pp. 991-1012 | Article Number: iejme.2016.090
Published Online: July 20, 2016
Article Views: 323 | Article Download: 369
The present study explored whether primary grades teachers chose probing questions, given two hypothetical mathematics lesson scenarios. After responding to the mathematics lesson scenarios, participating teachers completed the Problems in Schools survey assessing dispositions to support student autonomy, and the Mathematical Knowledge for Teaching (MKT) assessment for primary grades patterns, functions and algebra. Logistic multiple regression was used to examine the influence of teachers’ MKT and dispositions for supporting student autonomy. Results differed by format of scenario. In the scenario where the choice of a probing question would act as an initial prompt for description, results showed this choice was influenced more strongly by MKT score. In the scenario where a choice of probing question followed an already embedded student description, choosing a probing prompt as a follow-up question was more strongly influenced by support for student autonomy. Additionally, a negative, statistically significant interaction effect was found across both scenarios. Implications for these findings are discussed.
Keywords: Teacher knowledge, mathematical discussion, teacher questioning
Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407.
Boaler, J., & Brodie, K. (2004). The importance of depth and breadth in the analyses of teaching: A framework for analyzing teacher questions. In D. E. McDougall & J. A. Ross (Eds.), Proceedings of the 26th meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 773-782). Toronto, Canada.
Chazan, D., & Ball, D. (1999). Beyond being told not to tell. For the Learning of mathematics, 19(2), 2-10.
Cengiz, N., Kline, K., & Grant, T. J. (2011). Extending students’ mathematical thinking during whole-group discussions. Journal of Mathematics Teacher Education, 14, 355-374.
Clason, D. L., & Dormody, T. J. (1994). Analyzing data measured by individual Likert-type items. Journal of Agricultural Education, 35(4), 31-35.
Cross, D. I. (2009). Creating optimal mathematics learning environments: Combining argumentation and writing to enhance achievement. International Journal of Science and Mathematics Education, 7, 905-930.
Crocker, L., & Algina, J. (2006). Introduction to classical and modern test theory. Mason, OH: Wadsworth.
Deci, E. L., Schwartz, A. J., Sheinman, L., & Ryan, R. M. (1981). An instrument to assess adults’ orientations toward control versus autonomy with children: Reflections on intrinsic motivation and perceived competence. Journal of Educational Psychology, 73, 642-650.
Forman, E. A., Larreamendy-Joerns, J., Stein, M. K., & Browns, C. A. (1998). “You’re going to want to find out which and prove it”: Collective argumentation in a mathematics classroom. Learning and Instruction, 8(6), 527-548.
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.
Gokbel, E. N., & Boston, M. D. (2015). Considering students’ responses in determining the quality of teachers’ questions during mathematical discussions. In T. G., Bartell, K. N. Bieda, R. T. Putnam, K. Bradfield, & H. Dominguez (Eds.), Proceedings of the 37th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (p. 1172). East Lansing, MI: Michigan State University.
Grassetti, M. T. (2010). Engaging students in mathematics conversations: Discourse practices and the development of social and socialmathematical norms in three novice teachers’ classrooms (doctoral dissertation). Amherst, MA: University of Massachusetts – Amherst.
Herbst, P. & Chazan, D. (2012). On the instructional triangle and sources of justification for actions in mathematics teaching. ZDM, 44(5), 601-612.
Herbst, P., Chazan, D., Chen, C. L., Chieu, V. M., & Weiss, M. (2011). Using comics-based representations of teaching, and technology, to bring practice to teacher education courses. ZDM, 43(1), 91-103.
Herbst, P., Chazan, D., Kosko, K. , Dimmel, J., & Erikson, A. (2016). Studying decision making in instructional situations: How multimedia questionnaires can help. ZDM-Mathematics Education, 48(1), 167-183.
Herbst, P., & Chieu, V. M. (2011). Depict: A tool to represent classroom scenarios technical report. University of Michigan. Retrieved from http://hdl.handle.net/2027.42/87949.
Herbst, P., & Kosko, K. W. (2014). Mathematical knowledge for teaching and its specificity to high school geometry instruction. In J. Lo, K. R., Leatham, & L. R. Van Zoest (Eds.), Research trends in mathematics teacher education (pp. 23-46). New York: Springer.
Herbst, P., Kosko, K. W., & Dimmel, J. (2013). How are geometric proof problems preented? Conceptualzing and measuring teachers’ recognition of the diagrammatic register. In A. C. Superfine, M. Martinez, G. Larnell, T. Stoelinga, & D. Martin (Eds.), Proceedings of the 35th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 179-186), Chicago, IL: University of Illinois at Chicago.
Herbst, P., & Miyakawa, T. (2008). When, how, and why prove theorems? A methodology for studying the perspective of geometry teachers. ZDM, 40(3), 469-486.
Hiebert, J. & Wearne, D. (1993). Instructional tasks, classroom discourse, and students’ learning in second-grade arithmetic. American Educational Research Journal, 30(2), 393 – 425
Hill, H. C., Blunk, M. L., Charalambous, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L., & Ball, D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430-511.
Hill, H. C., Schilling, S. G., & Ball, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching. Elementary School Journal, 105, 11-30.
Hosmer, D. W., & Lemeshow, S. (2000). Applied logistic regression (2nd Ed.). New York: John Wiley & Sons, Inc.
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.
Jansen, A. (2006). Seventh graders’ motivations for participating in two discussion-oriented mathematics classrooms. The Elementary School Journal, 106(5), 409-428.
Jochums, B. L., & Pershey, E. J. (1993). Using the vignette method in formative evaluation. Evaluation Practice, 14(2), 155-161.
Kazemi, E., & Stipek, D. (2001). Promoting conceptual thinking in four upper-elementary mathematics classrooms. The Elementary School Journal, 102(1), 59-80.
Kersting, N. (2008). Using video clips of mathematics classroom instruction as item prompts to measure teachers’ knowledge of teaching mathematics. Educational and Psychological Measurement, 68(5), 845-861.
Kersting, N. B., Givvin, K. B., Sotelo, F. L., & Stigler, J. W. (2010). Teachers’ analyses of classroom video predict student learning of mathematics: Further explorations of a novel measure of teacher knowledge. Journal of Teacher Education, 61(1-2), 172-821.
Kim, H. J. (2011). An exploratory study of teachers’ use of mathematical knowledge for teaching to support mathematical argumentation in middle-grades (doctoral dissertation). Austin, TX: The University of Texas at Austin.
Kosko, K. W. (2012a). Geometry students’ hedged statements and their self-regulation of mathematics. The Journal of Mathematical Behavior, 31(4), 489-499.
Kosko, K. W. (2012b). Student enrollment in classes with frequent mathematical discussion and its longitudinal effect on mathematics achievement. The Mathematics Enthusiast, 9(1&2), 111-148.
Kosko, K. W. (2012). Geometry students’ self-determination and their engagement in mathematical whole class discussion. Investigations in Mathematics Learning, 8(2), 17-36.
Kosko, K. W., & Gao, Y. (2014). Perceptions and reality: One teacher’s use of prompts in mathematical discussions. In P. Liljedahl, S. Oesterle, C. Nicol, & D. Allan (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (Vol. 4, pp. 41-48), Vancouver, Canada: PME.
Kosko, K. W., & Herbst, P. G. (2013). Opening opportunities for discourse in the face of norms for posing proof problems. Round table paper presented at the 2013 Annual Meeting of the American Educational Research Association, Division C, San Francisco, CA.
Kosko, K. W., & Herbst, P. (2012). Evaluating teachers’ decisions in posing a proof problem. In L. R. Van Zoest, J. J. Lo, & J. L. Kratky (Eds.), Proceedings of the 34th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 813-820), Kalamazoo, MI: Western Michigan University.
Kosko, K. W., Rougee, A., & Herbst, P. (2014). ). What actions do teachers envision when asked to facilitate mathematical argumentation in the classroom? Mathematics Education Research Journal, 26(3), 459-476.
Kosko, K. W., & Wilkins, J. L. M. (2015). Does time matter in the growth of student-reported engagement in mathematical discussions? The influence of mathematical autonomy. Journal of Experimental Education., 83(3), 368-385.
Lobato, J., Clarke, D., Ellis, A. B. (2005). Initiating and eliciting in teaching: A reformulation of telling. Journal for Research in Mathematics Education, 36(2), 101-136.
Martino, A. M., & Maher, C. A. (1999). Teacher questioning to promote justification and generalization in mathematics: What research practice has taught us. Journal of Mathematical Behavior, 18(1), 53-78.
Moreno, R., & Ortegano-Layne, L. (2008). Do classroom exemplars promote the application of principles in teacher education? A comparison of videos, animations, and narratives. Educational Technology Research and Development, 56(4), 449-465.
Moyer, P. S., & Milewicz (2002). Learning to question: Categories of questioning used by preservice teachers during diagnostic mathematics interviews. Journal of Mathematics Teacher Education, 5(4), 293-315.
National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: Author.
O’Connor, M. C., & Michaels, S. (1993). Aligning academic task and participation status through revoicing: Analysis of a classroom discourse strategy. Anthropology and Education Quarterly, 24(4), 318-335.
Stein, M. K., & Lane, S. (1996). Instructional tasks and the development of student capacity to think and reason: An analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation: An International Journal on Theory and Practice, 2(1), 50-90.
Turner, J. C., Meyer, D. K., Midgley, C., & Patrick, H. (2003). Teacher discourse and sixth graders’ reported affect and achievement behaviors in two high-mastery / high-performance mathematics classrooms. The Elementary School Journal, 103(4), 357-382.
Webb, N. M., Franke, M. L., Ing, M., Chan, A., De, T., Freund, D., & Battey, D. (2008). The role of teacher instructional practices in student collaboration. Contemporary Educational Psychology, 33, 360-381.
Wilson, M. (2005). Constructing measures: An item response modeling approach. Mahwah, NJ: Lawrence Erlbaum.
Zahner, W. C. (2012). “Nobody can sit there”: Two perspectives on how mathematics problems in context mediate group problem solving discussions. Journal of Research in Mathematics Education, 1(2), 105-135.