Goals , aimed at forging links between the educational and commercial sectors Journal of Urban Mathematics Education July 2012, Vol. 5, No. 1, pp. 1–7 ©JUME. http://education.gsu.edu/JUME MAISIE L. GHOLSON is a recipient of NSF Graduate Research Fellows Program in STEM education and doctoral student in mathematics education in the Curriculum and Instruction Department in the College of Education, at the University of Illinois at Chicago, 1040 W. Harrison Street, M/C 147, Chicago, IL, 60607; e-mail: mghols2@uic.edu. Her research interests include the intersection of racial and mathematics identities, identity development through talk, and Black children’s experiences in first-year algebra courses. ERIKA C. BULLOCK is a doctoral candidate in mathematics education in the Department of Middle-Secondary Education and Instructional Technology in the College of Education, at Georgia State University, P.O. Box 3978, Atlanta, GA, 30303; e-mail: ebullock1@student.gsu.edu. Her research interests include exploring teacher professionalism and mathematics education policy from a critical postmodern theoretical (and methodological) perspective. She is a Southern Regional Education Board Doctoral Fellow and the assistant to the editor-in-chief of the Journal of Urban Mathematics Education. NATHAN N. ALEXANDER is a doctoral candidate in mathematics education in the Department of Mathematics, Science, and Technology at Teachers College, Columbia University and a Research Analyst at The Research Alliance for NYC Schools, 285 Mercer Street, 3rd Floor, New York, NY, 10003; email: nna2106@tc.columbia.edu. His research interests include academic peer networks, supplementary education, and self-efficacy in mathematics and science, specifically, among low income students and Black and Latina/o youth. GUEST EDITORIAL On the Brilliance of Black Children: A Response to a Clarion Call Maisie L. Gholson Erika C. Bullock Nathan N. Alexander University of Illinois– Chicago Georgia State University Teachers College, Columbia University n this special issue of the Journal of Urban Mathematics Education (JUME), we believe a new precedent was set in the mentoring and development of math- ematics education scholars in which we were fortunate enough to play a role. As three doctoral students from three different institutions, we were given the ex- traordinary opportunity and unique responsibility to serve as co-editors for the Proceedings of the 2010 Philadelphia and 2011 Atlanta Benjamin Banneker Asso- ciation (BBA) Conferences under the supervision of the editor-in-chief, Dr. David W. Stinson. Relying on the previous experience of the assistant to editor-in-chief, Erika C. Bullock, we managed the process from the issuing of invitations to the conference speakers to the final round of revisions. During the editing process we found ourselves continually referencing the clarion call by Dr. Danny B. Martin1 (Martin, 2011), who urged attendees of the 1 Unfortunately, Dr. Martin was not able to contribute to this special issue. The PowerPoint slides from his presentation, and those of the other 2011 conference presenters, are available on the Benjamin Banneker Association website (http://www.bannekermath.org). I about:/blank Gholson et al. Guest Editorial Bullock, E. C., Alexander, N. N, & Gholson, M. L. (Eds.). (2012). Proceedings of the 2010 Philadelphia and 2011 Atlanta Benjamin Banneker Association Conferences – Beyond the Numbers [Special issue]. Journal of Urban Mathematics Education, 5(2). 2 2011 BBA Conference to engage in research and argumentation with the bril- liance of Black children as axiomatic. It was evident in our conversations and in- teractions with each manuscript that we did not see this call as an exercise in slo- ganeering; rather, it moved us individually and collectively. In other words, taking the brilliance of Black children as an axiom seriously disrupted our sense of doing the work of mathematics education research related to Black children. We under- stood this call as a challenge to our work as emerging scholars and, in this imme- diate case, as editors. Although we acknowledged that editing (i.e., really concep- tualizing) with Black brilliance in mind would require modest shifts in our own thinking, we were unprepared for the intense and insidious gravity of our own deficit thinking, given we believed ourselves to be progressive thinkers, promis- ing scholars, and Black nonetheless. In this editorial we assume the responsibility to address some of the major issues that we have wrestled—and continue to wres- tle—with as it relates to Black mathematics education research. Thinking Axiomatically about Black Children In the talk, “Proofs and Refutations: The Making of Black Children in Mathematics Education,” Martin (2011) took a note from Imre Lakatos to de- scribe the production of mathematical knowledge relating to Black children as a series of axioms, conjectures, and counterexamples.2 According to Martin, there are two lines of argumentation within the process of proof and refutation, about Black children, both of which are equally problematic: (1) “Black children are mathematically illiterate and intellectually inferior to White and Asian children;” and, alternatively, (2) “Black children are brilliant.” Both are put forth as conjec- tures and lead mathematics education scholars to produce knowledge that main- tains the racial hierarchy of mathematics ability, wherein Black children are posi- tioned at the bottom. These conjectures also place those who hold opposing views in a position to produce counterexamples that disprove the conjectures, resulting in a stalemate. 2 In his presentation, Dr. Martin defined these terms as follows: An axiom is a logical statement that is assumed to be true. Axioms are not proven or demonstrated, but rather considered to be self-evident. Axioms serve as starting points for deducing and inferring other truths. A conjecture is a proposition that is unproven but is thought to be true and has not been disproven. A counterexample is an exception to a proposed general rule. Counterexamples are used to show that certain conjectures are false. Gholson et al. Guest Editorial Bullock, E. C., Alexander, N. N, & Gholson, M. L. (Eds.). (2012). Proceedings of the 2010 Philadelphia and 2011 Atlanta Benjamin Banneker Association Conferences – Beyond the Numbers [Special issue]. Journal of Urban Mathematics Education, 5(2). 3 For example, in the first conjecture, knowledge is produced via examples that focus on the inferiority of Black children’s mathematical ability, namely, the throngs of literature describing “achievement gaps” in standardized tests (see, e.g., U.S. Department of Education, 2003). Of course, this conjecture places criti- cal scholars who wish to refute such examples in the untenable position of prov- ing that Black children are not mathematically illiterate and inferior. In this case, as Martin notes, knowledge production continues to reify notions of deficiency. Contrary to how it may appear, the second conjecture, “Black children are bril- liant,” does not escape this pitfall. In this case, researchers concentrate their ef- forts on proving that Black children are brilliant, yet such evidence and examples are simply refuted by a return to the status quo, where de facto constructions of Black children as less than brilliant persist. The only escape from this quagmire is to treat the brilliance of Black children not as a conjecture, but as axiomatic—a self-evident, starting point for deducing and inferring other truths. Martin (2011) gives three key points for moving forward:  We must accept, and insist on, the brilliance of Black children as axiomatic.  We must avoid the trap of having to prove that Black children are brilliant.  We must avoid generating arguments, logic models, and counternarratives requiring proof that Black children are not brilliant. We suggest that taking Martin’s (2011) axiomatic stance calls into question many aspects of current scholarship. We first felt this need for questioning when discussing the lifeblood of Black mathematics education scholarship—critical race theory (CRT). One of the key tenets of CRT (see Jett, this issue) is the coun- ternarrative (as opposed to the master or dominant narrative), which works to re- fute hegemonic claims of Black inferiority. Consider that much of the scholarship on Black students in primary, secondary, and college in the last ten years relied on counternarratives generated by “successful” (read: brilliant) Black children, ado- lescents, and young adults. Despite honorable intentions, these counternarra- tives—and particularly the focus on successful Black children—reinforced the no- tion that successful Black children are the exception, not the rule. We certainly have the privilege of retrospection in reviewing this work and we recognize the imminent need at the time to push against the wave of deficit research on Black children in mathematics education of the 1980s and 1990s (which continues to- day). We also recognize that the BBA Conference marked a moment with poten- tial to pivot towards new forms of argumentation, that is, new axioms on which to build new truths about Black children. Our intent here is not to criticize our pre- decessors who have advanced the conversation regarding Black children in math- ematics by researching success and shining the light of research and teacher edu- cation efforts on Black children. To the contrary, we extend our gratitude toward those who have come before us and look toward the future to consider how our Gholson et al. Guest Editorial Bullock, E. C., Alexander, N. N, & Gholson, M. L. (Eds.). (2012). Proceedings of the 2010 Philadelphia and 2011 Atlanta Benjamin Banneker Association Conferences – Beyond the Numbers [Special issue]. Journal of Urban Mathematics Education, 5(2). 4 landscape of responsibility is changing as we take this sociopolitical turn in math- ematics education and mathematics education research (Gutiérrez, 2010). We do not purport to have answers; we are armed only with questions and an invitation to enter into a constant state of dis-ease by continually reflecting upon the ques- tions: What do I really believe about Black children and their abilities? How does my work reflect those beliefs? and Given that Black children are brilliant, how does this affect my research agenda? Questioning Prevailing Axioms Some may suggest that taking an axiomatic stance on Black children’s bril- liance is more intellectual posturing than substance. Yet, we only need to be re- minded of the current axioms on which knowledge about Black children are built to see the need for change. The recent tragedy of Trayvon Martin serves as an un- fortunate reminder of the axiom: “Black children are criminals.” This position dictates that the very presence of a Black male adolescent is cause for suspicion and presumed criminality—a criminal so heinous, in fact, that his presence poses an imminent threat against which the “victim” must “stand his ground.” This axi- om of criminality mediates Black children’s lived experiences in and out of the school system, as evidenced by the spring release of a U.S. Department of Educa- tion study that found Black and Latina/o students are three and a half times more likely to be suspended or expelled than White students (Adams & Robelen, 2012). The axioms that we choose have a material reality and, in Trayvon’s case, a dead- ly reality. An equally pernicious axiom that remains unspoken, unquestioned, and of- ten undetected is “White children are the standard.” Under this axiom, Black chil- dren’s test scores, behavioral and socioemotional patterns, as well as their dress and speech are subject to comparison of a fictitious, normalized White child. We (you may count yourself among us) have occasionally felt that pang of pride, however momentary, when a class or school of Black children are highlighted on the nightly news with their khaki pants, collared shirts, and blazers and singing in unison. These Black children create the optics of normalization; they appear to “do school” in an idyllic manner that is non-threatening to White middle-class sensibilities and is subconsciously part of our desire to see Black children reflect- ed as valuable and precious in larger society. This moment of pride comes with a cost—a clear subtext—namely, that Black children are only valuable to the extent that they reflect Whiteness. The axiom of White standardization harkens Frantz Fanon’s (1967) classic indictment in Black Skins, White Masks: “For the black man [and woman] there is only one destiny. And it is [to become] white” (p. 10). Thus, in the realm of mathematics education, the destiny of Black children has been confined to closing a so-called “racial achievement gap.” By assuming Gholson et al. Guest Editorial Bullock, E. C., Alexander, N. N, & Gholson, M. L. (Eds.). (2012). Proceedings of the 2010 Philadelphia and 2011 Atlanta Benjamin Banneker Association Conferences – Beyond the Numbers [Special issue]. Journal of Urban Mathematics Education, 5(2). 5 White children as our standard, we limit our imagination for generations of Black children to nothing more than what most of us have been taught since childhood: to work twice as hard and to be considered just as good as the average White child. Moreover, maintaining the axiom of White standardization requires that we cede to a set of beliefs that disallow Black children from being standard-bearers, because they are inevitably lacking in some “objective” capacity. Despite obvious problems, the axiom of standardization persists and is repeatedly invoked with every insinuation of an achievement gap. With an axiomatic stance of Black bril- liance, we consider achievement gap rhetoric to be a relic of deficit-research with diminishing returns and, thus, should be avoided, particularly, when used in the defense of Black children in mathematics. A Challenge to the Community So, what does it mean for the next generation of mathematics education scholars to take an axiomatic stance of Black brilliance? What possibilities does this stance create? What possibilities does it eliminate? Our work is most often a reflection of who we are and what we value. Even methodological approaches that claim little or no influence from researcher subjectivity are unable to avoid the residue of researcher bias. This evidence of our positionality as researchers of- ten not easily seen but becomes evident through careful reflection. As we consider the prevailing axioms about Black children, some of which we discussed above, we must assess our own complicity in the perpetuation and reproduction of these discourses through even those elements of our research that seem insignificant. The way that we select participants, frame interview or research questions, write up our research, solicit grant funding, or even focus on particular students during classroom observations are all influenced by and evidence of the axioms that we choose about teaching, learning, research, and Black children. Of course, this call to reflective caution is not limited to researchers. To the mathematics educator: how do you talk about Black children in the presence of the young, White, middle-class, and female preservice teachers who overwhelm- ingly fill your classrooms (Martin, 2009; Walker, 2007)? Do you dismiss subtle statements of deficiency as the comments of an exhausted and over-extended teacher? This call is one for accountability throughout the community of mathe- matics educators and researchers who are concerned with Black children. We must contemplate our own missteps, gently critique those of our colleagues, and remain open to that critique. We believe that exercising this reflexivity in the de- velopment of axiomatic stances is different than merely shifting discourses or re- framing the phenomenon of Black children’s mathematics education experiences. An axiomatic stance of brilliance transcends the offensive position (e.g., proving Black children are brilliant) and defensive position (e.g., refuting Black children’s Gholson et al. Guest Editorial Bullock, E. C., Alexander, N. N, & Gholson, M. L. (Eds.). (2012). Proceedings of the 2010 Philadelphia and 2011 Atlanta Benjamin Banneker Association Conferences – Beyond the Numbers [Special issue]. Journal of Urban Mathematics Education, 5(2). 6 illiteracy or inferiority) involved in framing and forecloses on the endless cycle of proving Black children’s brilliance. A new axiom of Black brilliance signals a new set of research questions and a new approach to mathematics teacher educa- tion that have nothing to do with Black children’s achievement, as their ability and potential is no longer in question. Although treating brilliance as axiomatic may forestall the surge of inter- view-based research in Black mathematics education (given counternarratives are no longer necessary as proof), new possibilities abound. Research questions can move beyond offensive or defensive positioning to locate and highlight unique characteristics of Black students, teachers, and classrooms. In response to differ- ent questions, the axiom of brilliance may encourage the influx of re-discovered methodologies such as microethnography, sociolinguistics, and (critical) dis- course analysis that make familiar (and strange) the circuitous rhythms of Black mathematics classrooms and communities. Finally, new questions and re- discovered methodologies will facilitate new modes of data representation and connections to the broader sociopolitical structures in the schools, communities, states, and nation. Equity in the Face of Brilliance To conclude, we note that the axiomatic stance of brilliance indexes a new conceptualization of equity research, wherein inequity, disparity, and marginaliza- tion are perhaps backdrops, but not foci for our questions and arguments. Equity based on the conjecture of Black brilliance begs for measurement, comparison, and legitimation, whereas an approach to equity based on axioms demands atten- tion and remuneration on principle, not evidence. In other words, we can no long- er afford to make equity arguments on evidentiary grounds, we have learned from those before us that no amount of evidence or proof will be sufficient to mandate systemic change—there is no silver study. We believe that forceful moral argu- mentation is the way forward for systemic change under the axiom of brilliance. We arrive with these arguments, questions, and conclusions humbly and largely by virtue of the incredible opportunity to serve as editors. For that, we are particularly thankful. As we considered this idea of axiomatic brilliance through editing the manuscripts in this issue and discussing those manuscripts and this editorial, we encountered a crisis of our own assumptions. For three young schol- ars who embarked upon the doctoral process with hopes of changing the lived ex- periences of Black children, their teachers, their communities, and their schools, this process of “rethinking [our] rethinking” (Stinson, 2004, p. xx) left us feeling rather uneasy. Despite our discomfort, we persist, knowing (or hoping) that our continual questioning of our own motivations will allow us to remain true to the people and communities that we intend to serve. Gholson et al. Guest Editorial Bullock, E. C., Alexander, N. N, & Gholson, M. L. (Eds.). (2012). Proceedings of the 2010 Philadelphia and 2011 Atlanta Benjamin Banneker Association Conferences – Beyond the Numbers [Special issue]. Journal of Urban Mathematics Education, 5(2). 7 Authors’ Note We, the guest editors of the special issue of the Journal of Urban Mathematics Education, would like to thank Dr. David Stinson and Dr. Jacqueline Leonard for extending this incredible opportunity. 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