Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education

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Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education

Viviane Durand-Guerrier, Sophie Soury-Lavergne, Ferdinando Arzarello

To cite this version:

Viviane Durand-Guerrier, Sophie Soury-Lavergne, Ferdinando Arzarello. Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education. Viviane Durand-Guerrier;

Sophie Soury-Lavergne; Ferdinando Arzarello. CERME6, INRP and ERME, 2010, Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education, 978-2-7342-1190-7.

�hal-02182374�

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INSTITUT NATIONAL DE RECHERCHE PÉDAGOGIQUE

Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education

January 28th-February 1st 2009 Lyon (France)

Viviane Durand-Guerrier, Sophie Soury-Lavergne

& Ferdinando Arzarello (eds.)

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Editorial board

Maha Abboud-Blanchard Janet Ainley

Paul Andrews

Ferdinando Arzarello Giorgio T. Bagni Patti Barber Christer Bergsten Morten Blomhøj Marianna Bosch Rosa Maria Bottino Leanor Camargo Susana Carreira José Carrillo Claire Cazes

Margarida Alexandra Cesar Giampaolo Chiappini Sarah Crafter

Guida de Abreu Jean-Luc Dorier Paul Drijvers Andreas Eichler Marie-Thérèse Farrugi

Marei Fetzer Fulvia Furinghetti Patrick Gibel Juan Godino Núria Gorgorió Ghislaine Gueudet Markku S. Hannula Matthias Hattermann Lisa Hefendehl–Hebeker Stephen Hegedus Alena Hospesova Elia Iliada

Eva Jablonka Uffe Jankvist Ivy Kidron Alain Kuzniak

Jean–Baptiste Lagrange Roza Leikin

Florence Ligozat Katja Maass

Joanna Mamona-Dawns Maria Alessandra Mariotti

Alain Mercier John Monaghan Candia Morgan

Maria Gabriella Ottaviani Marilena Panziara Birgit Pepin Dave Pratt

Susanne Prediger Kristina Reiss Tim Rowland Filip Roubicek Leonor Santos

Wolfgang Schloeglmann Gérard Sensevy

Nada Stehlikova Constantinos Tzanakis Paul Vanderlind

Jan van Maanen Kjersti Wæge Geoff Wake

Hans-Georg Weigand Floriane Wozniak

Publishing assistance

Service des publications, INRP

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I

CERME 6 – TABLE OF CONTENTS

GENERAL INTRODUCTION...XVIII

PLENARY 1

Signs, gestures, meanings: Algebraic thinking from a cultural semiotic perspective...XXXIII Luis Radford

PLENARY 2

Mathematics education as a network of social practices...LIV Paola Valero

SPECIAL PLENARY SESSION

Ways of working with different theoretical approaches in mathematics education research...1

Introduction...2

Tommy Dreyfus

Networking of theories: why and how? ...6

Angelika Bikner-Ahsbahs

People and theories ...16

John Monaghan

Discussion ...24

WORKING GROUP 1

Multimethod approaches to the multidimensional affect

in mathematics education...26

Introduction...28

Markku S. Hannula, Marilena Pantziara, Kjersti Wæge, Wolfgang Schlöglmann The effect of achievement, gender and classroom context

on upper secondary students' mathematical beliefs ...34

Markku S. Hannula

Changing beliefs as changing perspective ...44

Peter Liljedahl “Maths and me”:

software analysis of narrative data about attitude towards math ...54

Pietro Di Martino

Students’ beliefs about the use of representations in the learning of fractions...64

Athanasios Gagatsis, Areti Panaoura, Eleni Deliyianni, Iliada Elia

Efficacy beliefs and ability to solve volume measurement tasks in different representations ...74

Paraskevi Sophocleous, Athanasios Gagatsis

TABLE OF CONTENTS

Proceedings of CERME 6, January 28th-February 1st 2009, Lyon France © INRP 2010 <www.inrp.fr/editions/cerme6>

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II

Students’ motivation for learning mathematics in terms of needs and goals...84

Kjersti Wæge

Mathematical modeling, self-representation and self-regulation...94

Areti Panaoura, Andreas Demetriou, Athanasios Gagatsis

Endorsing motivation: identification of instructional practices ...104

Marilena Pantziara, George Philippou

The effects of changes in the perceived classroom social culture

on motivation in mathematics across transitions ...114

Chryso Athanasiou, George N. Philippou

“After I do more exercise, I won't feel scared anymore”

Examples of personal meaning from Hong-Kong ...124

Maike Vollstedt

Emotional knowledge of mathematics teachers – retrospective perspectives

of two case studies ...134

Ilana Lavy, Atara Shriki

Humour as a means to make mathematics enjoyable ...144

Pavel Shmakov, Markku S. Hannula

Beliefs: a theoretically unnecessary construct? ...154

Magnus Österholm

Categories of affect – some remarks...164

Wolfgang Schlöglmann

WORKING GROUP 2

Argumentation and proof...174

Introduction...176

Maria Alessandra Mariotti, Leanor Camargo, Patrick Gibel, Kristina Reiss

Understanding, visualizability and mathematical explanation ...181

Daniele Molinini

Argumentation and proof: a discussion about Toulmin's and Duval's models ...191

Thomas Barrier, Anne-Cécile Mathé, Viviane Durand-Guerrier

Why do we need proof ...201

Kirsti Hemmi, Clas Löfwall

Proving as a rational behaviour: Habermas' construct of rationality

as a comprehensive frame for research on the teaching and learning of proof...211

Francesca Morselli, Paolo Boero

Experimental mathematics and the teaching and learning of proof...221

Maria G. Bartolini Bussi

Conjecturing and proving in dynamic geometry: the elaboration of some research hypotheses...231

Anna Baccaglini-Frank, Maria alessandra Mariotti

The algebraic manipulator of alnuset: a tool to prove ...241

Bettina Pedemonte

Visual proofs: an experiment ...251

Cristina Bardelle

TABLE OF CONTENTS

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III

Teachers’ views on the role of visualisation and didactical intentions regarding proof...261

Irene Biza, Elena Nardi, Theodossios Zachariades

Modes of argument representation for proving – the case of general proof ...271

Ruthi Barkai, Michal Tabach, Dina Tirosh, Pessia Tsamir, Tommy Dreyfus

Mathematics teachers’ reasoning for refuting students’ invalid claims...281

Despina Potari, Theodossios Zachariades, Orit Zaslavsky

Student justifications in high school mathematics...291

Ralph-Johan Back, Linda Mannila, Solveig Wallin “Is that a proof?”: an emerging explanation

for why students don’t know they (just about) have one ...301

Manya Raman, Jim Sandefur, Geoffrey Birky, Connie Campbell, Kay Somers

“Can a proof and a counterexample coexist?” A study of students’ conceptions about proof ...311

Andreas J. Stylianides, Thabit Al-Murani

Abduction and the explanation of anomalies: the case of proof by contradiction ...322

Samuele Antonini, Maria Alessandra Mariotti

Approaching proof in school: from guided conjecturing and proving

to a story of proof construction ...332

Nadia Douek

WORKING GROUP 3

On “stochastic thinking”...343

Introduction...344

Andreas Eichler, Maria Gabriella Ottaviani, Floriane Wozniak, Dave Pratt

Chance models: building blocks for sound statistical reasoning ...348

Herman Callaert

Recommended knowledge of probability for secondary mathematics teachers ...358

Irini Papaieronymou

Statistical graphs produced by prospective teachers in comparing two distributions...368

Carmen Batanero, Pedro Arteaga, Blanca Ruiz

The role of context in stochastics instruction...378

Andreas Eichler

Does the nature and amount of posterior information affect preschooler’s inferences ...388

Zoi Nikiforidou, Jenny Pange

Student’s Causal explanations for distribution ...394

Theodosia Prodromou, Dave Pratt

Greek students’ ability in probability problem solving ...404

Sofia Anastasiadou

WORKING GROUP 4

Algebraic thinking and mathematics education...413

Introduction...415

Janet Ainley, Giorgio T. Bagni, Lisa Hefendehl-Hebeker, Jean-Baptiste Lagrange

TABLE OF CONTENTS

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IV

The effects of multiple representations-based instruction

on seventh grade students’ algebra performance ...420

Oylum Akkus, Erdinc Cakiroglu

Offering proof ideas in an algebra lesson in different classes and by different teachers...430

Michal Ayalon, Ruhama Even

Rafael Bombelli’s Algebra (1572) and a new mathematical “object”: a semiotic analysis ...440

Giorgio T. Bagni

Cognitive configurations of pre-service teachers

when solving an arithmetic-algebraic problem...449

Walter F. Castro, Juan D. Godino

Transformation rules: a cross-domain difficulty...459

Marie-Caroline Croset

Interrelation between anticipating thought and interpretative aspects

in the use of algebraic language for the construction of proofs in elementary number theory...469

Annalisa Cusi

Epistemography and algebra...479

Jean-Philippe Drouhard

Sámi culture and algebra in the curriculum ...489

Anne Birgitte Fyhn

Problem solving without numbers – An early approach to algebra...499

Sandra Gerhard

The ambiguity of the sign ...509

Bernardo Gómez, Carmen Buhlea

Behind students’ spreadsheet competencies: their achievement in algebra?

A study in a French vocational school ...519

Mariam Haspekian, Eric Bruillard

Developing Katy’s algebraic structure sense ...529

Maureen Hoch, Tommy Dreyfus

Children’s understandings of algebra 30 years on: what has changed?...539

Jeremy Hodgen, Dietmar Kuchemann, Margaret Brown, Robert Coe

Presenting equality statements as diagrams ...549

Ian Jones

Approaching functions via multiple representations: a teaching experiment with Casyopee ...559

Jean-Baptiste Lagrange, Tran Kiem Minh

Equality relation and structural properties ...569

Carlo Marchini, Anne Cockburn, Paul Parslow-Williams, Paola Vighi

Structure of algebraic competencies ...579

Reinhard Oldenburg

Generalization and control in algebra ...589

Mabel Panizza

From area to number theory: a case study ...599

Maria Iatridou, Ioannis Papadopoulos

Allegories in the teaching and learning of mathematics ...609

Reinert A. Rinvold, Andreas Lorange

TABLE OF CONTENTS

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V

Role of an artefact of dynamic algebra in the conceptualisation of the algebraic equality ...619

Giampaolo Chiappini, Elisabetta Robotti, Jana Trgalova

Communicating a sense of elementary algebra to preservice primary teachers ...629

Franziska Siebel, Astrid Fischer Conception of variance and invariance

as a possible passage from early school mathematics to algebra...639

Ilya Sinitsky, Bat-Sheva Ilany

Growing patterns as examples for developing a new view onto algebra and arithmetic...649

Claudia Böttinger, Elke Söbbeke

Steps towards a structural conception of the notion of variable ...659

Annika M. Wille

WORKING GROUP 5

Geometrical thinking...669

Introduction...671

Alain Kuzniak, Iliada Elia, Matthias Hattermann, Filip Roubicek

The necessity of two different types of applications in elementary geometry...676

Boris Girnat

A French look on the Greek geometrical working space at secondary school level ...686

Alain Kuzniak, Laurent Vivier

A theoretical model of students’ geometrical figure understanding ...696

Eleni Deliyianni, Iliada Elia, Athanasios Gagatsis, Annita Monoyiou, Areti Panaoura

Gestalt configurations in geometry learning...706

Claudia Acuña

Investigating comparison between surfaces...716

Paola Vighi

The effects of the concept of symmetry on learning geometry at French secondary school ...726

Caroline Bulf

The role of teaching in the development of basic concepts in geometry: how the concept

of similarity and intuitive knowledge affect student’s perception of similar shapes...736

Mattheou Kallia, Spyrou Panagiotis

The geometrical reasoning of primary and secondary school students ...746

Georgia Panaoura, Athanasios Gagatsis

Strengthening students’ understanding of ‘proof’ in geometry in lower secondary school ...756

Susumu Kunimune, Taro Fujita, Keith Jones

Written report in learning geometry: explanation and argumentation ...766

Sílvia Semana, Leonor Santos

Multiple solutions for a problem: a tool for evaluation of mathematical thinking in geometry...776

Anat Levav-Waynberg, Roza Leikin

The drag-mode in three dimensional dynamic geometry environments – Two studies ...786

Mathias Hattermann

3D geometry and learning of mathematical reasoning ...796

Joris Mithalal

TABLE OF CONTENTS

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VI

In search of elements for a competence model in solid geometry teaching

Establishment of relationships ...806

Edna González, Gregoria Guillén

Students’ 3D geometry thinking profiles ...816

Marios Pittalis, Nicholas Mousoulides, Constantinos Christou

WORKING GROUP 6

Language and mathematics...826

Introduction...828

Candia Morgan

Imparting the language of critical thinking while teaching probability...833

Einav Aizikovitsh, Miriam Amit

Toward an inferential approach analyzing concept formation and language processes ...842

Stephan Hußmann, Florian Schacht

Iconicity, objectification, and the math behind the measuring tape:

An example from pipe-trades training ...852

Lionel LaCroix

Mathematical reflection in primary school education:

theoretical foundation and empirical analysis of a case study ...862

Cordula Schülke, Heinz Steinbring

Surface signs of reasoning ...873

Nathalie Sinclair, David Pimm

A teacher’s use of gesture and discourse as communicative strategies

in concluding a mathematical task ...884

Raymond Bjuland, Maria Luiza Cestari, Hans Erik Borgersen

A teacher’s role in whole class mathematical discussion: facilitator of performance etiquette? ...894

Thérèse Dooley

Use of words – Language-games in mathematics education ...904

Michael Meyer

Speaking of mathematics – Mathematics, every-day life

and educational mathematics discourse ...914

Eva Riesbeck

Communicative positionings as identifications in mathematics teacher education...924

Hans Jørgen Braathe

Teachers’ collegial reflections of their own mathematics teaching processes

Part 1: An analytical tool for interpreting teachers` reflections...934

Kerstin Bräuning, Marcus Nührenbörger

Teachers’ reflections of their own mathematics teaching processes

Part 2: Examples of an active moderated collegial reflection...944

Kerstin Bräuning, Marcus Nührenbörger Internet-based dialogue: a basis for reflection

in an in-service mathematics teacher education program ...954

Mario Sánchez

TABLE OF CONTENTS

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VII

The use of algebraic language in mathematical modelling and proving

in the perspective of Habermas’ theory of rationality...964

Paolo Boero, Francesca Morselli

Objects as participants in classroom interaction ...974

Marei Fetzer

The existence of mathematical objects in the classroom discourse ...984

Vicenç Font, Juan D. Godino, Núria Planas, Jorge I. Acevedo

Mathematical activity in a multi-semiotic environment ...993

Candia Morgan, Jehad Alshwaikh

Engaging everyday language to enhance comprehension of fraction multiplication ...1003

Andreas O. Kyriakides

Tensions between an everyday solution and a school solution to a measuring problem...1013

Frode Rønning

Linguistic accomplishment of the learning-teaching processes

in primary mathematics instruction...1023

Marcus Schütte

Mathematical cognitive processes between the poles of mathematical technical terminology

and the verbal expressions of pupils ...1033

Rose Vogel, Melanie Huth

WORKING GROUP 7

Technologies and resources in mathematical education...1043

Introduction...1046

Ghislaine Gueudet, Rosa Maria Bottino, Giampaolo Chiappini, Stephen Hegedus, Hans-Georg Weigand

Realisation of mers (multiple extern representations) and melrs (multiple equivalent linked

representations) in elementary mathematics software ...1050

Silke Ladel, Ulrich Kortenkamp

The impact of technological tools in the teaching and learning of integral calculus...1060

Alejandro Lois, Liliana Milevicich

Using technology in the teaching and learning of box plots...1070

Ulrich Kortenkamp, Katrin Rolka

Dynamical exploration of two-variable functions using virtual reality ...1081

Thierry Dana-Picard, Yehuda Badihi, David Zeitoun, Oren David Israeli

Designing a simulator in building trades and using it in vocational education ...1091

Annie Bessot, Colette Laborde

Collaborative design of mathematical activities for learning in an outdoor setting ...1101

Per Nilsson, Håkan Sollervall, Marcelo Milrad

Student development process of designing and implementing exploratory

and learning objects ...1111

Chantal Buteau, Eric Muller

How can digital artefacts enhance mathematical analysis teaching and learning...1121

Dionysis I. Diakoumopoulos

TABLE OF CONTENTS

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VIII

A learning environment to support mathematical generalisation in the classroom ...1131

Eirini Geraniou, Manolis Mavrikis, Celia Hoyles, Richard Noss

Establishing a longitudinal efficacy study using SimCalc MathWorlds® ...1141

Stephen Hegedus, Luis Moreno, Sara Dalton, Arden Brookstein

Interoperable Interactive Geometry for Europe – First technological and educational results

and future challenges of the Intergeo project...1150

Ulrich Kortenkamp, Axel M. Blessing, Christian Dohrmann, Yves Kreis, Paul Libbrecht, Christian Mercat

Quality process for dynamic geometry resources: the Intergeo project...1161

Jana Trgalova, Ana Paula Jahn, Sophie Soury-Lavergne New didactical phenomena prompted by TI-Nspire specificities

The mathematical component of the instrumentation process...1171

Michèle Artigue, Caroline Bardini

Issues in integrating cas in post-secondary education: a literature review ...1181

Chantal Buteau, Zsolt Lavicza, Daniel Jarvis, Neil Marshall

The long-term project “Integration of symbolic calculator in mathematics lessons”

The case of calculus ...1191

Hans-Georg Weigand, Ewald Bichler

Enhancing functional thinking using the computer for representational transfer ...1201

Andrea Hoffkamp The Robot Race:

understanding proportionality as a function with robots in mathematics class ...1211

Elsa Fernandes, Eduardo Fermé, Rui Oliveira

Internet and mathematical activity within the frame of “Sub14” ...1221

Hélia Jacinto, Nélia Amado, Susana Carreira

A resource to spread math research problems in the classroom ...1231

Gilles Aldon, Viviane Durand-Guerrier

The synergy of students’ use of paper-and-pencil techniques and dynamic geometry software:

a case study ...1241

Núria Iranzo, Josep Maria Fortuny

Students’ utilization schemes of pantographs for geometrical transformations:

a first classification ...1250

Francesca Martignone, Samuele Antonini

The utilization of mathematics textbooks as instruments for learning ...1260

Sebastian Rezat

Teachers’ beliefs about the adoption of new technologies in the mathematics curriculum ...1270

Marilena Chrysostomou, Nicholas Mousoulides

Systemic innovations of mathematics education with dynamic worksheets as catalysts ...1280

Volker Ulm

A didactic engineering for teachers education courses in mathematics using ICT ...1290

Fabien Emprin

Geometers’ sketchpad software for non-thesis graduate students: a case study in Turkey ...1300

Berna Cantürk-Günhan, Deniz Özen

TABLE OF CONTENTS

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IX

Leading teachers to perceive and use technologies as resources

for the construction of mathematical meanings ...1310

Eleonora Faggiano

The teacher’s use of ICT tools in the classroom after a semiotic mediation approach...1320

Mirko Maracci, Maria Alessandra Mariotti Establishing didactical praxeologies:

teachers using digital tools in upper secondary mathematics classrooms ...1330

Mary Billington

Dynamic geometry software: the teacher’s role in facilitating instrumental genesis ...1340

Nicola Bretscher

Instrumental orchestration: theory and practice...1349

Paul Drijvers, Michiel Doorman, Peter Boon, Sjef van Gisbergen Teaching Resources and teachers’ professional development:

towards a documentational apProach of didactics ...1359

Ghislaine Gueudet, Luc Trouche

An investigative lesson with dynamic geometry:

a case study of key structuring features of technology integration in classroom practice...1369

Kenneth Ruthven

Methods and tools to face research fragmentation

in technology enhanched mathematics education...1379

Rosa Maria Bottino, Michele Cerulli

The design of new digital artefacts as key factor to innovate the teaching and learning of algebra:

the case of Alnuset ...1389

Giampaolo Chiappini, Bettina Pedemonte

Casyopée in the classroom: two different theory-driven pedagogical approaches ...1399

Mirko Maracci, Claire Cazes, Fabrice Vandebrouck, Maria Alessandra Mariotti

Navigation in geographical space ...1409

Christos Markopoulos, Chronis Kynigos, Efi Alexopoulou, Alexandra Koukiou

Making sense of structural aspects of equations by using algebraic-like formalism...1419

Foteini Moustaki, Giorgos Psycharis, Chronis Kynigos

Relationship between design and usage of educational software: the case of Aplusix ...1429

Jana Trgalova, Hamid Chaachoua

WORKING GROUP 8

Questions and thoughts for researching cultural diversity and mathematics education...1439

Introduction...1440

Guida de Abreu, Sarah Crafter, Núria Gorgorió

A survey of research on the mathematics teaching and learning of immigrant students...1443

Marta Civil

Parental resources for understanding mathematical achievement in multiethnic settings...1453

Sarah Crafter

Discussing a case study of family training

in terms of communities of practices and adult education...1462

Javier Díez-Palomar, Montserrat Prat Moratonas

TABLE OF CONTENTS

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X

Understanding Ethnomathematics from its criticisms and contradictions...1473

Maria do Carmo Domite, Alexandre Santos Pais

Using mathematics as a tool in Rwandan workplace settings: the case of taxi drivers ...1484

Marcel Gahamanyi, Ingrid Andersson, Christer Bergsten Parents’ experiences as mediators of their children’s learning:

the impact of being a parent-teacher ...1494

Rachael McMullen, Guida de Abreu

Batiks: another way of learning mathematics ...1506

Lucília Teles, Margarida César

The role of Ethnomathematics within mathematics education ...1517

Karen François

WORKING GROUP 9

Different theoretical perspectives and approaches in mathematics education research...1527

Introduction...1529

Susanne Prediger, Marianna Bosch, Ivy Kidron, John Monaghan, Gérard Sensevy

Research problems emerging from a teaching episode: a dialogue between TDS and ATD ...1535

Michèle Artigue, Marianna Bosch, Joseph Gascón, Agnès Lenfant

Complementary networking: enriching understanding...1545

Ferdinando Arzarello, Angelika Bikner-Ahsbahs, Cristina Sabena

Interpreting students’ reasoning through the lens of two different languages of description:

integration or juxtaposition? ...1555

Christer Bergsten, Eva Jablonka

Coordinating multimodal social semiotics and institutional perspective

in studying assessment actions in mathematics classrooms...1565

Lisa Björklund-Boistrup, Staffan Selander

Integrating different perspectives to see the front and the back: The case of explicitness ...1575

Uwe Gellert

The practice of (university) mathematics teaching:

mediational inquiry in a community of practice or an activity system...1585

Barbara Jaworski

An interplay of theories in the context of computer-based mathematics teaching:

how it works and why ...1595

Helga Jungwirth

On the adoption of a model to interpret teachers’ use of technology in mathematics lessons ...1605

Jean-Baptiste Lagrange, John Monaghan The joint action theory in didactics:

why do we need it in the case of teaching and learning mathematics?...1615

Florence Ligozat, Maria-Luisa Schubauer-Leoni

Teacher’s didactical variability and its role in mathematics education ...1625

Jarmila Novotná, Bernard Sarrazy

The potential to act for low achieving students

as an example of combining use of different theories ...1635

Ingolf Schäfer

TABLE OF CONTENTS

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XI

Outline of a joint action theory in didactics...1645

Gérard Sensevy

The transition between mathematics studies at secondary and tertiary levels;

individual and social perspectives...1655

Erika Stadler

Combining and Coordinating theoretical perspectives in mathematics education research...1665

Tine Wedege

Comparing theoretical frameworks in didactics of mathematics: the GOA-model...1675

Carl Winslow

WORKING GROUP 10

Mathematical curriculum and practice...1685

Introduction...1688

Leonor Santos, José Carrillo, Alena Hospesova, Maha Abboud-Blanchard Effective ‘blended’ professional development for teachers of mathematics:

Design and evaluation of the “UPOLA” Program ...1694

Lutz Hellmig

Teachers’ efficacy beliefs and perceptions regarding the implementation of new primary

mathematics curriculum...1704

Isil Isler, Erdine Cakiroglu

Curriculum management in the context of a mathematics subject group ...1714

Cláudia Canha Nunes, João Pedro da Ponte

Gestures and styles of communication: are they intertwined?...1724

Chiara Andrá

Teachers’ subject knowledge: the number line representation ...1734

Maria Doritou, Eddie Gray

Communication as social interaction. Primary School Teacher Practices...1744

Antonio Guerreiro, Lurdes Serrazina

Experimental devices in mathematics and physics standards

in lower and upper secondary school, and their consequences on teacher’s practices ...1751

Fabrice Vandebrouck, Cecile de Hosson, Aline Robert

Professional development for teachers of mathematics: opportunities and change...1761

Marie Joubert, Jenni Back, Els De Geest, Christine Hirst, Rosamund Sutherland

Teachers’ perception about infinity: a process or an object?...1771

Maria Kattou, Michael Thanasia, Katerina Kontoyianni, Constantinos Christou, George Philippou

Perceptions on teaching the mathematically gifted...1781

Katerina Kontoyianni, Maria Kattou, Polina Ioannou, Maria Erodotou, Constantinos Christou, Marios Pittalis

TABLE OF CONTENTS

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XII

The nature on the numbers in grade 10: A professional problem...1791

Mirène Larguier, Alain Bronner

A European project for professional development of teachers through a research based methodology: The questions arisen at the international level, the Italian contribution,

the knot of the teacher-researcher identity ...1801

Nicolina A. Malara, Roberto Tortora

Why is there not enough fuss about affect and meta-affect among mathematics teachers? ...1811

Manuela Moscucci

The role of subject knowledge in Primary Student teachers’ approaches

to teaching the topic of area ...1821

Carol Murphy

Developing of mathematics teachers’ community: five groups, five different ways ...1831

Regina Reinup

Foundation knowledge for teaching: contrasting elementary and secondary mathematics...1841

Tim Rowland

Results of a comparative study of future teachers from Australia, Germany and Hong Kong

with regard to competences in argumentation and proof...1851

Björn Schwarz, Gabriele Kaiser

Kate’s conceptions of mathematics teaching: Influences in the first three years ...1861

Fay Turner

Pre-service teacher-generated analogies for function concepts ...1871

Behiye Ubuz, Ayşegül Eryılmaz, Utkun Aydın, Ibrahim Bayazit

Technology and mathematics teaching practices: about in-service and pre-service teachers ...1880

Maha Abboud-Blanchard

Teachers and triangles...1890

Sylvia Alatorre, Mariana Saíz

Mathematics teacher education research and practice: researching inside the MICA program ...1901

Joyce Mgombelo, Chantal Buteau

Cognitive transformation in professional development: some case studies ...1911

Jorge Soto-Andrade

What do student teachers attend to?...1921

Nad’a Stehlíková

The mathematical preparation of teachers: A focus on tasks...1931

Gabriel J. Stylianides, Andreas J. Stylianides

Problem posing and development of pedagogical content knowledge

in pre-service teacher training...1941

Marie Tichá, Alena Hospesová

Sustainability of professional development ...1951

Stefan Zehetmeier

A collaborative project as a learning opportunity for mathematics teachers ...1961

Maria Helena Martinho, João Pedro da Ponte

Reflection on Practice: content and depth...1971

Christina Martins, Leonor Santos

Developing mathematics teachers’ education through personal reflection

and collaborative inquiry: which kinds of tasks?...1981

Angela Pesci

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XIII

The learning of mathematics teachers working in a peer group ...1991

Martha Witterholt, Martin Goedhart

Use of focus groups interviews in mathematics educational research...2000

Bodil Kleve

Analyses of interactions in a collaborative context of professional development ...2010

Maria Cinta Muñoz-Catalán, José Carrillo, Nuria Climent

Adapting the knowledge quarter in the Cypriot mathematics classroom ...2020

Marilena Petrou

Professional knowledge in an improvisation episode: the importance of a cognitive model ...2030

C. Miguel Ribeiro, Rute Monteiro, José Carrillo

WORKING GROUP 11

Applications and modelling...2040

Introduction...2042

Morten Blomhøj

Mathematical modelling in teacher education – Experiences from a modelling seminar ...2046

Rita Borromeo Ferri, Werner Blum

Designing a teacher questionnaire to evaluate professional development in modelling ...2056

Katja Maaß, Johannes Gurlitt

Modeling in the classroom – Motives and obstacles from the teacher’s perspective ...2066

Barbara Schmidt

Modelling in mathematics teachers’ professional development ...2076

Jeroen Spandaw, Bert Zwaneveld

Modelling and formative assessment pedagogies mediating change in actions of teachers

and learners in mathematics classrooms ...2086

Geoff Wake

Towards understanding teachers’ beliefs and affects about mathematical modelling...2096

Jonas Bergman Ärlebäck

The use of motion sensor can lead the students to understanding the cartesian graph ...2106

Maria Lucia Lo Cicero, Filippo Spagnolo

Interacing populations in a restricted habitat – Modelling, simulation

and mathematical analysis in class...2116

Christina Roeckerath

Aspects of visualization during the exploration of “quadratic world” via the ICT

Problem “fireworks” ...2126

Mária Lalinská, Janka Majherová

Mathematical modeling in class with and without technology...2136

Hans-Stefan Siller, Gilbert Greefrath

The ‘ecology’ of mathematical modelling: constraints to its teaching at university level ...2146

Berta Barquero, Marianna Bosch, Josep Gascón

The double transposition in mathematisation at primary school ...2156

Richard Cabassut

Exploring the use of theoretical frameworks for modelling-oriented instructional design ...2166

F.J. García, L. Ruiz-Higueras

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Study of a practical activity: engineering projects and their training context ...2176

Avenilde Romo Vázquez

Fitting models to data: the mathematising step in the modelling process ...2186

Lídia Serrano, Marianna Bosch, Josep Gascón

What roles can modelling play in multidisciplinary teaching...2196

Mette Andresen

Modelling in environments without numbers – A case study...2206

Roxana Grigoras

Modelling activities while doing experiments to discover the concept of variable...2216

Simon Zell, Astrid Beckmann

Modeling with technology in elementary classrooms...2226

N. Mousoulides, M. Chrysostomou, M. Pittalis, C. Christou

WORKING GROUP 12

Advanced mathematical thinking...2236

Introduction...2238

Roza Leikin, Claire Cazes, Joanna Mamona-Dawns, Paul Vanderlind

A theoretical model for visual-spatial thinking...2246

Conceição Costa, José Manuel Matos, Jaime Carvalho e Silva

Secondary-tertiary transition and students’ difficulties: the example of duality ...2256

Martine De Vleeschouwer

Learning advanced mathematical concepts: the concept of limit ...2266

António Domingos

Conceptual change and connections in analysis ...2276

Kristina Juter

Using the onto-semiotic approach to identify and analyze mathematical meaning

in a multivariate context...2286

Mariana Montiel, Miguel R. Wilhelmi, Draga Vidakovic, Iwan Elstak

Derivatives and applications; development of one student’s understanding ...2296

Gerrit Roorda, Pauline Vos, Martin Goedhart Finding the shortest path on a spherical surface:

“academics” and “reactors” in a mathematics dialogue...2306

Maria Kaisari, Tasos Patronis

Number theory in the national compulsory examination

at the end of the French secondary level: between organising and operative dimensions...2316

Véronique Battie

Defining, proving and modelling: a background for the advanced mathematical thinking...2326

Mercedes García, Victoria Sánchez, Isabel Escudero

Necessary realignments from mental argumentation to proof presentation ...2336

Joanna Mamona-Downs, Martin Downs

An introduction to defining processes ...2346

Cécile Ouvrier-Buffet

Problem posing by novice and experts: comparison between students and teachers ...2356

Cristian Voica, Ildikó Pelczer

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Advanced mathematical knowledge: how is it used in teaching?...2366

Rina Zazkis, Roza Leikin

Urging calculus students to be active learners: what works and what doesn't...2376

Buma Abramovitz, Miryam Berezina, Boris Koichu, Ludmila Shvartsman

From numbers to limits: situations as a way to a process of abstraction ...2386

Isabelle Bloch, Imène Ghedamsi

From historical analysis to classroom work:

function variation and long-term development of functional thinking ...2396

Renaud Chorlay

Experimental and mathematical control in mathematics ...2406

Nicolas Giroud

Introduction of the notions of limit and derivative of a function at a point...2416

Ján Gunčaga

Factors influencing teacher’s design of assessment material at tertiary level ...2426

Marie-Pierre Lebaud

Design of a system of teaching elements of group theory ...2436

Ildar Safuanov

WORKING GROUP 13

Comparative studies in mathematics education...2446

Introduction...2447

Eva Jablonka, Paul Andrews, Birgit Pepin

Comparing Hungarian and English mathematics teachers’ professional motivations...2452

Paul Andrews

Spoken mathematics as a distinguishing characteristic of mathematics classrooms

in different countries ...2463

David Clarke, Xu Li Hua

Mathematical behaviors of successful students from a challenged ethnic minority...2473

Tiruwork Mulat, Abraham Arcavi

A problem posed by J. Mason as a starting point

for a Hungarian-Italian teaching experiment within a European project...2483

Giancarlo Navarra, Nicolina A. Malara, András Ambrus A comparison of teachers’ beliefs and practices

in mathematics teaching at lower secondary and upper secondary school ...2494

Hans Kristian Nilsen

Mathematical tasks and learner dispositions: A comparative perspective...2504

Birgit Pepin

Elite mathematics students in Finland and Washington:

access, collaboration, and hierarchy ...2513

Jennifer von Reis Saari

International comparative research on mathematical problem solving:

Suggestions for new research directions...2523

Constantinos Xenofontos

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WORKING GROUP 14

Early years mathematics...2533

Introduction...2535

Patti Barber

Girls and boys in “the land of mathematics”

6 to 8 years old children’s relationship to mathematics interpreted from their drawings...2537

Päivi Perkkilä, Eila Aarnos

“Numbers are actually not bad”

Attitudes of people working in German kindergarten about mathematics in kindergarten ...2547

Christiane Benz

Learning mathematics within family discourses...2557

Birgit Brandt, Kerstin Tiedemann

Orchestration of mathematical activities in the kindergarten: the role of questions...2567

Martin Carlsen, Ingvald Erfjord, Per Sigurd Hundeland

Didactical analysis of a dice game...2577

Jean-Luc Dorier, Céline Maréchal

“Tell them that we like to decide for ourselves”

Children’s agency in mathematics education...2587

Troels Lange

Exploring the relationship between justification and monitoring

among kindergarten children ...2597

Pessia Tsamir, Dina Tirosh, Esther Levenson

Early years mathematics – The case of fractions...2607

Ema Mamede

Only two more sleeps until the school holidays: referring to quantities of things at home...2617

Tamsin Meaney

Supporting children potentially at risk in learning mathematics

Findings of an early intervention study...2627

Andrea Peter-Koop

The structure of prospective kindergarten teachers’ proportional reasoning...2637

Demetra Pitta-Pantazi, Constantinos Christou

How can games contribute to early mathematics education? – A video-based study ...2647

Stephanie Schuler, Gerald Wittmann

Natural differentiation in a pattern environment (4 year old children make patterns) ...2657

Ewa Swoboda

Can you do it in a different way?...2667

Dina Tirosh, Pessia Tsamir, Michal Tabach

WORKING GROUP 15

Theory and research on the role of history in mathematics education...2677

Introduction...2679

Fulvia Furinghetti, Jean-Luc Dorier, Uffe Jankvist, Jan van Maanen, Constantinos Tzanakis

The teaching of vectors in mathematics and physics in France during the 20th century ...2682

Cissé Ba, Jean-Luc Dorier

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Geometry teaching in Iceland in the late 1800s and the van Hiele theory...2692

Kristín Bjarnadóttir

Introducing the normal distribution by following a teaching approach inspired by history:

an example for classroom implementation in engineering education...2702

Mónica Blanco, Marta Ginovart

Arithmetic in primary school in Brazil: end of the nineteenth century ...2712

David Antonio Da Costa

Historical pictures for acting on the view of mathematics...2722

Adriano Demattè, Fulvia Furinghetti

Students’ beliefs about the evolution and development of mathematics ...2732

Uffe Thomas Jankvist

Using history as a means for the learning of mathematics without losing sight of history:

the case of differential equations ...2742

Tinne Hoff Kjeldsen

What works in the classroom

Project on the history of mathematics and the collaborative teaching practice ...2752

Snezana Lawrence

Intuitive geometry in early 1900s Italian middle school...2762

Marta Menghini

The appropriation of the New Math on the Technical Federal School of Parana

in 1960 and 1970 decades ...2771

Bárbara Winiarski Diesel Novaes, Neuza Bertoni Pinto

History, heritage, and the UK mathematics classroom...2781

Leo Rogers

Introduction of an historical and anthropological perspective in mathematics:

an example in secondary school in France...2791

Claire Tardy, Vivianne Durand-Guerrier

The implementation of the history of mathematics in the new curriculum and textbooks

in Greek secondary education ...2801

Yannis Thomaidis, Constantinos Tzanakis

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CERME 6 – GENERAL INTRODUCTION

GENERAL INTRODUCTION

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INTRODUCTION TO CERME 6

BY BARBARA JAWORSKI PRESIDENT OF ERME

EUROPEAN SOCIETY FOR RESEARCH IN MATHEMATICS EDUCATION

CERME is the two-yearly congress of ERME, the European Society for Research in Mathematics Education. CERME 6 marks more than a decade of ERME and it is important to recognise the achievements of the society over this time.

In May 1997, a group of 16 scholars from different European countries met in Osnabrück, Germany, for three days to discuss the formation of a European society in mathematics education. In true European spirit, we decided that we wanted a society which would bring together researchers from across Europe, particularly including colleagues from Eastern Europe, fostering communication, cooperation and collaboration. We wanted a conference that would explicitly provide such opportunity. We wanted especially to encourage and contribute to the education of young researchers. Thus ERME was born and began to take shape.

We decided on a two-yearly conference, or congress as it later became known, and the name CERME emerged – Congress of the European Society for Research in Mathematics Education. CERME should have a group structure in which researchers would have sufficient time to really get to know each other, share and discuss their research and engage in deep scholarly debate. The first CERME was planned for February 1999, at Osnabrück. The Program Committee took very seriously the aims for the conference expressed at the 1997 meeting. Seven working groups were planned and 12 hours were provided for work in a group. To avoid most of the conference time being taken up by paper presentation, it was decided there would be no oral presentations at the conference. Papers would be presented in written form before the conference with sufficient time for group participants to read the papers.

The 12 hours would be spent discussing the papers and working on themes and issues suggested by the papers and the group leaders. Over the succeeding years, a group led by Konrad Krainer (Austria) and Paolo Boero (Italy) developed a plan and style for a YERME summer school (YESS). The first summer school was held in Klagenfurt, Austria in August 2002. Like CERME, the summer school was based around groups, working on papers submitted by the young researchers, each with an international

“expert” as leader.

The pattern of CERME and YERME has developed so they take place in alternative years, the group structure being developed and carried forwards from one to the next.

We had CERME 2 in Marianske Lazne, Czech Republic in 2001; CERME 3 in Bellaria, Italy in 2003; and YESS 2 in Podebrady, Czech Republic in 2004. CERME 4 took place in Saint Feliu, Spain in February, 2005 and YESS 3 in Jyväskylä, Finland in August 2006. CERME 5 was held in Cyprus in February 2007, and YESS

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4 in Trabzon, Turkey in August, 2008. CERME 6 will take place in Lyon, France in 2009 and YESS 5 in Palermo, Italy in 2010. People came from these events speaking of inspirationalexperiences. It seemed clear that the events generated something that we came to call the CERME Spirit. Based fundamentally on the three Cs, communication, cooperation and collaboration, the CERME Spirit was about the inspiration that derives from serious scholarly tackling of ideas and concepts in key areas and of mathematics education research with colleagues from multiple nations, facilitated by the group design of the events.

However, the group design was not without its critics. Some critics felt constrained by the requirement to spend a conference, largely, in just one group. Some felt that a conference ought to offer a greater variety of opportunity to participants. Participants should be free to choose where to be at any time. However, the group work at CERME or YESS would be seriously disrupted if participants were to hop from group to group, not engaging seriously with the work in any one. Some suggested that perhaps planning could allow participants to take part in two groups, so that engagement in both could be serious. Such ideas have been considered by the ERME Board and Programme Committees but so far we have remained faithful to the initial conception. Many participants have said in evaluation of the events that the opportunity to spend serious time in one group allowed them to really get to know researchers from other countries, and that this contributed significantly to the depth of thinking that was possible.

We want to encourage wider participation to ongoing activity in our Society, with more nations contributing to hosting events and a secure financial platform for continuing our inclusive communication, cooperation and collaboration within Europe. Further details of ERME can be found at the following site:

http://ermeweb.free.fr/

Barbara Jaworski – President of ERME

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PRESENTATION OF CERME 6 BY FERDINANDO ARZARELLO, CHAIR OF THE SCIENTIFIC INTERNATIONAL COMMITTEE

As pointed out in the document written by our President, CERME is a Congress designed to foster a communicative spirit in European mathematics education according to the three Cs of ERME: communication, cooperation and collaboration. It deliberately moves away from research presentations by individuals towards collaborative group work. Its main feature is a number (15) of thematic groups whose members have worked together in a common research area.

In addition to the working group sessions, there was:

• Two plenary lectures and a panel;

• Two parallel 1 hour sessions where the participants had the opportunity of debating with the plenarists;

• A poster session;

• Final parallel sessions (repeated twice), where each group has presented its work to the interested participants;

• Policy and purpose sessions to negotiate the work and directions of ERME.

The philosophy of our Congress is based on the following two issues:

i. We need to know more about the research which has been done and is ongoing, and the research groups and research interests in different European countries;

ii. We need to provide opportunities for cooperation in research areas and for inter-European collaboration between researchers in joint research projects.

In organising this Conference we considered both the ERME spirit and the observations from the questionnaires filled by the participants, which mainly concerned the plenary events. Consequently, the following structure was planned:

• Two plenary lectures of 75 minutes; each plenarist had a reactor: they had 60 minutes for their two presentations, and then there was 15 minutes for questions from the floor. Moreover the interested people had the opportunity to meet the plenarists in an informal meeting in another day.

• An other event is the special 2 hour plenary of the last day, which had three participants: the aim was to discuss a topic emerging from previous CERMEs,

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analysing it from different standpoints and to give people the possibility of a wide debate.

The structure of the Working Groups was essentially the same: each group had more of 12 hours for discussing its topic. In the final Sunday session each group have presented the results of its work in two consecutive one hour slots, according to the model experienced in CERME 5, which had received the approval of the participants.

I think that all of us had a very exciting week, plenty of interesting scientific and social opportunities. In particular I underline the lecture of Prof. E. Ghys ⎯ http://www.dimensions-math.org ⎯ and the discussion on a Project of a European Journal of Mathematical Education.

I wish to thank the local organisers, and particularly Viviane Durand-Guerrier, for the enormous work they have done to make possible the realisation of this Conference.

Ferdinando Arzarello – Chair of the scientific international committee

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QUALITY AND INCLUSION IN CERME 6: A PROPOSED REVIEW

The European Society for Research in Mathematics Education (ERME), and its principal activities CERME (2-yearly Congress of ERME) and YERME (meetings of Young researchers in ERME) are committed to the three Cs: Communication, Cooperation and Collaboration in research in mathematics education. Over the years in which ERME has existed, the community has developed what has become known as “The CERME Spirit”. These words capture a practical manifestation of the objectives expressed in the three Cs. The phrase refers to an inclusivity of working in which people genuinely work together, in which all are welcome, and in which members work hard to ensure that all can take a full part in activity. A major factor and issue – that of the language of our work – has been addressed seriously; different groups devising their own approaches to their working language.

However, these things are not straightforward and issues arise as soon as we construct practical situations. The main example of this concerns the scientific quality of our work in mathematics education research. Of course we aspire to a high quality of scientific work, just as we aspire to operate in fully inclusive ways. Ideally we should like there to be compatibility between the two. But what does or can this look like in practice?

These issues face group leaders as soon as they set out to construct a programme of work for their group, starting with a call for papers. Responding to this call, we see that many papers are now received for all groups. This suggests that researchers in our field want to be part of CERME and offer their work to colleagues in CERME.

From an inclusive point of view, all papers should be welcome and all those wishing to participate should have a place. However, from a scientific point of view, papers should be reviewed according to scientific criteria, those that are of a suitable scientific quality (according to the group leaders) should be accepted and others rejected. In practice this means that authors of rejected papers may not be able to attend the congress since funding depends on an accepted paper. The practice seems to go against principles of inclusion.

The ERME Board, and Programme Committees of CERME conferences have been aware of these issues and have addressed them by creating a two stage review process. For presentation of papers at the congress, a much more open attitude should be taken to the criteria, aiming to include as many participants as possible. At this stage, feedback to prospective participants should detail what is required for a paper to be acceptable for the scientific proceedings following the congress. Papers not meeting these requirements would not be accepted for the proceedings. Of course, it is then up to the group leaders to determine how to make the necessary decisions:

what is acceptable for presentation, and what are the more strict criteria for publication? They also have to decide how to conduct the work of the group in an

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inclusive way. Similarly those organising YERME events have to decide how to ensure both quality and inclusion in practice.

Our sixth CERME achieved, it therefore feels like a time to review these issues and procedures. For this purpose, a small group of interested members of ERME has agreed to survey participants in CERME 6 and seek views on the processes and issues that are involved. We have included an opportunity to comment in the evaluation questionnaire for CERME 6 and possibility to send us a personal communication (written) to express your views in more detail. We have also asked group leaders, present and past, to tell us how they have made decisions and what difficulties if any there have been.

As a result of analysing the information received we hope to write a paper for a scientific edited book on the topic of inclusion and quality. Such a paper could also act as a basis for future policy in ERME, CERME and YERME.

Barbara Jaworski, Ferdinando Arzarello M. Alessandra Marriotti Constantinos Christou Joao Pedro da Ponte

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SCIENTIFIC PROGRAM

CERME 6 PLENARY CONFERENCES Jan 28, 15:30 - 16:45

Luis Radford, Université Laurentienne, Ontario, Canada.

SIGNS, GESTURES, MEANINGS: ALGEBRAIC THINKING FROM A CULTURAL SEMIOTIC PERSPECTIVE.

Reactor: Heinz Steinbring (Duisburg-Essen University)

Summary. In this presentation I will deal with the ontogenesis of algebraic thinking.

Drawing on a cultural semiotic perspective, informed by current anthropological and embodied theories of knowing and learning, in the first part of my talk I will comment on the shortcomings of traditional mental approaches to cognition. In tune with contemporary research in neuroscience, cultural psychology, and semiotics, I will contend that we are better off conceiving of thinking as a sensuous and sign- mediated activity embodied in the corporeality of actions, gestures, and artifacts. In the second part of my talk, I will argue that algebraic thinking can be characterized in accordance with the semiotic means to which the students resort in order to express and deal with algebraic generality. I will draw upon results obtained in the course of a 10-year longitudinal classroom research project to offer examples of students’ forms of algebraic thinking. Two of the most elementary forms of algebraic thinking identified in our research are characterized by their contextual and embodied nature;

they rely extensively upon rhythm and perceptual and deictic (linguistic and gestural) mechanisms of meaning production. Furthermore, keeping in line with the situated nature of the students’ mathematical experience, signs here usually designate their objects in an indexical manner. These elementary forms of algebraic thinking differ from the traditional one—based on the standard alphanumeric symbolism—in that the latter relies on sign distinctions of a morphological kind. Here signs cease to designate objects in the usual indexical sense to give rise to symbolic processes of recognition and manipulation governed by sign shape.

The aforementioned conception of thinking in general and the ensuing distinction of forms of algebraic thinking shed some light on the kind of abstraction that is entailed by the use of standard algebraic symbolism. They intimate some of the conceptual shifts that the students have to make in order to gain fluency in a cultural sophisticated form of mathematical thinking. Voice, gesture, and rhythm fade away.

Embodied and contextual ways of signifying are then replaced with a perceptual activity where differences and similarities are a matter of morphology, and where meaning becomes relational.

Jan 29, 9:15 - 10:30

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Paola Valero, Aalborg University, Denmark.

ATTENDING TO SOCIAL CHANGES IN EUROPE: CHALLENGES FOR MATHEMATICS EDUCATION RESEARCH IN THE 21ST CENTURY

Reactor: Margarida Alexandra da Piedade Silva Cesar (Lisbon University)

Summary. Based on an analysis of mathematics education research as an academic field and on current social, political and economic transformations in many European countries, I would argue for the need to rethink and enlarge definitions and views of mathematics education as a scientific field of study in order to provide better understandings and alternatives for practice in the teaching and learning of mathematics today. I will explore the notion of the “network of mathematics education practices” as a complex, multi-layered space of social practice where the meanings of the teaching and learning of mathematics are constituted. I will illustrate the potentiality of this notion to envision possible research paths in the field. I will illustrate these with the research that my colleagues and I have been carrying on multicultural classrooms in Denmark; as well as will offer examples of other research studies in Europe and other parts of the world where I see that the discipline is gaining newer insights that could allow attending to the social changes and challenges of the 21^st century.

Feb 1st, 11:00 – 13:00

SPECIAL PLENARY: WAYS OF WORKING WITH DIFFERENT THEORETICAL APPROACHES IN MATHEMATICS EDUCATION RESEARCH

Speakers: Angelika Bikner-Ahsbahs, Bremen University, Germany John Monaghan, University of Leeds, United Kingdom Chair: Tommy Dreyfus, Tel Aviv University, Israel

Structure : This plenary activity is planned to last 2 hours and will comprise five parts

Introduction (T. Dreyfus, 5 min)

Networking of theories – why and how? (A. Bikner-Ahsbahs, 25 min + 5 min for clarifications)

Taking the appropriate parts from a variety of theories (J. Monaghan, 25 min + 5 min for clarifications)

Questions to the floor (T. Dreyfus, 10 min)

Questions and contributions from the audience with reactions from the speakers (45 min)