Alison Clark-Wilson

The Mathematics Teacher in the Digital Era: An International Perspective on Technology Focused Professional Development

This volume addresses the key issue of the initial education and lifelong professional learning of teachers of mathematics to enable them to realize the affordances of educational technology for mathematics. With invited contributions from leading scholars in the field, this volume contains a blend of research articles and descriptive texts. In the opening chapter John Mason invites the reader to engage in a number of mathematics tasks that highlight important features of technology-mediated mathematical activity. This is followed by three main sections an overview of current practices in teachers use of digital technologies in the classroom and explorations of the possibilities for developing more effective practices drawing on a range of research perspectives (including grounded theory, enactivism and Valsiners zone theory). a set of chapters that share many common constructs (such as instrumental orchestration, instrumental distance and double instrumental genesis) and research settings that have emerged from the French research community, but have also been taken up by other colleagues. meta-level considerations of research in the domain by contrasting different approaches and proposing connecting or uniting elements

Hiccups within Technology Mediated Lessons: A Catalyst for Mathematics Teachers' Epistemological Development.

The notion of the lesson ‘hiccup’, defined as the perturbation experienced by a teacher during teaching that has been triggered by the use of mathematical technology, was first proposed in Clark-Wilson. Hiccups which are both unanticipated and unplanned, emerged from a study that sought to make sense of the process of secondary mathematics teachers’ situated learning as they began to use a particular new technological tool (TI-Nspire™ handheld devices and software) in their classrooms. The high frequency of the resulting hiccups enabled a categorisation of seven hiccup types that were shown to have influenced the development of teachers’ mathematical, pedagogic and technological knowledge. This article first reports and then extends this earlier work by articulating the design principles for a professional development approach within the Cornerstone Maths (CM) project that uses hiccups to try to address professional development ‘at scale’ concerning student use of dynamic digital technologies in mathematics classrooms.

A methodological approach to researching the development of teachers’ knowledge in a multi-representational technological setting.

This chapter details the methodological approach adopted within a doctoral study that sought to apply and expand Verillon and Rabardel’s (European Journal of Psychology of Education, 10, 77–102, 1995) triad of instrumented activity as a means to understand the longitudinal epistemological development of a group of secondary mathematics teachers as they began to integrate a complex new multi-representational technology (Clark-Wilson, How does a multi-representational mathematical ICT tool mediate teachers’ mathematical and pedagogical knowledge concerning variance and invariance? Ph.D. thesis, Institute of Education, University of London, 2010a). The research was carried out in two phases. The initial phase involved fifteen teachers who contributed a total of sixty-six technology-mediated classroom activities to the study. The second phase adopted a case study methodology during which the two selected teachers contributed a further fourteen activities. The chapter provides insight into the methodological tools and processes that were developed to support an objective, systematic and robust analysis of a complex set of qualitative classroom data. The subsequent analysis of this data, supported by questionnaires and interviews, led to a number of conclusions relating to the nature of the teachers’ individual technology-mediated learning.

Summary and Suggested Uses for the Book

This chapter provides an overview of the book’s content in relation to the ‘grain size’ of the focus and analysis of the different methodologies contained within the constituent chapters. In addition it offers some classification in terms of static, dynamic and more evolutionary approaches to researching teachers’ uses of digital technologies in classrooms, whilst emphasising the importance of the different approaches. The chapter ends by suggesting some possible approaches to the use of the book’s content for academic teaching scenarios, particularly those that involve practising mathematics teachers. The examples that are provided give ideas on how to engage teachers in both reflective thought alongside the provision of use of theoretical constructs that may support the ongoing development of their classroom practices with technology.

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).

Transforming Mathematics Teaching with Digital Technologies: A Community of Practice Perspective

Dynamic mathematical digital resources promise a transformation of the teaching and learning of mathematics by enabling teachers and learners to experience and explore difficult mathematical ideas in more tangible ways. However, reports of classroom practice reveal an underuse of such technologies—particularly by learners—and research findings articulate the complexities of the process of classroom integration by teachers. The work described in this chapter is set in the context of a large-scale multi-year study, Cornerstone Maths (CM), which aims to overcome known barriers to technology use in lower secondary mathematics with the professional development of the participating teachers as a central tenet. Here, the design and implementation of the CM professional development as experienced by a group of four teachers from one school’s mathematics department is examined from a Wengerian perspective as a means to understand the trajectories of teachers’ growth in both their mathematical knowledge for teaching and their associated emerging mathematical pedagogic practices with technology.