Orchestrating productive whole class discussions: The role of designed student responses
Keywords:
Mathematics discourse, whole class discussion, teacher tools, problem solving, designed student response, worked-out exampleAbstract
The value of students publicly sharing and discussing their solutions to unstructured problems is widely recognised. This can, however, be pedagogically challenging. The solutions may be partial, unclear and unpredictable. For many teachers, particularly those new to working with such problems with their students, the improvisation needed to orchestrate productive discussions can be unmanageably high. In this paper we present a pedagogical tool to help teachers. Specifically, teachers orchestrate discussions of designed, worked-out solutions to unstructured problems. In these lessons teachers are guaranteed a range of distinct solutions for which they can plan. The reduced need for improvisation means teachers are better placed to learn and practice new ways of probing students’ reasoning. These acquired practices may then be applied to discussions of students’ own responses to a problem.
In the study we explore the question: for a teacher new to working with unstructured problems, how do discussions of worked-out solutions (called in this paper designed student responses) differ from discussions of students’ own solutions? We find that discussions of authentic student solutions tend to focus on procedural descriptions, whereas the discussions of designed solutions also stimulated student explanation and evaluation. The findings reported here represent the initial part of an on-going study.
References
Ball, D. B., Thames, M. H., & Phelps, G. (2008). Content Knowledge for Teaching : What Makes It Special? Journal of Teacher Education, 59(5), 389-407.
Black, P., & Wiliam, D. (1998). Assessment and Classroom Learning. Assessment in Education: Principles, Policy & Practice, 5(1), 7-74.
Brousseau, G. (1997). Theory of Didactical Situations in Mathematics (N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield, Trans. Vol. 19). Dordrecht: Kluwer.
Carlson, M. P. (1999). The Mathematical Behaviour of Six Successful Mathematics Graduate Students:Influences Leading to Mathematical Success. Education Studies Mathematics, 40, 237-258.
Chazan, D., & Ball, D. L. (1999). Beyond being told not to tell. For the Learning of Mathematics, 19(2), 2-10.
Cole, M., & Scribner, S. (1975). Theorizing about the socialisation of cognition. . In T. Schwartz (Ed.), Socialization as cultural communication (pp. 157-176). Berkeley: University of California Press.
Franke, M. L., Webb, N. M., Chan, A. G., Ing, M., Freund, D., & Battey, D. (2009). Teacher Questioning to Elicit Students' Mathematical Thinking in Elementary School Classrooms. Journal of Teacher Education, 60(4), 380-392.
Lampert, M. (2001). Teaching problems and the problems of teaching. New Haven, CT: Yale University Press.
Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. New York: Campridge University Press.
Mercer, N. (1996). The quality of talk in children's collaborative activity in the classroom. Learning and Instruction, 6(4), 359-377.
Michaels, S., & O'Connor, C. (2015). Conceptualizing Talk Moves as Tools: Professional Development Approaches for Academically Productive Discussion. In A. E. R. Association (Ed.), Socializing Intelligence Through Academic Talk and Dialogue (pp. 347-362).
O'Connor, M. C. (1998). Language Socialization in the Classroom. In M.
Lampert & M. L. Blunk (Eds.), Talking Mathematics in Schools (pp. 17-56). UK: Cambridge University Press.
Remillard, J. T. (2000). Can curriculum materials support teachers’ learning? . Elementary School Journal, 100(4), 331-350.
Seufert, T., Janen, I., & Brunken, R. (2007). The impact of intrinsic cognitive load on the effectiveness of graphical help for coherence formation. Computers in human behavior, 23(3), 1055-1071.
Sfard, A. (1991). On the dual natureof mathematicalconceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1-36.
Sfard, A., & Kieran, C. (2001). Cognition as communication: Rethinging learning-by-talking through multi-faceted analysis of students' mathematical interactions. Mind, Culture, and Activity, 8(1), 42-76.
Sherin, M. G. (2002). When Teaching Becomes Learning. Cognition and Instruction, 20(2), 119-150.
Silver, A. E., Ghousseini, H., Gosen, D., Charalambous, C., & Font Strawhum, B. T. (2005). Moving from rhetoric to praxis: Issues faced by teachers in having students consider multiple solutions for problems in the mathematics classroom. Journal of Mathematical Behavior, 24, 287-301.
Smith, F., Hardman, F., Wall, K., & Mroz, M. (2004). Interactive whole class teaching in the National Literacy and Numercy Strategies. British Educational Research Journal, 30(3), 395-411.
Staples, M. (2007). Supporting Whole-class Collaborative Inquiry in a Secondary Mathematics Classroom,. Cognition and Instructy, 25(2-3), 161-217.
Stein, M. K., Eagle, R. A., Smith, M. A., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10, 313-340.
Van Someren, M. W., Reimann, P., Boshuisen, H. P. A., & de Jong, T. (1998). Learning with multiple representations. Amsterdam: Pergamon.
Vygotsky, L. (1978). Mind in Society. Harvard University Press.
Yackel, E., & Cobb, P. (1996). Sociomathematical Norms, Argumentation, and Autonomy in Mathematics. Journal for Research in Mathematics Education, 27(4), 458-477.
