Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben

2014 | Buch

Introduction Kapitel lesen Erstes Kapitel lesen

The Mathematics Teacher in the Digital Era

An International Perspective on Technology Focused Professional Development

herausgegeben von: Alison Clark-Wilson, Ornella Robutti, Nathalie Sinclair

Verlag: Springer Netherlands

Buchreihe : Mathematics Education in the Digital Era

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

Einloggen, um Zugang zu erhalten
insite
SUCHEN

Über dieses Buch

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 Valsiner’s 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

Inhaltsverzeichnis

Frontmatter
Introduction
Abstract
Teacher education is an important issue for society and it is framed within cultural, social, political and historical contexts. In recent years international research in mathematics education has offered a range of theoretical perspectives that provide different and interrelated frames and viewpoints (Ball and Bass 2003; Clark and Hollingworth 2002; Davis and Simmt 2006; Jaworski 1998; Wood 2008). The role of digital technologies within this discourse has an increasing relevance as the society and government place demands on teachers to integrate technology into their classroom practices so that students can experience its potential as a powerful learning tool (Drijvers et al. 2010; Lagrange et al. 2003; Trouche 2004).
Alison Clark-Wilson, Ornella Robutti, Nathalie Sinclair
Interactions Between Teacher, Student, Software and Mathematics: Getting a Purchase on Learning with Technology
Abstract
In this chapter three examples of teacher-guided use of ICT stimuli for learning mathematics (screencast, animation and applet) are critically examined using a range of distinctions derived from a complex framework. Six modes of interaction between teacher, student and mathematics are used to distinguish different affordances and constraints; five different structured forms of attention are used to refine the grain size of analysis; four aspects of activity are used to highlight the importance of balance between resources and motivation; and the triadic structure of the human psyche (cognition, affect and enaction, or intellect, emotion and behaviour) is used to shed light on how affordances may or may not be manifested, and on how constraints may or may not be effective, depending on the attunements of teachers and students. The conclusion is that what matters is the way of working within an established milieu. The same stimulus can be used in multiple modes according to the teacher’s awareness and aims, the classroom ethos and according to the students’ commitment to learning/thinking. The analytic frameworks used can provide teachers with structured ways of informing their choices of pedagogic strategies.
John Mason, John Mason

Current Practices and Opportunities for Professional Development

Frontmatter
Exploring the Quantitative and Qualitative Gap Between Expectation and Implementation: A Survey of English Mathematics Teachers’ Uses of ICT
Abstract
This chapter reports the results of a survey of English secondary school mathematics teachers’ technology use (n = 188). Set within the context of a broader study aiming to develop a deeper understanding of how and why mathematics teachers use technology in their classroom practice, the survey findings are used to explore the widely perceived quantitative gap and qualitative gap between the reality of teachers’ use of ICT and the potential for ICT suggested by research and policy. Teachers were asked about their access to hardware and software; their perception of the impact of hardware on students’ learning; the frequency of their use of ICT resources; their pedagogic practices in relation to ICT; and school and individual-level factors which may influence their use of ICT. This survey suggests that given the right conditions, at least those currently existing in England, ICT might contribute as a lever for change; however, the direction of this change might be construed as an incremental shift towards more teacher-centred practices rather than encouraging more student-centred practices.
Nicola Bretscher
Teaching with Digital Technology: Obstacles and Opportunities
Abstract
A key variable in the use of digital technology in the mathematics classroom is the teacher. In this chapter we examine research that identifies some of the obstacles to, and constraints on, secondary teachers’ implementation of digital technology. While a lack of physical resources is still a major extrinsic concern we introduce a framework for, and highlight the crucial role of, the intrinsic factor of teachers’ Pedagogical Technology Knowledge (PTK). Results from a research study relating confidence in using technology to PTK are then presented. This concludes that confidence may be a critical variable in teacher construction of PTK, leading to suggestions for some ways in which professional development of teachers could be structured to strengthen confidence in technology use.
Michael O. J. Thomas, Joann M. Palmer
A Developmental Model for Adaptive and Differentiated Instruction Using Classroom Networking Technology
Abstract
This paper presents a detailed explanatory model for adaptive and differentiated instruction. The model combines current practices for mathematics instruction with recommended practices for formative assessment. The model can best be implemented using classroom network technologies (such as TI-Nspire Navigator with TI handhelds), but it can also be used with manual data collection means such as personal whiteboards for each student. The model is presented for mathematics, but could be easily extended to science instruction or other subjects. Experience with adaptive and differentiated instruction suggests that teachers grow to full master level proficiency over time, often over a period of years, and that some teachers never reach that level. Accordingly, two transitional models are presented, an immediate (entry-level) model and an expert model for adaptive instruction. Fully differentiated instruction is incorporated in the ‘Master’ model. Growth from immediate, to expert, to master level requires development of skill with the technology, but more important are critical changes we infer in the teacher’s beliefs, as well as growth in their pedagogical content knowledge (PCK).
Allan Bellman, Wellesley R. Foshay, Danny Gremillion
Integrating Technology in the Primary School Mathematics Classroom: The Role of the Teacher
Abstract
In this chapter, we analyse the role of the teacher when using digital resources in the primary school mathematics classroom in Mexico and its relation to students’ mathematical learning. We carry out this analysis through the use of an instrument that we developed in which we relate five different aspects of the role of the teacher we consider important with the three different uses of technology classified by Hughes (Journal of Technology and Teacher Education, 13(2), 277–302, 2005) namely replacement, amplification and transformation. We use an enactivist perspective that considers learning as effective action in a given context (Maturana, H., & Varela, F. The tree of knowledge: The biological roots of human understanding, Revised Edition, Boston: Shambhala, 1992) in order to describe the way in which differences both in the uses of technology and in the role the teacher assumes in the classroom contribute to creating classroom contexts in which mathematical learning is promoted to different degrees.
María Trigueros, María-Dolores Lozano, Ivonne Sandoval
Technology Integration in Secondary School Mathematics: The Development of Teachers’ Professional Identities
Abstract
This chapter reports on research into the impact of digital technologies on Australian mathematics teachers’ classroom practice. The aim of the study was to identify and analyse individual and contextual factors influencing secondary mathematics teachers’ use of technology, and compare ways in which these factors come together to shape teachers’ pedagogical identities. The first section of the chapter examines the teacher’s role in terms of their pedagogical identities as users of technology, and introduces two theoretical frameworks for investigating trajectories of identity development. One framework classifies ways in which technology can change teaching and learning roles and mathematical practices. The other is concerned with teacher learning and development, and explains why teachers might embrace or resist technology-related change. The sections that follow provide case studies of two beginning teachers of secondary school mathematics who were integrating digital technologies into their classroom practice. Analysis of these case studies highlights issues related to identity development and demonstrates that identity trajectories are neither random nor fully determined, but instead are constrained by person-environment relationships.
Merrilyn Goos
Teaching Roles in a Technology Intensive Core Undergraduate Mathematics Course
Abstract
We discuss the dual teaching roles of university mathematics tutors, as teachers and policy makers, in relation to the classroom implementation of technology while guided by departmental policies. The main contribution of this chapter is the exemplification of these roles in an undergraduate mathematics programme, called Mathematics Integrated with Computers and Applications (MICA), with systemic technology integration. The current classroom practices of tutors in one of the MICA core courses for mathematics majors and future teachers of mathematics are examined. The role of the tutors in this course is to carefully guide the students’ instrumental genesis of programming technology for the investigation of both mathematics concepts and conjectures, and real-world applications. Acting as a mentor, the tutor encourages students’ mathematical creativity as they design, program, and use their own interactive mathematics Exploratory Objects.
Chantal Buteau, Eric Muller

Instrumentation of Digital Resources in the Classroom

Frontmatter
Digital Technology and Mid-Adopting Teachers’ Professional Development: A Case Study
Abstract
The integration of digital technology into secondary mathematics education is not yet a widespread success. As teachers are crucial players in this integration, an important challenge is not only to attract early adopters, but also to support mid-adopting teachers in their professional development on this point. The questions addressed in this Chapter are: which practices such mid-adopting teachers develop when starting to use technology in their mathematics classroom; and how these practices change over time while engaging in a project with colleagues and researchers. To answer these questions, theoretical notions of instrumental orchestration, TPACK and community of practice underpin the case study of two mathematics teachers from a group of twelve, who engaged in a project on technology-rich teaching. The data includes lesson observations, blogs and results from questionnaires. The results show the type of teaching practices the teachers develop and the changes in these practices. Even if these changes are modest and the impact of the community is limited, the teachers clearly became more confident in integrating technology in their teaching.
Paul Drijvers, Sietske Tacoma, Amy Besamusca, Cora van den Heuvel, Michiel Doorman, Peter Boon
Teaching Mathematics with Technology at the Kindergarten Level: Resources and Orchestrations
Abstract
In this chapter we study the use of software in mathematics by French kindergarten teachers who are working with 5 and 6-year-old children. We retain the theoretical perspective of the documentational approach, considering that teachers interact with a variety of resources, including technology. These interactions lead to the development, by the teachers, of documents, associating resources and professional knowledge. We focus here on the way teachers organise the available resources, for a given mathematical objective: the orchestrations they choose. Following in particular three teachers, we identify different types of orchestrations, evidencing teacher agency, and a specific attention to individual children's differences. Teacher knowledge of different kinds (pedagogical knowledge, knowledge about curriculum material, knowledge about the teaching of numbers at kindergarten) intervenes in the choice of orchestration.
Ghislaine Gueudet, Laetitia Bueno-Ravel, Caroline Poisard
Teachers’ Instrumental Geneses When Integrating Spreadsheet Software
Abstract
The spreadsheet is not a priori a didactical tool for mathematics education. It may progressively become such an instrument through the process of professional geneses on the part of teachers. This chapter describes the beginning of such a genesis, and presents some results concerning teachers’ professional development with ICT by examining the outcomes of two different sets of data. Theoretical notions, such as instrumental distance and double instrumental genesis supported the analysis of data leading to a comparison of a teacher integrating spreadsheets, for the first time in her practices, with the practices of teachers who are more expert with spreadsheets. The similarities found in the ways they use the tool leads to some hypotheses on the importance of these common elements as key issues in teachers’ ICT practices.
Mariam Haspekian
A Methodological Approach to Researching the Development of Teachers’ Knowledge in a Multi-Representational Technological Setting
Abstract
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.
Alison Clark-Wilson
Teachers and Technologies: Shared Constraints, Common Responses
Abstract
This chapter presents a synthesis of a set of studies focusing on teachers’ technology-based activity at the classroom level. Each of the studies is contextualised, singular and deals with individual teachers. Cross-analysing the findings of these separate situations aims to identify common characteristics in terms of common responses to shared constraints (in the French context) related to the use of technology by ordinary mathematics teachers. The synthesis is developed with the aim of analysing regularities in the practices of ordinary teachers integrating technologies into their teaching. These regularities are structured along three issues: How to simultaneously teach mathematics and use technology in class? (cognitive axis); How to teach mathematics in new teaching environments? (pragmatic axis); How to manage the time of teaching and learning when using technology? (temporal axis).
Maha Abboud-Blanchard
Didactic Incidents: A Way to Improve the Professional Development of Mathematics Teachers
Abstract
In this chapter the professional development of teachers is observed through the joint work of researchers and teachers. In the particular context of the European project EdUmatics, which focuses on mathematics education in a computer environment, the collaboration between researchers and teachers has helped both to build innovative situations and also to better understand the difficulties involved in the introduction of technology in classrooms. The theoretical framework of the theory of didactic situations, didactic incidents and documentational genesis allows the construction of analyses in order to better understand the students’ and teacher’s joint action and so to enhance teachers’ professional development. We highlight both the consistency of the framework and the contributions of our findings to the professional development of teachers.
Gilles Aldon

Theories on Theories

Frontmatter
Meta-Didactical Transposition: A Theoretical Model for Teacher Education Programmes
Abstract
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.
Ferdinando Arzarello, Ornella Robutti, Cristina Sabena, Annalisa Cusi, Rossella Garuti, Nicolina Malara, Francesca Martignone
Frameworks for Analysing the Expertise That Underpins Successful Integration of Digital Technologies into Everyday Teaching Practice
Abstract
This chapter examines contemporary frameworks for analysing teacher expertise which are relevant to the integration of digital technologies into everyday teaching practice. It outlines three such frameworks, offering a critical appreciation of each, and then explores some commonalities, complementarities and contrasts between them: the Technological, Pedagogical and Content Knowledge (TPACK) framework (Koehler & Mishra, Contemporary Issues in Technology and Teacher Education, 9(1), 2009); the Instrumental Orchestration framework (Trouche, L. (2005). Instrumental genesis, individual and social aspects. In D. Guin, K. Ruthven, & L. Trouche (Eds.), The didactical challenge of symbolic calculators: Turning a computational device into a mathematical instrument (pp. 197–230). New York: Springer.); and the Structuring Features of Classroom Practice framework (Ruthven, Education & Didactique, 3(1), 2009). To concretise the discussion, the use of digital technologies for algebraic graphing, a now well established form of technology use in secondary school mathematics, serves as an exemplary reference situation: each of the frameworks is illustrated through its application in a study of teacher expertise relating to this topic (respectively Richardson, Contemporary Issues in Technology and Teacher Education, 9(2), 2009; Drijvers, Doorman, Boon, Reed, & Gravemeijer, Educational Studies in Mathematics, 75(2), 213–234, 2010; Ruthven, Deaney, & Hennessy, Educational Studies in Mathematics, 71(3), 279–297, 2009).
Kenneth Ruthven
Summary and Suggested Uses for the Book
Abstract
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.
Alison Clark-Wilson, Ornella Robutti, Nathalie Sinclair
Backmatter
Metadaten
Titel
The Mathematics Teacher in the Digital Era
herausgegeben von
Alison Clark-Wilson
Ornella Robutti
Nathalie Sinclair
Copyright-Jahr
2014
Verlag
Springer Netherlands
Electronic ISBN
978-94-007-4638-1
Print ISBN
978-94-007-4637-4
DOI
https://doi.org/10.1007/978-94-007-4638-1

Premium Partner

    Bildnachweise