Microsoft Word - Final Confrey Vol 3 No 2.doc Journal of Urban Mathematics Education December 2010, Vol. 3, No. 2, pp. 25–33 ©JUME. http://education.gsu.edu/JUME 
 JERE CONFREY is the Joseph D. Moore Distinguished University Professor of Mathematics Education at the Friday Institute for Educational Innovation, College of Education, North Carolina State University, 1890 Main Campus Drive, Raleigh, NC 27606; email: jere_confrey@ncsu.edu. Her research focuses building diagnostic assessments for rational number reasoning using wireless technologies and on policy involving standards and assessments. RESPONSE COMMENTARY “Both And”—Equity and Mathematics: A Response to Martin, Gholson, and Leonard Jere Confrey North Carolina State University n the commentary “Mathematics as Gatekeeper: Power and Privilege in the Production of Knowledge,” this issue of JUME, authors Danny Martin, Maisie Gholson, and Jacqueline Leonard (2010) react to editor Kathleen Heid’s (2010) statements in the March 2010 issue of the Journal for Research in Mathematics Education (JRME), and to a panel presentation during the 2010 National Council of Teachers Research Presession (Harel, Ball, Battista, Thompson, & Confrey, 2010). I was the discussant for that panel. In summary, Martin et al. argue that by posing the question “Where’s the math in mathematics education research?” the scholars on the panel and the editor of JRME marginalize scholars who wish to study deep and complex factors that concern issues of identity, language, power, racialization, and socialization in mathematics education. They state that a call for more attention to mathematics content in mathematics education research is close- ly aligned with a “back to basics” agenda. Warning that focusing too heavily on the mathematics may sustain a tradition of deficit thinking about minority and indigent children, they intone that this focus fails to acknowledge the complex factors that limit these children’s access to rich opportunities to learn mathematics with the cultural resources that they bring to school. Further, Martin et al. (2010) observe the limited diversity in terms of race and to a lesser degree, gender, in many areas of mathematics education such as among the scholars who have focused on research on whole number concepts and operations (Nesher, 1980); rational number concepts (Confrey, 1988, 2008; Empson &Turner, 2006; Lamon, 2007; Steffe, 2002); proportional reasoning con- cepts (Behr, Harel, Post & Lesh, 1992; Confrey, 1995; Hart, 1988; Lamon, 1993; Lesh, Behr, & Post, 1987; Karplus, Pulos, & Stage, 1983; Noelting, 1980); alge- bra, problem solving, and proof (Harel & Sowder, 1998, 2007); and geometric and spatial thinking (Barrett & Clements, 2003; Barrett, Clements, Klanderman, Pennisi, & Polaki, 2006; Battista, 2007; Clements & Sarama 2009; Clements, Wilson, & Sarama, 2004; Hollebrands, 2002). They seem plainly offended by and critically challenge Harel’s assertion that the questions addressed by the preses- sion panel were apolitical and neutral; they characterize the questions instead as I Confrey Response Commentary 
 Journal of Urban Mathematics Education Vol. 3, No. 2 26 “displays [of] power and privilege” (p. 13). In their conclusion, they warn that to interpret their criticisms as personal rather than professional “would be disin- genuous and misses the point” (p. 21). I welcome Martin et al.’s (2010) highlighting these issues, and their chal- lenge of whether a call for a focus on mathematics content results in a call for the exclusion of broader issues of equity. I acknowledge some of the points raised by the authors and disagree with others. First, I outline my points of agreement with the authors: 1. Equity is not a “special issue” facing us in mathematics education; it is “the central issue” (Darling-Hammond, 1994, 2010; Bennett et al., 2004). In my opinion, the math wars (Wilson, 2002) have been a distraction from these fundamental issues just as the current media focus on the culture wars often distracts from more fundamental underlying perspectives on the distribution of wealth, corporate influence over democracy, and everyday injustices to people. 2. The tendency for educational professionals to treat children of color and of poverty solely in deficit terms is a devastating problem that severely con- strains our discourse and understanding of how to generate robust solutions to differences in performance and high failure rates in mathematics. 3. To address the magnitude of the inequity, one must understand how the en- tire education system, as a component of the larger system of human serv- ices, fails to provide fair and equal opportunities to learn for large segments of the population. Marilyn Frye (1983), a feminist scholar, describes a bird cage analogy, noting that if one looks at any single wire of a bird cage, one wonders why the bird does not fly away. Only by observing the whole con- figuration of wires does the inherent confinement of the cage become appar- ent. 4. The field of mathematics education needs to be more diverse—who does the scholarship does matter—due to differences in experiences, priorities, inter- pretive frameworks, and identification. When I recently hosted a discussion of Martin et al.’s (2010) commentary, of the women who participated (Afri- can American and Caucasian, and all them professionals in educational re- search), more than half, including myself, had been at one time or another explicitly counseled not to study issues of race or gender as a scholarly en- terprise for risk of being pigeonholed, and hence restricted in our subsequent professional opportunities. Therefore, I agree that the marginalization of scholarship referred to in the commentary is a widespread and unfortunate phenomenon reinforced by different forms of mentoring. Confrey Response Commentary 
 Journal of Urban Mathematics Education Vol. 3, No. 2 27 The concerns raised by Martin et al. (2010) clearly have merit. However, there is also merit in the perspective that the field of mathematics education re- search has drifted too far from close and careful attention to the mathematics we seek to have students learn. My advice to scholars interested in equity agendas can be communicated in relation to four particular issues; each focuses on the centrality of the mathematics in the agenda. 1. It is essential to stay current with research on cognition to be certain that the students one seeks to help are getting the most up-to-date ac- cess. For example, the Algebra Project (Moses & Cobb, 2001) quite properly and significantly asserted that algebra is a civil right; under the leadership of Robert Moses, the Algebra Project created community-based approaches to improving access and success. However, their curricular materials were slow to transition to a functions-based approach to algebra, and instead con- centrated on algebra as expressions and equations. I would argue that the de- lay in updating the Algebra Project’s approach constituted a disadvantage to students when the functions-based approach gained purchase in many intro- ductory college mathematics courses. 2. Serving the needs of all students requires one to stay abreast of, and make one’s opinions known concerning, the full range of mathematics that is of most importance and value to the communities one serves— from topics of basic arithmetic proficiency, to competence with funda- mental tools (Excel, statistical software, graphing software and hard- ware), to critical maths, to “Career and College Readiness,” and to twenty-first century skills (Confrey, 2009). During the development of the voluntary-state Common Core State Stan- dards for Mathematics (CCSS, 2010), a highly political decision was made to drop probability and statistics from the elementary curriculum. As a member of the National Validation Committee for the Common Core State Standards, I had access to many, but not all, of the comments. I witnessed a strong response from the learning scientists and the curriculum writing communities: vigorous evidence-based arguments to strengthen the statistics and probability content in the early grades—that research demonstrates chil- dren’s early rich probabilistic awareness, that these topics must be devel- oped over extended time, and that probability and statistics are critical mathematical topics for the 21st century. To what degree did the scholars on critical theory register concerns that the CCSS writers’ decision would in- crease students’ alienation from mathematics and weaken students’ ability to reason critically and quantitatively about the world around them? It is not Confrey Response Commentary 
 Journal of Urban Mathematics Education Vol. 3, No. 2 28 clear, for all comments were not made available, even to the validation committee. The writers’ final decision, however, to reduce the opportunity for all children to learn that they live in a world of probability, to incorpo- rate probability into their mathematical reasoning, and that fair opportunity is an issue of improving one’s odds, seems to me to reinforce an implicit impression communicated within the CCSS that mathematics is apolitical and objective. Scholars to whom Martin et al. (2010) refer, including M. Frankenstein, A. Powell, R. Gutiérrez, E. Gutstein, S. Lubienski, and others have raised ac- tive concerns about the role of critical mathematics and the effects of reform programs in high poverty settings. Martin et al. ask the question: “Is this the mathematics to which Heid, Harel, and perhaps the panelists might be refer- ring?” (p. 14). My answer would be yes, this and more. A continuation of the lines of research represented by those scholars, research that involves di- rect attention to the interaction of the mathematics and the lived experience of the student, is imperative. The work of some of the Centers for Learning and Teaching (CLT) such as the DiME (Diversity in Mathematics Educa- tion) Center and CEMELA (Center for the Mathematics Education of Lati- nos/as) keeps these linkages central to their work. It is also essential to rec- ognize that the mathematics one learns, the tools one has with which to learn, and the expectations and opportunities expressed in the schools are part of the lived experience of the student, and matter greatly. My question therefore is whether, in the research on increasing students’ success in mathematics and lessening the achievement gap, has there been enough at- tention paid to: (a) ensuring increased awareness of learning technologies and twenty-first century skills, (b) the development of career awareness and preparation, and (c) the intensification of topics like statistics and modeling? I emphasize the importance of this development, not so much for the identi- fication of research mathematicians, but for the education and empowerment of resourceful mathematicians (Confrey, 2007, 2010). To my mind, these topics are consistent with a call for more focus on the mathematics in mathematics education and are also central to a more effective equity agenda. 3. Good teaching that fosters rich classroom interactions and engagement is a key to a successful equity agenda. Many mathematics educators share with me the belief that good teaching and fair access to qualified teachers is the key route to increased equity. While improved teaching entails policy dimensions and actions at the sys- temic level, it also requires significant work in understanding teaching, in- terpreting classroom interactions, and improving professional development. Confrey Response Commentary 
 Journal of Urban Mathematics Education Vol. 3, No. 2 29 Much of the work around creating and supporting discourse communities (Hufferd-Ackles, Fuson, & Sherin, 2004; Thomas, 2010), building teaching capacity (Allen et al., 2006; NPTARS, 2005), and strengthening curricular implementation (Grouws, Reys, Papick, Tarr, & Chavez, 2010; McNaught, Tarr, & Sears, 2010) can transform students’ school learning experiences and enhance their opportunities to learn. This work requires precise, crea- tive, and extended attention to what happens within mathematics classrooms and how students develop their understandings over long periods of time. It could be further strengthened, to the benefit of students and teachers, by in- creased attention to the cultural resources students bring to school, sensitiv- ity to differences in linguistic nuances of region, culture, and class, and lev- eraging these characteristics for improved student mathematical under- standing. This is an arena in which scholars across mathematics education communities could help to produce massive change in children’s experi- ences in schools. Similarly, related development of uses of assessment to promote fair and engaging opportunities to learn would benefit from a more active role from the larger community committed to increased equity (Black & Wiliam, 1998). Formative assessment (assessment for learning) is one classroom process in which the imperatives of mathematical content, student engage- ment, and student ownership of their own learning intersect to the benefit of all students, and thus could itself be a productive focus for collaboration of mathematics educators of various subspecialties and perspectives. For in- stance, McManus (2008) studied how to instill formative assessment prac- tices in low-achieving schools. She identified three essential conditions for successful implementation of formative assessment: high level of content and pedagogical knowledge by the teacher, students trusting that they are partners in learning in the classroom environment, and dialogic mathemati- cal content discourse. These elements, along with the essential steps of for- mative assessment, were the basis of successful formative assessment lead- ing to increased student motivation, ownership of their own learning, and improved self-efficacy. My own research team is undertaking designing new forms of classroom-embedded diagnostic assessment based on learning tra- jectories to help all students to participate more fully in classroom activities (Confrey & Maloney, in press). 4. A lack of significant attention to mathematics in mathematics education research results in the marginalization of the entire field, threatening the preparation of the next generation of scholars and teachers. While I fully agree with Martin et al.’s (2010) view that Harel’s characteri- zation of the issues as apolitical (during the panel) was in error, I do believe Confrey Response Commentary 
 Journal of Urban Mathematics Education Vol. 3, No. 2 30 that the advice of the collective group of mathematics education scholars— to pay closer attention to the mathematics—represents wise and pragmatic counsel to which all members of the mathematics education must attend. Mathematics educators have been effectively sidelined in many policy deci- sions and related expert panels. The worst example was reflected in the Na- tional Mathematics Advisory Panel Report (National Mathematics Advisory Panel, 2008), in which the chapter on learning and serving the needs of spe- cial education students virtually mandated direct instruction; the whole doc- ument severely limited attention to context, technologies, and modeling (Kelly, 2008). Some of those problems may turn out to be amplified in the Common Core State Standards (CCSS, 2010), which virtually eliminated statistics and algebra in the early grades, and in which the consequent inten- sity of the mathematics assigned to middle school is likely to have negative consequences for impoverished schools that lack sufficient teaching capac- ity. Scholars as well as policy specialists need to keep a very close eye on this development. One can argue that the displacement of the mathematics education commu- nity by mathematicians and cognitive scientists (primarily experimental psychologists) was simply a product of the prior federal administration’s bi- ases. But this marginalization continues in the current administration, and attacks on colleges of education continue. In light of these developments, the counsel to keep mathematics central in our work seems to me to be wise counsel. Concluding Remarks We must not underestimate the value of the type of debate and discussion that Martin et al.’s (2010) commentary facilitates. The group mentioned previ- ously who took part in the discussion at North Carolina State University left in a state of excitement and an increased sense of community, which resulted from spirited debate and attempts to discuss the “wicked problems”1 raised by the commentary. The exercise of debate, strong calls for self-examination, and em- phasis on inclusion are key values, particularly in a national culture in which en- lightened thought and debate seem to be increasingly attenuated, and local poli- cies that increase segregation, attacks on public schooling, bullying on sexuality, and excessive blaming of teachers for societies’ woes are rampant. I can under- stand the undertone of anger, urgency, and critical concern in Martin, Gholson, and Leonard’s commentary. However, I would have preferred to have seen less 























































 1 For an explanation of wicked problems, see http://en.wikipedia.org/wiki/Wicked_problem#Formal_definitions. Confrey Response Commentary 
 Journal of Urban Mathematics Education Vol. 3, No. 2 31 rhetorical devices, such as the link to “back to basics” which was relatively un- founded and implies an unduly conservative agenda, and more emphasis on the fact that the statement represents differences in opinions among scholars all of whom are exercising leadership. While critical theory is essential in raising con- sciousness, there is also a need for heavy lifting on the practical problems that cause inequity to persist. My voice in this debate is to call for “both and.” We cer- tainly need attention to both equity and mathematics, and in some critical areas with the potential to improve the situation, we have too few hands to lift and too few scholars gaining the technical know-how of methods and technological ad- vances to be keeping pace with the opportunities that are arising. A new synthesis of research methodologies that combines attention to equity and mathematics has the potential to benefit more children and teachers as well as to improve the strength of mathematics education. Acknowledgments I acknowledge the contributions of Alan Maloney, Allison McCulloch, and Kenny Nguyen in re- viewing and commenting on this commentary. All opinions expressed in the paper are solely the responsibility of the author. References Allen, M., Coulter, T., Dwyer, C. A., Goe, L., Immerwahr, J., Jackson, A., Johnson, J., Oliver, R. M., Ott, A., et al. (2006). America’s challenge: Effective teachers for at-risk schools and students. Washington, DC: National Comprehensive Center for Teacher Quality. Barrett, J. E., & Clements, D. H. (2003). Quantifying path length: Fourth-grade children’s developing abstractions for linear measurement. Cognition and Instruction, 21, 475–520. Barrett, J. E., Clements, D. H., Klanderman, D., Pennisi, S., & Polaki, M. V. (2006). Students’ coordination of geometric reasoning and measuring strategies on a fixed perimeter task: Developing mathematical understanding of linear measurement. Journal for Research in Mathematics Education, 37, 187–221. Battista, M. T. (2007). The development of geometric and spatial thinking. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 843–908). Charlotte, NC: Information Age. Behr, M., Harel, G., Post, T., & Lesh, R. (1992). Rational number, ratio and proportion. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 296–333). New York: Macmillan. Bennett, A., Bridglall, B. L., Cauce, A. M., Everson, H. T., Gordon, E. W., Lee, C. D., Mendoza- Denton, R., Renzulli, J. S., & Stewart, J. K. (2004). All students reaching the top: Strategies for closing academic achievement gaps. Naperville, IL: National Study Group for the Affirmative Development of Academic Ability. Black, P., & Wiliam, D. (1998). Inside the black box: Raising standards through classroom assessment. Phi Delta Kappan, 80,(2), 139–148. CCSS (2010). Common Core State Standards for Mathematics, retrieved from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf Confrey Response Commentary 
 Journal of Urban Mathematics Education Vol. 3, No. 2 32 Clements, D. H., & Sarama, J. (2009). Learning and teaching early math: The learning trajectories approach. New York: Routledge. Clements, D. H., Wilson, D. C., & Sarama, J. (2004). Young children’s composition of geometric figures: A learning trajectory. Mathematical Thinking and Learning, 6, 163–184. Confrey, J. (1988). Multiplication and splitting: Their role in understanding exponential func- tions. In M. Behr, C. LaCompagne, & M. Wheeler (Eds.), Proceedings of the 10th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 250–259). DeKalb, IL: Northern Illinois University Press. Confrey, J. (1995). Student voice in examining “splitting” as an approach to ratio, proportions and fractions. Proceedings of the 19th annual meeting of the International Group for the Psy- chology of Mathematics Education (Vol. 1, pp. 3–29). Recife, Brazil: Universidade Federal de Pernambuco. Confrey, J. (2007). Tracing the evolution of mathematics content standards in the United States: Looking back and projecting forward. Paper presented at K–12 mathematics: What should students learn and when should they learn it?, Arlington, VA. Confrey, J. (2008). A synthesis of the research on rational number reasoning: A learning progres- sions approach to synthesis. Paper presented at the 11th International Congress of Mathe- matics Instruction, Monterrey, Mexico. Confrey, J. (2009). Steering a course for preparing students for the mathematical sciences in the 21st century. Paper presented at the annual meeting of the Research in Undergraduate Mathematics Education Conference, Raleigh, NC. Confrey, J. (2010). What now? Priorities in implementing the Common Core State Standards for Mathematics. Paper presented at the Kick-Off for the Institute for Research in Mathematics and Science Education, Washington, D.C. Confrey, J., & Maloney, A. P. (in press). Next generation digital classroom assessment based on learning trajectories in mathematics. In C. Dede & J. Richards (Eds.), Steps toward a digital teaching platform. NewYork: Teachers College Press Darling-Hammond, L. (1994). Performance-based assessment and educational equity. Harvard Educational Review, 64, 5–29. Darling-Hammond, L. (2010). The flat world and education: How America’s commitment to equity will determine our future. New York: Teachers College Press. Empson, S. B., & Turner, E. (2006). The emergence of multiplicative thinking in children’s solu- tions to paper folding tasks. Journal of Mathematical Behavior, 25, 46–56. Frye, M. (1983). The politics of reality: Essays in feminist theory. Trumansberg, NY: The Crossing Press. Grouws, D., Reys, R. E., Papick, I., Tarr, J. E., & Chavez, O. (2010). Comparing options in secondary mathematics: Investigating curriculum (COSMIC). Retrieved from http://cosmic.missouri.edu/. Harel, G., Ball, D. L., Battista, M. T., Thompson, P., & Confrey, J. (2010). Where’s the mathematics in mathematics education? Paper presented at the Research Presession of the annual meeting of the National Council of Teachers of Mathematics, San Diego, CA. Harel, G., & Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. In A. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research in collegiate mathematics education III (pp. 234–283). Providence, RI: American Mathematical Society. Harel, G., & Sowder, L. (2007). Toward a comprehensive perspective on proof. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 805–842). Charlotte, NC: Information Age. Hart, K. A. (1988). Ratio and proportion. In J. Hiebert & M. J. Behr (Eds.), Number concepts and operations in the middle grades (pp. 198–219). Mahwah, NJ: Erlbaum. Confrey Response Commentary 
 Journal of Urban Mathematics Education Vol. 3, No. 2 33 Heid, M. K. (2010). Where’s the math (in mathematics education research)? Journal for Research in Mathematics Education, 41, 102–103. Hollebrands, K. (2002). The role of a dynamic software program for geometry in high school students’ developing understandings of geometric transformations. In D. Mewborn (Ed.), Proceedings of the 24th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 695–706). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education. Hufferd-Ackles, K., Fuson, K. C., & Sherin, M. G. (2004). Describing levels and components of a math-talk learning community. Journal for Research in Mathematics Education, 35, 81– 116. Karplus, R., Pulos, S., & Stage, E. (1983). Proportional reasoning of early adolescents. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 45–90). Or- lando, FL: Academic Press. Kelly, A. E. (Ed.). (2008). Special issue on foundations for success: The final report of the National Mathematics Advisory Panel [Special Issue]. Educational Researcher, 37(3). Lamon, S. J. (1993). Ratio and proportion: Connecting content and children’s thinking. Journal for Research in Mathematics Education, 24, 41–61. Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical frame- work. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629–668). Charlotte, NC: Information Age. Lesh, R., Behr, M., & Post, T. (1987). Rational number relations and proportions. In C. Janiver (Ed.), Problems of representations in the teaching and learning of mathematics (pp. 41– 58). Hillsdale, NJ: Erlbaum. Martin, D. B., Gholson, M. L., & Leonard, J. (2010). Mathematics as gatekeeper: Power and privilege in the production of knowledge. Journal of Urban Mathematics Education, 3(2), 12–24. Retrieved from http://ed-osprey.gsu.edu/ojs/index.php/JUME/article/view/95/51. McManus, S. (2008) A study of formative assessment and high stakes testing: Issues of student efficacy and teacher views in the mathematics classroom. Unpublished doctoral dissertation, North Carolina State University, Raliegh. McNaught, M., Tarr, J. E., & Sears, R. (2010). Conceptualizing and measuring fidelity of implementation of secondary mathematics textbooks: Results of a three–year study. Paper presented at the annual meeting of the American Educational Research Association, Denver, CO. Retrieved from http://cosmic.missouri.edu/aera10/. Moses, R. P., & Cobb., C. E. (2001). Radical equations: Math literacy and civil rights. Boston: Beacon Press. National Mathematics Advisory Panel (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education. Nesher, P. (1980). The stereotyped nature of school word problems. For the Learning of Mathematics, 1, 41–48. Noelting, G. (1980). The development of proportional reasoning and the ratio concept, part I – Differentiation of stages. Educational Studies in Mathematics, 11, 217–253. NPTARS (2005). Qualified teachers for at-risk schools: A national imperative. Washington, DC: National Partnership for Teaching in At-Risk Schools. Steffe, L. P. (2002). A new hypothesis concerning children’s fractional knowledge. Journal of Mathematical Behavior, 102, 1–41. Thomas, S. (2010). Examining the impact of the North Carolina integrated mathematics (NCIM) project professional development on two teachers’ instructional practices: A case study. Unpublised doctoral dissertation, North Carolina State University, Raleigh. Wilson, S. (2002). California dreaming: Reforming mathematics education. New Haven, CT: Yale University Press.