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1. A Sociocultural Perspective on Beginning Teachers Enacting Reasoning and Proving Practices

   Weingarden, M.; Buchbinder, O. (January 2022, Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)

   Karunakaran, S. S.; Higgins, A. (Ed.)

   The critical role of teachers in supporting student engagement with reasoning and proving has long been recognized (Nardi & Knuth, 2017; NCTM, 2014). While some studies examined how prospective secondary teachers (PSTs) develop dispositions and teaching practices that promote student engagement with reasoning and proving (e.g., Buchbinder & McCrone, 2020; Conner, 2007), very little is known about long-term development of proof-related practices of beginning teachers and what factors affect this development (Stylianides et al., 2017). During the supervised teaching experiences, interns often encounter tensions between balancing their commitments to the university and cooperating teacher, while also developing their own teaching styles (Bieda et al., 2015; Smagorinsky et al., 2004; Wang et al., 2008). Our study examines how sociocultural contexts of the teacher preparation program and of the internship school, supported or inhibited proof-related teaching practices of beginning secondary mathematics teachers. In particular, this study aims to understand the observed gap between proof-related teaching practices of one such teacher, Olive, in two settings: as a PST in a capstone course Mathematical Reasoning and Proving for Secondary Teachers (Buchbinder & McCrone, 2020) and as an intern in a high-school classroom. We utilize activity theory (Leont’ev, 1979) and Engeström’s (1987) model of an activity system to examine how the various components of the system: teacher (subject), teaching (object), the tasks (tools), the curriculum and the expected teaching style (rules), the cooperating teacher (community) and their involvement during the teaching (division of labor) interact with each other and affect the opportunities provided to students to engage with reasoning and proving (outcome). The analysis of four lessons from each setting, lesson plans, reflections and interviews, showed that as a PST, Olive engaged students with reasoning and proving through productive proof-related teaching practices and rich tasks that involved conjecturing, justifying, proving and evaluating arguments. In a sharp contrast, as an intern, Olive had to follow her school’s rigid curriculum and expectations, and to adhere to her cooperating teacher’s teaching style. As a result, in her lessons as an intern students received limited opportunities for reasoning and proving. Olive expressed dissatisfaction with this type of teaching and her desire to enact more proof-oriented practices. Our results show that the sociocultural components of the activity system (rules, community and division of labor), which were backgrounded in Olive’s teaching experience as a PST but prominent in her internship experience, influenced the outcome of engaging students with reasoning and proving. We discuss the importance of these sociocultural aspects as we examine how Olive navigated the tensions between the proof-related teaching practices she adopted in the capstone course and her teaching style during the internship. We highlight the importance of teacher educators considering the sociocultural aspects of teaching in supporting beginning teachers developing proof-related teaching practices. 

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2. Counterfactually Fair Representation

   Zuo, Zhiqun; Khalili, Mohammad_Mahdi; Zhang, Xueru (May 2024, Proceedings of the 37th International Conference on Neural Information Processing Systems)

   The use of machine learning models in high-stake applications (e.g., healthcare, lending, college admission) has raised growing concerns due to potential biases against protected social groups. Various fairness notions and methods have been proposed to mitigate such biases. In this work, we focus on Counterfactual Fairness (CF), a fairness notion that is dependent on an underlying causal graph and first proposed by Kusner et al. (2017); it requires that the outcome an individual perceives is the same in the real world as it would be in a "counterfactual" world, in which the individual belongs to another social group. Learning fair models satisfying CF can be challenging. It was shown in (Kusner et al. 2017) that a sufficient condition for satisfying CF is to not use features that are descendants of sensitive attributes in the causal graph. This implies a simple method that learns CF models only using non-descendants of sensitive attributes while eliminating all descendants. Although several subsequent works proposed methods that use all features for training CF models, there is no theoretical guarantee that they can satisfy CF. In contrast, this work proposes a new algorithm that trains models using all the available features. We theoretically and empirically show that models trained with this method can satisfy CF. 

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3. Technological knowledge of mathematics pre-service teachers at the beginning of their methodology courses / Conocimiento tecnológico de los futuros maestros de matemáticas al iniciar sus cursos de metodología

   https://doi.org/10.51272/pmena.42.2020-135  

   Choque Dextre, Yency Edith; Moreno-Concepción, Juliette; Hernández-Rodríguez, Omar; Villafañe-Cepeda, Wanda; González, Gloriana (December 2020, Proceedings of the 42nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   Sacristán, A. I.; Cortés-Zavala, J. C.; Ruiz-Arias, P. M. (Ed.)

   Mathematics pre-service teachers must learn how to use tools like scientific calculators, Computer Algebra System (CAS), text processors and dynamic mathematical environments. These tools allow users to work with mathematical objects, perform specialized tasks, respond in a defined mathematical way, and transmit mathematical knowledge (Dick & Hollebrands, 2011). To achieve the integration of technology in Mathematics Education, the teacher’s role is very important, since their beliefs and knowledge will dictate how they use technology in the classroom (Julie et al., 2010). The goal of this research is to determine the beliefs and knowledge about technology and its integration into the teaching of mathematics by a group of pre-service teachers at the beginning of their first course of methodology in the teaching of mathematics at the secondary level (N=11). Interviews were conducted, and a questionnaire was administered to determine the profile participants use of technology at their schools and universities. 

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4. Engaging Teachers in the Combination of Statistical Investigation and Social Justice: Fairness in School Funding

   https://doi.org/10.5951/MTE.2022.0016  

   Casey, Stephanie; Bondurant, Liza; Ross, Andrew (February 2023, Mathematics Teacher Educator)

   This Perspectives on Practice manuscript focuses on an innovation associated with “Engaging Teachers in the Powerful Combination of Mathematical Modeling and Social Justice: The Flint Water Task” from Volume 7, Issue 2 ofMTE. We built on Aguirre et al.’s (2019) integration of mathematical modeling and social justice issues in mathematics teacher education to similarly integrate statistical investigations with social justice issues. 

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5. Computational Classrooms: A Research-Based Approach to Designing a Computer Science Course for Elementary and Middle School Teachers

   Rivera, J; Radoff, J (March 2025, National Association for Research in Science Teaching)

   To address the complex threats to Earth's life-sustaining systems, students need to learn core concepts and practices from various disciplines, including mathematics, civics, science, and, increasingly, computer science (NRC, 2012; United Nations, 2021). Schools must therefore equip students to navigate and integrate these disciplines to tackle real-world problems. Over the past two decades, STEM educators have advocated for an interdisciplinary approach, challenging traditional barriers between subjects and emphasizing contextualized real-world issues (Hoachlander & Yanofsky, 2011; Vasquez et al., 2013; Ortiz-Revilla et al., 2020; Honey et al., 2014; Takeuchi et al., 2020). Despite extensive evidence supporting integrated approaches to STEM education, subject boundaries remain, with disciplines often taught separately and computer science and computational thinking (CS & CT) not consistently included in elementary and middle school curricula. In today's digital age, CS and CT are crucial for a well-rounded education and for addressing sustainability challenges (ESSA, 2015; NGSS Lead States, 2013; NRC, 2012). While there's consensus on the importance of introducing computational concepts and practices to elementary and middle school students, integrating them into existing curricula poses significant challenges, including how to effectively support teachers to deliver inquiry instruction confidently and competently (Ryoo, 2019). Existing frameworks and tools for teaching CS and CT often focus on maintaining fidelity to canonical concepts and formalized taxonomies rather than on practical applications (Grover & Pea, 2013; Kafai et al., 2020; Wilkerson et al., 2020). This focus can lead teachers to learn terminology without fully understanding its relevance or application in different contexts. In response, some researchers suggest using a learning sciences perspective to consider “how the complexity of everyday spaces of learning shapes what counts, and what should be counted, as ‘computational thinking’” (Wilkerson et al., 2020, p. 265). These scholars emphasize the importance of drawing on learners’ everyday experiences and problems to make computational practices more meaningful and contextually relevant for both teachers and their students. Thus, this paper aims to address the following question: How can we design learning experiences for in-service teachers that support (1) their authentic engagement with computational concepts, practices, and tools and (2) more effective integration within classroom contexts? In the limited space of this proposal, we primarily address part 1. 

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