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1. Teacher Actions to Foster Creativity in Calculus

   Satyam, V.R. (January 2022, Proceedings of the 24rd Annual Conference on Research in Undergraduate Mathematics Education)

   S. Karunakaran, Z. Reed (Ed.)

   Fostering mathematical creativity in the classroom requires intentional actions on the part of the instructor. We examine the teaching actions that students in a creativity-based Calculus I course report as contributing to their sense of creativity. Based on interview data, we found the four overall types of teaching actions: Task-Related, Teaching-Centered, Inquiry Teaching, and Holistic Teaching. We discuss subtypes as well as concrete actions, to provide actionable steps practitioners can take to foster students’ creativity. 

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2. Teaching Humans When to Defer to a Classifier via Exemplars

   https://doi.org/10.1609/aaai.v36i5.20469  

   Mozannar, Hussein; Satyanarayan, Arvind; Sontag, David (June 2022, Proceedings of the AAAI Conference on Artificial Intelligence)

   Expert decision makers are starting to rely on data-driven automated agents to assist them with various tasks. For this collaboration to perform properly, the human decision maker must have a mental model of when and when not to rely on the agent. In this work, we aim to ensure that human decision makers learn a valid mental model of the agent's strengths and weaknesses. To accomplish this goal, we propose an exemplar-based teaching strategy where humans solve a set of selected examples and with our help generalize from them to the domain. We present a novel parameterization of the human's mental model of the AI that applies a nearest neighbor rule in local regions surrounding the teaching examples. Using this model, we derive a near-optimal strategy for selecting a representative teaching set. We validate the benefits of our teaching strategy on a multi-hop question answering task with an interpretable AI model using crowd workers. We find that when workers draw the right lessons from the teaching stage, their task performance improves. We furthermore validate our method on a set of synthetic experiments. 

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3. Children's sensitivity to automatic behavior relates to pedagogical reasoning and Theory of Mind

   https://doi.org/10.3389/fdpys.2025.1574528  

   Bass, Ilona; Colantonio, Joseph; Aboody, Rosie; Wong, Michelle; Ullman, Tomer; Bonawitz, Elizabeth (April 2025, Frontiers in Developmental Psychology)

   Pedagogy is a powerful way to learn about the world, and young children are adept at both learning from teaching and teaching others themselves. Theoretical accounts of pedagogical reasoning suggest that an important aspect of being an effective teacher is considering what learners need to know, as misconceptions about learners' beliefs, needs, or goals can result in less helpful teaching. One underexplored way in which teachers may fail to represent what learners know is by simply “going through the motions” of teaching, without actively engaging with the learner's beliefs, needs, and goals at all. In the current paper, we replicate ongoing work that suggests children are sensitive to when others are relying on automatic scripts in the context of teaching. We then look at the potential link to two related measures. First, we hypothesize that sensitivity to a teacher's perceived automaticity will be linked to classic measures of pedagogical sensitivity and learning—specifically, how children explore and learn about novel toys following pedagogical vs. non-pedagogical demonstrations. Second, we hypothesize that the development of Theory of Mind (ToM) (and age differences more broadly) relate to these pedagogical sensitivities. Our online adaptation of the novel toy exploration task did not invoke pedagogical reasoning as expected, and so we do not find robust links between these tasks. We do find that ToM predicts children's ability to detect automaticity in teaching when controlling for age. This work thus highlights the connections between sensitivity to teaching and reasoning about others' knowledge, with implications for the factors that support children's ability to teach others. 

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4. Orienting to Student Sense-Making: Using Simulations to Support the Development of Equitable Mathematics Teaching

   https://doi.org/10.4018/979-8-3693-1164-6.ch011  

   Shaughnessy, Meghan; Boerst, Timothy A; Garcia, Nicole; Claiborne, Brit (November 2024, IGI Global)

   This chapter reports on work from a decade-long project to develop and study the use of teaching simulations focused on the teaching practices of eliciting and interpreting student thinking to support preservice teachers' (PSTs') learning. The chapter describes how teaching simulations focused on these practices allow teacher educators to support PSTs in orienting to student sense-making that is at the heart of equitable mathematics instruction. The teaching simulation approach is described. Examples illustrate how the approach is designed and facilitated in ways that make visible PSTs' engagement with three teaching performance areas (eliciting the student's process, using mathematical knowledge and skill, and conveying respect for the student as a mathematical thinker and learner) that are crucial for more equitable mathematics instruction. Connections between each of the performance areas and more equitable eliciting and interpreting of student thinking are described alongside the ways in which teacher educators can provide feedback that supports PSTs' development. 

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5. The Potential Impact of Opportunities to Apply Mathematics to Teaching on Prospective Secondary Teachers’ Competence

   Lai, Y.; Strayer, J.F.; Ross, A.; Adamoah, K.; Anhalt, C.; Bonnesen, C; Casey, S.; Kohler, B.; Lischka, A.E. (March 2023, Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)

   In the past two decades, there has been a trend in materials for mathematics courses for prospective secondary teachers: more opportunities for teachers to “apply mathematics to teaching”. That is, materials increasingly highlight how mathematical knowledge learned in the course can be useful in secondary teaching, and provide opportunities for teachers to harness this knowledge in simulations of teaching. There is little known about the effects of this curricular reform on teachers’ competence. In this report, we use data from the Mathematics of Doing, Understanding, Learning, and Educating for Secondary Schools MODULE(S2) project to examine the potential impact of using such curricular materials. The data include over 300 prospective secondary teachers’ responses to 3 sets of Likert pre-/post-term surveys addressing: mathematical knowledge for teaching; expectancy for enacting selected core teaching practices; and valuing of enacting these practices. We found mean increases across the survey results. We conclude with directions for future research on the impact of this curricular reform. 

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