+ A Response to Dr. Na’ilah Suad Nasir’s Plenary Address – Why Should Mathematics Educators Care About Race and Culture? David W. Stinson Georgia State University PME-NA 2013 Chicago, IL

+ Mathematics as Gatekeeper: Power and Privilege in the Production of Knowledge Danny B. Martin, Maisie L. Gholson – University of Illinois at Chicago Jacqueline Leonard – University of Colorado Denver “Both And”—Equity and Mathematics: A Response to Martin, Gholson, and Leonard Jere Confrey – North Carolina State University Engaging Students in Meaningful Mathematics Learning: Different Perspectives, Complementary Goals Michael T. Battista – The Ohio State University Vol. 3, No. 2 Fall/Winter Issue 2010

+ Instructional Triangle Instruction, Capacity, and Improvement Consortium for Policy Research in Education, 1999, p. 3 D. K. Cohen and D. L. Ball

+ Instructional Triangle SOURCE: Adapted from Cohen and Ball, 1999, 2000, in press. Adding It Up: Helping Children Learn Mathematics National Research Council, 2002, p. 314 Editors: J. Kilpatrick, J. Swafford, and B. Findell

+ Expanding, Elaborating, and Rethinking the Instructional Triangle… Nipper, K., & Sztajn, P. (2008). Expanding the instructional triangle: Conceptualizing mathematics teacher development. Journal of Mathematics Teacher Education, 11, 333–341. Herbst, P., & Chazan, D. (2012). On the instructional triangle and sources of justification for action in mathematics teaching. Retrieved from Stinson, D. W., & Bullock, E. C. (2012). Transitioning into contemporary theory: Critical postmodern theory in mathematics education research. In L. R. Van Zoest, J. J. Lo, & J. L. Kratky (Eds.), Proceedings of the 34 th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1163–1169). Kalamazoo, MI: Western Michigan University.

+ Instructional Triangle “ Inequity in Mathematics Education: Questions for Educators” The Mathematics Educator, 2002, p. 35 J. Weissglass

+ Learning Pathways: A Conceptual Tool for Understanding Culture and Learning Na’ilah Suad Nasir, University of California Berkeley Brigid Barron, Stanford University Roy Pea, Stanford University Shelly Goldman, Stanford University Reed Stevens, Northwestern University Phil Bell, University of Washington, Seattle Maxine McKinney de Royston, University of California, Berkeley The LIFE (Learning in Formal and Informal Environments) Center is an NSF-funded Science Learning Center, which conducts research on the social foundations of learning. “Conceptualizing learning as occurring along culturally organized learning pathways—the sequences of consequential participations and transitions (Beach, 1999) in learning activities that move one toward greater social recognition as competent in particular learning domains and situations” (p. 2)

+ Four Key Characteristics of Learning Pathways… “Characteristic 1: Learning pathways are taken up in relation to identities, and have a relational, affective, and motivational component” “Characteristic 2: Learning pathways are socially constructed by self and others, and they build up over multiple instances” “Characteristic 3: Learning pathways are made up of related sets of practices and routines, which over time support repertoires of practices, often organized with one or more goals in mind” “Characteristic 4: Learning pathways include enactments of privilege and marginalization that occur in relation to structural constraints and supports from families and institutions”

+ Instructional Triangle & Learning Pathways Learning pathways are taken up in relation to identities, and have a relational, affective, and motivational component Learning pathways are socially constructed by self and others, and they build up over multiple instances Learning pathways are made up of related sets of practices and routines, which over time support repertoires of practices, often organized with one or more goal in mind Learning pathways include enactments of privilege and marginalization that occur in relation to structural constraints and supports from families and institutions

+ Instructional Triangle & Learning Pathways

+ What are some of the questions on race, ethnicity, culture, language, diversity, and equity that we might ask ourselves and one another as we engage as a community in the next few days…