Presentations

Abstract/Description: Presentations consider (1) the nature of student thinking (ST) available to teachers during instruction, (2) teachers’ perceptions of productive use of ST, and (3) teachers’ abilities to recognize and respond to ST. The work will be discussed in the broader context of developing a theory of productive use of ST.

Abstract/Description: Analyses of new middle grades textbooks across Ratio and Proportion and Geometry domains of the Common Core will be reported. Data will be shared related to mathematical content, types of representations, and comparisons. We will discuss how access to mathematics based on curriculum use poses a potential equity gap in implementing the Common Core.

Abstract/Description: The Common Core State Standards describes eight Mathematical Practice Standards for students’ engagement in mathematical work. NCTM introduced eight Mathematics Teaching Practices in Principles to Actions. How are these sets of practices related? Using video vignettes we will examine how effective teaching elicits authentic mathematical work.

Abstract/Description: The derivative is an important foundational concept in calculus that has applications in many fields of study. Existing frameworks for student understanding of the derivative are largely descriptive in nature, and there is little by way of theoretical frameworks that can explain or predict student difficulties in working with the derivative concept. In this paper we combine Zandieh’s framework for understanding the derivative with “analogical reasoning” from psychology into the “merged derivative-analog framework.” This framework allows us to take the useful descriptive capabilities of Zandieh’s framework and add a layer of explanatory power for student difficulties in applying the derivative to novel situations.

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.