Teachers' Orientations Toward Using Student Mathematical Thinking As a Resource During WholeClass Discussion
Stockero, S. L., Leatham, K. R., Ochieng, M. A., Van Zoest, L. R., & Peterson, B. E. (2019). Teachers' orientations toward using student mathematical thinking as a resource during wholeclass discussion. Journal of Mathematics Teacher Education. https://doi.org/10.1007/s10857018094210
Using student mathematical thinking during instruction is valued by the mathematics education community, yet practices surrounding such use remain difficult for teachers to enact well, particularly in the moment during wholeclass instruction. Teachers' orientations—their beliefs, values, and preferences—influence their actions, so one important aspect of understanding teachers' use of student thinking as a resource is understanding their related orientations. To that end, the purpose of this study is to characterize teachers' orientations toward using student mathematical thinking as a resource during wholeclass instruction. We analyzed a collection of 173 thinkingasaresource orientations inferred from scenariobased interviews conducted with 13 teachers. The potential of each orientation to support the development of the practice of productively using student mathematical thinking was classified by considering each orientation's relationship to three frameworks related to recognizing and leveraging highpotential instances of student mathematical thinking. After discussing orientations with different levels of potential, we consider the cases of two teachers to illustrate how a particular collection of thinkingasaresource orientations could support or hinder a teacher's development of the practice of building on student thinking. The work contributes to the field's understanding of why particular orientations might have more or less potential to support teachers' development of particular teaching practices. It could also be used as a model for analyzing different collections of orientations and could support mathematics teacher educators by allowing them to better tailor their work to meet teachers' specific needs.
Teachers' Responses to Instances of Student Mathematical Thinking with Varied Potential to Support Student Learning
Stockero, S. L., Freeburn, B., Van Zoest, L. R., Peterson, B. E., & Leatham, K. R. (2018). Teachers' responses to instances of student mathematical thinking with varied potential to support student learning. In T. E. Hodges, G. J. Roy, & A. M. Tyminski (Eds.), Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 10761083). Greenville, SC: University of South Carolina & Clemson University.
A Characterization of Student Mathematical Thinking That Emerges During WholeClass Instruction: An Exploratory Study
Van Zoest, L. R., Leatham, K. R., Arslan, O., Ochieng, M. A., Ruk, J. M., Peterson, B. E., & Stockero, S. L. (2018). A characterization of student mathematical thinking that emerges during wholeclass instruction: An exploratory study. In T. E. Hodges, G. J. Roy, & A. M. Tyminski (Eds.), Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 11261129). Greenville, SC: University of South Carolina & Clemson University.
This exploratory study investigated 164 instances of student mathematical thinking that emerged during wholeclass instruction in a highschool geometry course. The MOST Analytic Framework provided a way to categorize these instances according to their Building Potential—that is, the potential for learning to occur if the student thinking of the instance were made the object of consideration by the class. We discuss variations in Building Potential found in these instances by examining the subcategorizations that emerged from our additional analyses. The variations in the building potential of student thinking revealed in the study highlight the complexity of teaching, and the need to support teachers in identifying and appropriately responding to instances with different levels of Building Potential.
Teachers' Responses To a Common Set of High Potential Instances of Student Mathematical Thinking
Stockero, S. L., Van Zoest, L. R., Peterson, B. E., Leatham, K. R., & Rougée, A. O. T. (2017). Teachers' responses to a common set of high potential instances of student mathematical thinking. In E. Galindo, & J. Newton (Eds.), Proceedings of the 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1178–1185). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.
This study investigates teacher responses to a common set of high potential instances of student mathematical thinking to better understand the role of the teacher in shaping meaningful mathematical discourse in their classrooms. Teacher responses were coded using a scheme that disentangles the teacher move from other aspects of the teacher response, including who the response is directed to and the degree to which the student thinking is honored. Teachers tended to direct their response to the student who had shared their thinking and to explicitly incorporate ideas core to the student thinking in their response. We consider the nature of these responses in relation to principles of productive use of student mathematical thinking.
Beyond the "Move": A Scheme for Coding Teachers' Responses To Student Mathematical Thinking
Peterson, B. E., Van Zoest, L. R., Rougée, A. O. T., Freeburn, B., Stockero, S. L., & Leatham, K. R. (2017). Beyond the "move": A scheme for coding teachers' responses to student mathematical thinking. In B. Kaur, W. K. Ho, T. L. Toh, & B. H. Choy. (Eds.), Proceedings of the 41st annual meeting of the International Group for the Psychology of Mathematics Education, Vol. 4 (pp. 17–24). Singapore: International Group for the Psychology of Mathematics Education.
To contribute to the field's understanding of the teachers' role in using student thinking to shape classroom mathematical discourse, we developed the Teacher Response Coding Scheme (TRC). The TRC provides a means to analyze teachers' inthemoment responses to student thinking during instruction. The TRC differs from existing schemes in that it disentangles the teacher move from the actor (the person publically asked to consider the student thinking), the recognition (the extent to which the student recognizes their idea in the teacher move), and the mathematics (the alignment of the mathematics in the teacher move to the mathematics in the student thinking). This disentanglement makes the TRC less valueladen and more useful across a broad range of settings.
Conceptualizing the Teaching Practice of Building On Student Mathematical Thinking
Van Zoest, L. R., Peterson, B. E., Leatham, K. R., & Stockero, S. L. (2016). Conceptualizing the teaching practice of building on student mathematical thinking. In M. B. Wood, E. E. Turner, M. Civil, & J. A. Eli (Eds.), Proceedings of the 38th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1281–1288). Tucson, AZ: University of Arizona.
An important aspect of effective teaching is taking advantage of inthemoment expressions of student thinking that, by becoming the object of class discussion, can help students better understand important mathematical ideas. We call these highpotential instances of student thinking MOSTs and the productive use of them building. The purpose of this paper is to conceptualize the teaching practice of building on MOSTs as a first step toward developing a common language for and an understanding of productive use of highpotential instances of student thinking. We situate this work in the existing literature, introduce core principles that underlie our conception of building, and present a prototype of the teaching practice of building on MOSTs that includes four subpractices.
We conclude by discussing the need for future research and our research agenda for studying the building prototype.
Uncovering Teachers' Goals, Orientations, and Resources Related to the Practice of Using Student Thinking
Stockero, S. L., Van Zoest, L. R., Rougee, A., Fraser, E. H., Leatham, K. R. & Peterson, B. E. (2015). Uncovering teachers' goals, orientations, and resources related to the practice of using student thinking. Proceedings of the 37th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. East Lansing, MI: Michigan State University, MI.
Despite years of efforts to promote using student thinking during instruction, the practice of productively using student thinking is still difficult for teachers to enact well. Improving teachers' use of this practice requires an understanding of why teachers currently respond to student thinking as they do; that is, an understanding of the goals, orientations and resources (Schoenfeld, 2011) that underlie their enactment of this practice. We describe a scenariobased interview tool developed to prompt teachers to discuss their decisions and rationales related to using student thinking. We examine cases of three individual teachers to illustrate how the tool allows us (1) to infer individual teachers' goals, orientations and resources and (2) to differentiate among teachers' uses of student thinking. Understanding reasons behind teachers' use of student thinking will help us to match professional development to teachers' needs.
Teachers' Perceptions of Productive Use of Student
Mathematical Thinking
Leatham, K. R., Van Zoest, L. R., Stockero, S. L., & Peterson, B. E. (2014). Teachers' perceptions of productive use of student mathematical thinking. In P. Liljedahl, S. Oesterle, C. Nicol, & D. Allan (Eds.), Proceedings of the Joint Meeting of PME 38 and PMENA 36 (Vol. 4, pp. 73–80). Vancouver, Canada: PME.
We argue that the teaching practice of productively using student
mathematical thinking [PUMT] needs to be better conceptualized
for the construct to gain greater traction in the classroom and
in research. We report the results of a study wherein we explored
teachers' perceptions of PUMT. We interviewed mathematics teachers
and analyzed these interviews using and refining initial conjectures
about the process teachers might go through in learning PUMT.
We found that teachers' perceptions of PUMT ranged from valuing
student participation, to valuing student mathematical thinking,
to using that thinking in a variety of ways related to eliciting,
interpreting and building on that thinking.
