Olive Chapman

Professional Development of Mathematics Educators: Trends and Tasks

In this chapter the professional growth of mathematics educators — including teachers, teacher educators, and educators of teacher educators — is presented as an ongoing lifelong process. So far as teachers are concerned, it occurs in various stages and contexts, beginning with their experiences as school students, followed by formal preservice preparation towards an academic qualification and teaching certificate. It continues in formal and informal inservice settings and, sometimes, in graduate studies. In this chapter we focus on trends in the thinking about, and practices within, inservice professional development programmes for mathematics educators — inservice teachers as well as inservice teacher educators. We begin by offering a unifying conceptual framework which takes into account interrelations between the different groups covered by the term ‘mathematics educators’. This framework, which acknowledges the central role of tasks and programmes in which participants engage, facilitates thinking about the complexities and underlying processes involved in professional development in mathematics education. We describe in detail the main types of programmes reported in the literature. Examples of tasks with special potential for enhancing the professional development of both teachers and teacher educators are discussed.

Research Methods in Mathematics Teacher Education

As the field of mathematics education grows so too do the research methods used to study the field. In the special area of teacher education, the last decade has witnessed a substantial increase in attention. New perspectives and new methodologies have been constituted and new research techniques established. Choosing the “right” method is not a trivial task for any researcher, and increasingly we are seeing more sophisticated research methods, including different forms of mixed methods. A main concern of research these days relates to the fact that as well as studying teachers and teaching, researchers want to see their findings applied to the professional development of teachers and to a critical modification of teacher education practices, in the frame of social changes. This has led to more research with teachers rather than on teachers. After surveying state-of-the-art of methods in research on mathematics teacher education published in renowned international journals, this chapter focusses on participatory action research as an example of a research method from the politicized periphery of the field.

Mathematical Modelling in High School Mathematics: Teachers’ Thinking and Practice

Modelling in the mathematics classroom is discussed based on the thinking and practice of a sample of exemplary high school mathematics teachers. These teachers held conceptions of mathematics, word problems and problem solving that placed importance on real world connections and influenced the creation of a classroom culture to support modelling. Their teaching strategies that allowed students to develop flexibility to engage in modelling are highlighted.

Mathematics Teacher Educators' Knowledge for Teaching

The aims of DG12 were to: Facilitate discussion of key issues related to the knowledge required by mathematics teacher educators (MTEs), Identify different emergent strands in research that can be related to this area.

Overall Commentary: Understanding and Changing Mathematics Teachers

This overall commentary examines the research studies presented in all three sections of this book; first by discussing issues from within the three central themes of the book (mathematical knowledge for teaching, teacher identity, and tools to facilitate teachers’ learning) and then by looking at contributions the studies make to three important areas of research in mathematics teacher education: understanding the teacher, supporting teachers’ learning, and research tools. In doing so, the chapter discusses the nature of research in identified areas of research, highlights specific contributions of the studies in this book to those areas, and suggests implications for future research in the field of mathematics teacher education.

Steps Toward a More Inclusive Mathematics Pedagogy

This chapter is based on an action research project with the mathematics teaching staff of a school that serves special needs students from grades 2 to 12. Now in its fifth year, and with the aim of refining practices to ensure that all students have the opportunity to learn, the collaboration has adopted the analogy that “learning to teach differently is like learning another language.” This framing has highlighted the complexities, difficulties, and strategies associated with shifting from highly familiar standardized, teacher-centered classroom practices to more authentic emphases that are consonant with reform efforts. In this chapter, we report on the power of this frame to effect transformations in teachers’ beliefs and actions, while also highlighting how easily one’s “native language” can seep into, undermine, and obscure efforts at transformation. By way of initial example, through action research, strategies have been implemented to ensure teachers are constantly aware of multiple learner interpretations, yet there is a persistent recurrence in classrooms of questions of the form “Can anyone tell me…?” We argue that such questions may be indicative of a mode of directive teaching that is aimed at a “representative learner,” in contrast to a mode of responsive teaching that is attentive to the sense(s) that each learner might actually be making.

Improving Teachers’ Assessment Literacy in Singapore Mathematics Classrooms: Authentic Assessment Task Design

In this chapter, we present a school-based, practice-oriented professional development approach to mathematics authentic assessment task design and examine its impact on elementary mathematics teachers’ assessment literacy. The quality of teachers’ assessment tasks used in the day-to-day mathematics instruction was used as an indicator of teachers’ assessment literacy. We believe that authentic assessment tasks provide rich learning opportunities for students to develop their mathematical literacy, which was evident in students’ work. In addition, teachers’ active involvement in the design and implementation of mathematics authentic assessments has the potential to increase their diagnostic competence. Singapore, one of the high-performing education systems in the world, was used as an example to demonstrate the importance of improving mathematics teachers’ assessment literacy in the context of twenty-first century teaching and learning. The chapter ends with some recommendations for using mathematics authentic assessments to increase teachers’ diagnostic competence. It also includes some suggestions for future research.

Mathematics Teachers Working and Learning Through Collaboration

The authors of this paper were tasked by ICME-13 organisers with conducting a survey on the topic “Mathematics Teachers Working and Learning through Collaboration”. Four research questions guided the survey, concerned with: the nature of collaborative working; the people who engage collaboratively; the methodological and theoretical perspectives used; what learning could be observed and how it related to collaboration? The resulting survey drew from a wide range of sources, identifying papers relevant to the topic—316 papers were identified, analysed against a set of criteria and organised into three major themes, each relating to one or more of our research questions: Different contexts and features of mathematics teachers working in collaboration; Theories and methodologies framing the studies; Outcomes of collaborations. In addition to the papers revealed by the survey, the team sought contributions from projects around the world which are not represented in the published literature. Members from these projects offered ‘narratives’ from the work of teachers in the projects. This paper reports on the nature of the projects revealed by the survey and the narratives, their theoretical and methodological focuses, and the range of findings they expressed. While we offer a significant range of factors and findings, resulting from a very considerable work, we are aware of limitations in our study: we missed relevant papers in journals outside our range; papers reviewed were usually not authored by teachers so the teachers’ voice was often missing; narratives came from projects with which we were familiar, so we missed others. The survey team is in the process of initiating an ICMI study which can take this work into these missing areas. This paper follows closely the presentation made by the survey team at the ICME-13 congress. In presenting findings from the survey, we have tried to provide examples from and make reference to the survey papers. Because the set of references would be too large to fit within our word limit, we have had to reduce the number of references made. However, readers can find a full set of references in a more detailed paper, Robutti et al. in (ZDM Mathematics Education, 48(5), 651–690, 2016).