Past Presentations

Abstract/Description: An important aspect of effective teaching is taking advantage of in-the-moment expressions of student thinking that, by becoming the object of class discussion, can help students better understand important mathematical ideas. We call these high-potential instances of student thinking MOSTs and the productive use of them building. The purpose of this paper is to conceptualize the teaching practice of building on MOSTs as a first step toward developing a common language for and an understanding of productive use of high-potential instances of student thinking. We situate this work with the existing literature, introduce core principles that underlie our conception of building, and present a prototype of the teaching practice of building on MOSTs that include four sub-practices. We conclude by discussing the need for future research and our research agenda for studying the building prototype.

Abstract/Description: The calculus concepts of concavity and inflection points are often given meaning through the shape or curvature of a graph. However, there appear to be deeper core ideas for these two concepts, though the research literature has yet to give explicit attention to what there core ideas might be or what it might mean to “understand” them. In this paper, I propose a framework for the concavity and inflection point concepts, using the construct of covariation, wherein I propose conceptual (as opposed to mathematical) definitions that can be used for both research and instruction. I demonstrate that the proposed conceptual definitions in this framework contain important implications for the teaching and learning of these concepts, and that they provide more powerful insight into student difficulties than more traditional graphical interpretations.

Abstract/Description: In this session we present findings from our analysis of six middle school textbooks purported to align to the Common Core State Standards for Mathematics (CCSSM). We specifically report on the approach and connection of isometries and congruence in grade 8. We found the majority of the curriculum materials to be lacking in three important mathematical ideas related to isometries: properties of isometries, congruence in terms of isometries, and orientation of figures. This lack of connections will impact teachers as they implement the CCSSM and students as their opportunities to learn isometries as outlined in CCSSM will vary depending on their teachers’ understanding of isometries and congruence as well as the textbook that they are using.

Abstract/Description: In this session, we share results of our work that examined how new middle grades textbooks are organizing and presenting transformational geometry concepts aligned to CCSSM. We explore what happens when there is a mismatch and how to identify a mismatch between the mathematical content presented in the books and what CCSSM teachers are held accountable to teach.

Abstract/Description: Once students share their ideas, creating meaningful mathematics discourse requires that teachers decide which ideas are worth pursuing and how to capitalize on those ideas. We share a framework for determining which student ideas have significant potential to support mathematics learning and discuss how teachers might productively use those ideas.

Abstract/Description: Explore examples of teacher and student imprecision in classroom mathematics discourse. Discuss types of imprecision that occur in classrooms, the ramifications of this imprecision, and strategies for addressing that imprecision. Learn how to minimize your own imprecision and to view student imprecision as an opportunity to learn mathematics.

Abstract/Description: Principles to Action endorses “Supporting Productive Struggle in Learning Mathematics.” With a common societal belief that student struggle indicates poor teaching, allowing and supporting student struggle seems foreign. We will discuss research on the benefits of this practice and some suggestions to effectively support student productive struggle.

Abstract/Description: The Comprehensive Mathematics Instruction Framework, developed by the Brigham Young University Public School Partnership, highlights the relationship between conceptual, procedural and representational understanding. The three components of the framework: Teaching Cycle, Learning Cycle and Continuum of Understanding will be described and illustrated.

Abstract/Description: We will introduce the teaching practice of building and its constituent components as the most productive use of worthwhile student mathematical thinking, analyze teaching examples for evidence of building, and consider how to support teachers’ development of this practice.

Abstract/Description: We discuss evidence that preservice secondary mathematics teachers who participated in focused video analysis, watching, analyzing and discussing videos through the lens of a specific theoretical framework, are able to transfer their noticing into the real-time classroom.