The Mathematics Educator2004, Vol. 14, No. 1, 47–51

47 Book Review

Amy Hackenberg is at work on her doctoral dissertation on theemergence of sixth graders’ algebraic reasoning from theirquantitative reasoning in the context of mathematically caringteacher-student relations. In addition to her fascination withmathematical learning and the orchestration of it, she iscompelled by issues of social justice, the nature andconsequences of social interaction, and the relationship betweenthe “social” and the “psychological” in mathematics education.

Book Review…Diverse Voices Call for Rethinking and Refining Notions of

EquityAmy J. Hackenberg

Burton, L. (Ed.). (2003). Which way social justice in mathematics education? Westport, CT:Praeger. 344 pp. ISBN 1-56750-680-1 (hb). $69.95.

Editor Leone Burton remarks that the title of thisbook reflects a “shift in focus from equity to a moreinclusive perspective that embraces social justice as acontested area of investigation within mathematicseducation” (p. xv). What’s interesting is that thequestion in the title lacks a verb—is the question“which are ways to social justice in mathematicseducation?” Or more tentatively, “which ways mightbring about social justice in mathematics education?”Or perhaps the focus is more on research, either up tonow or in the future: “which ways have research onsocial justice in mathematics education taken? Or“which ways could (should?) research on social justicein mathematics education take?” Each of the thirteenchapters in the volume addresses at least one of thosefour questions. Overall, this book responds to its titlequestion through diverse voices that call for expandingwork on gender issues into broader sociocultural,political, and technological contexts; rethinking andrefining key notions such as equity, citizenship, anddifference; and considering how to conduct studies thatreach beyond school and university boundaries towardfamilies, communities, and policy-makers.

The collection is the third volume in theInternational Perspectives on Mathematics Educationseries for which Burton has served as series editor.1 Inher introduction she describes the origin of the book inthe activities of the International Organization ofWomen in Mathematics Education (IOWME) at theNinth International Congress of Mathematics

Education (ICME9) in Tokyo, Japan, in 2000. Perhapsthis context explains why approximately half of thechapters focus primarily on gender, while otherchapters include issues related to differences in race,class, language, and thinking styles. Burton notes thatthis book, as the fourth publication of IOWME,“reflects the development of the group’s interests thathave evolved over 16 years from a sharp focus ongender issues to its present wider interest in socialjustice” (p. xiii).

In the introduction Burton also outlines the processby which the book developed. After a general call forpapers, an international review panel of mathematicseducators reviewed submissions. Chapter authors werethen paired to give feedback to each other on theirwork in order to promote dialogue as well as “cross-referencing possibilities” (p. xv). As perhaps is alwaysthe case in an edited book without summary pieces tohighlight connections between chapters, the cross-referencing of concepts in this volume could beexpanded. Burton does a nice job of drawing someconnections in her introduction, but otherwise suchresonance is largely left to the reader. Fortunately, as Ihope to demonstrate in this review, there is ampleopportunity to draw connections between chapters (andalso occasionally to wish that an author had heededanother author’s points or ideas!)

Organization of the BookThe thirteen chapters in the book are organized

into three sections. The four chapters in the firstsection focus on definitional work, conceptualframeworks, and reviews of and recommendations forresearch, thereby “setting the scene” (p. 1). The authorsof this section are from Australia (Brew), Germany(Jungwirth), the United Kingdom (Povey), and theUnited States (Hart). The second section consists ofseven chapters primarily about studies that take placein classrooms and address the question “what does

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social justice mean in classrooms?” (p. 101). Theauthors of this section are from Australia (Forgasz,Leder, and Thomas; Zevenbergen), Germany (Ferriand Kaiser), Malawi (Chamdimba), the United Statesand Peru (Secada, Cueto, and Andrade), and the UnitedKingdom (Mendick; Wiliam). The last section includestwo chapters focused specifically on “computers andmathematics learning” (p. 261) with regard to socialjustice. The authors (Wood, Viskic, and Petocz; Vale)come from Australia and Eastern Europe, but all nowpractice mathematics education in Australia.

The placement of chapters within this organizationis a little puzzling. Wiliam’s illuminating chapter onthe construction of statistical differences and itsimplications is included in the second section onclassroom studies, but since it grapples with definitionsand conceptual ideas (and is not a classroom study), itmight have been better placed in the first moretheoretically-oriented section. Brew’s chapter, a studyabout reasons that mothers return to studymathematics, is included in the first section but seemsto fit better in the second, despite the fact that the studydoes not take place in mathematics classrooms.Support for changing the placement of Brew’s chapteris provided by the position of Mendick’s: Her report ofyoung British men’s choices to study mathematicsbeyond compulsory schooling is only peripherallylocated in classrooms and was still placed in the secondsection.

The other weak organizational aspect of the bookis the inclusion of only two chapters in the third sectionon computers and mathematics learning. One wondersif there were intentions for a more substantial sectionbut some papers did not make the publication deadline.In any case, because both chapters in this section reporton studies set in classrooms, it seems that they couldhave been included in the second section—or thatperhaps two sections about studies might have beenwarranted, one that focused directly on studies inmathematics classrooms and one that included researchon mathematics education outside of immediateclassroom contexts.

Conceptually-Oriented Chapters: What Is Equity?What Is Social Justice?

Organizational difficulties aside, I focus first onthe more conceptually-oriented chapters, which arecontained in the first three chapters of the first sectionof the book as well as in Wiliam’s chapter from thesecond section. These authors engage in definitionaland conceptual work that forms a foundation forresearch on social justice. All four authors ponder the

nature of equity and justice within different contexts: atypology of gender-sensitive teaching, previous andcurrent research on equity and justice in mathematicseducation, citizenship education in the UnitedKingdom, and statistical analyses of gender differencesin mathematics education.

Jungwirth describes a typology of gender-sensitiveteaching that consists of three types distinguished bymodifications made according to gender, the degree towhich gender groups are identified and treated asmonolithic, and corresponding conceptions of equity.In Type I teaching, teachers are “gender-blind” andmake no modifications according to gender since theybelieve that boys and girls can do math equally well. InType II teaching, teachers adjust practices based ongender but tend to treat students of a single gender asmonolithic (i.e., tend to essentialize.) Jungwirthbelieves that in the third (and implicitly mostadvanced) type, the concept of equity “no longerapplies…Equity here refers to the individual, withrespect to learning arrangements and, somewhatqualified, to outcomes” (p. 16). Teachers engaging inType III teaching attend to individual differenceswithin gender groups and tailor teaching to individuals.

Although Jungwirth’s typology offers a conceptualframework for examining the equitable implications ofteachers’ orientations toward mathematics teaching andmathematics classrooms, her dichotomizing of groupsand individuals is problematic. For example, in theirattention to individuals, might not Type III teacherscreate classrooms in which mathematics could bedevoid of women, which Jungwirth sees asconsiderably less evolved than even Type I teaching?The problem seems to be in characterizing equitybased on group-individual dichotomies—to adhere toostrongly to group identities can result in essentializing,while to focus primarily on the individual can leave outtrends and broad characteristics of groups that areimportant considerations in work toward equity andsocial justice (cf. Lubienski, 2003).

These issues are reflected in Hart’s review ofscholarship on equity and justice in mathematicseducation over the last 25 years. Her chapter is notablefor explicit discussion about different ways researchershave used equity and justice (and equality); for herclearly stated choice to use equity to mean justice; andfor her formulation of calls for future research. Inparticular, she calls for research on pedagogies thatcontribute to justice; self-study of educators’ ownpractices; and more research that explores studentmotivation, socialization, identity, and agency withrespect to mathematics. Hart highlights Martin’s

Amy J. Hackenberg 49

(2000) study on factors contributing to failure andsuccess of African American students in mathematicsas an exemplar for future research because of itsmultilevel framework for analyzing mathematicssocialization and identity. Although her points abouthis work are well taken, the considerable space shegives to this relatively recent study seems odd givenher aims to review 25 years of research.

Povey continues Jungwirth’s and Hart’sdefinitional work by considering the complex andcontested notion of citizenship in relation to socialjustice and mathematics education. She describes howrecent mandates for citizenship education in Englandreinforce a conservative perspective by focusing onpolitical and legal citizenship (the right to vote, forexample), without questioning the nature and characterof social citizenship, let alone its connections to “the(mathematics) education of future citizens” (p. 52).Povey believes that for citizenship to be a usefulconcept in democratizing mathematics classrooms theconcept “will have to be more plural, more active, andmore concerned with participation in the here andnow” (p. 56).

Perhaps the strongest chapter of these four (andone of the strongest in the collection) is Wiliam’s onthe construction of statistical differences inmathematical assessments. He demonstrates that ingender research in mathematics education, effect sizesof standardized differences between male and femaletest scores are relatively small, and the variabilitywithin a gender is greater than between genders. Basedon this analysis, Wiliam concludes that differencesbetween genders depend on what counts asmathematics on assessments. In particular, what countsas mathematics may be maintained because it supportspatriarchal hegemony.

As an implication of his argument, Wiliamproposes “random justice” (p. 202) to produce equityin selection based on test scores. Wiliam calls thepercentage of the population that reaches a certainstandard (for, say, entrance to medical school) arecruitment population. Usually, selecting from arecruitment population (i.e., creating a selectionpopulation) involves choosing a small top percentageof it. This mode of selection perpetuates selecting moremales than females, largely because males showgreater variability in their test scores compared tofemales (males produce more highs and lows.) Wiliamproposes that a random sample of the recruitmentpopulation that sustains the gender (or racial, class,etc.) make-up of it is “the only fair way” (p. 204) ofcreating a selection population. Although this proposal

may seem counterintuitive (and certainly differs fromtypical U.S. selection processes!), Wiliam makes acompelling argument that is worth reading.

Chapters on Studies in or SurroundingMathematics Classrooms

In these chapters—Brew’s chapter from the firstsection as well as the other 8 chapters in the book—thediverse voices in the volume become quite apparent,not only because of the different geographical locationsor ethnic heritages of the authors but because of thediverse ways in which the authors focus on issues ofsocial justice in relation to mathematics classrooms andmathematical study. These nine chapters can also beloosely grouped as exemplifying, supporting,informing, or aligning with the more conceptually-oriented chapters.

In particular, two chapters that focus specificallyon teaching practices in relation to social justice mayexemplify and inform Jungwith’s typology. Theauthors of these chapters attend to how teachersapproach students who belong to disadvantagedgroups. Chamdimba, whose research took place in thesouthern African country of Malawi, studied the year11 students of a Malawian teacher who agreed to usecooperative learning to potentially promote a “learner-friendly classroom climate” (p. 156) for girls. As aresearcher, Chamdimba might exemplify a Type IIorientation out of her concerns over Malawian girls’lack of representation and achievement in mathematicsand subsequent Malawian women’s lack of bargainingpower as a group for social and economic resources inthe country. Chamdimba’s conclusion that femalestudents experienced largely positive effects mighthelp Jungwirth refine her typology so that recognizingstudents as part of disenfranchised groups and actingon that recognition to address the group is seen aslegitimate and useful (i.e., not necessarily less evolvedthan Type III teaching.) However, Chamdimba’s studyis also subject to scrutiny over whether a particularclassroom structure can bring about improvements inall Malawian females’ educational, social, andeconomic status.

Perhaps a better example of the subtlety involvedin the group-individual distinctions with regard tosocial justice is found in Zevenbergen’s study.Zevenbergen used Bourdieu’s tools as a frame forunderstanding teachers’ beliefs about students fromsocially disadvantaged backgrounds in the South-EastQueensland region of Australia. Eight of the 9 teachersinterviewed expressed views of students as deficientdue to poverty and cultural practices. Stretching

50 Book Review

Jungwirth’s typology beyond gender-sensitivity, theninth teacher had more of a Type III orientation in herrespect for these students as individuals. However, byexpressing an understanding of how parents’ lack ofcultural capital prevented them from challenging theways in which schools (under)served their children,this teacher did not ignore these students as belongingto a disadvantaged group. This teacher’s ability tounderstand and value students as both individuals andpart of a group might allow Jungwirth to amplify andfurther articulate her typology.

These two chapters and three others exhibit workthat aligns with Hart’s call for research on pedagogiesthat contribute to social justice and on one’s ownteaching in relation to social justice. Vale’s two casestudies of computer-intensive mathematics learning intwo junior secondary mathematics classrooms focus onhow teachers’ practices with technology impede (butmight facilitate) more just classroom environments.Vale’s work is complemented by the three universityclassroom studies presented by Wood, Viskic, andPetocz. In studying their own computer-intensiveteaching of differential equations, statistics, andpreparatory mathematics classes, these threeresearchers found positive attitudes toward the use oftechnology across gender. Finally, Ferri and Kaiser’scomparative case study on the styles of mathematicalthinking of year 9 and 10 students (ages 15-16) hasimplications for developing pedagogies that recognizedifferences other than due to gender, race, or class, andthat thereby contribute to justice and diversity inclassrooms.

However, Secada, Cueto, and Andrade’s large-scale, comprehensive study of the conditions ofschooling for fourth and fifth-grade children who speakAymara, Quechua, and Spanish in Peru may be thestrongest example of work toward Hart’srecommendation of multilevel frameworks in researchon social justice. These researchers intended to create a“policy-relevant study” (p. 106). To do so theyarticulated their conceptions of equity as distributivesocial justice (opportunity to learn mathematics is asocial good and should not be related to accidents ofbirth) and socially enlightened self-interest (it is ineveryone’s interest for everyone to do well so as not tocause great cost to society). In addition, the researcherstook as a premise that equity must come with both highquality and equality (i.e., lowering the bar does notfoster equity). Thus they contribute to definitionalwork while formulating “practical” conclusions andrecommendations for Peruvian governmental policy.

Finally, the remaining three chapters in the bookconnect with Povey’s chapter in exploring a particularcontested and complex concept or relate to Wiliam’swork on considering the construction of difference.Brew’s study entails rethinking aspects of the complexconcept of mothering in the context of mathematicallearning of both mothers and their children. Byincluding voices of the children in the study, Brew isable to show the fluid roles of care-taking betweenstudying mothers and their children (e.g., childrensometimes acted as carers for their mothers) and “thepivotal role that children can play…in providing notonly a consistent motivating factor but also enhancingtheir mother’s intellectual development” (p. 94).

What Povey does for citizenship and Brew does formothering, Mendick does for masculinity in thecontext of doing mathematics. In a very strong andthoughtful chapter, she describes stories of three youngBritish men who have opted to study mathematics intheir A-levels even though they do not enjoy it.Mendick’s smart use of a poststructuralist perspectivethat deconstructs the classic opposition betweenstructure and agency allows her to argue that taking upmathematics is a way for the men to “do masculinity”in a variety of ways: to prove their intelligence toemployers and others as well as to secure a future inlabor market. The stories of the three males prompt thequestion: “why is maths a more powerful proof ofability than other subjects?” (p. 182). To respond,Mendick contrasts the men’s stories with youngwomen’s stories (part of her larger research project.)

This artful move is not intended to drawdichotomies between how men and women “do maths”differently—Mendick cautions against such simplisticconclusions and notes that some females usemathematics the way these three males do. Instead thecontrast allows her to demonstrate and deepen hertheorizing of masculinity as a relational configurationof a practice, as well as to argue for more complexityin gender reform work. Thus for her, “maths andgender are mutually constitutive; maths reform work isgender reform work” (p. 184). By examining gender inthis way, like Wiliam, she calls into questiondifferences between males and females in relation tomathematics and supports his contention that whatcounts as mathematics (and, Mendick would add, asmasculine and feminine) is the basis for thesedifferences.

Differences between males and females are alsothe subject of the chapter by Fogasz, Leder, andThomas. They used a new survey instrument to capturethe beliefs of over 800 grade 7–10 Australian students

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regarding gender stereotyping of mathematics. Theirfindings revealed interesting reversals of expected(stereotyped) beliefs. For example, their participantsbelieved that boys are more likely than girls to give upwhen they find a problem too difficult, and that girlsare more likely than boys to like math and find itinteresting. However, through an examination ofparticipation rates and achievement levels of male andfemale grade 12 mathematics students from 1994 to1999 in Victoria, Australia, the researchers refuterecent, media-hyped contentions (see, e.g., Conlin,2003; Weaver-Hightower, 2003) that males are nowdisadvantaged in mathematics. Frankly, Fogasz andcolleagues might have benefited from Wiliam’s adviceon examining effect size—it is hard to know how muchsignificance to give to the differences they found.Nevertheless, their work supports the notion thatmathematics may be maintained as a male domaindespite certain advances of females.

Overall, I agree with Burton that the chapters inthis volume achieve the goal of providing “anintroduction for new researchers as well as stimulationfor those seeking to develop their thinking in new orunfamiliar directions” (p. xiii). Although theorganization is a bit puzzling and some chapters areclearly stronger than others, the book is a useful readfor researchers in mathematics education. Moreimportant, the diversity of voices—and the connectionsthat readers can draw among this diversity—gives acomplex and layered picture of how resources,sociocultural contexts, governmental policy, teacherand student practices, human preferences andexpectations, and researchers’ theorizing andinterpretations, all contribute to “…who does, and whodoes not, become a learner of mathematics” (p. xviii).

REFERENCESConlin, M. (2003, May 26). The new gender gap. Business Week

online. Retrieved September 1, 2003, fromhttp://www.businessweek.com

Lubienski, S. T. (2003). Celebrating diversity and denyingdisparities: A critical assessment. Educational Researcher,32(8), 30–38.

Martin, D. B. (2000). Mathematics success and failure amongAfrican-American youth: The roles of sociohistorical context,community forces, school influence, and individual agency.Mahwah, NJ: Lawrence Erlbaum.

Weaver-Hightower, M. (2003). The “boy turn” in research ongender and education. Review of Educational Research, 73(4).471–498.

1 The first volume was Multiple Perspectives on MathematicsTeaching and Learning (2000) edited by Jo Boaler; the secondvolume was Researching Mathematics Classrooms: A CriticalExamination of Methodology (2002) edited by Simon Goodchildand Lyn English.