Past Presentations

Abstract/Description: Mathematics teachers make numerous decisions that form lessons that in turn greatly influence what students learn. In making these decisions, teachers rely on their curricular reasoning (CR) to decide on what mathematics to teach, how to structure their lesson, and what problems or tasks to use to achieve their lesson goals. However, teachers differ with respect to the sophistication of their CR and the diversity of CR aspects used in their reasoning. In this paper, we detail two ways to classify teachers’ CR: a leveled approach to capture the increasing sophistication of teachers’ CR, and a heat map approach that highlights the extent to which teacher use various CR aspects in their planning. These methods provide stakeholders avenues by which CR can be studied and that teachers’ CR abilities can be further developed.

Abstract/Description: We seek to extend the understanding and application of the interrelatedness of professional noticing (Jacobs et al., 2010) by identifying the student mathematical thinking to which (STs’) ability to attend to and interpret student mathematical thinking while student teaching and the ways they interpret the student mathematical thinking that was available to them. We report findings from STs’ individual professional noticing skills of attending to and interpreting students’ mathematical thinking. We then compare these findings to the combination of the two professional noticing skills (i.e. interrelated skills). In this poster, we answer the following research questions, How do STs’ individual skills of attending to and interpreting student mathematical thinking differ from their interrelated professional noticing?

Abstract/Description: This poster presents a multi-researcher team’s process of engaging in qualitative data analysis. Three subgroups, each including an experienced researcher and a graduate student, applied iterative approaches to code and identify data patterns regarding ways middle school mathematics teachers use curricular reasoning (CR) to engage learners. Teachers use CR as they design and enact instruction with their students, curriculum materials, and standards in mind. This poster will present ways each subgroup of researchers analyzed the following CR aspects: analyzing curricular materials, viewing mathematics from the learner perspective, and considering mathematical meaning. The poster will illustrate how we created space for dialogue about data analysis, wove seven researchers' perspectives together, and discussed different approaches to analyzing data. Our process has implications for other researchers as they consider data analysis approaches in their contexts, especially when analyzing complex data sets focused on teaching and learning.

Abstract/Description: This paper reports the results of a survey of 404 US mathematics education faculty regarding the research expectations for obtaining tenure. Survey questions asked about expected numbers of publications per year, how much different types of publications (e.g., journal articles, book chapters) and scholarly activities (e.g., giving presentations, obtaining funding) were valued. Statistical analyses were used to examine differences in these results across three demographic characteristics (institution type, research commitment, department). We found statistically significant differences related to each of these variables. Research expectations varied substantially across institution type. For example, the average expected number of yearly publications was 2.23, 1.63, and .99 papers at R1, R2, and Other institutions respectively. By contrast, research expectations seldom varied by department.

Abstract/Description: Scholars suggest that students’ difficulties in making sense of and meaningfully manipulating algebraic expressions is due to their lack of structural reasoning. Research studies have documented that students seldom use expert structural reasoning but give little insight into the nature of students’ non-expert structural reasoning. Our study examines how six AP students identify structure, match structures to rules for manipulation, and evaluate their matches as they solve problems involving rational expressions. We found that students were engaged in structural reasoning throughout the hour-long interviews, and that successful solutions were characterized by students identifying structures by breaking expressions into smaller parts based on the highest level of operation (HLO), matching those structures to valid rules, and evaluating the correctness and progress made by the match they constructed.

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.

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.

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.

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.

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.