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Meaningful discourse in the mathematics classroom involves creating a learning community that empowers students to articulate their reasoning and make sense of the contributions of their peers while advancing the learning of mathematics for the entire class. This study assessed the degree to which secondary mathematics (Grades 7–12) teacher candidates incorporated discourse into their lessons and the factors influencing their decisions. An explanatory mixed methods design was used, in which data were collected sequentially. Lesson videos were analyzed, followed by interviews of teacher candidates with high-discourse lessons. This study found that participants showed significant growth in their use of effective teaching practices from the beginning of the semester to the end of the semester, including mathematics discourse. The interviews revealed four contributing factors: intentional effort, learning experiences, professional relationships, and pedagogical knowledge. Understanding the experiences of teacher candidates during their own learning of mathematics, their mathematical identities, and beliefs about mathematics could help generate knowledge regarding the implementation of mathematics discourse and other reform-based practices in teacher instruction. 

This paper clarifies and expands the definition of teacher professional practice, grounded in the commonplaces of professionalism outlined by Lee Shulman. We present the Professional Development: Research, Implementation, and Evaluation (PrimeD) framework as a lens for transforming professional development into a practice that engages teachers as professionals. This discussion explores teachers’ roles in both their classrooms and the profession. The inclusion of PrimeD evaluation and research in the development and practice of mathematics teachers addresses Shulman’s professionalism commonplaces. PrimeD was tested as a lens for professionalism in mathematics teacher education programs at four universities. In the study, teachers collaborated as professionals on developing and testing novel ways to approach mathematics lessons. In general, teachers’ efforts to conduct structured experimentation in their lessons were disconnected from traditional views of the role of a teacher. As a result, teachers who did develop and test lesson trials in this PD program did not frequently continue experimentation. Typically, teachers wanted to collaborate on testing classroom activities but did not have resources to do so (e.g., time, collaborative planning). Systemic changes are needed to promote sustainable change, allowing teachers to collaborate and share the results of classroom research. 

Quantitative data for Mathematics Discourse in Secondary Teacher Candidates’ Lessons: A Mixed Methods Analysis. 

This paper describes how plan-do-study-act cycles engaged a classroom mentor teacher and student teacher in a professional collaboration that resulted in two inquiry activities for high-school geometry classes. The PDSA cycles were carried out in four high school geometry classes, each with 30 to 35 students, in a mid-Atlantic urban school district in the U.S. The four geometry classes were co-taught by the second and third authors of this paper. The data consisted of classroom documents (e.g., activity prompts, tasks), classroom observations, student feedback about activities, and monthly PDSA reports. The PDSA cycles had a direct effect on the professional learning of the teachers. The resultant classroom activities used a data collection approach to engaging students in inquiry to learn about trigonometry functions and density. Student learning behaviors were noticeably improved during these activities compared with traditional mathematics instruction. We concluded that the data collection sequence provided an accessible entry point for students to begin scientific inquiry in mathematics. The process opened the conceptual space for students to develop curiosity about mathematical phenomena and to explore their own research questions. The use of culturally relevant topics was especially compelling to students, and the open-ended nature of these exploratory activities allowed students to see mathematics through their own cultural lenses. 

This study examined the use of the PrimeD framework to improve secondary (Grades 7-12) mathematics teacher preparation. The study used design-based research through a four-year treatment-only mixed methods triangulation design. Data sources were program documents and assessments, focus groups, interviews, and field experience observations. The Reformed Teaching Observation Protocol with Performance Descriptors (RTOP+) measured candidates’ teaching quality at three time points during the student teaching internship. As the program incorporated more features of PrimeD, supervisors and mentor teachers increasingly took on leadership roles and each subsequent cohort demonstrated stronger growth on the RTOP+. 

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. 

These data are for 17 secondary mathematics teacher candidates (TCs) in four university teacher preparation programs, who 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, a Networked Improvement Community (NIC) was formed by teacher candidates, classroom mentor teachers, field experience supervisors, and university faculty 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 (Lyublinskaya & Tournaki, 2011) were used to examine how teacher candidates implemented technology for Mathematics conceptual understanding. The Mathematics Classroom Observation Protocol for Practices (MCOP^2; Gleason, Livers, & Zelkowski, 2015) was used to further examine how effective mathematics teaching practices (e.g., student engagement) were implemented by TCs.