Ornella Robutti

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

Meta-Didactical Transposition: A Theoretical Model for Teacher Education Programmes

We propose a new model for framing teacher education projects that takes both the research and the institutional dimensions into account. The model, which we call Meta-didactical Transposition, is based on Chevallard’s anthropological theory and is complemented by relevant elements that focus on the specificity of both researchers’ and teachers’ roles, while enabling a description of the evolution of their praxeologies over time. The model is illustrated with examples from different Italian projects, and it is discussed in light of current major research studies in mathematics teacher education.

Technology and the Role of Proof: The Case of Dynamic Geometry

This chapter brings together two intersecting areas of research in mathematics education: teaching and learning with dynamic geometry environments (DGEs) and the teaching and learning of proof. We focus on developments in the literature since 2001 and, in particular, on (a) the evolution of the notion of “proof” in school mathematics and its impact on the kinds of research questions and studies undertaken over the past decade—including increasing use of DGEs at the primary school level; and (b) the epistemological and cognitive nature of dragging and measuring as they relate to proof.

A method for quantifying focused versus overview behavior in AOI sequences

We present a new measure for evaluating focused versus overview eye movement behavior in a stimulus divided by areas of interest. The measure can be used for overall data, as well as data over time. Using data from an ongoing project with mathematical problem solving, we describe how to calculate the measure and how to carry out a statistical evaluation of the results.

An investigation on the effectiveness of physics teaching in Italy

A nationwide investigation was carried out involving about 6000 students with the aim of collecting data on student appraisal of the teaching of physics in Italian secondary schools (age 14‐19). The analytical techniques employed are described and the main conclusions which can be drawn by comparing the ratings by different categories of students and the correlation with different ways of teaching physics are summarized.

TEACHER’S SEMIOTIC GAMES IN MATHEMATICS LABORATORY

Pesquisa realizada para verificar a relacao pesquisador-educador infantil na introducao da contagem. Duas educadoras foram acompanhadas em sessoes de planejamento e atividades de sala de aula com vinte e quatro criancas de dois anos e meio a tres anos. Em 6 visitas a creche na fase inicial, 29 na central e 6 na de afastamento, os dados foram coletados com registro escrito das conversas informais, entrevistas abertas e individuais com as educadoras; e relatorios das observacoes das sessoes de planejamento e aulas. Os resultados evidenciaram avancos na relacao pesquisadora-educadora na insercao de atividades de contagem nos dialogos com as criancas. Observou-se instabilidade e retrocesso nas formas de explorar a contagem na ausencia da pesquisadora. O tempo e modo de intervencao podem ter relacao com a permanencia e retorno as praticas anteriores. Mais tempo e outras formas de cooperacao pesquisadora-educadora que propiciassem uma reflexao critica sobre seus atos educativos, provavelmente acarretariam implicacoes de ambas no processo de analise e compreensao da acao pedagogica.

Teaching mechanical oscillations using an integrated curriculum

Abstract A set of teaching materials dealing with harmonic oscillations was developed as part of a research project investigating the influence of different pedagogical tools on physics learning. The materials incorporate simulation software and laboratory activities associated with Teacher and Student Units. The project involved research groups at seven Italian universities and the materials have been trialled in high schools nation‐wide. This paper describes the experimental protocol for the use of these materials in pilot classes and the evaluation of student learning and teacher training results. The intervention was found to improve physics education at school praxis level and to promote understanding of the content area as well as appreciation of the role of experiments and simulations in the construction of scientific knowledge

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.

MOOC: repository di strategie e metodologie didattiche in Matematica

Abstract – This paper focuses on MOOC (Massive Open Online Courses) as a new paradigm in e-learning educational projects: it presents MOOCs for lower and upper secondary school mathematics teachers. On the one hand, a MOOC, with rich materials in innovative didactic methodologies and specific technological tools, can be understood as a repository from which teachers can draw inspiration. On the other hand - by allowing teachers from different geographic locations an opportunity for communication – a MOOC is also the place where these teachers - in a community of peers, supported by a vigilant but non-intrusive presence of trainers – have the rare opportunity to reflect together to organise strategies, processes and materials that are linked not only to age, type of school and social/individual situation, but also to the content of the discipline that has specific cognitive obstacles. The aim of this contribution is, therefore, to present our teacher education experiences through MOOCs, with a focus on the methodologies of mathematics teaching that were shared and debated with the teachers who attended the course, using as theoretical lens a new elaborated framework to analyse these new online training environments. Riassunto – Il focus di questo articolo verte su MOOC (Massive Open Online Courses) per docenti di matematica di scuola secondaria (I e II grado), da considerarsi come nuovo paradigma nei progetti educativi in e-learning. Da un lato, un MOOC, con materiali ricchi di metodologie didattiche innovative e specifici strumenti tecnologici, si puo intendere come un archivio informatico (repository) da cui gli insegnanti possono trarre spunto. Dall’altro lato, consentendo un’opportunita di comunicazione a vari insegnanti, provenienti da diverse realta geografiche, un MOOC e anche il luogo in cui tali insegnanti – in una comunita unicamente di pari, sostenuta dalla vigile, ma non invadente presenza dei formatori – si ritrovano ad avere la rara occasione di poter riflettere insieme per orientare opportunamente strategie, processi e materiali, legati non solo a fascia di eta, tipologia di scuola e situazione sociale/individuale, ma anche ai contenuti stessi della disciplina che presentano ostacoli cognitivi specifici. L’obiettivo di questo contributo e dunque quello di esporre le nostre esperienze di formazione insegnanti tramite MOOC, con un focus sulle metodologie di didattica della matematica che sono state condivise e approfondite con i corsisti, utilizzando come lente d’analisi un nuovo quadro elaborato proprio per analizzare questi nuovi ambienti di formazione insegnanti online. Keywords – MOOCs, teacher education, professional development, peer collaboration, community of practice, repository Parole chiave – MOOC, formazione insegnanti, sviluppo professionale, collaborazione tra pari, comunita di pratica

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).