Mathematics, critical literacy, and youth participatory action research

Mathematics learning can be transformed andenhanced through youth research.

6Mathematics, critical literacy, andyouth participatory action research

K. Wayne Yang

currently there is no constitutional guarantee for quality educa-tion in the United States. No Child Left Behind leaves definitionsof quality and equity to individual states, and the resulting statelaws tend to provide only minimal elementary-level schooling orminimal standards for resources.1 Thus, the federal governmentdefers responsibilities for any educational outcomes or standardsin resources for schooling, and this facilitates the devolution ofaccountability from federal to state government, then to localboards, then individual schools, and ultimately to individual class-room teachers. One such tool of devolution is California’s SchoolAccountability Report Card (SARC), which provides that everyschool must provide a public document that evaluates its facilities,programs, instruction, student achievement, and so forth. In prin-ciple, the SARC is meant to keep schools accountable. In practice,because schools produce these reports themselves, the SARC is adevice of self-promotion. Youth and families are caught betweenthe callousness of an unaccountable state and the defensiveness ofinadequate schools.

99NEW DIRECTIONS FOR YOUTH DEVELOPMENT, NO. 123, FALL 2009 © WILEY PERIODICALS, INC.Published online in Wiley InterScience (www.interscience.wiley.com) • DOI: 10.1002/yd.317

This article presents a youth-conducted school accountabilityreport card wherein students researched and evaluated all aspects oftheir urban high school in Oakland, California. No Child LeftBehind has produced a policy environment with no one left respon-sible for the “savage inequalities” between affluent schools and thosein poor communities of color.2 These youth researchers, then, exer-cised their only recourse, which is to repossess the SARC. In poorcommunities, the property of buyers who default on promised pay-ments is repossessed. Here, the state has defaulted on its promise ofadequate education, and the youth have repossessed the master’stools and schools to hold themselves, their teachers, and the stateaccountable. Youth assessed all aspects of school life through mul-tiple methodologies, including field notes, videotaping classrooms,interviews of students and staff, and surveys of staff, teachers, par-ents, and students. The youth created several culminating researchproducts: statistical reports, a written SARC, documentary films, aWeb site, and community presentations. This article highlights therole of mathematics in this endeavor.

Theoretical frameworkWhen Freire and his colleagues first convened literacy circles inRecife, Brazil, adult literacy learners began with the interrogationof texts as a means to produce meaning about the world. Thesetexts were illustrations of familiar settings in the Brazilian camponêsexperience, such as a pictorial scene of a farm with men and womenworkers, a landlord, and crops. Thus, discussions built from thecamponês’ funds of knowledge to unlock generative themes latent insociety.3 The first literate act was to learn and produce codes withwhich to speak these latent themes; these codes are “a complex ofideas, concepts, hopes, doubts, values, and challenges” that consti-tute a larger critical framework about the world.4 Freire did notimmediately provide men and women with pen and paper andsolicit descriptions of the world. Rather, reading of text precededwriting.

100 YOUTH IN PARTICIPATORY ACTION RESEARCH

new directions for youth development • DOI: 10.1002/yd

Our youth participatory action research (PAR) project followeda similar two-phase process: intensive reading of texts, followed byintensive production of original texts. The first phase was heavilyteacher centered and the second youth centered. In this way, ourapproach differs from those that create a youth-centered space atthe outset, based on abstract ideals of democratic participation.5

This pedagogical approach is developmentally appropriate foryouth, as compared to adult literacy learners, and for a media-richworld of print, visual, and digital texts.

I describe these two phases of critical pedagogy as critical con-sumption and critical production of texts. In critical discourse analy-sis, consumption and production (followed by distribution)comprise the cycle for textual practices.6 Consumption, or reading,is a nonneutral activity, subject to unequal power relationships inthe creation and interpretation of texts. Critical consumption, then,is reading for codes about society and the power inequalities behindrepresentations. The youth in our program call this the differencebetween “overstanding” and “understanding,” a common distinc-tion made by hip-hop poets.7 This reading of worldviews is alwaysslightly ahead in phase of writing in an effective critical pedagogyproject.

Youth PAR is threatened by two fallacies: the fallacy of idealizeddemocracy and the fallacy of predetermined criticism. Ideal-ized democracy reifies the student-centered dogma that somehowdemocratic participation equals effective pedagogy.8 The art ofteaching is not to produce a world without teachers, but to distin-guish between authority and authoritarianism in knowledge pro-duction.9 Predetermined criticism, by contrast, occurs whenpedagogical exercises merely reproduce the critical worldviews heldby the teacher. If the teacher’s worldviews are acceptable to youth,this process appears harmless, even liberating, and can be confusedwith a Freirian approach, but it amounts to a form of epistemo-logical benevolent dictatorship. Ideologies are affirmed, and no newideas are constructed.

In mathematics, the fallacy of predetermined criticism is thegreater of the two threats. Social justice teaching in mathematics

101MATHEMATICS, CRITICAL LITERACY, AND YOUTH PAR


often forefronts quantitative inquiries into social inequalities. Thiskind of “reading and writing the world with mathematics” can bea powerful tool in describing injustice.10 An increasing number oflessons, carefully constructed by experienced educators, havebecome available through Internet sharing.11 Typically lessons offerstatistical analysis of some social disparity, such as racial profilingin discretionary police automobile stops, followed by generativediscussions of social inequalities.12 The connections to academicstandards are often meticulously explored. However, mathematicseducation has not realized its full potential in developing youthresearchers capable of producing critical texts at the level of pub-lic intellectuals.

Equipped with rigorous literacies, youth researchers can reposi-tion themselves as “organic intellectuals,” or specialized, powerfulpolitical actors with wide influence not only within formal politicsbut also within the broader realm of common sense.13 Organicintellectuals are constructed when subaltern voice transforms intoauthoritative voice within the political arena.14 Unlike subalternvoice, which is largely voiceless within mainstream institutions andcivil society, authoritative voice is by definition influential amongnonsubaltern groups.15 This is a crucial distinction between othertheorizations of youth voice, which often either celebrate16 orlament17 the forms of youth agency that operate below the currentof mainstream society.

Youth knowledge production, rather than their reproduction ofcritique, is far more developed outside the field of mathematics.Ernest Morrell’s work delineates three skills needed in youthresearch: critical literacy, academic literacy, and new media literacy.18

Critical literacy refers to youth analysis of social structures in thereproduction of inequality, as well as metacognitive proficiency inthe “codes of power.”19 Traditional literacy refers to academic read-ing and writing. New media literacy underscores the rigorous pro-duction of new media texts, such as film, Internet blogs, and digitaltexts, rather than their simple consumption. That is, although youthmay come with extensive funds of knowledge in new media, rigor-ous training develops their skills in manipulating media. According



to Morrell, these combinations of literacies comprise a holistic setof skills for youth liberatory practice. Morrell provides a theory ofliteracy that can inform youth PAR in mathematics.

Project background, participants, and methodsThis article describes the mathematics component of a multiyearyouth PAR project. Specifically, I focus on the math texts con-sumed and produced by youth rather than the actual results of theyouth SARC. The youth researchers were trained as part of a soci-ology course taught by university professors, as well as a mathe-matics class designed as an intervention to both remediate gaps inmath preparation and accelerate students into higher-order mathliteracy.

Approximately thirty high school youth participated in threeyears of critical research, beginning as sophomores and continuingthrough the end of their senior year. They enrolled in formal classesin sociology, mathematics, and English through which they weretrained in research methods and textual analysis. The classes were cotaught by two university professors who raised all theresources for the project. Each year the youth engaged in a differ-ent culminating PAR project. In year 1, they researched social issuesin their East Oakland neighborhoods, a project called “Doc YourBlock.” In year 2, they evaluated their high school: the youth SARC.In year 3, they researched human rights issues as manifested glob-ally and locally. This article examines the pedagogy of the mathe-matics course work and corresponding SARC project in year 2.

First, youth analyzed and critiqued the SARC, a formulaic toolused by all California schools as required by the state. Youth col-lected SARCs from schools of diverse socioeconomic communities,including their own, and examined their format and content, theircontributions and inadequacies. To inform their critique, studentsalso conducted a literature review in the sociology of education.The literature review and SARC critique took five months andwere also informed by their prior year’s study.



Second, youth designed their own SARC process, which involveda comprehensive mixed-methods approach. In research teams, theyaddressed different areas of focus in schooling, and conducted inter-views, surveys, classroom observations, videotaping, and artifact col-lection. They also conducted a few pilot studies, surveys, interviews,and observations, and presented their SARC design in a publicforum for critical feedback before continuing. Finally, they spentthe remaining five months in fieldwork and analysis. During thistime, each research team was divided into several specialists whowere trained in SPSS statistics, Dreamweaver Web design, and FinalCut Pro film editing software. The youth presented their work in aculminating public forum of parents, teachers, students, and com-munity members. The following year, they presented again at various national research conferences. The final SARC productsincluded a Web site where the public could access evaluations of individual teachers, classes, or areas of focus; several short docu-mentary films exploring each area of focus; statistical and writtenreports; and elaborate audiovisual presentations.

Socially engaged research requires university co-researchers to fully commit to the struggles of the community. Our responsi-bility was to provide resources as needed, including tutors, com-puting equipment, video cameras, travel expenses to national conferences, and books.

The project was based at East Oakland Community HighSchool, a three-year-old public (noncharter) school that wasfounded by the students and their families in this research project.In a traumatic turn of events, the state-controlled school districtclosed the school after its second year, despite massive communityoutcry and support from a majority of the locally elected schoolboard. Among the state’s justifications were low test scores fromthe previous year, although, ironically, the closure decision came afew months before the school showed the largest test score gainsof any other high school in the San Francisco Bay Area. The schoolclosure will not be the topic of this article; however, it sets a dra-matic context for the SARC project.



East Oakland is an urban community suffering the consequencesof economic and educational divestment. Nearly 80 percent ofincoming high school freshmen do not graduate, and only 6 per-cent were eligible to apply for college in 2003—fewer than onehundred out of an entering class of sixteen hundred students in anygiven year across all comprehensive high schools in the area.20 Notsurprisingly, this high school’s demographics reflected the “reseg-regation” of U.S. schools.21 Over 70 percent of the students quali-fied for free and reduced-price lunch; approximately 65 percentwere Latino/a, and 35 percent were African American.

Our youth researchers were thirty high school juniors: thirteenAfrican American (eight girls and six boys) and sixteen Latina/o(ten girls and six boys). The class was detracked, although given theschool’s academic achievement context, the overwhelming major-ity of the students in the class would be considered low achieversby traditional academic measures. The students were selected inpart at random and in part to represent the academic margins ofthe school. In fact, special attention was made to recruit studentswho were the most disinvested in their schooling, with the theorythat they would tend to have the strongest critique of schoolinginequality and be among the strongest contributors.

In the prior year, after a series of substitute and unqualified mathteachers, 79 percent of these students scored far below basic and19 percent below basic on state exams in mathematics. As a result,any pedagogical project in mathematics would need to simultane-ously remediate gaps in student learning, while accelerating theiracquisition of higher-order math skills.

Use of texts in mathematicsMany math classes are characterized by a single text: the textbook.In teaching critical mathematics literacy, we have to expand ourrange of allowable texts and how students use them. This PAR proj-ect had two textual phases: the students’ consumption, or reading



of texts, followed by their production of youth-authored mathemat-ical texts.

Critical consumption of texts

In designing this project, the first question was what math texts touse. We began by identifying generative themes. In sociology, thesethemes were readily apparent because of the social analysis embed-ded in the curriculum. In mathematics, this was a bit more difficult.If we had simply thought in terms of “political math,” we mighthave just assumed these themes to be incarceration, violence, insti-tutional racism, and police brutality, for example. However, if peo-ple are to pursue their “ontological and historical vocation to bemore fully human,”22 then from this perspective, the humanity ofthe East Oakland youth cannot be reduced to these neo-Marxistconcerns. Students’ relationship to mathematics as a schooled sub-ject, and through mathematics to the world, was indeed “a complexof ideas, concepts, hopes, doubts, values, and challenges.”23 Somegenerative themes of greatest concern were their identities asraced-classed-gendered math learners, the absence or presence ofculture and history in math, the oppressive nature of institutionalmathematics, the applicability of math to social justice, problem-solving methodologies, theories of numbers and numerology, andthe epistemology of mathematics. Therefore, we searched for textsthat corresponded to these themes, as summarized in Table 6.1.

Students received the print texts in a university reader format.In addition, they were assigned precalculus and geometry text-books, SAT and trigonometry drill books, and three pages of ref-erence material to be memorized that covered topics fromarithmetic to trigonometry.

The second design question was how to implement these texts.In Freire’s adult literacy work, group discussions took place in “cul-ture circles” around a pictorial text. In the Cuban literacy cam-paign, for example, the pedagogical interface was often a singlestudent and tutor, and they used a literacy primer comprisinglessons of political relevance to campesinos, such as land reform.31

In sociology, we often paired a film, such as Bus 174, with academic



literature with similar generative themes, such as Bourdieu’s “Struc-ture, Habitus, Practices.”32 Because films in mathematics were farless available, we created multimedia presentations to correspondto readings. These were delivered in a modified Socratic lectureformat with teacher-initiated questions and student responses.

Students also engaged these math texts through writing and talk-ing assignments. Youth wrote a “math autobiography” in responseto the film Stand and Deliver. After reading “The Numbers ofAncient Egypt” and “The Amazing Achievements of the Maya,” andanalyzing Pythagoras and Irrational Numbers in comparison to TupacConspiracy Theories, each student selected a unique number toresearch and kept journals of relevant number theories, culminatingin a PowerPoint presentation. After discussing “Mathematics andEngineering in the Nile Valley,” students selected a unique trigono-metric application to analyze and teach. After reading Harper’s Index,they combed the local newspaper for data to create their own EastOakland Index. Each student also selected a math mentee: a sibling,elder, neighbor, friend, or peer with whom they would discuss math-ematics outside of school.



Table 6.1. Sample mathematics texts, medium, and generativethemesTexts Medium Generative Themes

“Mathematics and Engineering Print and Identity, history, problemin the Nile Valley”24 audiovisual solving

Pythagoras and Irrational Audiovisual Numerology, epistemology, Numbers25 number theory

Tupac Conspiracy Theories Audiovisual Identity, culture, numerologyStand and Deliver26 Film Identity, racism, institutional

mathematicsHarper’s Index27 Print Social justice, cultureThe Ishango Bone Audiovisual History, identityExcerpts from Euclid’s Print Geometric postulates, Elements28 philosophy, history

“The Numbers of Ancient Print Number theory, history, Egypt”29 culture, identity

“The Amazing Achievements Print Number theory, history, of the Maya”30 culture, identity

These mathematical discussions generated a diverse complex ofideas, analyses, values, and memories of personal experiences—athematic math universe. Through this critical consumption of text,students began to articulate their understanding of quality mathe-matics education and its relationship to social justice—essential forthe sophistication with which youth conducted their SARCresearch.

Critical production of texts

An intermediary step between critical consumption of texts andparticipatory action research (PAR) was the production of texts:print, graphical, multimedia, and oratorical student-authored mate-rials. We used highly structured projects to developed specific lit-eracies: data analysis, multimedia representation of data, and publicpresentation. For example, each student chose a trigonometricapplication from the textbook, analyzed it, created a PowerPointpresentation for it, and then taught it in a formal public lecture.

Monique, an African American girl with stronger academic skillsin mathematics, had disproportionately underdeveloped public pre-sentation skills. She selected an application that modeled the rev-enue trends of an outerwear manufacturer as a function of time,using trigonometric functions. Figures 6.1 and 6.2 are reproduc-tions of slides from her presentation.

In order to create this trigonometric model, Monique had tolearn Microsoft Excel as a new media tool for plotting actual datapoints (Figure 6.1) and for generating hypothetical data points froma trigonometric function (Figure 6.2). Her digital slides were highlyrated by peers, parents, and teachers. However, her public speak-ing skills were less developed; with head bowed, she would readquietly and rapidly from her notes.

The explicit standard for student presentations was that of a pub-lic intellectual speaking before a hypothetically hostile audience,such as cynical school district officials, policymakers, andresearchers. Students were trained to endure challenging questionsand to give incisive criticism to one another. As a general practice,





Figure 6.1. Revenue over time (actual)

Figure 6.2. Trigonometric model of revenue over time

they debated, interrogated, and challenged each other’s statementsin class discussions. Often they would stand before the entire classand defend a prepared position, and then receive critical feedbackon their presentation skills. Through this training, Moniquelearned to make eye contact with the audience, speak at a measuredrate, and interweave humor into her presentations. Eventually shewent on to present at a national conference on mathematics andsocial justice in New York City.

We followed three design principles for all of our math text pro-duction projects: each student must produce a unique text, eachproject demands rigorous forms of new media and academic liter-acy, and each is delivered in a public setting. These precursor exer-cises to action research conditioned the youths’ academic and newmedia literacies to a rigor befitting a public intellectual. They out-line our efforts at developmentally moving youth from consumersto producers of text.

As an important aside, we found improvements in traditionalacademic assessments as well. On the math SAT, students improvedan average of 34 points, ranging from 0 to 110 points. On statestandardized tests, 20 percent of students tested at grade level com-pared to none the year before, and 40 percent moved up at leastone level of proficiency. Seventy-five percent of students passedassessments of remediated topics, which included oral and writtenexams in math mnemonics. Although the progress was modest, therate of growth and concurrent transformation of youth academicidentities were significant. Students increasingly self-identified asmathematically talented learners. For example, two students pro-fessed that they aspired to become math teachers, a particularlydramatic change for one of them who had failed algebra in theninth grade. Through these structured research exercises, studentsbecame mathematical anthropologists, historians, philosophers, andanalysts through explorations of the cultural, historical, conceptual,and applied aspects of mathematics.

The production of critical texts in mathematics offered perfor-mance measures of academic literacy. Although these texts do not



assess problem-solving speed and precision, they illuminated criti-cal thinking, mathematical reasoning and method, and conceptualmastery.33 These academic literacies, along with new media liter-acy and critical code fluency, proved to instrumental in the youthSARC project.

Mathematics in youth PAR

Youth literate skills with math texts directly transferred to theSARC project, which demanded the production of highly sophis-ticated texts: written reports, statistical analyses, documentaryvideos, interactive Web sites, and public presentations of results.

The SARC project took place primarily in sociology class butrequired vast hours of work outside school. Toward its culmination,students worked intensively around the clock, editing video, creat-ing slides, writing reports, entering data from hundreds of surveys,and practicing their talks. Frequently these work sessions took placeat one of the professor’s homes, often past midnight.

Furthermore, youth were also compelled to learn new skillsalong the way. In these instances, their ability to confidently enteruncharted territory was made possible through the transference ofpreviously developed skills. For example, students had no priortraining in statistics. However, the SARC demanded (1) new aca-demic literacy in producing descriptive statistics, analyzing distri-butions, and comparing means; (2) new media literacy in SPSS(Statistical Package for the Social Sciences), a powerful professionalresearch software package; and (3) critical code fluency in inter-preting statistics with respect to the social world. Figures 6.3, 6.4,6.5, and 6.6 are reproductions of some slides from student presen-tations of their findings. These slides reveal both the students’ lit-eracy in statistical analysis and their ability to teach complicatedstatistical methods to a public audience.

These figures capture the sophisticated statistical analysis thatstudents learned informally along the way as part of the SARCproject. They could analyze the social significance between normaland nonnormal distributions, low and high standard deviations, and





Figure 6.3. Example of a normal distribution

Figure 6.4. Nonnormal distribution with low standard deviation

Note: I.o.E. is an abbreviation for Indicators of Excellence: Seven key indicators of effec-tive pedagogy developed by the students.



Figure 6.5. Possible outlier

Note: I.o.E. is an abbreviation for Indicators of Excellence: Seven key indicators of effec-tive pedagogy developed by the students.

Figure 6.6. Comparison of means (significance test)

skews and outliers (Figures 6.3, 6.4, and 6.5). For example, Figure6.5 shows that students overwhelmingly reported teacher Z to havestrong classroom discipline, but that the outlier distorted the meanor average response. With such sophisticated mathematical liter-acy, youth researchers could give useful interpretations of their dataas feedback to individual teachers.

Youth researchers used these quantitative indicators, triangulatedwith qualitative interviews and observations, with the goal of devel-oping analyses that would be useful to improving classroom prac-tices. They found that in general, the official school report cardstended to be overly quantitative—sharing reductionist test scores andbasic, underanalyzed demographic information—without practicalways for teachers to improve their practice. By contrast youthresearchers developed critical interpretative skills with respect to sta-tistical information. For example, they noticed differences betweenmale and female responses in a particular classroom, conducted a t-test of statistical significance (Figure 6.6), and then triangulatedthose data with observations and interviews of students from theclass. The resulting analysis provided specific feedback to the teacher.

Transforming mathematics educationAlthough at an immediate level, youth employed statistics in theirPAR project, mathematics was more than just a tool to critiquesocial inequalities. It was also a sociocultural activity through whichto examine complex codes of power, identity, and culture in humansociety. Thus, they developed critical theories of mathematics edu-cation itself that redefined the form, function, and agenda of mathin schools. They began to critically rewrite their educational worldand schooled identities.

As one of the students, Michael Navarro, prepared for a panel atthe Social Justice in Mathematics Conference in New York, hewrote: “Our cultures are misrepresented in the mainstream and ineducation. At our school, we learn where mathematics originated,



and how relatively easy the methods we learn are compared to howour ancestors had to struggle and work through the math.”

Michael was a young Latino, struggling to establish U.S. citi-zenship. His grade in the math class hovered near a B+, higher thanwhat he had attained in the past. By “the methods we learn,” he wasreferring to the development of algebra and its familiar textbooksteps in problem-solving algorithms, compared to the Kemeticmethods of aha calculus that required precise error estimations34

or the calculations of the Maya whose unparalleled astronomicalmeasurements were conducted without the benefit of fractions.35

His statements also reflected several layers of identity formationcommon in student writing: an identification with ancient Africanand Maya mathematicians, a view of self within mathematics edu-cation as a collective project, and an implicit identification of selfas a math learner with a hard work ethic.

Youth also articulated different social justice agendas in mathe-matics education. Although they were consistent in their critiqueof social inequality, their recommendations were quite diverse. ForMichael, it centered on the curricular connection of mathematicsto ancestry and heritage culture: “By learning about your ancestors,you are going back to your roots and figuring out what your cul-ture is, your religious habits, and the things that your culture usedto do before we were colonized. We need to learn about how weused to be and then critically analyze how we can apply that to ourdaily modern lives.”

For Monique, it was the pragmatics of self-determination. Shedescribed “three aspects of social justice in mathematics.” She termed“economic self-determination” as requiring an education to providetools for the financial well-being of the larger community, “repre-sentational self-determination” as providing the tools for people toshape their own identities, and educational self-determination as pro-viding an opportunity structure for the collective advancement ofoppressed people.

Thus, youth articulated critiques of math education withoutresorting to predetermined criticisms of simple liberal dogma.



These math projects served as problem-posing scenarios, throughwhich multiple articulations of social justice could emerge.

Mathematics in youth PAR has been underexplored and is oftenreduced to the practice of making statistically based statementsabout injustice. But mathematics can be more than a tool of advo-cacy. It can lead to increased skills across literate domains. It canalso be a condensing point for a social justice movement in educa-tion by posing the question of what quality education in mathe-matics should be. A just mathematics education does more thanengage the external world of justice in housing, shelter, criminal-ity, and other aspects of human rights; it creates an internal worldof humane intellectual activity, characterized by rigor in mathe-matical theory and problem-solving methodologies, a philosophicaland historical foundation that forefronts the ancestral and con-temporary mathematical ponderings of oppressed people, and thedisciplined development of literate skills that can be criticallyapplied to the real world.

Notes1. Liu, G. (2006). Education, equality, and national citizenship. The Yale

Law Journal, 116(2), 330.2. Kozol, J. (1991). Savage inequalities: Children in America’s schools. New

York: Crown.3. Moll, L. (1992). Funds of knowledge for teaching: Using a qualitative

approach to connect homes and classrooms. Theory into Practice, 31(2),132–141.

4. Freire, P. (1970). Pedagogy of the oppressed. New York: Continuum, 101.5. Ellsworth, E. (1989). Why doesn’t this feel empowering? Working

through the repressive myths of critical pedagogy. Harvard Education Review,59(3), 297–324.

6. Drawing from Fairclough, N. (1995). Critical discourse analysis: Papers inthe critical study of language. New York: Longman.

7. Cee-Lo. (1998). The experience. Still Standing [CD]. LaFace Records.8. Ellsworth. (1989).9. Delpit, L. D. (1988). The silenced dialogue: Power and pedagogy in edu-

cating other people’s children. Harvard Educational Review, 58(3), 280–298.10. Gutstein, E. (2006). Reading and writing the world with mathematics:

Toward a pedagogy for social justice. New York: Routledge.11. An example is www.radicalmath.org.12. Gutstein. (2006).



13. Gramsci, A. (1999). Intellectuals and hegemony. In C. C. Lemert (Ed.),Social theory: The multicultural and classic readings (pp. 259–261). Boulder, CO:Westview Press.

14. Spivak, G. C. (1999). A critique of postcolonial reason: Toward a history ofthe vanishing present. Cambridge, MA: Harvard University Press.

15. This distinction is not a judgment of subaltern intellectual activity.Gramsci states that all people “are intellectuals, but not all [people] have insociety the function of intellectuals.” Therefore one cannot speak of “non-intellectuals, because non-intellectuals do not exist.” Gramsci. (1999). P. 259.

16. Kelley, R.D.G. (1994). Race rebels: Culture, politics, and the black workingclass. New York: Free Press.

17. Willis, P. (1977). Learning to labor: How working class kids get working classjobs. New York: Columbia University Press.

18. Morrell, E. (2004a). Becoming critical researchers: Literacy and empower-ment for urban youth. New York: Peter Lang.

19. Delpit. (1988). P. 14.20. Based on California Department of Education 2003 data for Castlemont

and Fremont High Schools, the two comprehensive high schools in East Oakland.

21. Orfield, G. (1999). Resegregation in American schools. Cambridge, MA:Harvard University Press.

22. Freire. (1970). Pp. 40–41.23. Freire. (1970). P. 110.24. Lumpkin, B. (1994). Mathematics and engineering the Nile Valley. In

I. Van Sertima (Ed.), Egypt: Child of Africa (pp. 323–340). Journal of Africancivilizations, vol. 12. New Brunswick, NJ: Transaction.

25. Pythagoras and irrational numbers, Tupac conspiracy theories, and The Ishangobone all refer to audiovisual presentations created by the math teachers.

26. Musca, C. (Producer), & Menéndez, R. (Director). (1988). Stand anddeliver [Motion picture]. United States: Warner Bros.

27. Harper’s Magazine Foundation. (2005–2006). Various excerpts fromHarper’s Index. In Harper’s. New York: Harper’s Magazine Foundation.http://www.harpers.org/subjects/HarpersIndex.

28. Euclid, Heiberg, J. L., & Fitzpatrick, R. (2005). Euclid’s elements in Greek:From Euclidis elementa. Austin, TX: Richard Fitzpatrick.

29. Ifrah, G. (2000a). The numbers of Ancient Egypt. In D. Bellos, E. F.Harding, S. Wood, & I. Monk [French Translators], The universal history ofnumbers: From prehistory to the invention of the computer (pp. 162–177). NewYork: Wiley.

30. Ifrah, G. (2000b). The amazing achievements of the Maya. In D. Bellos,E. F. Harding, S. Wood, & I. Monk [French Translators], The universal his-tory of numbers: From prehistory to the invention of the computer. (pp. 297–322).New York: Wiley.

31. Kozol, J. (1991). Savage inequalities: Children in America’s schools. NewYork: Crown.

32. Bourdieu, P. (1999). Structure, habitus, practices. In C. Lemert (Ed.),Social theory: The multicultural and classic readings. Boulder, CO: Westview.



33. To address speed and precision, we created trigonometry and SAT drillbooks and frequently assessed students’ test-taking performance.

34. Lumpkin, B. (1994).35. Ifrah, G. (2000b).

k. wayne yang is an assistant professor of ethnic studies at the Univer-sity of California, San Diego.



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Mathematics, critical literacy, and youth participatory action research