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1. WHAT DOES IT MEAN FOR GEOMETRY TEACHERS TO IMPROVE A LESSON? A MULTIMODAL ANALYSIS

   Schwarts, Gil; Jeon, Jeon; Herbst, Patricio; Brown, Amanda (October 2023, Proceedings of the 45th Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Lamberg, T; Moss, D (Ed.)

   A central goal of lesson-centered professional development programs (PD) for mathematics teachers is to learn by constructing an artifact, for example, by designing and improving a lesson plan together. That leads to the questions, what does it mean, for mathematics teachers, to improve a lesson? And how can improvements be accounted for in the analysis of the resulting artifacts, especially when these are multimodal? This paper lays the groundwork for answering such questions by drawing on empirical data from a lesson-centered PD program for secondary geometry teachers. We show how semiotic choices were made to convey that the teacher would need to support students when geometry instruction moves from a construction task to a proof, by (1) addressing students’ confusion; and (2) creating a shared language to discuss diagrams. We relate these findings to teachers’ professional growth and the conference theme. 

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2. What does it mean for geometry teachers to improve a lesson? A multimodal analysis.

   Schwarts, Gil (November 2023, Paper to be included in the proceedings of the 45th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Reno, NV.)

   A central goal of lesson-centered professional development programs (PD) for mathematics teachers is to learn by constructing an artifact, for example, by designing and improving a lesson plan together. That leads to the questions, what does it mean, for mathematics teachers, to improve a lesson? And how can improvements be accounted for in the analysis of the resulting artifacts, especially when these are multimodal? This paper lays the groundwork for answering such questions by drawing on empirical data from a lesson-centered PD program for secondary geometry teachers. We show how semiotic choices were made to convey that the teacher would need to support students when geometry instruction moves from a construction task to a proof, by (1) addressing students’ confusion; and (2) creating a shared language to discuss diagrams. We relate these findings to teachers’ professional growth and the conference theme. 

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3. Teacher learning to teach mathematics via reasoning and proving: a discursive analysis of lesson plans modifications

   https://doi.org/10.3389/feduc.2023.1154531  

   Weingarden, Merav; Buchbinder, Orly (August 2023, Frontiers in Education)

   Christiansen, I (Ed.)

   Despite the importance of reasoning and proving in mathematics and mathematics education, little is known about how future teachers become proficient in integrating reasoning and proving in their teaching practices. In this article, we characterize this aspect of prospective secondary mathematics teachers’ (PSTs’) professional learning by drawing upon the commognitive theory. We offer a triple-layer conceptualization of (student)learning,teaching, andlearning to teachmathematics via reasoning and proving by focusing on the discourses students participate in (learning), the opportunities for reasoning and proving afforded to them (teaching), and how PSTs design and enrich such opportunities (learning to teach). We explore PSTs’ pedagogical discourse anchored in the lesson plans they designed, enacted, and modified as part of their participation in a university-based course:Mathematical Reasoning and Proving for Secondary Teachers. We identified four types of discursive modifications: structural, mathematical, reasoning-based, and logic-based. We describe how the potential opportunities for reasoning and proving afforded to students by these lesson plans changed as a result of these modifications. Based on our triple-layered conceptualization we illustrate how the lesson modifications and the resulting alterations to student learning opportunities can be used to characterize PSTs’ professional learning. We discuss the affordances of theorizing teacher practices with the same theoretical lens (grounded in commognition) to inquire student learning and teacher learning, and how lesson plans, as a proxy of teaching practices, can be used as a methodological tool to better understand PSTs’ professional learning. 

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4. Classifying curricular reasoning: Ways for capturing teachers’ curricular decision

   Dingman, Shannon; Teuscher, Dawn; Olson, Travis; Roth_McDuffie, Amy (October 2023, Proceedings for the forty-fifth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Lamberg, T; Moss, D (Ed.)

   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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5. Classifying curricular reasoning: Ways for capturing teachers’ curricular decisions.

   Dingman, S; Teuscher, D; Olson, T; Roth_McDuffie, A (October 2023, PME-NA)

   Lamberg, T; Moss, D (Ed.)

   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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