Exploring the central role of student authority relations in collaborative mathematics
Abstract
How students build mathematics knowledge together in classrooms is of central concern in research focused on the role of language in learning and doing mathematics. This paper explores how students compose mathematics knowledge together in relation to the social construction of influence. Drawing on the influence framework (Engle et al. in J Learn Sci 23(2):245–268, 2014), core interactional components are made salient: gaining access to the conversational floor and interactional space, being perceived as intellectually meritorious, and being positioned with social and intellectual authority. Of these, being positioned with social and intellectual authority is argued to be most important. This paper highlights both the centrality of authority and its discursive nature and connects these ideas to collaborative mathematics activity. Finally, the paper concludes with a discussion of the theoretical generativity of focusing on the functions of language in mathematics classrooms, in addition to its forms, to better articulate discursive mechanisms at play during collaborative mathematics learning activities.
Keywords
Authority Influence Collaboration Language IdentityReferences
- Amit, M., & Fried, M. N. (2005). Authority and authority relations in mathematics education: A view from an 8th grade classroom. Educational Studies in Mathematics, 58(2), 145–168.CrossRefGoogle Scholar
- Anderson, K. (2009). Applying positioning theory to the analysis of classroom interactions: Mediating micro-identities, macro-kinds, and ideologies of knowing. Linguistics and Education, 20(4), 291–310.CrossRefGoogle Scholar
- Bell, C. V., & Pape, S. J. (2012). Scaffolding students’ opportunities to learn mathematics through social interactions. Mathematics Education Research Journal, 24(4), 423–445.CrossRefGoogle Scholar
- Bishop, J. P. (2012). “She’s always been the smart one. I’ve always been the dumb one”: Identities in the mathematics classroom. Journal for Research in Mathematics Education, 43(1), 34–74.CrossRefGoogle Scholar
- Brodie, K. (2007). Dialogue in mathematics classrooms: Beyond question-and-answer methods. Pythagoras, 66, 3–13.Google Scholar
- Cvencek, D., Nasir, N. I. S., O’connor, K., Wischnia, S., & Meltzoff, A. N. (2015). The development of math-race stereotypes: “They say Chinese people are the best at math”. Journal of Research on Adolescence, 25(4), 630–637.CrossRefGoogle Scholar
- DeJarnette, A. F., & González, G. (2015). Positioning during group work on a novel task in algebra II. Journal for Research in Mathematics Education, 46(4), 378–422.CrossRefGoogle Scholar
- Engle, R. A., & Conant, F. R. (2002). Guiding principles for fostering productive disciplinary engagement: Explaining an emergent argument in a community of learners classroom. Cognition and Instruction, 20(4), 399–483.CrossRefGoogle Scholar
- Engle, R. A., Langer-Osuna, J. M., & McKinney de Royston, M. (2014). Toward a model of influence in persuasive discussions: Negotiating quality, authority, privilege, and access within a student-led argument. Journal of the Learning Sciences, 23(2), 245–268.CrossRefGoogle Scholar
- Erickson, F., & Shultz, J. J. (1981). Talking to “The Man’: Organization of communication in school counseling interviews. New York: Academic Press.Google Scholar
- Esmonde, I. (2017). Power and sociocultural theories of learning. In I. Esmonde & A. N. Booker (Eds.), Power and privilege in the learning sciences: Critical and sociocultural theories of learning. New York: Routledge.Google Scholar
- Esmonde, I., & Langer-Osuna, J. M. (2013). Power in numbers: Student participation in mathematical discussions in heterogeneous spaces. Journal for Research in Mathematics Education, 44(1), 288–315.CrossRefGoogle Scholar
- Gerson, H., & Bateman, E. (2010). Authority in an agency-centered, inquiry-based university calculus classroom. The Journal of Mathematical Behavior, 29(4), 195–206.CrossRefGoogle Scholar
- Halliday, M. A. K. (1978). Language as social semiotic. London: Edward Arnold.Google Scholar
- Hamm, J. V., & Perry, M. (2002). Learning mathematics in first-grade classrooms: On whose authority? Journal of Educational Psychology, 94(1), 126–137.CrossRefGoogle Scholar
- Hand, V., & Gresalfi, M. (2015). The joint accomplishment of identity. Educational Psychologist, 50(3), 190–203.CrossRefGoogle Scholar
- Harré, R., & Langenhove, L. Van (Eds.). (1998). Positioning theory: Moral contexts of international action. Oxford: Blackwell Publishers.Google Scholar
- Herbel-Eisenmann, B. A., & Otten, S. (2011). Mapping mathematics in classroom discourse. Journal for Research in Mathematics Education, 42(5), 451–485.CrossRefGoogle Scholar
- 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(2), 81–116.CrossRefGoogle Scholar
- Kotsopoulos, D. (2014). The case of Mitchell’s cube: Interactive and reflexive positioning during collaborative learning in mathematics. Mind, Culture, and Activity, 21(1), 34–52.CrossRefGoogle Scholar
- Langer-Osuna, J. (2015). From getting ‘fired’ to becoming a collaborator: A case of the co-construction of identity and engagement in a project-based mathematics classroom. Journal of the Learning Sciences, 24(1), 53–92.CrossRefGoogle Scholar
- Langer-Osuna, J., Gargroetzi, E., Munson, J., & Chavez, R. (2018). The role of off-task interactions in supporting productive disciplinary engagement in elementary mathematics. Paper presented as part of structured symposium: Understanding the transformative power of teacher and student agency in changing educational contexts at the annual meeting of the American Educational Research Association, New York.Google Scholar
- Langer-Osuna, J. M. (2011). How Brianna became bossy and Kofi came out smart: Understanding the trajectories of identity and engagement for two group leaders in a project-based mathematics classroom. Canadian Journal of Science, Mathematics, and Technology Education, 11(3), 207–225.CrossRefGoogle Scholar
- Langer-Osuna, J. M. (2016). The social construction of authority among peers and its implications for collaborative mathematics problem solving. Mathematical Thinking and Learning, 18(2), 107–124.CrossRefGoogle Scholar
- Langer-Osuna, J. M. (2017). Authority, identity, and collaborative mathematics. Journal for Research in Mathematics Education, 48(3), 237–247.CrossRefGoogle Scholar
- Lerman, S. (2000). The social turn in mathematics education research. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 19–44). Westport: Ablex Publishing.Google Scholar
- McGee, E. (2013). Young, black, mathematically gifted, and stereotyped. The High School Journal, 96(3), 253–263.CrossRefGoogle Scholar
- Mehan, H. (1979). Learning lessons. Cambridge: Harvard University Press.CrossRefGoogle Scholar
- Morgan, C., Craig, T., Schuette, M., & Wagner, D. (2014). Language and communication in mathematics education: An overview of research in the field. ZDM—The International Journal on Mathematics Education, 46(6), 843–853.CrossRefGoogle Scholar
- Moschkovich, J. (1999). Supporting the participation of English language learners in mathematical discussions. For the Learning of Mathematics, 19(1), 11–19.Google Scholar
- Moschkovich, J. N. (1996). Moving up and getting steeper: Negotiating shared descriptions of linear graphs. The Journal of the Learning Sciences, 5(3), 239–277.CrossRefGoogle Scholar
- Pace, J. L., & Hemmings, A. (2007). Understanding authority in classrooms: A review of theory, ideology, and research. Review of Educational Research, 77(1), 4–27.CrossRefGoogle Scholar
- Pimm, D. (2014). Authority, explanation, contention and register: Language data and the surface search for essence. ZDM—The International Journal on Mathematics Education, 46(6), 967–976.CrossRefGoogle Scholar
- Planas, N., Morgan, C., & Schütte, M. (2018). Mathematics education and language. Lessons from two decades of research. In T. Dreyfus, M. Artigue, D. Potari, S. Prediger & K. Ruthven (Eds.), Developing research in mathematics education. Twenty years of communication, cooperation and collaboration in Europe (pp. 196–210). London: Routledge.CrossRefGoogle Scholar
- Rowland, T. (1992). Pointing with pronouns. For the Learning of Mathematics, 12(2), 44–48.Google Scholar
- Schleppegrell, M. J. (2007). The linguistic challenges of mathematics teaching and learning: A research review. Reading & Writing Quarterly, 23(2), 139–159.CrossRefGoogle Scholar
- Sfard, A. (2001). There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning. Educational Studies in Mathematics, 46(1–3), 13–57.CrossRefGoogle Scholar
- Shah, N., & Leonardo, Z. (2017). Learning discourses of race and mathematics in classroo interaction: A poststructural perspective. In I. Esmonde & A. N. Booker (Eds.), Power and privilege in the learning sciences: Critical and sociocultural theories of learning. New York: Routledge.Google Scholar
- Sullivan, F. R., & Wilson, N. C. (2015). Playful talk: Negotiating opportunities to learn in collaborative groups. Journal of the Learning Sciences, 24(1), 5–52.CrossRefGoogle Scholar
- Varelas, M., Martin, D. B., & Kane, J. M. (2012). Content learning and identity construction: A framework to strengthen African American students’ mathematics and science learning in urban elementary schools. Human Development, 55(5–6), 319–339.CrossRefGoogle Scholar
- Wagner, D., & Herbel-Eisenmann, B. (2014). Identifying authority structures in mathematics classroom discourse: a case of a teacher’s early experience in a new context. ZDM—The International Journal on Mathematics Education, 46(6), 871–882.CrossRefGoogle Scholar
- Walkerdine, V. (1997). Redefining the subject in situated cognition theory. In D. Kirshner & J. A. Whitson (Eds.), Situated cognition: Social, semiotic, and psychological perspectives (pp. 57–70). Mahwah: Lawrence Erlbaum.Google Scholar
- Wilson, M. S., & Lloyd, G. M. (2000). Sharing mathematical authority with students: The challenge for high school teachers. Journal of Curriculum and Supervision, 15(2), 146–169.Google Scholar
- Wood, M. B. (2013). Mathematical micro-identities: Moment-to-moment positioning and learning in a fourth-grade classroom. Journal for Research in Mathematics Education, 44(5), 775–808.CrossRefGoogle Scholar
- Wortham, S. (2006). Learning identity: The joint emergence of social identification and academic learning. Cambridge: Cambridge University Press.Google Scholar