Leveraging MOSTs (July 2016 – Sept. 2017) was a collaborative project among researchers at Brigham Young University, Michigan Technological University and Western Michigan University. The project contributed to the improvement of the teaching of secondary school mathematics by studying the practice of productively using student mathematical thinking.

Conceptualizing Teachable Moments

The work began by conceptualizing "teachable moments" in mathematics classrooms. This theorizing led to the development of the MOST Analytic Framework. MOSTs are Mathematically Significant Pedagogical Opportunities to build on Student Thinking, and the framework describes how one can distinguish such instances of student thinking from among all the instances that might occur in a given mathematics lesson. This framework is thus a way to define mathematical "teachable moments" and it provides a lens to examine—and a vocabulary to talk about—instances of student mathematical thinking. This lens also allows researchers to determine whether and to what degree instruction attends to student thinking, significant mathematics, and pedagogical opportunities.

Exploring MOSTs in Different Kinds of Classrooms

Having defined MOSTs, the project turned to applying the framework to videotapes of classroom mathematics lessons in order to learn more about the nature of these moments. Although MOSTs occurred in all of the classroom lessons that were analyzed, the rate at which they occurred varied. MOSTs occurred more frequently when students were given more opportunity to share their thinking. The vast majority of the MOSTs could be categorized into three types according to what made them "compelling moments." Half of the MOSTs occurred when students showed evidence of grappling with a mathematical idea (Sense Making). The next highest category involved instances of student thinking that were Incorrect or Incomplete (32%). Student thinking that led to Multiple Ideas or Solutions being available for students to consider occurred in 15% of the MOSTs.

Uncovering Teachers' Orientations about Using Student Thinking

Throughout the project the team explored teacher's perceptions of "productive use of student thinking." These efforts resulted in the development and use of an interview protocol that gives teachers classroom scenarios and asks them to describe their thinking about and potential responses to instances of student mathematical thinking. Results from analyzing these interviews include the following: (a) We identified high-potential teacher orientations that position student thinking as a particularly valuable resource during whole-class discussion, where teachers value students directly interacting with one another by hearing other students' explanations, and questioning, comparing, critiquing, and discussing their peers' ideas; (b) We identified hindering orientations that position student thinking as needing to be evaluated and corrected, where teachers value highly scaffolded learning experiences in which their role is to explain and demonstrate mathematical ideas; (c) We found that teachers tended to: direct their responses to the same student who created the instance (as opposed to turning that thinking over to the class to consider), use only a few select type of moves (often not availing themselves of a wider range of potentially productive moves), and explicitly incorporate students' thinking (thus making it quite clear that they were indeed taking up those ideas).

This project advanced knowledge by enhancing the field's understanding of: (a) the student thinking that teachers have available to them in their classrooms; and (b) teachers' perceptions and use of student thinking during instruction. The project provided tools for teachers, teacher educators, and researchers that make more tangible the often abstract but fundamental goal of productively using students' mathematical thinking. These tools have the potential to enhance teachers' practice of productively using student thinking during instruction, thus improving students' opportunities to learn mathematics.

More information about the project can be found in the project proposal.


 

This project was funded by the National Science Foundation, grant #'s:

WMU DRL-1220148
MTU DRL-1220357
BYU DRL-1220141

Any opinions, findings, and conclusions or recommendations expressed in these materials are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.