Overview:
Building on MOSTs: Investigating Productive Use of HighLeverage Student Mathematical 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 exploring the teaching practices that allow teachers to elicit and take advantage of MOSTs.
We have developed an initial theoretical conceptualization of a productive way teachers can coordinate their work around MOSTs—a teaching practice we refer to as building. Our current conceptualization of building includes four subpractices:
 Make the object of consideration clear (make precise)
 Turn the object of consideration over to the students with parameters that put them in a sensemaking situation (grapple toss)
 Orchestrate a wholeclass discussion in which students collaboratively make sense of the object of consideration (orchestrate)
 Facilitate the extraction and articulation of the mathematical point of the object of consideration (make explicit)
Although this conceptualization of building and its subpractices makes sense in theory, our experience studying MOSTs suggests that the practice is seldom enacted in classrooms. We thus will study the practice of building on MOSTs by working together with teachers to generate and then analyze instantiations of the practice.
During the first year of the project, we developed and piloted MOSTEliciting Prompts (MEPs)—brief mathematical undertakings that have a high likelihood of surfacing particular MOSTs as students share their thinking in response to the prompt. These MEPs were developed by drawing on our prior work studying MOSTs, the literature, and our own teaching experiences. MEPs were constructed around broad mathematical ideas so they could be "dropped into" different 612 grade classes at almost any time during the year.
After the MEPs were developed, we held a teacherresearcher retreat with a group of 13 teacherresearchers (TRs) in summer of 2018 and taught them about our theorized building practice so they could create instantiations around the MEPs in their classrooms. During the second year of the project, the TRs engaged in cycles of (a) implementing a MEP, (b) providing initial reactions and feedback, (c) participating in a smallgroup debriefing meeting, and (d) participating in a largegroup research meeting. The goal of these cycles was to capture increasingly better enactments of the building practice.
Our Current Work:
We are in the fourth year of our project. We had originally anticipated using our analysis of the building enactments that were generated by the TRs during the second year of the project (2018–2019), to create and present refinements of the theorized building practice to the TRs before a second round of enactments this school year (2020–2021). Unfortunately, the COVID19 pandemic has greatly complicated this effort. Now, rather than presenting our refinements to the TRs as a group and working to collect data from all of the TRs on a specific schedule, we are instead working with the TRs individually to update them on our refinements of the building practice, and to determine the best times throughout the year to collect building enactment data of these refinements. Nevertheless, over the next year, we still anticipate that our work with the TRs will result in a refined, theorized building practice, that can be utilized by teachers to help them take advantage of the MOSTs that occur in their classrooms.
The core research questions of the project are:
 What does it look like to build on MOSTs in a way that coordinates the core principles underlying their productive use?
Our work to answer this research question will involve analysis of records of the
teacherresearchers' attempts to implement the building practice during six MEP enactment cycles. Drawing heavily on the procedures we have established for analyzing MOSTs and for analyzing teacher responses to student thinking, this analysis will have two main foci. The first focus is understanding whether our current building prototype—including the four building subpractices—satisfies core principles of quality mathematics instruction that we have gleaned from mathematics education literature. These
principles are that student mathematics is at the forefront, students are positioned as legitimate mathematical thinkers, students are engaged in sensemaking, and students work collaboratively. The second focus is understanding whether there are other
collections of subpractices that also satisfy the core principles. In answering this research question, we hope to better understand how the coordination of subpractices produces the teaching practice of building.
 What are variations in how enacting the building subpractices coordinate the core
principles?
Our work to answer this research question, like the previous research question, will
involve the retrospective analysis of records of the teacherresearchers' attempts to implement the building practice during the six MEP enactment cycles. However, to answer this particular question we will focus specifically on the enactment of each of the subpractices of the teaching practice of building on MOSTs. By focusing on these subpractices, we hope to better understand what the individual subpractices look like, and which enactments of these subpractices do and do not work well.
 What are teachers' experiences in attempting to build on MOSTs?
Our work to answer this question will involve the ongoing analysis of the teacherresearchers' attempts to implement the building practice and their reflections on these attempts during the six MEP enactment cycles. This work will include watching MEP enactment videos and reviewing teacher feedback to select segments or collections of segments that will be the focus of group discussion among the project PIs and the teacherresearchers. Subsequent analysis of teacher feedback and meeting discussions, as well as the video of the MEP enactments, will allow us to ascertain what aspects of building are particularly accessible or challenging, and consider how teachers can be supported in their enactment of building on MOSTs. This analysis will also inform the ongoing planning of our work, including modifications to the building prototype and the work we do with the teacherresearchers to prepare them for future MEP enactments.
This project is funded by the National Science Foundation, grant
#'s:
WMU DRL1720613
MTU DRL1720566
BYU DRL1720410
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.
