Past Presentations

Abstract/Description: While scholars have noted that variables are used in multiple ways during algebraic activity, little empirical research has been conducted to study which variable types middle school students typically encounter in their mathematics classes. To address this need, we present a study that examined the different types of variables used in three 7th-8th grade mathematics curricula. Using qualitative methods, we identified 8 main variable types. These 8 variable types were present in every year of each curriculum. Most lessons required students to distinguish between 2-5 different variable types. Our findings imply that students need to develop sophisticated and nuanced understandings of variables to meaningfully participate in middle school mathematics.

Abstract/Description: Approaches to integration based on quantitative reasoning have largely developed along two parallel lines. One focuses on continuous accumulation from rate, with accumulation functions as the primary object. The other focuses on summing infinitesimal bits of a quantity, with definite integrals as the primary object. No work has put these two approaches in direct conversation with each other, which is the purpose and contribution of this theoretical paper. In this paper, we unpack both approaches in terms of meanings and reasoning. Because modeling is a key motive for using quantitatively-grounded approaches in the first place, we then analyze and discuss each approach’s method of modeling two example contexts.

Abstract/Description: Intellectual need (IN) is a powerful way to support learning by engaging students and helping them view mathematics as less arbitrary. While IN has been developed theoretically, much less has been done to build frameworks for how to actually create IN provoking tasks – both in terms of what a task designer might attend to and how to attend to those things. In this theoretical paper, we review key premises in IN, from which we extract several components that should be taken up in IN task design. We then describe a process one can use to address these components systematically in constructing a task specifically meant to provoke IN.

Abstract/Description: "Work on the teaching and learning of definite integrals has expanded significantly in recent years, with the specific conceptualization "adding up pieces" being a promising foundational meaning for integrals. Yet, work in this area has largely focused on student understanding and reasoning, with only small attention to the detailed work of how task-based learning over an entire unit of integration could support students in coming to develop these understandings. This poster presents an outline of a learning trajectory for a unit on integration based on adding up pieces and how students come to learn the individual parts that make up the larger integral concept.

Abstract/Description: Four groups of mathematics teacher educators share the ways they are exploring the creation, organization, and use of public records of student mathematical thinking--physical and visual representations of student mathematics that are publicly accessible to all participants within a classroom.

Abstract/Description: Student teaching has long been plagued by a lack of coherence and sustained institutional and research support. In this working group participants will identify challenges and share strategies to support efforts to improve secondary mathematics clinical practice.