The Tale of Two Teachers’ Use of Prompts in Mathematical Discussions
Keywords:Institutional obligation, mathematical discussion, practical rationality, teacher questioning
Facilitating mathematical discussions has consistently been identified as beneficial to students’ mathematical learning, with teachers’ use of questioning a primary identifier of appropriate facilitation. Although many teachers report familiarity with appropriate questioning techniques, we hypothesized that some teachers may not work in contexts where they can implement what they understand as best practices in their classroom. To explore this potential interaction, two primary teachers with similar dispositions towards mathematics pedagogy, but dissimilar institutional obligations were observed over a 10-week period. The types and frequencies of teachers’ questioning and their students’ responses during whole class mathematical discussions were observed. Despite both teachers holding similar conceptions of and dispositions towards facilitating mathematical discussion, the effectiveness of teachers’ various prompts in eliciting students’ mathematical descriptions was substantially different. Findings suggest that differences in the respective teachers’ institutional obligations may have affected the effectiveness of one teacher’s probing questions.
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: PME-NA.
Cengiz, N., Kline, K., & Grant, T. J. (2011). Extending students’ mathematical thinking during whole-group discussions. Journal of Mathematics Teacher Education, 14, 355-374. https://doi.org/10.1007/s10857-011-9179-7
Clotfelter, C. T., Ladd, H. F., & Vigdor, J. L. (2007). Teacher credentials and student achievement: Longitudinal analysis with student fixed effects. Economics of Education Review, 26(6), 673–682. https://doi.org/10.1016/j.econedurev.2007.10.002
Cohen, D. K., Raudenbush, S. W., & Ball, D. L. (2003). Resources, instruction, and research. Educational Evaluation and Policy Analysis, 25(2), 119–142.https://doi.org/10.3102/01623737025002119
Creswell, J. W., & Plan Clark, V. L. (2007). Designing and conducting mixed methods research. Thousand Oaks, CA: Sage Publications.https://doi.org/10.1177/1558689806298644
Delice, A., Aydin, E., & Cevik, K. S. (2013). Mathematics teachers’ use of questions: Is there a change of practice after the curriculum change? Eurasia Journal of Mathematics, Science & Technology Education, 9(4), 417–427.
Franke, M. L., et al. (2009). Teacher questioning to elicit students’ mathematical thinking in elementary school classrooms. Journal of Teacher Education, 60(4),380–392. https://doi.org/10.1177/0022487109339906
Heid, M. K., et al. (2014). A processes lens on a beginning teacher’s personal and classroom mathematics. In J. J. Lo, K. R. Leatham, & L. R. Van Zoest (Eds.), Research Trends in Mathematics Teacher Education (pp. 67–82). New York: Springer International Publishing. https://doi.org/10.1007/978-3-319-02562-9_4
Herbst, P., & Chazan, D. (2011). Research on practical rationality: Studying the justification of actions in mathematics teaching. The Mathematics Enthusiast, 8(3), 405–462.
Herbst, P., & Chazan, D. (2012). On the instructional triangle and sources of justification for actions in mathematics teaching. ZDM, 44(5), 601–612.https://doi.org/10.1007/s11858-012-0438-6
Hiebert, J. & Wearne, D. (1993). Instructional tasks, classroom discourse, and students’ learning in second-grade arithmetic. American Educational Research Journal, 30(2), 393–425 https://doi.org/10.3102/00028312030002393
Hill, H. C. (2005). Content across communities: Validating measures of elementary mathematics instruction. Educational Policy, 19, 447–475.https://doi.org/10.1177/0895904805276142
Hill, H. C., et al. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430–511. https://doi.org/10.1080/07370000802177235
Hill, H. C., Schilling, S. G., & Ball, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching. The Elementary School Journal, 105(1), 11–30. https://doi.org/10.1086/428763
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. https://doi.org/10.2307/30034933
Hunter, R. (2007). Can you convince me: Learning to use mathematical argumentation. In J. H. Woo, H. C., Lew, K. S., Park, & D. Y. Seo (Eds.), Proceedings of the 31st conference of the International Group for the Psychology of Mathematics Education, Volume 3 (pp. 81-88), Seol: PME.
Ihrig, L. M. (2014). The effects of socialization on beginning science teachers’ pedagogical decision making and science instruction (Unpublished doctoral dissertation). Iowa State University, Ames, Iowa.
Karaağaç, M. K., & Threlfall, J. (2004). The tension between teacher beliefs and teacher practice: The impact of the work setting. In Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, 137–144). Toronto, Canada: PME-NA.
Kazemi, E., & Stipek, D. (2001). Promoting conceptual thinking in four upper-elementary mathematics classrooms. The Elementary School Journal, 102(1), 59–80.https://doi.org/10.1086/499693
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. (2016). Primary teachers’ choice of probing questions: Effects of MKT and supporting student autonomy. IEJME – Mathematics Education, 11(4), 991–1012.
Kosko, K. W. (2012). 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. & Miyazaki, Y. (2012). The effect of student discussion frequency on fifth-grade students’ mathematics achievement in U.S. schools. The Journal of Experimental Education, 80(2), 173–195.https://doi.org/10.1080/00220973.2011.566588
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.https://doi.org/10.1007/s13394-013-0116-1
Kosko, K. W., & Wilkins, J. L. M. (2015). Does time matter in improving mathematical discussions? The influence of mathematical autonomy. The Journal of Experimental Education, 83(3), 368–385. https://doi.org/10.1080/00220973.2014.907225
Kosko, K. W., & Wilkins, J. L. M. (2012). Students’ quality of mathematical discussion and their self-determination in mathematics. Investigations in Mathematics Learning, 4(3), 15–30.
MacLure, M. (2003). Discourse in educational and social research. Philadelphia: Open University Press.
Mercer, N., & Littleton, K. (2007). Dialogue and the development of children’s thinking: A sociocultural approach. London: Routledge.
Newton, H. Z. (2011). Chinese teachers’ self-reported beliefs and practices related to majority and minority students in Xinjiang Uygur Autonomous Region (Unpublished doctoral dissertation). University of Washington, Seattle, WA.
Oliveira, A. W. (2009). “Kindergarten, can I have your eyes and ears?” politeness and teacher directive choices in inquiry-based science classrooms. Cultural Studies of Science Education, 4, 803–846. https://doi.org/10.1007/s11422-009-9193-6
Reeve, J., Bolt, E., & Cai, Y. (1999). Autonomy-supportive teachers: How they teach and motivate students. Journal of Educational Psychology, 91, 537–548.https://doi.org/10.1037/0022-06188.8.131.527
Siegel, S., & Castellan, N. J. (1988). Nonparametric statistics for the behavioural sciences (2nd Ed.). New York: McGraw-Hill.
Streeck, J., & Mehus, S. (2005). Microethnography: The study of practices. In K. L. Fitch & R. E. Sanders (Eds.), Handbook of language and social interaction (pp. 381–404). Mahwah, NJ: Lawrence Erlbaum Associates, Publishers.
Temple, C., & Doerr, H. M. (2012). Developing fluency in the mathematical register through conversation in a tenth-grade classroom. Educational Studies in Mathematics, 81, 287–306. https://doi.org/10.1007/s10649-012-9398-6
Tobin, K. (1986). Effects of teacher wait time on discourse characteristics in mathematics and language arts classes. American Educational Research Journal, 23(2), 191–200. https://doi.org/10.3102/00028312023002191
Truxaw, M. P., Gorgievski, N., & DeFranco, T. C. (2008). Measuring K-8 teachers’ perceptions of discourse use in their mathematics classes. School Science and Mathematics, 108(2), 58–70. https://doi.org/10.1111/j.1949-8594.2008.tb17805.x
Webel, C., & Platt, D. (2015). The role of professional obligations in working to change one’s teaching practices. Teaching and Teacher Education, 47, 204–217.https://doi.org/10.1016/j.tate.2015.01.007
Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27, 458–477. https://doi.org/10.2307/749877
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Based on a work at https://iie.chitkara.edu.in