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1. 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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2. Shaping the professional growth of mathematics faculty who teach prospective secondary teachers

   Czap, L.; Ahrens, S.; Lai, Y.; Lischka, A. E. (January 2021, Proceedings of the forty-third annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   D. Olanoff; K. Johnson; S. Spitzer (Ed.)

   Professional development (PD) that supports faculty in teaching courses for prospective secondary teachers, especially courses focused on mathematical knowledge for teaching, are largely absent from higher education, despite the need to improve instruction in these courses. This study examines a novel PD program whose structure was inspired by rehearsals (Lampert et al., 2013). We analyzed PD discussions throughout the year using an instructional triad framework, and we interpreted the PD structure using Clarke and Hollingsworth’s (2002) Interconnected Model for Professional Growth. We suggest that a rehearsal-inspired pedagogy offered opportunities for faculty growth in attending to student contributions. 

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3. Professional development for mathematics teacher education faculty: Need and design

   Jackson, B.; Hauk, S.; Tsay, J. J.; Ramirez, A. (June 2020, The Montana math enthusiast)

   null (Ed.)

   The purpose of this report is to share a conceptual model useful in the design of professional learning about teaching for university mathematics faculty. The model is illustrated by examples from a particular design effort: the development of an online shortcourse for faculty new to teaching mathematics courses for prospective primary school teachers. How novice mathematics teacher educators grow as instructors is an emerging area of research and development in the United States. At the same time, it is well established that effective instructional design of any course, including a course for faculty, requires breadth first: understanding and anticipating the needs of the learner. Therefore, given the sparse knowledge base in the new arena of mathematics teacher educator professional growth, effective design requires leveraging the scant existing research while also exploring and iteratively refining broad goals and objectives for faculty learning. Only after a conceptual foundation is articulated for what is to be learned and what will constitute evidence of learning, can cycles of design productively examine and test-bed particular course features such as lesson content, structures (like scope and sequence), and processes (like communication and evaluation). In the example used in this report, several researchbased perspectives on learning in/for/about teaching guided design goals and short-course objectives. These valued perspectives informed creation and prioritization of principles for short-course design which, in turn, informed evaluation of faculty learning. With these conceptual foundations in place, design of lessons to realize the goals, principles, and objectives rapidly followed. The work reported here contributes to the knowledge base in two ways: (1) it addresses faculty professional development directly by describing and illustrating a model for supporting instructional improvement and (2) it provides metanarrative to scaffold the professional growth of those who design professional learning opportunities for post-secondary mathematics faculty. 

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4. Facilitating collaborative inquiry into practice around artifacts of mathematics teaching

   https://doi.org/10.1007/s10857-024-09649-z  

   Ebby, Caroline_B; Hess, Brittany; Pecora, Lizzy; Valerio, Jennifer (August 2024, Journal of Mathematics Teacher Education)

   Abstract Although there has been increasing attention to the importance of teacher agency in professional development, there has been little attention to what it takes to facilitate collaborative work that both centers teachers’ assets and expertise and leads to productive learning. This paper presents a framework for focused and responsive facilitation of productive discourse around instructional practice in teacher learning communities. Drawing on a situative perspective, we trace the development of six novice teacher leaders as they were mentored to lead online collaborative lesson design groups focused on analyzing artifacts of K-8 mathematics instruction in a large urban district in the US. Our framework articulates how leaders facilitated the discussions in ways that both built on teacher knowledge, experiences, and contributions while also focusing on professional learning goals. Our analysis also shows how rich learning opportunities were co-constructed and sustained by the mentors, teacher leaders, and participants in each group over time. Through narrative descriptions of one group, we show how the teacher participants began to take on some of the facilitation practices themselves as they apprenticed into the practices of the community. This approach to professional learning positions teachers’ experience and knowledge as important assets while supporting them to try out and reflect on new classroom practices. 

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5. Preservice Secondary Mathematics Teachers’ Reflective Noticing from 360-degree Video Recordings of Their Own Teaching.

   Buchbinder, O.; Brisard, S.; Butler, R.; McCrone, S. (January 2021, Journal of technology and teacher education)

   The benefits of using video in teacher education as a tool for reflection and for developing professional expertise have long been recognized. Recent introduction of 360 video technology holds promise to extend these benefits as it allows prospective teachers to reflect on their own performance by considering the classroom from multiple perspectives. This study examined nine prospective secondary teachers’ (PSTs) noticing and self-reflection on the 360 recordings of their own teaching. The PSTs, enrolled in a capstone course Mathematical Reasoning and Proving for Secondary Teachers, taught a proof-oriented lesson to small groups of students in local schools while capturing their teaching with 360 video cameras. We analyzed the PSTs’ written comments on their video and reflection reports to identify the categories of noticing afforded by the 360 technology as well as the instances of PSTs’ learning. The results point to the powerful potential of 360 videos for supporting PSTs’ self-reflection and professional growth. 

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