This project focuses on three mathematics teaching practices --posing mathematical problems, responding to students' mathematical ideas, and interpreting students' mathematical thinking -- that are discussed in teacher preparation courses as practices that directly affect student learning. These practices are essential to the improvement of mathematics teaching and learning and demand a deep understanding of mathematics in the context of teaching. Research has found these practices to be underdeveloped in prospective teachers of mathematics and to be challenging to learn. In spite of the amount of attention they tend to receive in teacher preparation courses little is known about how these practices develop at the beginning stages of a teacher's career. This means that the field of mathematics teacher education has incomplete knowledge about how best to help prospective teachers move towards more sophisticated understandings and enactments of these practices. The research and educational agenda proposed in this project are critical to improving the design and implementation of mathematics teacher preparation programs and experiences.
This project will study the practices of posing, interpreting, and responding using cross-sectional and longitudinal research designs. The cross-sectional study will characterize the focal practices at each of three stages in the elementary teacher preparation program at Michigan State University. The longitudinal study will focus on the development of the focal practices as prospective elementary school teachers move through the teacher preparation program and into their first and second year of teaching. Factors that afford and constrain the development of these practices will also be examined through in-depth case studies of ten participants. The educational goal of the project is to provide professional development for mathematics teacher education instructors. This professional development will consist of regular instructor meetings throughout the length of the project that will parallel the activities of the research group. As the research group works to develop the research instruments, for example, the instructor group will focus on adapting the research instruments to their teacher education classrooms. The goal of these educational activities is to, in collaboration with practicing mathematics education instructors, make the research tools and findings generated by this project useful to the teaching practice of mathematics teacher educators.
This project investigated the development of prospective teachers’ understanding and enactments of mathematics teaching practice, as they move from course work, to preparatory teaching, and into regular teaching positions. The project involved conceptual and empirical work related to three specific practices of mathematics teaching---Posing mathematical tasks, Interpreting students’ mathematical reasoning, and Responding to students’ mathematical ideas (PIR) ---that teachers constantly perform in classrooms. The main argument for this study was that PIR practices are embedded within the everyday work of mathematics teaching. Teachers pose mathematical tasks, they interpret students’ work on those tasks and make assumptions about what they are and not understanding, and they respond based on those assumptions. Therefore PIR practices open and close mathematics learning opportunities to students every day. Although it is not hard to see the important role these practices play, these are not studied explicitly during teacher preparation courses. It is important to note that since the time this project was funded, attention to the study of practices has increased at the teacher education institution where this study took place and elsewhere. The project sought to define and then unpack these practices with greater precision and with the goal of broadening what might be considered competent performance of these practices, especially for those just beginning their formal studies of mathematics teaching. It used cross-sectional and longitudinal study designs to explore how prospective teachers who had not studied these practices explicitly during their teacher preparation program imagined and enacted these practices over time. The educational goal of the project is to explore ways of making these practices an object of explicit study in mathematics teacher education classrooms. This project generated new research tools to study envisioned (or imagined) mathematics teaching practice using prompts that requested dialogical representation of mathematics teaching. Additionally the project generated classroom observation and interview protocols. The project also generated pedagogical applications of some of the project research tools to be used as instructional tools with pre-service and in-service teachers. Opportunity to Learn Findings: Of the three PIR practices the practice of posing mathematical tasks to students is more prominently emphasized across all teacher preparation courses in the institution where this study took place. However, this is likely to be the case in other programs as this is a practice that is easier to study without access to an actual mathematics classroom. This tends to be the case in University-based teacher preparation programs. The practices of interpreting students’ mathematical reasoning were the focus on the mathematics methods courses rather than content courses and the practice of responding to students’ thinking was barely mentioned in course materials or by the course instructors interviewed. Cross-Sectional Study Findings Despite the lack of explicit attention in most teacher preparation programs (at the time the project’s cross-sectional data was collected), this project found that even without such explicit emphasis, the more experienced teacher education students (interns) produced a greater collection and higher quality PIR practices in the project’s PIR teaching scenarios than the less experienced teacher education students (juniors). Longitudinal Case Studies The Longitudinal study of the project consisted of two concurrent longitudinal studies; one within the teacher preparation program at MSU (7 participants: from junior-to senior-to intern) and the other beyond the teacher preparation program (7 participants: from intern-to first year of teaching- to second year-to third year). These studies documented the development of PIR practice as prospective teachers transitioned from studying to enacting mathematics teaching. The "within teacher preparation" study further confirmed the cross-sectional study findings, that there were differences in the PIR practices of those in the senior and the intern year phase of teacher preparation and illuminated contextual factors that supported and limited the development of these practices. The "beyond teacher preparation" study painted a more complicated picture of what it takes for new teachers to enact high quality PIR practices and by the third year of teaching the participating beginning teachers became more confident, intentional, and experimental in their enactments and explaining their PIR practices over time. By their third year of teaching they had settled into well-established routines for posing tasks, interpreting, students’ work, and responding to their thinking, but were also experimenting and stretching some aspect of their posing-interpreting-responding practices (typically based on mentors’ or evaluators’ feedback and/or students’ outcomes data). Factors that supported and constrained their growth of PIR practices in the context of beginning years of teaching include: the mathematics textbook, the stability of their teaching assignment, continued education (Master’s Degree and/or Professional Development Opportunities), and the school culture and how it supports their new teachers.
