Leveraging MOSTs (Mathematically Significant Pedagogical Opportunities to build on Student Thinking) is a collaborative project among researchers at Brigham Young University, Michigan Technological University and Western Michigan University that focuses on improving the teaching of secondary school mathematics by improving teachers’ abilities to use student thinking during instruction to develop mathematical concepts.

The project is developing a Theory of Productive Use of Student Mathematical Thinking (PUMT Theory) that articulates what the practice of productively using student mathematical thinking looks like, how one develops this practice, and how that development can be facilitated.

The core research questions of the project are:

  • What is the nature of high-leverage student thinking that teachers have available to them in their classrooms?
    The work to answer this research question began with the conceptualization and development of the MOST framework (see Conceptualizing Mathematically Significant Pedagogical Opportunities to Build on Student Thinking or Recognizing Opportunities for Productive Use of Student Thinking for more details). Currently, the project is working on defining and exploring attributes of student thinking (e.g., whether the student mathematics is incorrect or correct, what prompted the thinking) to see whether these attributes might distinguish MOSTs from non-MOSTs (see Attributes of Student Mathematical Thinking that is Worth Building on in Whole Class Discussion for more details). These distinctions may provide another way to better understand the nature of MOSTs. In addition, the project is looking at the occurrence of different types of instances (MOSTs and non-MOSTs) across a lesson. This analysis of the occurrence, or ebb and flow, of MOSTs could also provide additional information about MOSTs, such as at what points in a lesson they might be more likely to occur.
  • How do teachers use student thinking during instruction and what goals, orientations and resources underlie that use?
    This work began by exploring the ways in which teachers perceive "productive use of student thinking" through a card sort activity in which teachers engaged in sorting various teacher moves based on their productivity (see Teachers' Perceptions of Productive Use of Student Mathematical Thinking paper or presentation). Since then, the project has used a scenario interview to explore the goals, orientations and resources (per Schoenfeld, A., 2011, How we think) teachers describe in responding to student thinking (see Uncovering Teachers' Goals, Orientations, and Resources Related to the Practice of Using Student Thinking). Currently, this work is exploring the types of teacher responses given in these scenario interviews as well as in classroom videos. These analyses will provide insight into the relationship among teachers' goals, orientations and resources, the type of student thinking shared and how teachers respond to that thinking.
  • What is a hypothetical learning process for the teaching practice of productively using student thinking?
    The project's work exploring the ways in which teachers perceive "productive use of student thinking" led to the development of a hypothetical learning process for this teaching practice (see Teachers' Perceptions of Productive Use of Student Mathematical Thinking paper or presentation). The conception of a hypothetical learning trajectory is based on Simon’s (1995) description in Reconstructing mathematics pedagogy from a constructivist perspective. The next steps in this work include: collecting expert opinions to refine the HLP, conceptualizing how various positions on the HLP might be defined and connected together, exploring how one might determine where along the HLP a teacher is currently, and understanding how a teacher’s goals, orientations and resources might be related to where they are on the HLP.
  • What supports can be provided to move teachers along this hypothetical learning process?
    In analyzing classroom videos for MOSTs, the project noticed that some of the challenges in the analysis and classroom conversation arose because of imprecision in the language of the teacher and/or the students. Hence, work on this imprecision is ongoing to better understand how imprecision in language might affect the student thinking that is available in classrooms and how teachers might address imprecision in classroom discourse. It is anticipated that a focus on precision of language could be a leverage point to move teachers along the HLP. Future work in this area will include working with teachers in teacher development experiments to better understand what supports might best move teachers who are at various starting points along the HLP.

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

 

This project is 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.