Presentations

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.

Abstract/Description: We explore a wide sample of currently available instructional materials intended for college mathematics instructors (textbooks, magazines, teacher editions, lesson plans, teaching articles, classroom notes for flipped classrooms, books, etc.) in order to assess how available materials are building a knowledge base for teaching. We modify a framework from Hiebert & Morris (2009) to look for key categories of knowledge that are fundamental for a knowledge base for teaching mathematics. We found that few articles contained meaningful amounts of multiple categories. We use the categories to describe the nature of current available materials and argue that a new genre of instructional material and scholarly work to create the missing knowledge is needed.

Abstract/Description: The Pathways to College Algebra curriculum aims to build concepts that cohere with the big ideas in Calculus, and initial results suggest improved readiness for Calculus by students who use the curriculum. Our study examines similarities and differences of Pathways and non-Pathways students understanding and reasoning about the calculus concept of the limit. We compare students’ understanding of limits at the beginning and at the end of the unit. Our findings suggest that (1) students reliance on procedures, combined, or quantitative reasoning was dependent on the calculus instructors’ emphasis in the class; (2) students who begin their Calculus class with high covariational reasoning gain a more sophisticated understanding of limits; and (3) when curriculum is coherent students will identify mathematical connections.

Abstract/Description: We will discuss the teaching practice of building on student mathematical thinking, unpacking important nuances of this practice. Together we will consider how we as mathematics teacher educators can help teachers to develop skills related to these nuances.

Abstract/Description: This session highlights examples of praxis that challenge traditional grading practices. Drawing on collective insights of participating MTEs, we will identify next steps in our praxis of humanizing grading, brainstorm strategies for systemic change, and develop a shared resource.

Abstract/Description: Join us in a discussion around the purposes of student teaching, the design of existing paired-placement student teaching experiences, and how such experiences can be designed to better aligned with current purposes of student teaching.

Abstract/Description: In this session, we examine multiple middle grades teachers’ mathematical goals and how much time students spend during class working towards these goals. We also examine if the teachers’ goals are aligned or not aligned with research-based learning trajectories.

Abstract/Description: Teachers are using more online materials and often modify their existing textbook sequences as they plan and enact lessons. These decisions impact the scope and sequence of the mathematics for students. We will discuss teachers’ reasoning for these decisions.

Abstract/Description: We focus on data collected within a larger study into middle grades mathematics teachers’ curricular reasoning. Specifically, we present data from three teachers’ integration of Desmos’ Transformation Golf: Rigid Motion activity into their 8th grade unit on geometric transformations.

Abstract/Description: The teaching practice of building has been conceptualized as a productive way to take advantage of student contributions during whole-class instruction that provide leverage for supporting student learning and accomplishing mathematical goals. In this theoretical paper that is informed by empirical data, we elaborate on four subpractices of building: make precise, grapple toss, orchestrate, and make explicit. We provide illustrations from our efforts to make sense of building through work with teacher-researchers who are enacting the building practice in their classrooms and explore different aspects of the subpractices and relationships between these aspects and principles underlying productive use of student thinking.

Abstract/Description: Mathematics teachers are vital components in determining what mathematics students have the opportunity to learn. There are a vast number of factors and reasons that influence a teacher’s instructional decisions. As such, teachers rely heavily on their curricular reasoning (CR) to make decisions about what content to teach, how that content is taught, and the tasks to use to facilitate student learning. In this paper, we outline five strands of CR gleaned from research with middle grades mathematics teachers as they plan and implement instruction with unfamiliar curricular resources. These strands lay the foundation for our Instructional Pyramid model of CR and provide a lens through which teacher decision-making can be further understood and enhanced.

Abstract/Description: How teachers reason with their mathematical meanings when making curricular decisions

Abstract/Description: Teachers utilizing student mathematical thinking is important when teaching, yet many inservice teachers find it difficult to implement. The Standards for Preparing Teachers of Mathematics (AMTE, 2017) outline the knowledge, skills, and dispositions that beginning teachers should have after graduating including the importance of attending to and interpreting student mathematical thinking. In this paper, we present results from two focused video analysis assignments that our pre-service teachers engaged in to identify their images of student mathematical thinking and their ability to attend to and interpret student mathematical thinking.