Past Presentations

Abstract/Description: Prior research has shown how the multiplicatively-based summation conception (MBS) is important for making sense of definite integral expressions in science contexts. This study attempts to accomplish two goals. First, it describes introductory lessons on integration from two veteran calculus teachers as a way to possibly explain why so few students draw on the MBS conception when making sense of definite integrals. Second, it reports the results from a design experiment intended on promoting not only the construction of the MBS conception, but its priming for activation when students see and interpret definite integrals expressions.

Abstract/Description: Little research has been conducted into student understanding of concavity and inflection points. Much of what we know comes incidentally from studies looking at the calculus activity of sketching the graphs of functions. However, since concavity and inflection points can be useful in conveying information in disciplines like science, engineering, technology, and economics, it seems important to study how students understand these two concepts in these contexts. This study attempts to provide insight into this area.

Abstract/Description: Prior research has documented several conceptualizations students have regarding the definite integral, though the conceptualizations are largely based off of single-variable integral expressions. No research to date has documented how students’ understanding of integration becomes generalized for multivariate contexts. This paper describes six conceptualizations of multivariate definite integrals and how they connect to students’ prior conceptions of single-variable definite integrals.

Abstract/Description: We analyzed video of three Japanese lesson study sessions connected to elementary or middle school math lessons. We use the discussion to better understand what Japanese teachers view as most important in a lesson and the frame which they use to view a lesson. We discuss how some ideas used by the Japanese could potentially be useful for US teachers and US professional developers.

Abstract/Description: PSTs curricular reasoning is necessary to analyze curriculum and make decisions about planning, implementation, and reflecting. This session will provide participants an opportunity to examine textbooks and participate in a curriculum analysis activity that we have used with our PSTs.

Abstract/Description: We will share the iterative video-based See it, Try it, and Reflect on it (STiR) model of making practice studyable was implemented in methods courses at two universities. We share our findings that the model promotes preservice teachers’ learning as they probe student thinking.

Abstract/Description: Anticipating student mathematical thinking is broadly discussed as a valuable teaching practice. Specifically, it is emphasized as part of the lesson study process and is the first of the five practices discussed by Smith and Stein (2011). Learning to anticipate student thinking requires teachers to see mathematics through their students’ eyes. In my own teaching as well as in my work with preservice teachers, I have come to value seeing mathematics through students’ eyes as well as to recognize the challenges in doing so. In this talk, I will share some interesting ways students see mathematics and discuss the pedagogical benefits of looking at mathematics through their eyes.

Abstract/Description: This session builds on research on professional noticing of students’ mathematical thinking by unpacking different ways of conceptualizing the teaching practice of responding to student thinking. Four projects focused on defining and developing this practice will be presented and discussed.

Abstract/Description: Policy-makers in the U.S. have asked teachers both to implement Common Core Standards and improve student achievement. While many assume that these goals work in concert, research suggests that links between teaching quality and student outcomes may be more tenuous. We explore whether implementation of new Common Core-aligned achievement tests might strengthen these relationships, focusing on a test considered a model for these assessments and an observational instrument aligned with the Common Core.