Secondary Pre-Service Teachers’ Images and Interpretations of Student Mathematical Thinking

Presenters: Dawn Teuscher, Brigham Young University and J Matt Switzer, Texas Christian University
Location: PMENA in St Louis, Missouri
Teachers utilizing student mathematical thinking is important when teaching, yet many inservice teachers find it difficult to implement. The Standards for Preparing Teachers of Mathematics (AMTE, 2017) outline the knowledge, skills, and dispositions that beginning teachers should have after graduating including the importance of attending to and interpreting student mathematical thinking. In this paper, we present results from two focused video analysis assignments that our pre-service teachers engaged in to identify their images of student mathematical thinking and their ability to attend to and interpret student mathematical thinking.

Dissecting Curricular Reasoning: An Examination of Middle Grade Teachers’ Reasoning Behind Their Instructional Decisions

Presenters: Shannon Dingman, University of Arkansas; Dawn Teuscher, Brigham Young University; Lisa Kasmer, Grand Valley State University; and Travis Olson, University of Nevada Las Vegas
Location: PMENA in St Louis, Missouri
Mathematics teachers are vital components in determining what mathematics students have the opportunity to learn. There are a vast number of factors and reasons that influence a teacher’s instructional decisions. As such, teachers rely heavily on their curricular reasoning (CR) to make decisions about what content to teach, how that content is taught, and the tasks to use to facilitate student learning. In this paper, we outline five strands of CR gleaned from research with middle grades mathematics teachers as they plan and implement instruction with unfamiliar curricular resources. These strands lay the foundation for our Instructional Pyramid model of CR and provide a lens through which teacher decision-making can be further understood and enhanced.

What Japanese Lesson Plans Teach us About Sharing Knowledge of Teaching?

Presenters: Doug Corey, Eula Monroe and Michelle Wagner, Brigham Young University
Location: NCTM 2017 Research Conference, San Antonio, Texas
US mathematics education has failed to find a robust way to develop and store a knowledge base for teaching. We explore the use of detailed lesson plans as a solution to the storage problem for a knowledge base for teaching. We gather lesson plans and lesson-plan like documents from seven different sources (2 in Japan, 5 in the US) and analyze them to see which ones tend to best capture the key elements of high quality lessons and, moreover, makes the reasoning behind the instructional decisions explicit. We found that Japanese lesson study lesson plans tended to be the best examples of a knowledge base for teaching, although activity articles from Mathematics Teaching in the Middle School and Teaching Children Mathematics also did very well on a few dimensions and fairly well overall. Lessons from the Chicago School Lesson Study Group also scored high. One feature that was common among the better example lessons plans was that they tied together three elements: (1) specific instructional decisions based on (2) student mathematical thinking around a (3) a particular mathematical topic or idea. The good examples integrated these three things differently, and some specific examples were shared about how these were integrated into the lesson plans or lesson-plan like documents.

A Framework for Thinking Through a Unit: Implications for Task, Instructional Practices and Student Outcomes

Presenters: Scott Hendrickson and Sterling Hilton, Brigham Young University
Location: NCSM Annual Conference, San Antonio, Texas
The Comprehensive Mathematics Instruction Framework developed by the BYU Public School Partnership informs teachers in making decisions regarding the selection and sequencing of tasks, in implementing instructional practices that intentionally align with the nature and purpose of tasks (e.g., level of cognitive demand), and in assessing expected student outcomes. Classroom video and student work will be used to illustrate the Framework.