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1. 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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2. 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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3. Messages about valued knowledge products and processes embedded within a suite of transformed high school chemistry curricular materials

   https://doi.org/10.1039/d2rp00124a  

   Schafer, Adam G.; Kuborn, Thomas M.; Schwarz, Cara E.; Deshaye, Megan Y.; Stowe, Ryan L. (January 2023, Chemistry Education Research and Practice)

   The way high school chemistry curricula are structured has the potential to convey consequential messages about knowledge and knowing to students and teachers. If a curriculum is built around practicing skills and recalling facts to reach “correct” answers, it is unlikely class activities will be seen (by students or the teacher) as opportunities to figure out causes for phenomena. Our team of teachers and researchers is working to understand how enactment of transformed curricular materials can support high school chemistry students in making sense of perplexing, relatable phenomena. Given this goal, we were surprised to see that co-developers who enacted our materials overwhelmingly emphasized the importance of acquiring true facts/skills when writing weekly reflections. Recognition that teachers’ expressed aims did not align with our stated goal of “supporting molecular-level sensemaking” led us to examine whether the tacit epistemological commitments reflected by our materials were, in fact, consistent with a course focused on figuring out phenomena. We described several aspects of each lesson in our two-semester curriculum including: the role of phenomena in lesson activities, the extent to which lessons were 3-dimensional, the role of student ideas in class dialogue, and who established coherence between lessons. Triangulation of these lesson features enabled us to infer messages about valued knowledge products and processes materials had the potential to send. We observed that our materials commonly encouraged students to mimic the structure of science practices for the purpose of being evaluated by the teacher. That is, students were asked to “go through the motions” of explaining, modeling etc. but had little agency regarding the sorts of models and explanations they found productive in their class community. This study serves to illustrate the importance of surfacing the tacit epistemological commitments that guide curriculum development. Additionally, it extends existing scholarship on epistemological messaging by considering curricular materials as a potentially consequential sources of messages. 

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4. Relevance as perceived by high school students in decontextualized mathematics lessons

   Adil, Aamina; Lee, Kihoon L.; Dietiker, Leslie (January 2022, Proceedings of the forty-fourth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Lischka, A. E.; Dyer, E. B.; Jones, R. S.; Lovett, J. N.; Strayer, J.; Drown, S. (Ed.)

   When mathematics educators work towards making mathematics more relevant, they often think about including more real-world applications into mathematics lessons. But what happens when a lesson is devoid of real-world contexts? In what ways can students find it relevant? This study explores how high school students perceived relevance when they were asked to describe their experiences during decontextualized mathematics lessons. Students highlighted how they found certain characteristics of the lessons to be useful in their learning and how they perceived relevance through different feelings experienced in the lessons. 

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5. Narrative characteristics of captivating secondary mathematics lessons

   https://doi.org/10.1007/s10649-022-10184-y  

   Dietiker, Leslie; Singh, Rashmi; Riling, Meghan; Nieves, Hector I.; Barno, Erin (January 2022, Educational Studies in Mathematics)

   Why do some mathematics lessons captivate high school students and others not? This study explores this question by comparing how the content unfolds in the lessons that students rated highest with respect to their aesthetic affordances (e.g., using terms like “intriguing,” “surprising”) with those the same students rated lowest with respect to their aesthetic affordances (e.g., “just ok,” “dull”). Using a framework that interprets the unfolding content across a lesson as a mathematical story, we examine how some lessons can provoke curiosity or enable surprise. We identify eight characteristics that distinguish captivating lessons and show how some, such as the average number of questions under consideration at any point in the lesson, are strongly related to student aesthetic experiences. In addition, the lessons that students described as more interesting included more instances of misdirection, such as when students’ false assumptions provide opportunities for surprising results. These findings point to the characteristics of future lesson designs that could enable more students to experience curiosity and wonder in secondary mathematics classrooms. 

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