the social order, covertly, institutionally,
and with the appearance of not being racial. Color blindness then bolsters
whiteness by its resistance to framing, defining, or pathologizing whiteness
(Bonilla-Silva, 2003). This racial ideology fits with Martin’s (2009) discussion about the framing of White achievement versus that of students of
color along two lines. First, it shows the denial to recognize how institutional inequality bestows unearned advantages on Whites. This allows the
dominant ideology to locate racism in a few prejudiced individuals.
Second, it fits with framing lower achievement by students of color as a
matter of cultural deficiency. An unwillingness to question how institutions benefit Whites, coupled with statistics showing lower achievement
scores for African American and Latinos, transfers the blame to students,
families, and culture. Therefore, color blindness has shifted explicit racial
arguments about genetics to supposed nonracial arguments of student
failure, uncaring parents, and devaluing of education, which leaves whiteness invisible, allowing many to defend their views in apparent nonracial
ways (Bobo & Hutchings, 1996; Bobo & Smith, 1994; Bonilla-Silva, 2003;
Bonilla-Silva & Forman, 2000; Carmines & Merriman, 1993; Jackman,
1994).
These ideological frameworks play out, in very real ways, through divvying up such resources as housing, earnings, and wealth. Sewell (1992) and
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Lewis (2004) discuss racism both ideologically and concretely through
considering its dual nature: symbolic (ideological) and material (structural
resources). Ideologies produce very real material consequences. In mathematics education, there are common perceptions (symbolic racism) about
who is biologically better mathematically—namely, Whites and Asians.
These perceptions are then made real (material racism) by how African
Americans are treated in mathematics classrooms, the forms of instruction
available, and what courses (AP or not) schools provide, which in turn lead
to different testing outcomes (gaps). By giving African Americans impoverished forms of instruction through tracking and reduced funding
through property taxes, material racism concretizes racist ideologies. In
this sense, race is more dynamic than having racial ideologies create material differences; racial ideologies are also reproduced by material circumstances. Sewell (1992), in his analysis of this dialectic relationship, explains
that it
[m]ust be true that schemas are the effects of resources, just as resources are the
effect of schemas. . . . If resources are instantiations or embodiments of schemas,
they therefore inculcate and justify the schemas as well. . . . If schemas are to be
sustained or reproduced over time . . . they must be validated by the accumulation
of resources that their enactment engenders. (p. 12)
Therefore, in the case of mathematics education, achievement “gaps” serve
to reify ideologies about mathematics intelligence and effort in favor of
Whites and Asians. The dialectic relationship between ideologies that
create more racial disparity and racial disparity that produce these ideologies is critical in understanding the consequences of policy and educational
institutions.
Symbolically and materially, Whiteness creates racialized spaces and
resource distribution to pass on to future generations. For example, we
are born into racially separate spaces, with housing segregation affecting
who lives, shops, and goes to school with each other. In addition, this
results in stratified work environments, home values, property taxes, and
school funding. In his article, Lipsitz (1995) discusses federal policies in
the United States that authorized attacks on Native Americans, restricted
naturalized citizenship to “White” immigrants, and supported slavery and
segregation. Many policies seem neutral, yet their effects are anything but
that.
Through housing, taxation, and educational practices, supposed colorblind policies advantage Whites. In the United States, the Federal Housing
Administration’s (FHA’s) practices and policies have shifted loan money
and therefore future investment in real estate away from communities of
color and toward Whites since 1934 (Lipsitz, 1995; Logan & Molotch,
1987). Studies have shown that African Americans are more likely than
Whites to be turned down for loans (controlling for credit qualifications),
disqualified for loans three times as much, and are four times less likely to
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receive conventional financing (Campen, 1991; Logan & Molotch, 1987;
Massey, 1996; Ong & Grigsby, 1988; Orfield & Ashkinaze, 1991; Zuckoff,
1992). Federal tax policies have also advantaged Whites from higher taxation on goods and services rather than taxing profits from investments
(Lipsitz, 1995). This policy allowed Whites to build more wealth by lowering investment taxes on capital gains advantaging Whites who benefited
from home ownership, increased home values, and generational wealth
(Oliver & Shapiro, 1997). Educationally, the fact that there is a similar level
of segregation in schools to the 1960s means resource distribution is just as
central an issue today as it was 40 years ago (Fairclough, 2007; Orfield,
Losen, Wald, & Swanson, 2004; Walker, 1996).4 Policies of school funding
tied mostly to local property taxes have maintained differential funding for
suburban schools at levels twice that for urban schools (Kozol, 1991). This
is significant considering the current racial segregation of urban schools
with less than 3% of all White students attending schools that are 83%
non-White (Frankenberg, Lee, & Orfield, 2003).
There are numerous other examples of nonneutral policies that advantage Whites as well (see Conley, 1999; Dyson, 2000; Kivel, 2002; Wynn,
1976). These forms of color-blind policies advantage Whites by guaranteeing that they will continue to benefit materially from historic advantages. Meanwhile the attack on affirmation action for people of color
threatens the one policy trying to balance the playing field from a history
of “neutral policies.” The irony is that housing, tax, and educational policies that purport an ideology of color blindness actually advantage
Whites. This in turn has served to increase racial stratification, rather
than ameliorate it.
APPLYING PERLO’S MODEL FOR MATERIAL RACISM TO
MATHEMATICS EDUCATION
Centuries of bestowing land, education, and stored wealth means that
many Whites born today begin their lives with more familial wealth stored
in houses, educational attainment, and economic investments. Policies that
place wealth in the hands of certain groups and take it away from other
groups are a form of exploitation. Perlo (1996) calculates this racial exploitation as the “wage differentials against African Americans, Hispanics, etc.,
multiplied by the number of workers employed in private enterprises” (p.
170). For instance, if the median income differential between Whites and
Blacks was $5,000 in a given year, we would multiply that by the number of
Black workers to get the total differential that represents the exploitation of
Black workers. Hypothetically, for 100,000 Black workers, the financial
exploitation would result in $500 million that year. Perlo contends that the
profits from these wage differentials are benefits of racism for Whites.
Given this framing, Perlo (1996) computes that the total profits due to
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racism in 1947 were $56 billion (in 1995 dollars). That number rose to $88
billion in 1972, $112 billion in 1980, and $197 billion in 1992. African
Americans were exploited for $48, $60, $74, and $107 billion in those years,
while Latinos were exploited for $8, $28, $34, and $84 billion.
While the link between race and wage differential is clearly correlational,
the connection may carry more meaning than mere association. For
instance, because there is no biological reason for race, the idea that it is a
fictive construct would mean that we should not find racial income differences unless there was a system that stratified access and opportunity along
racial lines (e.g., slavery and segregation). Perlo, therefore, considers that
the differences are indicative of the racist exploitation of workers. These
numbers do not include the exploitation of White women or Whites in
poverty, even though they are also likely exploited by the White elite. Even
so, these numbers speak to a widening divide in wealth between Whites and
people of color. They are a symbol of centuries of policies invested in the
education, wealth, and maintenance of wealth to advantage Whites on the
backs of African Americans and Latinos.
Because mathematics serves as a gatekeeper for entrance into elite colleges and for higher-paying careers, mathematics education is also a system
used to stratify society. Through the availability of AP classes in suburban
schools, tracking students of color into lower mathematics coursework, and
counselors referring students to less-advanced coursework, different access
and opportunities are available to students of color (Noguera, 2004; Oakes
et al., 2003). In addition, deficit ideologies of teachers can result in negative and sometimes hostile environments for students, when some teachers
do not believe that students of color have the intellectual ability to think
abstractly (Perry, 1993). All of these processes serve to reduce mathematics
coursework, college opportunities, and earning potential for people of
color. Taking these forms of stratification into account, Perlo’s calculations
for the exploitation of people of color can be computed for the mathematics curriculum. Wage differentials are related to educational attainment
and mathematics coursework. In considering these differentials, the mathematical attainment of various races can be considered and their subsequent relationship with future wages. Therefore, the portion of racial wage
differentials related to the mathematics curriculum is a more specific
example of Perlo’s calculation.
In this article, I calculate the material racism, using a similar formula to
Perlo’s, related to differential mathematics coursework. As an example, we
can take the average mathematics attainment of a Latino student and
compare this to the average attainment by a White student in 1982. Rose
and Betts (2001) compared differential mathematics coursework to differential job pay. As an example, according to their calculations, if the average
Latino student completed Algebra 1 and the average White student completed Algebra 2, this would be associated with about a $5,000 wage differential 10 years after high school. In expanding this differential over a
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40-year work-life, we would multiply the wage differential by 40 giving the
Latino student $200,000 less in earned income. Multiplying the average
differential across the entire class of Latino high school seniors in 1982
would correspond to the income advantage that Whites hold over that class
of Latino students. So if there were 200,000 Latino seniors in 1982, the
advantage Whites would gain over that senior class would total $40 billion
(200,000 x $5,000). Using these calculations, mathematics coursework
serves as a representation of racial investment in which Whites reproduce
job, earning, and wealth differentials.5
Rose and Betts (2001) contend that SES-related background
variables—specifically parental income, parental education, and school
characteristics—account for the racial differences in earnings. However,
as suggested in the above review of the literature, I argue that material
racism takes the form of differential economic, housing, and educational
outcomes for future generations. While Rose and Betts consider such
outcomes as part of SES, in my view, these are racialized variables as well.
When Rose and Betts considered race and ethnicity, they were less significant factors in their analysis because the variables they use for SES
partially account for their variable on race. Therefore, their analysis does
not fully account for race because they use variables that confound race
and SES.
In looking further into their analysis, the minimization of race is even
more evident. Rose and Betts (2001) state that “the effect that curriculum
could play in decreasing the earnings gap related to parental income is
quite remarkable15” (p. 74). While they claim, as noted in the previous
paragraph, that curriculum is not related to racial income differences, they
consider the curriculum as critical in reducing the income gap connected
to parental earnings. The footnote along with that statement asserts:
15
It is important to bear in mind that although we did not explicitly find that
standardizing the curriculum can help narrow the ethnic earnings gap, the
ethnic composition of students in the lowest-parental-income group is such that
narrowing this gap would be a step toward narrowing the ethnic earnings gap as
well. (p. 74)
The claims by Rose and Betts that curriculum plays a major role in income
differentials in terms of SES and that race is interrelated with their variables
for SES furthers the case that race is minimized in their analysis. From the
viewpoint that their analysis minimizes race, their finding that the mathematics curriculum is responsible for 26.1% of differences in income in
terms of SES will be modified to approximate the role of the mathematics
curriculum on racial income differences. In addition to this statistic, they
also include the percentage of racial income differences and the role of
mathematics coursework related to these differences. Their calculation
of the proportion of racial income differences related to mathematics
coursework will be used in this article.
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Their argument that the curriculum does not explain racial income
differences is further complicated by the data set. Rose and Betts (2001) say
that “The [High School and Beyond] dataset underrepresents workers who
drop out of school or immigrants who have never attended American high
schools, which may explain our surprising finding that standard background variables fully account for ethnic earnings gaps14” (pp. 73–74). The
footnote then states: “14This dataset especially underrepresents Hispanic
dropouts because they are especially likely to leave school before grade 10”
(p. 74). So above and beyond the confounding of their SES variables with
race, they acknowledge the underestimation of their data set for racialized outcomes due to poor data on dropouts. A number of researchers
have demonstrated that poorer math grades, not taking math, and
lower achievement scores in math are linked to a higher likelihood of
students dropping out (Battin-Pearson, Newcomb, Abbott, Hill, Catalano,
& Hawkins, 2000; Ekstrom, Goertz, Pollack, & Rock, 1986; Lee & Burkam,
2003). In the analysis presented in this article, I build on Rose and Betts’s
analysis by using a better statistic for dropouts—the status dropout rate. I
revisit and reanalyze the data provided by Rose and Betts to examine the
relationship between Whites investment in mathematics education and a
larger system that perpetuates material racism. Additionally, I consider data
for two more time points to understand patterns of math coursework
and wage differentials across a 23-year span. The following three research
questions guide this study:
1. How does mathematics coursework relate to racial differences in
potential wage earnings for three time points (1982, 1992, and 2004)?
2. What do these wage differentials predict in terms of earnings over a
40-year work-life and across a generation for different racial groups?
3. What is the projected economic investment in racial groups based on
differential mathematics coursework?
METHODS
The data used in this study were taken from national databases: High
School and Beyond (HSB) 1980 (and follow-ups), National Education
Longitudinal Study (NELS) 1988 (and follow-ups), Education Longitudinal Study 2002 (and follow-ups), and Current Population Survey (CPS)
1972–2005.6 This article presents a secondary analysis of these data with
respect to mathematics course completion. All dollar amounts are in 2010
dollars adjusted using the Consumer Price Index.
The surveys change somewhat over time in terms of mathematics course
classifications. Because of this, the classifications I use here are reclassifications of the various surveys. Calculus remained the same, but depending on
the survey, some collected data on Trigonometry and Precalculus, while
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others considered this Algebra III. Additionally, vocational math, no math,
and Prealgebra have been grouped because each source classifies this
differently. Algebra I, Algebra II, and Geometry II were consistent across
data sets. Therefore, these data should be considered approximations
across different but similar national data sets.
Rose and Betts (2001) use the cohort dropout rate from HSB in their
analysis. This considers only the change in student population for a cohort
from sophomore to senior year of high school. This calculation is a major
underestimate because it does not consider those who dropped out prior to
sophomore year of high school. Here, I use the only data available across all
3 years—the status dropout rate (for an understanding of the problems with
dropout rates in national data sets, see Orfield et al., 2004). For these data
sets, I use dropout data from the National Center for Educational Statistics,
specifically the status dropout rate (Chapman, Laird, Ifill, & KewalRamani,
2011). This measures the percentage of noninstitutionalized individuals
aged 16 through 24 who are not enrolled in high school and who do not
have a high school credential. The advantage is that it accounts for those
who completed high school after the expected date of graduation, can be
compared over time, and considers those students that HSB, NELS, and ELS
would miss because students dropped out prior to sophomore year of high
school. Even the status dropout rate, though, underestimates dropouts. For
an idea of the scale of the underestimate, Orfield and colleagues (2004)
calculate the dropout rate of African Americans and Latinos to be 50.2% and
53.2%, respectively in 2001 (as compared to the status rates of 10.5% and
13.4%, respectively). Rose and Betts (2001) did calculate the income of
dropouts 10 years after graduation and that statistic is used in this article.
Similar to the example presented earlier, the equation for the average
yearly income for each ethnic/racial group is as follows:
% completed calculus ¥ average earnings by mathematics coursework
% completed trigonometry/algebra III ¥ average earnings by mathematics
coursework
% completed algebra II ¥ average earnings by mathematics coursework
% completed algebra I/geometry ¥ average earnings by mathematics
coursework
% completed low academic/no math ¥ average earnings by mathematics
coursework
+% dropouts ¥ average earnings for dropouts
Multiplying the above sum by the number of students each year gives the
result of differential investments in mathematics coursework by each
ethnic/racial group. The projected earnings across all students in a racial
group serve as a way to see economic investment related to mathematics.
Comparing racial groups for the same number of students shows differences in economic investment.
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DAN BATTEY
The above changes to Rose and Betts’s (2001) analysis allow for a comparison of ethnic/racial groups across three time points instead of one,
speaking to the first research question. The article also uses a better statistic
for dropouts in calculating earnings related to mathematics coursework
giving a more accurate projection for earning differentials across years.
Finally, I project these differences across a generation and work-life to view
the economic differences related to differential mathematics coursework.
Results
The results begin with data across 1982, 1992, and 2004 on the highest level
of mathematics completed by racial/ethnic group. I have also included
dropouts in Table 1 because the national data included only the highest
level of mathematics completed for high school graduates. The analysis
then shifts to the income levels 10 years after graduation by mathematics
achieved and by race/ethnicity. These data are then used to calculate the
incomes for different racial groups in comparison to Whites 10 years after
graduation, over a lifetime, and across generations. Last, I calculate the
percentage of the racial earnings differentials related to mathematics
coursework according to Rose and Betts (2001).
Table 1 shows the highest level of mathematics completed for high
school graduates in 1982, 1992, and 2004 by ethnic/racial group. The right
column also presents the status dropout rate. Hispanics, American Indians,
and Blacks took advanced mathematics at lower rates across years and were
more likely than Asians and Whites to take no mathematics. While these
data could be used to reaffirm the lack of interest in mathematics of
students of color to support cultural deficit theories or to promote a
discussion of racial “gaps,” all three groups (Hispanics, American Indians,
and Blacks) increased their mathematics course taking across the years.
These data actually speak to the continued valuing of mathematics across
groups rather than singling out one culture or ethnicity as valuing it and
another as not valuing it. Additionally, the data point to a bar being raised
mathematically as subsequent classes achieve more mathematical coursework, raising concerns about access to higher-level mathematics. First, in
urban schools, which have higher populations of Hispanics and Blacks in
the United States, researchers have documented the lack of AP mathematics and science courses available (Oakes et al., 2003). Even if students of
color wanted to take this coursework, it is not available to many, often
because they do not have teachers certified to teach AP mathematics. Also,
for decades, tracking as a schooling phenomenon has routed students of
color to lower levels of mathematics (Oakes, 1985, 1990; Oakes et al.,
2003). And counselors often steer students of color away from college
preparatory courses (Cicourel & Kitsuse, 1963; DiMaggio, 1982; Erickson &
Schultz, 1982; Oakes et al., 2003; Rosenbaum, 1976). These three factors
22.9
37.6
11.2
11.3
8.6
28.9
32.4
18.7
23.9
13.7
39.1
35.5
36.3
28.1
16.8
39,581
11.5
22.1
6.9
5.0
1.0
16.2
33.8
4.9
7.0
5.4
42,625
Trig/Algebra III
6.8%
15.4
2
2.6
2.3
Calculus
Advanced
23.8
17.5
31.5
31.9
40.8
35,014
26.9
23.9
23.5
26.3
28
18.9
19.1
18.5
13.8
13.4
Alg 2
16.4
11.1
18.7
26.5
23.7
30,447
20.8
12.5
32
30.9
28.5
30.9
17.2
27.7
33.1
27.8
Alg 1/Geo1
Middle
Graduates
4.6
2.1
6.6
6.4
13.3
28,163
11.9
9.2
18.9
14.2
28.9
20.5
10.6
40.6
39.1
48
Low Academic/
No Math
4.7
4.6
10.5
13.4
15.2
23,928
4.3
4.6
7.6
10.9
18.2
8.8
2.2
11.3
16.8
25.1
Dropouts2
2
Excludes prealgebra.
Source: Chapman, C., Laird, J., Ifill, N., & KewalRamani, A. (2011). Trends in High School Dropout and Completion Rates in the United States: 1972–2009 (NCES 2012-006).
U.S. Department of Education. Washington, DC: National Center for Education Statistics. Retrieved December 12, 2011, from http://nces.ed.gov/pubsearch
3
Rose & Betts, 2001.
SOURCE: U.S. Department of Education, National Center for Education Statistics. High School and Beyond Longitudinal Study of 1980 Sophomores,
“First Follow-Up” (HS&B-So:80/82); National Education Longitudinal Study of 1988 (NELS:88/92), “Second Follow-Up, High School Transcript Survey, 1992”;
Education Longitudinal Study of 2002 (ELS:2002/04), “High School Transcript Study”; and National Assessment of Educational Progress (NAEP), 1987, 1990, 1994,
1998, and 2000 High School Transcript Studies (HSTS).
1
1982
White
Asian/Pacific Islander
Black
Hispanic
American Indian/Native Alaskan (AI/NA)
1992
White
Asian/Pacific Islander
Black
Hispanic
AI/NA
2004
White
Asian/Pacific Islander
Black
Hispanic
AI/NA
Avg. Earnings 10 Years After High School
(2010 dollars)3
Year and Ethnicity/Race
TABLE 1
Highest Mathematics Completed by Year, Ethnicity/Race, and Average Yearly Earnings 10 Years After High School Graduation
ACCESS TO MATHEMATICS
345
346
DAN BATTEY
should remind us that educational mechanisms are in place that treat
students differentially according to race, rather than jumping to conclusions based on cultural myths of disinterest in mathematics.
Using the mathematics coursework data allows for a calculation that also
includes the average earnings 10 years after graduation (2010 dollars), in
the bottom row of Table 1 (see Rose & Betts, 2001). The bottom row shows
the average earnings attributable to mathematics coursework 10 years after
high school ends, not yet factoring in course completion by ethnicity/race.
Multiplying the percent of Whites who completed calculus in 1982 (6.8%)
by the average income of that group of students 10 years later ($46,625)
along with the percentage who completed Trigonometry/Advanced
Algebra (22.9%) by their income ($39,581) and so forth down the line
results in the average wage earned for Whites across mathematics course
work completed and dropouts. In doing this across years for each ethnic/
racial group, the calculations show the average earnings 10 years after
graduation (or expected graduation in the case of dropouts). However, this
does not include data about who goes to college. Additionally, those with
higher-paying jobs also see larger increases in wages over time as well
(Autor, Katz, & Kearney, 2006). Therefore these numbers should be seen as
a conservative approximation. The numbers for these calculations can be
seen in the first column of Table 2. This gives a sense of the earning
potential for different groups according to mathematics coursework.
In Table 2, I present the total earnings for each ethnic/racial group
based on the number of students in each high school class multiplied by
their average earnings related to mathematics coursework. The adjusted
column compares the total earnings of different racial groups with that of
Whites, using the same number of students (as each ethnic/racial group)
multiplied by the average earnings for Whites. For instance, to compare
Asians and Whites, I multiplied the population of Asians by their average
earnings and multiplied the population of Asians by the average earnings
of Whites. This way we can compare the average earnings of both groups
over a population of various ethnic/racial groups. The last column, which
compares total and adjusted earnings, represents the financial advantage
given to Whites through mathematics preparation (rounded to the nearest
million). The negative sign represents an investment in favor of Asians (see
Table 2). However, comparing the same number of students, Whites would
be accorded an income advantaged of $1.23–$1.73 billion over African
Americans. For Hispanics the advantage ranges from $1.24–$2.55 billion,
in part due to an increase in the U.S. population for this racial group. And
finally, for Alaskan Indian/Native American the range is from $133–$166
million. This accumulation of wealth in favor of Whites over Native Americans is for fewer than 50,000 high school students. This does not include
statistics for people of color earning lower wages with the same education
working in the same job, SES, or other factors that would make these
differentials greater. So again, these calculations should be considered an
3,607
59
524
284
45
2,631
163
431
362
43
2,376
157
701
634
47
34,887
36,533
32,021
30,862
31,107
36,405
38,289
33,481
32,215
32,771
Population of
18-Year-Olds
(rounded to
thousands)1
$33,129
36,187
29,830
28,753
29,458
Average Earnings
From Mathematics
Coursework
(2010 dollars)
U.S. Department of Education’s Common Core of Data.
1
1982
White
Asian/Pacific Islander
Black
Hispanic
American Indian/Native Alaskan
(AI/NA)
1992
White
Asian/Pacific Islander
Black
Hispanic
AI/NA
2004
White
Asian/Pacific Islander
Black
Hispanic
AI/NA
Year and Ethnicity/Race
91,907
6,982
18,044
19,581
1,195
91,804
5,951
13,793
11,171
1,351
$119,507
2,124
15,623
8,179
1,330
Total Earnings
Based on Mathematics
Coursework
(millions)
TABLE 2
Annual Earnings Related to Mathematics Coursework and Investment, by Year and Ethnicity/Race
—
6,639
19,621
22,128
1,328
—
5,683
15,027
12,628
1,515
0
$1,944
17,350
9,423
1,496
Adjusted Earnings
for Whites With
Same Population
(millions)
—
-344
1,576
2,547
133
—
-268
1,234
1,457
164
0
-$179
1,728
1,244
166
Investment
Relative
to Whites
(millions)
ACCESS TO MATHEMATICS
347
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DAN BATTEY
underestimate. These numbers are for only 1 year of work, 10 years after
high school, and do not include the years in between the dates included.
Over the course of the 23-year span contained in this study, using the
average yearly advantage (see column 1 in Table 3), Whites earned more
than Blacks ($38.4 billion), Hispanics ($41.1 billion), and Native Americans ($3.84 billion). For an estimated 40-year work-life, also called a synthetic work-life (see Day & Newburger, 2002), the total earnings differential
ranged from $6.67 to $71.4 billion. Across a synthetic 40-year work-life, the
average income differential for all graduates in a single year results in over
$144 billion in advantages for White students. Notice as well that Asians still
show advantages over Whites totaling $5.69 billion (23-year span) and $9.90
(40-year work-life) billion (see Table 3). As noted earlier, these numbers do
not consider that differentials at one point are more likely to grow due to
raises, accumulated income, and interest. The last column in Table 3
reports the aggregate advantages for 23 years of high school classes (1982–
2004) across a synthetic 40-year work-life. The aggregate earnings advantage for Whites is over $3 trillion. However, these differences do not factor
in the portion of differences in racial earnings that are related to mathematics coursework.
In their regression analysis, Rose and Betts (2001) report the percentage
of the racial income differences that are attributable to differences in
mathematics coursework. This means that if there is a 10% difference in
income between Whites and Hispanics, say, and that half of this difference
is related to the differences in mathematics coursework, then 50% of
difference in racial earnings is accounted for by the mathematics curriculum. These numbers range from 9.8% for African Americans to 53.3% for
Asian Americans (see column 1 in Table 4). These percentages represent a
large variance in how differences in earnings are accounted for with respect
to mathematics coursework. It is possible that because Rose and Betts used
data that underreported dropouts for Hispanics in particular, that their
analysis overestimated the proportion that mathematics plays in explaining
earning differentials in comparison to Whites.
TABLE 3
Investment Relative to Whites for 23-Year Span and 40-Year Synthetic Work-Life
Investment Compared
to Whites
Asian/Pacific Islander
Black
Hispanic
American Indian/Native
Alaskan
Total
Average
(1982–2004
in millions)
Cumulative
Over 23 Years
(1982–2004)
Synthetic
40-Year
Work-Life
Synthetic
Work-Life*
23 Years
-$247
1,670
1,785
166
-5,693
38,414
41,077
3,837
-9,901
66,808
71,438
6,674
-227,724
1,536,588
1,643,093
153,507
3,374
83,329
144,921
3,333,188
53.3%
9.8
50.0
14.8
Asian/Pacific Islander
Black
Hispanic
American Indian/Native Alaskan
Total
Taken from Rose & Betts (2001).
1
Percentage of
Investment Related
to Math Coursework1
Investment Compared to Whites
Cumulative
Over 23 Years
(1982–2004)
-3,032
3,765
20,539
570
21,841
Average
(1982–2004
in millions)
-$132
163
893
25
950
-5,273
6,547
35,719
991
37,984
Synthetic
40-Year
Work-Life
TABLE 4
Investment Relative to Whites for 23-Year Span and 40-Year Synthetic Work-Life Related to Mathematics Coursework
-121,288
150,586
821,547
22,791
873,635
Synthetic
Work-Life*
23 Years
ACCESS TO MATHEMATICS
349
350
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Calculating the portion of racial wage differentials attributed to mathematics coursework results in average yearly advantages for Whites between
$25 and $893 million (see column 2 in Table 4). Asians are advantaged
over Whites by $132 million. The cumulative 23-year advantage for Whites
is over $21 billion and the total across a 40-year work-life is over $37 billion.
Taken together, across a work-life for the 23 high school classes in this
analysis, $873 billion is invested in Whites over other racial groups through
mathematics coursework. Other considerations not included in this analysis such as raises, retirement accounts, home values, and interest would
seem to make these approximations all the more conservative.
DISCUSSION
From a racial justice standpoint, the earning differentials attributable to
mathematics education are appalling and could be worse with access to
better data. Possibly even more alarming is that for the most part, these
earning differentials have maintained or increased over the last 20-plus
years. These numbers lend support for the mathematics curriculum as a
racialized social system. Bonilla-Silva (1997) defines this as a social system
that places people in racial hierarchies economically, politically, and ideologically. Those at the top of the racial hierarchy receive economic compensation, better jobs, and higher social respect. Therefore, this analysis
supports the idea that the mathematics curriculum functions as a racialized
social system investing more in Whites than Blacks, Hispanics, and American
Indians. Mathematics coursework is associated with higher earnings, better
jobs, and social esteem based on who is mathematically able. Much like
previously discussed color-blind policies of housing and taxes, the mathematics curriculum espouses neutrality while racial stratification continues
in terms of mathematics coursework and potential earnings. One mechanism that might be producing these racial differences is mathematics use as
an unfixed gatekeeper while also reifying who is innately mathematical.
In deconstructing the supposed racial neutrality surrounding the mathematics curriculum (Martin, 2003), we can examine its gatekeeping force
with respect to access to universities and occupations. Moses and Cobb
(2001) termed access to mathematics as the next civil rights issue, citing its
position as a gatekeeper in society, and according to this analysis, they are
certainly right. Moses’s “Algebra Project” provides culturally appropriate,
community-based, high-quality mathematics instruction to students of
color giving students access to mathematics through improving public
schools. This push for more students of color to take mathematics is evident
in the data presented here. From 1982 through 2004, African Americans,
Latinos, and Native Americans completed significantly more mathematics
coursework. In fact, about 83% of African American high school students
completed Algebra 1 or higher in 2004, an increase that is likely connected
ACCESS TO MATHEMATICS
351
to the agency of communities of color in gaining more access to mathematics courses over a 23-year period. In invoking their agency, these marginalized groups have chosen to take advantage of the perceived instrumental
value of mathematics education. This is consistent with the growing body of
work documenting African American success in mathematics and viewing
mathematics access as a form of liberatory pedagogy (Berry, 2005; Martin,
2000, 2006a, 2006b; Moody, 2001; Stinson, 2008; Thompson & Lewis,
2005). However, taking mathematics courses alone will not solve the
problem of access to universities, living-wage jobs, and affordable housing
because all groups are taking more mathematics. So as math increases its
status as a gatekeeper, the gate itself is being raised.
To illustrate how the gate is being raised in mathematics, I examine the
case of AP courses and their link to universities over the last 2 decades.
Oakes and colleagues (2000) noted the disparity of access to AP math in
suburban and urban schools in the 1990s. As universities began valuing AP
courses more, the disparity began to diminish as more urban schools
provided access to AP mathematics coursework (Oakes et al., 2003). In
recent years, however, there has been a devaluing of AP courses in the
media and society. With the widespread adoption of AP courses in mathematics came criticism about these courses, largely focused on concerns
about teaching to the test, lacking depth, and not being college caliber (see
Wallis & Miranda, 2004). As students of color got access to AP courses, elite
high schools began dropping the coursework, offering their own courses
billed as being more rigorous (Schneider, 2008). This has facilitated a
devaluing of AP mathematics courses at the university level such that
Harvard no longer rewards grades in AP mathematics coursework and will
only count a score of 5 on the AP calculus exam. From valuing AP courses
when they are exclusive, to devaluing them once students of color gain
access, to the subsequent dropping of the AP course framework, recent
history speaks to the continual repositioning of the mathematical gate to
maintain elite access to college institutions.
Shifting the notion of the mathematics curriculum from a gatekeeper
determining who is qualified to an unfixed gatekeeper would mean that it
could be seen as a racial sorting mechanism. Students across racial groups
took more mathematics from 1982 through 2004; however, as discussed
earlier, the AP gate was shifting at the same time. What this means is that if
universities select mathematics’ elite, they will still disproportionally select
Whites and Asians. Therefore, access to the curriculum of mathematics
alone will not give students access to equitable power and wealth. Consistent with this, Rose and Betts (2001) found that one-half to three-quarters
of income differences attributable to mathematics coursework functioned
through educational attainment and college major. Even as a person of
color advances in mathematics, achieving more earning potential, mathematics coursework still continued to feed the mathematical elite to universities and jobs. Rather than mathematics serving as a marker of sufficient
352
DAN BATTEY
academic attainment, it is a stratifying system. I anticipate that similar
systems to AP will be erected to maintain differential access to top universities and higher-paying jobs, reproducing material racism through
mathematics acting as an unfixed gatekeeper.
Some might cite the advantage Asians have over Whites as proof that the
mathematics curriculum is not racialized. However, the racial positioning
of Asian American success in mathematics is complex. Prior work notes that
the model minority myth is invoked when society wants to compare good
and bad minorities (Bonilla-Silva, 2001). The positioning of Asians as
mathematically successful is often more about framing African Americans,
Latinos, and Native Americans as mathematically incapable. What this
ignores is the history of Asians being excluded from union membership
and their limited access to noneducational endeavors during the technological advancements made post World War II and the resulting need for
educated professionals (Sue & Okazaki, 1990). Subsequently the honorary
White status afforded to Asians during the civil rights movement was meant
to position African American dissent against a “successful” minority group
(Mura, 1996). The successful minority myth is then used to dispel notions
that racism is a factor for other groups (Bonilla-Silva, 2001, 2003).
However, this positioning is disingenuous when considering Asian subgroups such as the Hmong, Vietnamese, Filipino, and Laotians that are not
served well in the workforce or by educational institutions (Martin, 2009).
The consequence in mathematics education of the positioning of Asian
students as “models” is to frame them as a group that is culturally and
biologically predisposed to mathematical success. The corollary being that
African American, Latino, and Native American students are culturally and
biologically deficient with respect to mathematics. The positioning of
Asians and Whites at the top of a biological hierarchy in mathematics
furthers the case that it is being used as a sorting mechanism to stratify
society through symbolic racism. The mathematics curriculum is then a
system that supposedly filters the most innately intelligent students, meanwhile legitimating a racial ideology of who is more intelligent, can access
elite universities, and deserves high-paying jobs. As the mathematics curriculum becomes increasingly implicated in material racism through its use
as an unfixed gatekeeper, it also serves to reify symbolic racism in terms of
mathematics aptitude. This is not to say that students of color should not
take more mathematics, just that this needs to be coupled with challenges
to material and symbolic racism through challenging notions of who is
mathematically capable and examining whether the gatekeeping function
of mathematics is being used for or against racial justice.
Conclusion
Critiquing whiteness and color-blind ideologies in the mathematics curriculum reframes the struggle that Latinos, African Americans, and Native
ACCESS TO MATHEMATICS
353
Americans face when pursuing mathematics. This color-conscious framing
moves us out of thinking about deficits and failures toward the struggle to
be educated (Martin, 2000). There are institutional reasons that students
of color are not increasing their course-taking in mathematics at a higher
rate. From counselor recommendations, to teacher beliefs, to tracking,
and the lack of rigorous mathematics courses being offered, educators can
examine student opportunity in mathematics within a racialized social
system, examining the potential of different movements to progress toward
or regress from racial justice. Additionally, this framing can help educators
envision points of convergence with policies in mathematics education.
This requires a critical framing that examines efforts through the lenses of
interest convergence and divergence.
Building on Bell’s (1979) work, Lamos (2011) discussed the notion of
interest convergence and divergence with respect to college writing programs. Interest convergence theorizes that those whom racial stratification
serves, those who hold the power, dictate progress on racial issues. Therefore, Lamos’s construct of interest divergence references racial issues
where the interests of those in power halt or reverse momentum for racial
justice. Using this framework, Lamos argued to move forward racially, we
must be strategic about finding or creating areas of convergence.
One example of using interest convergence in mathematics education
is the recent push by mathematics professors to teach calculus at the
university level (Posamentier, 2007). The Mathematical Association of
America and the National Council of Teachers of Mathematics (2012)
came out with a joint statement that high school should not be about
getting students through calculus. This movement away from squeezing
more mathematics into K–12 education could potentially support removal
of calculus from the high school curriculum. This would remove the AP
credit for everyone, lowering the unfixed gate. A second example of convergence is international mathematics comparisons. While many view the
mathematics curriculum from an economic perspective in terms of competitiveness in the global market, we obviously have not invested enough
in African Americans, Latinos, and Native Americans. Prendergast (2003)
argued that current practice is to give standards rather than actual
property to ameliorate racial injustice in education. This is currently
in practice with the Common Core State Standards in the United States.
Achievement tests are used in this argument to monitor success in reducing racial gaps as if the tests themselves will impel social movement rather
than reify existing ideologies about racial inferiority (Prendergast, 2003).
Convergence can be found in uniting with the economic concerns by
investing property in communities not served well mathematically to
compete in the global market. This would take the form of giving more
resources, including providing more money, high-quality teachers and
teacher support, curricula, and technology to schools with high populations of students of color to support continued growth in mathematics.
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DAN BATTEY
The convergence would be a strategic area to shift property to invest in
communities of color.
Both of these areas of convergence need to be coupled with a focus on
the institutional constraints that restrict access for students of color. Tracking is the most common mechanism cited as restricting access to mathematics, but the literature is barren with respect to other mechanisms. A
concerted effort needs to be made to research and document the ways in
which opportunities are racially stratified, studying mechanisms that contribute to differential access and gaps. The goal of this program of scholarship would be to shift the national discourse away from discussing
outcomes of a racialized social system (e.g., gaps) separate from mechanisms that influence those outcomes. Future research on achievement
differences should not be published without also noting mechanisms that
contributed to those differences. The goal of these efforts is to break the
symbolic racism as to who is mathematically able and therefore teachable.
By taking this perspective, hopefully educators can continue to work toward
racial justice in mathematics education.
ACKNOWLEDGMENT
The author would like to thank Jessica Hunsdon and Nora Hyland for their
extensive and thoughtful feedback on this paper.
NOTES
1. The phrase “A Possessive Investment in Whiteness” is taken from George
Lipsitz’s (1995) seminal paper. Here I use it as a way to discuss mathematics
education’s role in perpetually advantaging whiteness.
2. Advanced Placement courses are classes taken in high school that when completed, students receive college credit. For example, in mathematics, courses
in AP Calculus and Statistics can receive college credit. There is also an AP
exam aligned with the classes that when passed, some universities recognize as
completion of college coursework.
3. Perlo (1996) calculates racial exploitation as wage differentials against people of
color multiplied by the number of employed workers. In this way, the difference
in wages between the average Latino worker and average White worker is the
exploitation of the Latino worker. Multiplying that differential across the population of workers would give the advantaging of the population of White workers
or alternatively the exploitation of the population of Latino workers.
4. While racial segregation was initially due to law (considered de jure segregation), racial segregation is now due to housing prices, loan practices, and neighborhood choices (considered de facto segregation). De facto segregation is not
by law, but this means that the current racial separation of schools is similar to
that of the 1960s in the United States.
ACCESS TO MATHEMATICS
355
5. Of course, issues such as SES, gender, and geographic location are important,
but for the purposes of this article on racial differences, and not having access to
the entire national data sets, these are not calculated here. This limits the
calculations shared in the article because intersections such as SES would
allow for a more nuanced consideration of how these constructs affect racial
differences rather than attributing differences solely to race.
6. The data sets cover a random sampling of the 3.6–4.5 million high school
students depending on the year. High School and Beyond collected data on
sophomores in 1980 and high school graduates in 1982. This is a longitudinal
study of a cohort of students from sophomore to senior year of high school and
continued studying the students long after high school until 1992. Similarly the
National Education Longitudinal Study of 1988 and the Education Longitudinal
Study of 2002 follow students from sophomore year in high school and beyond.
REFERENCES
Anhalt, C. O., Allexsaht-Snider, M., & Civil, M. (2002). Middle school mathematics
classrooms: A place for Latina parents’ involvement. Journal of Latinos and Education, 1(4), 255–262.
Autor, D. H., Katz, L. F., & Kearney, M. S. (2006). The polarization of the U.S. labor
market. American Economic Review, 96(2), 189–194.
Battin-Pearson, S., Newcomb, M. D., Abbott, R. D., Hill, K. G., Catalano, R. F., &
Hawkins, J. D. (2000). Predictors of early high school dropout: A test of five
theories. Journal of Educational Psychology, 92(3), 568–582.
Bell, D. A. (1979). Brown v. the Board of Education and the interest-convergence
dilemma. Harvard Law Review, 93, 518–533.
Berry, R. Q. (2005). Voices of success: Descriptive portraits of two successful AfricanAmerican male middle school students. Journal of African American Studies, 8(4),
46–62.
Bobo, L., & Hutchings, V. (1996). Perceptions of racial competition in a multiracial
setting. American Sociological Review, 61(6), 951–972.
Bobo, L., & Smith, R. A. (1994). Anti-poverty, affirmative action, and racial attitudes. In S. Danziger, G. Sandefur, & D. Weinberg (Eds.), Confronting poverty:
Prescriptions for change (pp. 365–395). Cambridge, MA: Harvard University Press.
Bonilla-Silva, E. (1997). Rethinking racism: Toward a structural interpretation.
American Sociological Review, 62, 465–480.
Bonilla-Silva, E. (2001). White supremacy and racism in the post-civil rights era. Boulder,
CO: Lynne Rienner.
Bonilla-Silva, E. (2003). Racism without racists: Color-blind racism and the persistence of
racial inequality in the United States. Lanham, MD: Rowman & Littlefield.
Bonilla-Silva, E., & Forman, T. (2000). “I am not a racist, but . . .”: Mapping White
college students’ racial ideology in the USA. Discourse and Society, 11, 50–85.
Brewley-Kennedy, D. (2005). The struggles of incorporating equity into practice in
a university mathematics methods course. The Mathematics Educator, 1, 16–28.
Campen, J. (1991, January–February). Lending insights: Hard proof that banks
discriminate. Dollars and Sense, 191.
Carmines, E. G., & Merriman, W. R. (1993). The changing American dilemma:
Liberal values and racial policies. In P. M. Snideman, P. E. Tetlock, & E. G.
Carmines (Eds.), Prejudice, politics, and the American dilemma (pp. 237–255). Stanford, CA: Stanford University Press.
Chapman, C., Laird, J., Ifill, N., & KewalRamani, A. (2011). Trends in high school
dropout and completion rates in the United States: 1972–2009 (NCES 2012-006). U.S.
356
DAN BATTEY
Department of Education. Washington, DC: National Center for Education
Statistics. Retrieved December 12, 2011, from http://nces.ed.gov/pubsearch
Cicourel, A. V., & Kitsuse, J. I. (1963). Educational decision makers. Indianapolis, IN:
Bobbs-Merrill.
Civil, M., & Bernier, E. (2006). Exploring images of parental participation in
mathematics education: Challenges and possibilities. Mathematical Thinking and
Learning, 8(3), 309–330.
Conley, D. (1999). Being Black, living in the red: Race, wealth, and social policy in
America. Berkeley: University of California Press.
Day, J. C., & Newburger, E. C. (2002). The big payoff: Educational attainment and
synthetic estimates of work-life earnings. Washington, DC: U.S. Census Bureau.
DiMaggio, P. (1982). Cultural capital and school success. American Sociological
Review, 47, 189–201.
Diversity in Mathematics Education Center for Learning and Teaching (DiME).
(2007). Culture, race, power, and mathematics education. In F. Lester (Ed.), The
second handbook of research on mathematics teaching and learning (pp. 405–433).
Charlotte, NC: Information Age.
Dyson, M. E. (2000). I may not get there with you: The true Martin Luther King Jr. New
York: The Free Press.
Ekstrom, R. B., Goertz, M. E., Pollack, J. M., & Rock, D. A. (1986). Who drops out
of high school and why? Findings from a national study. Teachers College Record,
87(3), 356–373.
Erickson, F., & Schultz, J. (1982). The counselor as gatekeeper. New York: Academic
Press.
Fairclough, A. (2007). A class of their own: Black teachers in the segregated South.
Cambridge, MA: Belknap Press of Harvard University Press.
Fleischman, H. L., Hopstock, P. J., Pelczar, M. P., & Shelley, B. E. (2010). Highlights
from PISA 2009: Performance of U.S. 15-year-old students in reading, mathematics, and
science literacy in an international context (NCES 2011-004). Washington, DC: U.S.
Department of Education, National Center for Education Statistics.
Foley, N. (2002). Mexican Americans and whiteness. In P. Rothenberg (Ed.), White
privilege: Essential readings on the other side of racism (pp. 49–59). New York: Worth.
Frankenberg, E., Lee, C., & Orfield, G. (2003). A multiracial society with segregated
schools: Are we losing the dream? Cambridge, MA: The Civil Rights Project.
Gutiérrez, R. (1996). Practices, beliefs, and cultures of high school mathematics
departments: Understanding their influence on student advancement. Journal of
Curriculum Studies, 28, 495–529.
Gutiérrez, R. (1999). Advancing urban Latina/o youth in mathematics: Lessons
from an effective high school mathematics department. Urban Review, 31(3),
263–281.
Gutiérrez, R. (2000). Advancing African American, urban youth in mathematics:
Unpacking the success of one mathematics department. American Journal of
Education, 109(1), 63–111.
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.
Gutstein, E. (2005). Reading and writing the world with mathematics: Toward a pedagogy
for social justice. London: Routledge.
Gutstein, E. (2006). “The real world as we have seen it”: Latino/a parents’ voices on
teaching mathematics for social justice. Mathematical Thinking and Learning, 8(3),
331–358.
Haney-Lopez, I. (2006). White by law: The legal construction of race. New York:
New York University Press.
ACCESS TO MATHEMATICS
357
Hobson v. Hansen, 265 F. Supp. 902 (D.D.C., 1967).
Jackman, M. (1994). Velvet glove: Paternalism and conflict in gender, class, and race
relations. Berkeley: University of California Press.
Kivel, P. (2002). Uprooting racism: How White people can work for racial justice. Gabriola
Island, BC: New Society.
Kozol, J. (1991). Savage inequalities: Children in America’s schools. New York: Harper
Perennial.
Ladson Billings, G., & Tate, W. F. (1995). Toward a critical theory of education.
Teachers College Record, 97, 47–68.
Lamos, S. (2011). Interests and opportunities: Race, racism, and university writing instruction in the post-civil rights era. Pittsburgh, PA: University of Pittsburgh Press.
Lee, V. E., & Burkam, D. T. (2003). Dropping out of high school: The role of
school organization and structure. American Educational Research Journal, 40(2),
353–393.
Lewis, A. E. (2004). “What group?” Studying Whites and whiteness in the era of
“color-blindness.” Sociological Theory, 22(4), 623–646.
Lipsitz, G. (1995). The possessive investment in whiteness: Racialized social democracy and the “White” problem in American studies. American Quarterly, 47(3),
369–387.
Lipsitz, G. (1998). The possessive investment in whiteness: How White people profit from
identity politics. Philadelphia, PA: Temple University Press.
Logan, J. R., & Molotch, H. (1987). Urban fortunes: The political economy of place.
Berkeley: University of California Press.
Martin, D. B. (2000). Mathematics success and failure among African American youth: The
roles of sociohistorical context, community forces, school influence, and individual agency.
Mahwah, NJ: Erlbaum.
Martin, D. B. (2003). Hidden assumptions and unaddressed questions in mathematics for all rhetoric. The Mathematics Educator, 13(2), 7–21.
Martin, D. B. (2006a). Mathematics learning and participation as racialized forms of
experience: African American parents speak on the struggle for mathematics
literacy. Mathematical Thinking and Learning, 8(3), 197–229.
Martin, D. B. (2006b). Mathematics learning and participation in African American
context: The co-construction of identity in two intersecting realms of experience. In N. Nasir & P. Cobb (Eds.), Diversity, equity, and access to mathematical ideas
(pp. 146–158). New York: Teachers College Press.
Martin, D. B. (2009). Researching race in mathematics education. Teachers College
Record, 111(2), 295–338.
Massey, D. S. (1996). American apartheid: Segregation and the making of the
underclass. American Journal of Sociology, 96(2), 329–357.
Mathematical Association of American and the National Council of Teachers of
Mathematics. (2012, April 3). Calculus: A joint position statement of the Mathematical
Association of America and the National Council of Teachers of Mathematics. Retrieved
April 13, 2012, from http://www.maa.org/news/2012_maanctm.html
Moody, V. (2001). The social constructs of the mathematical experiences of
African-American students. In B. Atweh, H. Forgasz, & B. Nebres (Eds.), Sociocultural research on mathematics education (pp. 255–278). Mahwah, NJ: Erlbaum.
Morrison, T. (1993). On the backs of Blacks. Time, 142(21), 57.
Moses, R. P., & Cobb, C. E. (2001). Radical equations: Civil rights from Mississippi to the
Algebra Project. Boston: Beacon.
Mura, D. (1996, May 17). Re-examining Japanese Americans: From honorary
Whites to model minorities. Asian Week, 17(38), 7.
Noguera, P. A. (2004). Racial isolation, poverty, and the limits of local control in
Oakland. Teachers College Record, 106(11), 2146–2170.
358
DAN BATTEY
Oakes, J. (1985). Keeping track: How schools structure inequality. New Haven, CT: Yale
University Press.
Oakes, J. (1990). Opportunities, achievement, and choice: Women and minority
students in science and mathematics. In C. Cazden (Ed.), Review of research
in education (pp. 153–222). Washington, DC: American Educational Research
Association.
Oakes, J., Joseph, R., & Muir, K. (2003). Access and achievement in mathematics
and science: Inequalities that endure and change. In J. Banks & C. Banks (Eds.),
Handbook of research in multicultural education (2nd ed., pp. 69–90). San Francisco:
Jossey-Bass.
Oakes, J., Rogers, J., McDonough, P., Solorzano, D., Mehan, H., & Noguera, P.
(2000). Remedying unequal opportunities for successful participation in Advanced Placement courses in California high schools. Unpublished report, ACLU of Southern
California, Los Angeles, CA.
Oliver, M. L., & Shapiro, T. M. (1997). Black wealth/White wealth. New York:
Routledge.
Ong, P., & Grigsby III, J. G. (1988). Race and life-cycle effects on home ownership
in Los Angeles, 1970 to 1980. Urban Affairs Quarterly, 23, 601–615.
Orfield, G., & Ashkinaze, C. (1991). The closing door: Conservative policy and Black
opportunity. Chicago: University of Chicago Press.
Orfield, G., Losen, D., Wald, J., & Swanson, C. (2004). Losing our future: How minority
youth are being left behind by the graduation rate crisis. Cambridge, MA: The Civil
Rights Project at Harvard University.
Paul, F. G. (2003, October). Re-tracking within algebra one: A structural sieve with
powerful effects for low-income, minority, and immigrant students. Paper presented at
the Harvard University of California Policy Conference, Sacramento, CA.
People Who Care v. Rockford Board of Education, 851 F. Supp. 905 (N.D.IL. 1994).
Perlo, V. (1996). Economics of racism II: The roots of inequality. New York: International
Publishers.
Perry, T. (1993). Toward a theory of African American achievement (Report No. 16).
Boston: Center on Families, Communities, Schools, and Children.
Posamentier, A. (2007, September 9). AP math class should be dropped. Newsday.
Retrieved April 13, 2011, from http://www.newsday.com/opinion/ap-mathclass-should-be-dropped-1.688830
Prendergast, C. (2003). Literacy and racial justice: The politics of learning after Brown v.
Board of Education. Carbondale: Southern Illinois University Press.
Reed, R. J., & Oppong, N. (2005). Looking critically at teachers’ attention to equity
in their classrooms. The Mathematics Educator, 1, 2–15.
Roediger, D. R. (2002). Colored White: Transcending the racial past. Berkeley: University of California Press.
Rose, H., & Betts, J. R. (2001). Math matters: The links between high school curriculum, college graduation, and earnings. San Francisco: Public Policy Institute of
California.
Rosenbaum, J. (1976). Making inequality. New York: Wiley Interscience.
Schneider, J. (2008, May 28). Schools’ unrest over the AP test: Elite schools are
dropping it, striking a blow to public education. The Christian Science Monitor.
Retrieved March 23, 2012, from http://www.csmonitor.com/Commentary/
Opinion/2008/0528/p09s01-coop.html
Sewell, W. H. (1992). A theory of structure: Duality, agency, and transformation.
American Journal of Sociology, 98, 1–29.
Stinson, D. W. (2008). Negotiating sociocultural discourses: The counterstorytelling of academically (and mathematically) successful African American
male students. American Educational Research Journal, 45(4), 975–1010.
ACCESS TO MATHEMATICS
359
Sue, S., & Okazaki, S. (1990). Asian-American educational experience. American
Psychologist, 45, 913–920.
Tate, W., & Rousseau, C. (2002). Access and opportunity: The political and social
context of mathematics education. In L. English (Ed.), Handbook of international
research in mathematics education (pp. 271–299). Mahwah, NJ: Erlbaum.
Thompson, L., & Lewis, B. (2005). Shooting for the stars: A case study of the
mathematics achievement and career attainment of an African American male
high school student. High School Journal, 88(4), 6–18.
Walker, V. S. (1996). Their highest potential: An African American school community in the
segregated South. Chapel Hill: University of North Carolina Press.
Wallis, C., & Miranda, C. A. (2004, November 1). How smart is AP? Time, 1–3.
Wynn, N. A. (1976). The Afro-American and the second world war. New York: Holmes &
Meier.
Zuckoff, M. (1992, October 9). Study shows racial bias in lending. Boston Globe,
pp. 77–78.