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Using Rehearsal Debriefs with Experienced Teachers to Negotiate an Understanding of an Ambitious Teaching Practice

Presenters: Shari Stockero, Michigan Technological University; Ben Freeburn, Western Michigan University; Jessica Postma, Western Michigan University; Nishat Alam, Michigan Technological University; Keith Leatham, Brigham Young University; Blake Peterson, Brigham Young University; and Laura Van Zoest, Western Michigan University
Location: AMTE in Nashville, Tenneessee
Abstract/Description:
We use rehearsal debrief discussion excerpts to consider how rehearsals with experienced teachers might be planned and structured to position the debrief as a mechanism for mathematics teacher educators and teachers to negotiate an understanding of a complex teaching practice.

Viewing Classroom Mathematics Discourse through Two Complementary Lenses

Presenters: AnnaMarie Conner, University of Georgia; Keith Leatham, Brigham Young University; Laura Singletary, Lee University; Laura Van Zoest, Western Michigan University, Jonathan Foster, University of Virginia; Shari Stockero, Michigan Technological University; Hyejin Park, Drake University; Blake Peterson, Brigham Young University; and Yuling Zhuang, Emporia State University
Location: AMTE in Nashville, Tenneessee
Abstract/Description:
We explore teachers’ facilitation of whole class discussions by comparing and contrasting the analysis of such discussions through two different lenses: 1) teachers’ support of collective argumentation; and 2) teachers’ productive use of student mathematical contributions.

How Students Reason about Compound Unit Structures: m/s2, ft-lbs, and (kg*m)/s

Presenters: Steven Jones, Leilani Fonbuena, Michelle Chambers and Spencer Young from Brigham Young University
Location: RUME in Omaha Nebraska
Abstract/Description:
Intensive quantities result from quantitative operations on two or more extensive quantities. As such, their units of measure consist of “compound units.” Students regularly encounter symbolically-written compound unit structures that are directly given to them, rather than constructed or developed, such as m/s 2 , ft-lbs, or kg∙m/s. It is consequently important to understand how students might try to reason about such symbolically-presented compound unit structures, which is the focus of this study. We examined “ways of reasoning” students used to make sense of such units, and describe in this paper five themes that emerged during analysis: (1) decomposing into separate units, (2) treating units as variables, (3) using covariational/ multivariation reasoning, (4) posing a quantification, and (5) bringing in pure math concepts.

Graphical Resources: Different Types of Knowledge Elements Used in Graphical Reasoning

Presenters: Steven Jones, Brigham Young University and Jon-Marc Rodriquez, University of Wisconsin - Madison
Location:
Abstract/Description:
In broad terms, much of the research on graphical reasoning can be characterized as focusing on misconceptions, covariational and quantitative reasoning, and graphing as a social practice. In contrast, other research has focused on graphing as a cognitive process, emphasizing the fine-grained knowledge elements related to graphing, with a focus on characterizing ideas students associate with graphical patterns (i.e., graphical forms). This paper moves beyond graphical forms to characterize other categories of fine-grained knowledge – “graphical resources” – that are activated and used in concert when constructing and interpreting graphs. In this study, we identified six categories of graphical resources: graphical forms resources, framing resources, ontological resources, convention resources, quantitative resources, and function resources. We posit that holistically considering different categories of fine-grained graph-related knowledge resources can connect various bodies of research on graphing.

Theoretical Considerations for Designing and Implementing Intellectual Need-Provoking Tasks

Presenters: Aaron Weinberg, Ithaca College; Michael Tallman, Oklahoma State University; and Steven Jones, Brigham Young University
Location:
Abstract/Description:
The idea of intellectual need (IN) has received much interest from instructors in trying to design tasks that engage students in impasse-driven learning. However, we argue that the literature on IN is currently insufficient for supporting the careful design and implementation of tasks meant to provoke IN. In this paper, we examine two particular shortcomings: (1) What exactly IN can be created for, and (2) How an instructor might support students in navigating the experience of resolving the confusion and constructing the targeted meanings. For the first of these, we describe the category error of thinking of producing IN for a “topic”, and use the idea of conceptual analysis to suggest a way to address this shortcoming. For the second, we bring in control-value theory to explain what an instructor might attend to in order to ensure that the disequilibrium stays productive and does not lead to frustration and disengagement.