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Presentations

Professional Noticing: What Difference Do We See in Analyzing Interrelated Noticing...

Thursday, February 08 - Saturday, February 10
Abstract/Description: Noticing activities are abundant in teacher education. We will discuss an implicit methodology used by many that may mask key details about teachers' professional noticing skills. We will engage in two activities to demonstrate the importance of interrelating noticing skills.
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Presentations

Student Teachers’ Professional Noticing in Written Justifications Compared to...

Thursday, February 08 - Saturday, February 10
Abstract/Description: We will discuss findings from employing a methodology to study student teachers interrelated professional noticing skills, differences in findings when studying professional noticing as individual skills, and share implications for developing preservice mathematics teacher educators professional noticing.
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Enhancing Mathematics Teachers’ Curricular Reasoning through Professional Development

Thursday, February 08 - Saturday, February 10
Abstract/Description: Mathematics teachers rely heavily on their curricular reasoning (CR) when making decisions regarding curriculum. In this session, we highlight the Instructional Pyramid model for CR and discuss approaches teacher educators can use to enhance teachers' CR.
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Presentations

Mathematics Standards: Authority or Guidance?

Thursday, February 08 - Saturday, February 10
Abstract/Description: We report on how teachers use the CCSSM to make decisions about what they teach or do not teach. This has implications for mathematics teacher educators as we help preservice teachers learn to use policy documents to improve student learning.
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Presentations

Noticing With Respect To

Thursday, February 08 - Saturday, February 10
Abstract/Description: The common practice of focusing on noticing a singular event is too simplified to account for teachers’ noticing during responsive teaching. We unpack the complexity of noticing WRT (with respect to) during responsive teaching and the iterative noticing it entails.
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Classifying Curricular Reasoning: Ways for Capturing Teachers’ Curricular Decisions

Sunday, October 01 - Wednesday, October 04
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.
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Presentations

Professional Noticing: The Interrelated Skills of Attending to and Interpreting...

Sunday, October 01 - Wednesday, October 04
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?
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Developing a Qualitative Data Analysis Process with a Multi-Research Team

Sunday, October 01 - Wednesday, October 04
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.
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Research Expectations for Mathematics Education Faculty in US Institutions...

Sunday, October 01 - Wednesday, October 04
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.
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Students’ Structural Reasoning about Rational Expressions

Sunday, October 01 - Wednesday, October 04
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.
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Presentations

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

Thursday, February 23 - Saturday, February 25
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.
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Graphical Resources: Different Types of Knowledge Elements Used in Graphical Reasoning

Thursday, February 23 - Saturday, February 25
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.
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Theoretical Considerations for Designing and Implementing Intellectual...

Thursday, February 23 - Saturday, February 25
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.
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Using Rehearsal Debriefs with Experienced Teachers to Negotiate an Understanding...

Thursday, February 02 - Saturday, February 04
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.
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Viewing Classroom Mathematics Discourse through Two Complementary Lenses

Thursday, February 02 - Saturday, February 04
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.
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An Introduction to Lesson Analysis

Wednesday, January 04
Abstract/Description: John Dewey pointed out that one of the problems with the US K-12 educational system is that when a teacher retires, they take all of their accumulated knowledge with them out of the educational system. This is largely the case with undergraduate mathematics education as well. The available instructional resources for undergraduate mathematics instructors lack key features required to build a robust knowledge base for teaching. Few resources address the everyday work of teaching undergraduate mathematics by exploring the details of teaching specific content in a specific context, how to reason through various possible instructional decisions, and how the instructional decisions connect with or help to deepen student mathematical thinking. In this talk I discuss the idea of Lesson Analysis (LA), a process for generating instructional knowledge, and the closely associated written genre, Lesson Analysis Manuscripts (LAMs), to store and share important instructional knowledge largely absent in current resources. LAMs are a type of detailed lesson plan developed to solve a particular problem of practice. However, the emphasis is on understanding the reasoning behind the instructional decisions, usually justified through student mathematical thinking, not on the particular instructional choices of the lesson. I discuss how LA fits into a broad SoTL umbrella, the key features of a LAM, and explain where to publish LAMs for the undergraduate mathematics teaching community.
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Geometric Rotations and Angles: How are they Connected?

Thursday, November 17 - Sunday, November 20
Abstract/Description: With the adoption of the Common Core State Standards for Mathematics 12 years ago, the topic of geometric transformations was shifted from high school to grade 8. In our research with middle grades teachers, they often discussed their difficulty in teaching geometric rotations. Therefore, we analyzed 444 middle grade students’ responses, across four states, to eight rotation questions from the SMART assessment. The results corroborate teachers’ challenges with teaching and student learning of rotations. Results indicate that students have a rigid understanding of angle measure that may be impacting their understanding of geometric rotations. Although angle measure is introduced in grade 4, we hypothesize that teachers need to provide additional opportunities for students to expand their rigid understanding of angle measure.
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Using Public Records to Support the Productive Use of Student Mathematical Thinking

Thursday, November 17 - Sunday, November 20
Abstract/Description: The more researchers understand the subtleties of teaching practices that productively use student thinking, the better we can support teachers to develop these teaching practices. In this paper, we report the results of an exploration into how secondary mathematics teachers’ use of public records appeared to support or inhibit their efforts to conduct a sense-making discussion around a particular student contribution. We use cognitive load theory to frame two broad ways teachers used public records - manipulating and referencing - to support establishing and maintaining students’ thinking as objects in sense-making discussions.
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