Past Presentations

Abstract/Description: This poster reports our findings of how teachers used public records of student mathematical thinking throughout whole class discussions. In our work, we consider a public record to be a physical and visual representation of a student contribution that is accessible to all classroom members. We will share how teachers' explicit referencing of public records helped teachers to establish student thinking and engage students with each other’s ideas in whole class discussions.

Abstract/Description: Covariation and covariational reasoning are key themes in mathematics education research. Recently, these ideas have been expanded to include cases where more than two variables relate to each other, in what is termed multivariation. Building on the theoretical work that has identified different types of multivariation structures, this study explores students’ reasoning about these structures. Our initial assumption that multivariational reasoning would be built on covariational reasoning appeared validated, and there were also several other aspects of reasoning employed in making sense of these structures. There were important similarities in reasoning about the different types of multivariation, as well as some nuances between them.

Abstract/Description: The sampling distribution (SD) is a foundational concept in statistics, and simulations of repeated sampling can be helpful to understanding them. However, it is possible for simulations to be misleading and it is important for research to identify possible pitfalls in order to use simulations most effectively. In this study, we report on a key misconception students had about SDs that we call the “multi-sample distribution.” In this misconception, students came to believe that a SD was composed of multiple samples, instead of all possible samples, and that the SD must be constructed by literally taking multiple samples, instead of existing theoretically. We also discuss possible origins of this misconception in connection with simulations, as well as how some students appeared to resolve this misconception.

Abstract/Description: The activities that teacher educators prepare for preservice teachers should be intentional in their purpose for improving teaching practices. We report on a video database activity that our preservice teachers engaged in and their improvement in attending to student mathematics.

Abstract/Description: To productively use student mathematical thinking, it must be 1) made clear and 2) established as the object of discussion. The nuances of these two aspects of the teaching subpractice, Make Precise, will be discussed through examples from the data.

Abstract/Description: We share our research on uses of a public record to support whole-class discussions, show examples of revising a public record in real-time to support the discussion, and consider how this information can be used in developing well-prepared beginning teachers.

Abstract/Description: Students can learn more deeply when conceptual understanding is at the forefront and connections are made between topics. We hypothesize that such understanding and connections can be achieved for the chain rule, implicit differentiation, and related rates through the construct of nested multivariation (NM). In this first paper, we describe the process of creating a hypothetical learning trajectory (HLT) rooted in NM for this sequence of topics. This theoretical paper contains our conceptual analysis, literature review, and construction of the HLT.

Abstract/Description: Students learn more deeply when conceptual understanding is at the forefront and connections are made between topics. While previous work has examined the chain rule, implicit differentiation, and related rates separately, we have created a hypothetical learning trajectory (HLT) for these topics to teach them in a conceptual, connected way. In a previous paper we outlined the creation of the HLT based on the construct of nested multivariation (NM). In this second paper, we describe a small-scale teaching experiment done to test the HLT. Our results suggest NM was an appropriate construct to base the HLT on, and we present the students’ developing understandings as they progressed through the HLT. Based on the results, we made final adjustments to the HLT, in preparation for a full-scale classroom teaching experiment.

Abstract/Description: Using engaging problem contexts is important in instruction, and the literature contains themes of contexts being realistic, worthwhile, or enjoyable, as well as motivating. Yet, the literature largely lacks detailed student perspectives on what helps problem contexts achieve these characteristics. In this study, eleven calculus students were interviewed to identify features of problems that made them engaging. This led to a new top-level characteristic “variety,” and the identification of features that helped contexts have the characteristics described in the literature. In particular, problems that were realistic/motivating contained features including: (a) expansion of awareness, (b) need for math, and/or (c) explicit purpose. Contexts that were enjoyable/motivating contained features including: (a) insertion into problem, (b) teacher’s personal story, or (c) absurd story. At the end, we show the usefulness of these results by critiquing problems from the literature in terms of how engaging they might be to students.

Abstract/Description: Intellectual need is the need that students feel to understand how and why a particular mathematical idea came to be. We are interested in creating tasks that calculus instructors can use to provoke intellectual need. However, the current suggestions for designing such tasks lack detail and don’t account for several issues specific to undergraduate introductory calculus. In this theoretical paper, we discuss the idea of intellectual need, explore three issues related to the teaching of calculus, and present a theoretical model that task-designers can use to frame important factors that affect the development and use of these tasks.