Leveraging MOSTs (Mathematically Significant Pedagogical Opportunities to build on Student Thinking)

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Keith R Leatham and Blake E Peterson, Mathematics Education

Progress on academic objectives and description of initial findings

Phase 1, Goal 1: Purposefully create a data set of videotapes and transcripts of secondary classroom mathematics discourse that reflects the student mathematical thinking that can occur in diverse classrooms.

We have found that the 25+ classroom videos that were collected in previous projects and in the first year of this project were sufficient to complete much of the work related to the development and refinement of the MOST framework. To diversity our data set further, we collected data in one classroom with a Native American student population and also obtained access to data collected by another researcher in a diverse classroom.

Phase 1, Goal 2: Test and refine the MOST (Mathematically Significant Pedagogical Opportunity to build on Student Thinking) framework by using it to analyze a diverse set of classroom video.

A significant part of the work of year 2 involved continuing to refine our MOST framework and the related coding protocols that are used to code classroom video. We have now developed a protocol that is used by undergraduate and graduate student researchers to code each classroom video for context and to identify potential instances of student mathematical thinking to be analyzed by the research group. We have also refined the protocol for identifying MOSTs and documenting why instances of student thinking fall short of being MOSTs. This protocol for identifying MOSTs was tested by the evaluation team and clarifications to the protocol have been made based on their feedback. We have developed a codebook that clearly describes the process for identifying potential instances of student mathematical thinking and for analyzing these instances using the MOST framework.

We have tested and refined the MOST framework by using it to code classroom video data and now believe that our framework “holds up” in the analysis of classroom video from diverse contexts. We have received feedback on the framework from journal reviewers and conference session attendees. We continue to test the framework by applying it to additional classroom video from diverse classrooms.

Phase 1, Goal 3: Develop and pilot-test the interview protocols and surveys we will be using later in the project.

In year 1, an initial classroom observation interview protocol was developed and pilot-tested with seven teachers. Based on this pilot test, we identified problems with the protocol and refined it before it is used with additional teachers. In particular, we found that the interview questions did not elicit the information that we wanted to gather without providing the teacher with information that was too leading with regard to what we were looking for (i.e., our view of what it means to productively use student mathematical thinking). To date, the revised protocol has only been used with one teacher, but we plan to use it with more teachers in year 3.

In an attempt to gather better information about teachers’ perceptions of productive use of student thinking, we developed a card sort interview that asked teachers to sort a collection of teachers moves related to the use of student thinking on a continuum from “least productive” to “most productive”. We used this interview with 12 teachers. The data from these interviews allowed us to develop a hypothetical learning progression related to productive use of student mathematical thinking, as well as to describe different ways that teachers “use” student thinking, ranging from engaging students in the lesson to having other students think about the student thinking. We found, however, that this interview did not give us detailed information about the specific ways that teachers might respond to student ideas, which led us to develop a new interview protocol based on classroom scenarios (described under Phase 2, Goal 1).

Phase 2, Goal 3: Develop a hypothetical learning trajectory for the mathematics teaching practice of productively using student thinking during instruction to develop mathematical concepts.

We have made some progress on both goals 2 and 3 using data from the card sort and classroom scenario interviews, but will continue to refine our theory and learning trajectory in subsequent years of the project. At this point, we have articulated a hypothetical learning progression that includes the following stages:

  • Reject Active Student Participation
  • Value Student Participation
  • Value Student Mathematical Thinking
  • Elicit Student Mathematical Thinking
  • Interpret Student Mathematical Thinking
  • Build on Student Mathematical Thinking

In addition, we have identified a range of “uses” of student thinking that correspond to the eliciting, interpreting and building stages of this progression. At this point, we conjecture that teachers can only engage in some subset of the “uses” depending on what stage they are at on the HLP. We plan to test this conjecture and continue to refine the HLP and the associated “uses” of student thinking using interview and observation data, as well as during our work with teachers in teacher development experiments.

Evaluation of the mentoring environment

We anticipated that the graduate student and undergraduate students involved in this mentored experience would benefit from four main aspects of their work: research, mentoring, observation and presentation. We evaluate each of these areas briefly in the following paragraphs.

Research: The graduate student took an active role in the research project by attending research team meetings and participating in the ongoing, day-to-day work of carrying out the research. She also participated in significant ways in our week-long summer research retreat. One primary responsibility was for her to develop a deep understanding of our MOST coding framework and then use that framework to code video of mathematics lessons. This knowledge was crucial as the graduate student played a critical role in supervising the undergraduate students who worked on the processing, transcribing and initial coding of data. Through this research experience, we feel that the graduate student and undergraduate students learned how to translate a theoretical framework into a workable coding scheme and how to develop that coding into workable, evidence-supported theory.

Mentoring: The graduate student supervised undergraduate research assistants as they learned and applied the aforementioned coding scheme. The graduate student acted as a mentor to help undergraduate research assistants understand the framework that drives the codes, the computer program (StudioCode) in which the coding takes place, and the application and refinement of the codes themselves. We found this graduate student mentoring to be invaluable to the progress of our work. For example, our typical weekly research meeting began with the graduate student meeting with the undergraduate students for the first hour, during which time the undergraduates reported on their progress and raised questions for the group to discuss. The PIs then joined in for the second hour of the meeting, discussing unresolved issues and joining in making new assignments for the coming week.

Observing: The mentored students spent a significant number of hours observing mathematics classrooms wherein teachers are trying (to varying degrees of success) to effectively elicit and use students mathematical thinking. The students were required to think deeply about this important teaching practice over an extended period of time and in numerous different classroom contexts (with diversity of content, teachers and students), something very few novice teachers have the opportunity to do. We believe (based on our own observations as well as on conversations with the students) that this experience of watching and analyzing the teachers and the students in these classrooms had a strong impact on the students and helped them better understand important perspectives and issues in the field of mathematics education.

Presentations: The graduate student presented a poster at the 35th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education in Chicago. One undergraduate student (Allyson Rugg) presented at the Student Research Conference.

Students who participated

Graduate Student:

  • Lindsay Merrill

Undergraduate Students:

  • Alicia Heninger
  • Maggie Flanders
  • Morgan Matsen
  • Allyson Rugg
  • Sydney Bracha

Academic deliverables they helped to produce

  • MOST Coding Instructions (2014, July)
  • Ochieng, M. A., Van Zoest, L.R., Merrill, L., Peterson, B. E., Leatham, K. R., & Stockero, S. L. (2014, April). Teachers’ perception of “use” of students’ mathematical thinking in whole class discussion. WMU Poster Day. 9th Annual Western Michigan University Research and Creative Activities Poster Day, Western Michigan University, April 2014.
  • Johnson, K. R., Steele, Michael D., Herbel-Eisenmann, B. A., Leatham, K. R., & Peterson, B. E., Stockero, S. L., Van Zoest, L. R., Almeida, I., and Merrill, L. (2013). Classroom mathematics discourse: Broadening perspectives by integrating tools for analysis. In M. V. Martinez & A. Castro Superfine (Eds.), Proceedings of the 35th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1340–1348). Chicago: University of Illinois at Chicago.
  • Almeida, I., Merrill, L. Van Zoest, L. R., Stockero, S. L., Leatham, K. R., & Peterson, B. E. (2013). A framework for identifying mathematically significant pedagogical openings to build on student thinking. In Martinez, M. & Castro Superfine, A (Eds.). Proceedings of the 35th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (p. 1264). Chicago, IL: University of Illinois at Chicago.

Description of how the budget was spent

We were awarded $10,500. We spent the funds as follows:

  • $6150 to pay the undergraduate research assistants
  • $1500 to the graduate student
  • $1500 to purchase student versions of the StudioCode software
  • $1500 to partially pay for the graduate student to attend the conference in Chicago