Professional development of teachers and mentor teachers: A case study from the German Center for Mathematics Teacher Education in the domain of teaching probability and statistics

Prof. Rolf Biehler, Universität Paderborn (Germany) and DZLM (German Centre for Mathematics Teacher Education)

The DZLM (German Centre for Mathematics Teacher Education) exists since 2011 and develops research-based programs for mathematics teacher education and mathematics mentor teacher education that are continually evaluated.  New standards for courses for teachers and mentor teachers are emerging from its various fields of activity. The growing network inside and outside the DZLM, including its strong collaboration with other teacher educating institutions, is an important source for its development.

The presentation will build on several projects the author is responsible for in the domain of probability and statistics: A course for mentor teachers for lower secondary schools, a course for out-of-field teachers for lower secondary schools and courses for teachers and mentor teachers at upper secondary level. Mentor teachers, “normal” teachers and out-of-field teachers of mathematics represent the different major addressees of the DZLM. Based on research in probability and statistics education on the one hand and on research on the design of professional development courses for the various addressees on the other, the presented examples will provide an insight into the practical work of DZLM and its theoretical basis.

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Preparing Mathematics Teachers to Facilitate the Problem-Solving Cycle Professional Development

Prof. Hilda Borko, Stanford University, California, USA

In recent years, there has been a growing demand for professional development opportunities for classroom teachers. A major impediment to meeting this demand is the lack of attention to preparing PD leaders. Although our understanding of what PD leaders must know and be able to do has increased, we know less about how to prepare and support these leaders. In the area of mathematics, the preparation of PD leaders has been the focus of a small number of research and development projects, including my work with colleagues to develop and study the Problem-Solving Cycle (PSC) model of professional development and Mathematics Leadership Preparation (MLP) model of PD leader preparation. The PSC consists of a series of three interconnected workshops, organized around a rich mathematical problem.  During the workshops teachers solve the problem and prepare to teach it (Workshop 1), and then use video clips and student work from their PSC lessons to analyze student reasoning and instructional practices (Workshops 2 and 3). The MLP program is designed to prepare Math Leaders to plan and lead PSC workshops. It includes multiple opportunities for participants to plan and rehearse PD facilitation practices, and to receive feedback from both the facilitators of the MLP development experiences and their fellow Math Leaders. Because video clips from participating teachers’ mathematics lessons are an integral part of PSC workshops, our team has developed activities and tools for supporting Math Leaders to select video clips, plan and rehearse video-based discussions, and debrief the rehearsals. In the presentation I will describe the two models and share some of our research findings, highlighting what we have learned about preparing for and leading video-based discussions.

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Using video for mathematics teacher development: The role of error and judgment.

Dr. Alf Coles, University of Bristol, Bristol, UK

In this presentation, I will report on findings, related to the role of the facilitator, from a UK government-funded project to promote the use of video clubs for the professional development of teachers of mathematics. Teachers meet on six occasions, over a three-month period and share video recordings of their own classrooms. The meetings of one club were themselves video recorded. While it is a common finding that discussion norms can be hard to establish, participants in this club adapted to intended norms from the first meeting. The way this was achieved is analyzed, within the enactivist methodology of the project. There is an apparent paradox that a move away from judgment is achieved through the use of judgment. Bateson’s (1972) levels of learning, error and communication are offered as one explanation of the observed phenomena. Implications are drawn out for facilitating professional development with mathematics teachers more generally.

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Educating educators to work in the field of mathematics teaching development

Prof. Ruhama Even, Weizmann Institute of Science, Israel

There is general agreement today that the continued professional development of teachers is key to improving students' opportunities to learn mathematics. Yet, past experience suggests that supporting practicing teachers’ learning is not a trivial task. Consequently, there is a growing interest in the international community in the education of educators that will be able to work with practicing mathematics teachers on developing their teaching. The talk addresses the challenges associated with this undertaking by attending to three issues. The first two issues are related to the field of teaching development of practicing mathematics teachers: one issue centers on the practice of mathematics educators who work in the field of teaching development, and the other on the nature of this field. The third issue is the professional education and development of mathematics educators who work in the field of teaching development, proposing the construct of knowtice (a combination of knowledge and practice) as a lens to capture the essence of what these educators need to learn and develop. Finally, directions for future research will be suggested.

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Students, teachers, teachers of teachers, teachers of teachers of teachers… Reflections on the “learning-teaching pyramid”

Prof. Abraham Arcavi and Dr. Ronnie Karsenty, Weizmann Institute of Science, Israel

Mathematics education has been focusing on students and how they learn for about 4-5 decades. Teacher learning is the focus of research and development for about three decades. In the last decade and a half attention was directed to teachers of teachers, teacher educators and teacher mentors. In the VIDEO-LM project our attention is on teachers of teachers, and ourselves (teachers of teachers of teachers) within a specific environment of using video to foster reflection on the teaching practice. We will present our two cycles of preparing teacher mentors for the VIDEO-LM project, the design principles that led us, the plans and the challenges to implement them. We will also reflect on the percolation of what we do throughout the “learning- teaching pyramid”.

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