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1. Analyzing the development of MKT in content courses

   Lai, Y. ; Strayer, J. F. ; Lischka, A. E. ( November 2018 , In T.E. Hodges, G.J. Roy, & A.M. Tyminski, A. M. (Eds.), Proceedings of the 40th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)

   To improve teaching and learning in content courses for secondary mathematics teachers, we take the approach of supporting faculty who teach these courses – often mathematics faculty – in developing their own mathematical knowledge for teaching (MKT) at the secondary level. We describe a framework that has informed the design of educative curricula for a set of these courses. This framework integrates theory for knowledge development, empirical work on dimensions of knowledge used in teaching, and findings on observable behaviors in teaching that reveal prospective secondary teachers’ knowledge development. 

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2. 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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3. Mathematics instructors’ attention to instructional interactions in discussions of teaching rehearsals

   Czap, L. ; Ahrens, S. ; Lischka, A.E. ( January 2020 , Mathematics Education Across Cultures: Proceedings of the 42nd 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.)

   In our project, we develop curricular materials to support prospective secondary teachers’ development of MKT and provide professional development (PD) opportunities for instructors ho will teach with these materials. In this paper, we examine the ways in which mathematics faculty engage in the teaching rehearsal debriefs included in the PD to answer the question: To what instructional interactions do instructors of mathematics content courses attend during rehearsal debriefs enacted in PD? Findings show that mathematics instructors attend to all types of interactions but attention is influenced by instructors’ mathematical knowledge. 

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4. 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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5. Teaching Mathematics with Technology: TPACK and Effective Teaching Practices

   https://doi.org/10.3390/educsci12020133  

   Rakes, Christopher R. ; Stites, Michele L. ; Ronau, Robert N. ; Bush, Sarah B. ; Fisher, Molly H. ; Safi, Farshid ; Desai, Siddhi ; Schmidt, Ashley ; Andreasen, Janet B. ; Saderholm, Jon ; et al ( February 2022 , Education Sciences)

   This paper examines how 17 secondary mathematics teacher candidates (TCs) in four university teacher preparation programs implemented technology in their classrooms to teach for conceptual understanding in online, hybrid, and face to face classes during COVID-19. Using the Professional Development: Research, Implementation, and Evaluation (PrimeD) framework, TCs, classroom mentor teachers, field experience supervisors, and university faculty formed a Networked Improvement Community (NIC) to discuss a commonly agreed upon problem of practice and a change idea to implement in the classroom. Through Plan-Do-Study-Act cycles, participants documented their improvement efforts and refinements to the change idea and then reported back to the NIC at the subsequent monthly meeting. The Technology Pedagogical Content Knowledge framework (TPACK) and the TPACK levels rubric were used to examine how teacher candidates implemented technology for Mathematics conceptual understanding. The Mathematics Classroom Observation Protocol for Practices (MCOP2) was used to further examine how effective mathematics teaching practices (e.g., student engagement) were implemented by TCs. MCOP2 results indicated that TCs increased their use of effective mathematics teaching practices. However, growth in TPACK was not significant. A relationship between TPACK and MCOP2 was not evident, indicating a potential need for explicit focus on using technology for mathematics conceptual understanding. 

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