Description: Mathematics Education Professors at BYU are collaborating with researchers from two other universities to improve how math teachers facilitate student thinking in the classroom.

Start: October 1, 2012
End: September 30, 2016

• Sponsor: National Science Foundation
• Principal Investigator: Keith Leatham
• Co-PI: Blake Peterson
• Website: http://leveragingMOSTs.org/

Project Description
Any middle-schooler knows that a whole variety of student ideas and questions can surface during a teacher’s 8th grade mathematics lesson. When this happens, it is the teacher’s responsibility to determine which ideas are most beneficial to the students and should be pursued during the class’ limited time together. However, deciding what ideas to pursue isn’t always black and white. This is why BYU Professors Keith Leatham and Blake Peterson are teaming up with Shari Stockero from Michigan Technological University and Laura Van Zoest from Western Michigan University in collaborative research on the matter.

These veteran educators seek to improve valuable teaching moments in the classroom through the development of an accessible PUMT Theory (A Theory of Productive Use of Student Mathematical Thinking). The focus of the PUMT theory is to use student thinking effectively to drive the learning in the classroom. Student thinking includes comments, written or verbal ideas, questions, or even mistakes presented by students. The researchers have termed advantageous instances of student thinking as Mathematical Opportunities in Student Thinking, or MOSTs. Using these types of thinking in the right way builds on students’ critical thinking skills and extends their understanding of the concepts being taught. The PUMT theory developed by the researchers and their teams will serve as a guide to all teachers in capitalizing on specific instances of MOSTs.

Intellectual Merit:
Throughout the four-year project, the researchers will use new and existing video-taped classroom lessons, as well as interviews from teachers participating in the research. Data will vary over many regions, ethnic groups, and levels of classes. Separated into four integrated phases, the project first focuses on researching what kind of student thinking will most likely come up in a diverse range of classroom settings. Next, researchers will investigate how teachers currently build on and take advantage of the thinking in their classrooms. Hundreds of instances of student thought happen each day in a teacher’s classroom, and the teacher has to make on-the-spot decisions about which lines of thinking to pursue or not. Taking the right opportunities grows the students’ understanding of the content, and directs them to develop high levels of critical thinking. Phase three draws on improving the teacher’s ability to effectively recognize and use MOST experiences in their lessons. The researchers will collaborate in helping the teacher employ an effective PUMT model that can be studied and improved upon in the last phase of the project.

Broader Impact:
The overall result of the project is to produce a polished and revised PUMT Theory to be shared and put to use in the classroom. Based on concrete data, the results of this research will enrich the pedagogy (teaching abilities and strategies) of not only mathematics teachers, but all teachers seeking to develop high cognitive skills in their students. The work in this research has already led to several presentations and publications, including a presentation this month at the annual Association of Mathematics Teachers Educators meeting in Irvine, California. Taking the right opportunities in the classroom scaffolds student understanding and their ability to think cognitively. The combined efforts of these researchers contribute to both the educational world and to individual lives as they help students in the classroom to get the most out of MOSTs.