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Signs, gestures, meanings: Algebraic thinking from a cultural semiotic perspective /

Luis Radford, Université Laurentienne, Ontario, Canada

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Mathematics education as a network of social practices /

Paola Valero, Aalborg University, Denmark

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>> Download the Margarida Cesar's reaction

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Introduction / Tommy Dreyfus

Networking of theories: why and how? / Angelika Bikner-Ahsbahs

People and theories / John Monaghan

Multimethod approaches to the multidimensional affect in mathematics education

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Introduction / Markku S. Hannula, Marilena Panziara, Kjersti Wæge, Wolfgang Schloeglmann

The effect of achievement, gender and classroom context on upper secondary students' mathematical beliefs / Markku S. Hannula

Changing beliefs as changing perspective / Peter Liljedahl

“Maths and me”: software analysis of narrative data about attitude towards math / Pietro Di Martino

Students’ beliefs about the use of representations in the learning of fractions / Athanasios Gagatsis, Areti Panaoura, Eleni Deliyianni, Iliada Elia

Efficacy beliefs and ability to solve volume measurement tasks in different representations / Paraskevi Sophocleous, Athanasios Gagatsis

Students’ motivation for learning mathematics in terms of needs and goals / Kjersti Wæge

Mathematical modeling, self-representation and self-regulation / Areti Panaoura, Andreas Demetriou, Athanasios Gagatsis

Endorsing motivation: identification of instructional practices / Marilena Pantziara and George Philippou

The effects of changes in the perceived classroom social culture on motivation in mathematics across transitions / C. Athanasiou, G. N. Philippou

“After I do more exercise, I won't feel scared anymore” Examples of personal meaning from Hong-Kong / Maike Vollstedt

Emotional knowledge of mathematics teachers – retrospective perspectives of two case studies / Ilana Lavy and Atara Shriki

Humour as a means to make mathematics enjoyable / Pavel Shmakov, Markku S. Hannula

Beliefs: a theoretically unnecessary construct? / Magnus Österholm

Categories of affect – some remarks / Wolfgang Schlöglmann

Argumentation and proof

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

Understanding, visualizability and mathematical explanation / Daniele Molinini

Argumentation and proof: a discussion about Toulmin's and Duval's models / Thomas Barrier, Anne-Cécile Mathé, Viviane Durand-Guerrier

Why do we need proof / 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 / Francesca Morselli, Paolo Boero

Experimental mathematics and the teaching and learning of proof / Maria G. Bartolini Bussi

Conjecturing and proving in dynamic geometry: the elaboration of some research hypotheses / Anna Baccaglini-Frank, Maria alessandra Mariotti

The algebraic manipulator of alnuset: a tool to prove / Bettina Pedemonte

Visual proofs: an experiment / Cristina Bardelle

Teachers’ views on the role of visualisation and didactical intentions regarding proof / Irene Biza, Elena Nardi, Theodossios Zachariades

Modes of argument representation for proving – the case of general proof / Ruthi Barkai, Michal Tabach, Dina Tirosh, Pessia Tsamir, Tommy Dreyfus

Mathematics teachers’ reasoning for refuting students’ invalid claims / Despina Potari, Theodossios Zachariades, Orit Zaslavsky

Student justifications in high school mathematics / 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 / Manya Raman, Jim Sandefur, Geoffrey Birky, Connie Campbell, Kay Somers

“Can a proof and a counterexample coexist?” A study of students’ conceptions about proof / Andreas J. Stylianides, Thabit Al-Murani

Abduction and the explanation of anomalies: the case of proof by contradiction / Samuele Antonini, Maria Alessandra Mariotti

Approaching proof in school: from guided conjecturing and proving to a story of proof construction / Nadia Douek

Stochastic thinking

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

Chance models: building blocks for sound statistical reasoning / Herman Callaert

Recommended knowledge of probability for secondary mathematics teachers / Irini Papaieronymou

Statistical graphs produced by prospective teachers in comparing two distributions / Carmen Batanero, Pedro Arteaga, Blanca Ruiz

The role of context in stochastics instruction / Andreas Eichler

Does the nature and amount of posterior information affect preschooler’s inferences / Zoi Nikiforidou, Jenny Pange

Student’s Causal explanations for distribution / Theodosia Prodromou, Dave Pratt

Greek students’ ability in probability problem solving / Sofia Anastasiadou

Algebraic thinking and mathematics education

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Introduction / Janet Ainleya, Giorgio T. Bagnib, Lisa Hefendehl–Hebekerc, Jean–Baptiste Lagranged

The effects of multiple representations-based instruction on seventh grade students’ algebra performance / Oylum Akkus, Erdinc Cakiroglu

Offering proof ideas in an algebra lesson in different classes and by different teachers / Michal Ayalon, Ruhama Even

Rafael Bombelli’s Algebra (1572) and a new mathematical “object”: a semiotic analysis / Giorgio T. Bagni

Cognitive configurations of pre-service teachers when solving an arithmetic-algebraic problem / Walter F. Castro, Juan D. Godino

Transformation rules: a cross-domain difficulty / Marie-Caroline Croset

Epistemography and algebra / Jean-Philippe Drouhard

Sámi culture and algebra in the curriculum / Anne Birgitte Fyhn

Problem solving without numbers – An early approach to algebra / Sandra Gerhard

The ambiguity of the sign / Bernardo Gómez, Carmen Buhlea

Behind students’ spreadsheet competencies: their achievement in algebra? A study in a French vocational school / Mariam Haspekian, Eric Bruillard

Developing Katy’s algebraic structure sense / Maureen Hoch, Tommy Dreyfus

Children’s understandings of algebra 30 years on: what has changed? / Jeremy Hodgen, Dietmar Kuchemann, Margaret Brown, Robert Coe

Presenting equality statements as diagrams / Ian Jones

Approaching functions via multiple representations: a teaching experiment with Casyopee / Jean-Baptiste Lagrange, Tran Kiem Minh

Equality relation and structural properties / Carlo Marchini, Anne Cockburn, Paul Parslow-Williams, Paola Vighi

Structure of algebraic competencies / Reinhard Oldenburg

Generalization and control in algebra / Mabel Panizza

From area to number theory: a case study / Maria Iatridou, Ioannis Papadopoulos

Allegories in the teaching and learning of mathematics / Reinert A. Rinvold, Andreas Lorange

Role of an artefact of dynamic algebra in the conceptualisation of the algebraic equality / Giampaolo Chiappini, Elisabetta Robotti, Jana Trgalova

Communicating a sense of elementary algebra to preservice primary teachers / Franziska Siebel, Astrid Fischer

Conception of variance and invariance as a possible passage from early school mathematics to algebra / Ilya Sinitsky, Bat-Sheva Ilany

Growing patterns as examples for developing a new view onto algebra and arithmetic / Claudia Böttinger, Elke Söbbeke

Steps towards a structural conception of the notion of variable / Annika M. Wille

Geometrical thinking

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Introduction / Alain Kuzniak, Iliada Elia, Matthias Hattermann, Filip Roubicek

The necessity of two different types of applications in elementary geometry / Boris Girnat

A French look on the Greek geometrical working space at secondary school level / Alain Kuzniak, Laurent Vivier

A theoretical model of students’ geometrical figure understanding / Eleni Deliyianni, Iliada Elia, Athanasios Gagatsis, Annita Monoyiou, Areti Panaoura

Gestalt configurations in geometry learning / Claudia Acuña

Investigating comparison between surfaces / Paola Vighi

The effects of the concept of symmetry on learning geometry at French secondary school / 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 / Mattheou Kallia, Spyrou Panagiotis

The geometrical reasoning of primary and secondary school students / Georgia Panaoura, Athanasios Gagatsis

Strengthening students’ understanding of ‘proof’ in geometry in lower secondary school / Susumu Kunimune, Taro Fujita, Keith Jones

Written report in learning geometry: explanation and argumentation / Sílvia Semana, Leonor Santos

Multiple solutions for a problem: a tool for evaluation of mathematical thinking in geometry / Anat Levav-Waynberg, Roza Leikin

The drag-mode in three dimensional dynamic geometry environments – Two studies / Mathias Hattermann

3D geometry and learning of mathematical reasoning / Joris Mithalal

In search of elements for a competence model in solid geometry teaching. Establishment of relationships / Edna González, Gregoria Guillén

Students’ 3D geometry thinking profiles / Marios Pittalis, Nicholas Mousoulides, Constantinos Christou

Language and mathematics

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Introduction / Candia Morgan

Imparting the language of critical thinking while teaching probability / Einav Aizikovitsh, Miriam Amit

Toward an inferential approach analyzing concept formation and language processes / Stephan Hußmann, Florian Schacht

Iconicity, objectification, and the math behind the measuring tape: An example from pipe-trades training / Lionel LaCroix

Mathematical reflection in primary school education: theoretical foundation and empirical analysis of a case study / Cordula Schülke, Heinz Steinbring

Surface signs of reasoning / Nathalie Sinclair, David Pimm

A teacher’s use of gesture and discourse as communicative strategies in concluding a mathematical task / Raymond Bjuland, Maria Luiza Cestari, Hans Erik Borgersen

A teacher’s role in whole class mathematical discussion: facilitator of performance etiquette? / Thérèse Dooley

Use of words – Language-games in mathematics education / Michael Meyer

Speaking of mathematics – Mathematics, every-day life and educational mathematics discourse / Eva Riesbeck

Communicative positionings as identifications in mathematics teacher education / Hans Jørgen Braathe

Teachers’ collegial reflections of their own mathematics teaching processes. Part 1: An analytical tool for interpreting teachers reflections / Kerstin Bräuning, Marcus Nührenbörger

Teachers’ reflections of their own mathematics teaching processes. Part 2: Examples of an active moderated collegial reflection / Kerstin Bräuning, Marcus Nührenbörger

Internet-based dialogue: a basis for reflection in an in-service mathematics teacher education program / Mario Sánchez

The use of algebraic language in mathematical modelling and proving in the perspective of Habermas’ theory of rationality / Paolo Boero, Francesca Morselli

Objects as participants in classroom interaction / Marei Fetzer

The existence of mathematical objects in the classroom discourse / Vicenç Font, Juan D. Godino, Núria Planas, Jorge I. Acevedo

Mathematical activity in a multi-semiotic environment / Candia Morgan, Jehad Alshwaikh

Engaging everyday language to enhance comprehension of fraction multiplication / Andreas O. Kyriakides

Tensions between an everyday solution and a school solution to a measuring problem / Frode Rønning

Linguistic accomplishment of the learning-teaching processes in primary mathematics instruction / Marcus Schütte

Mathematical cognitive processes between the poles of mathematical technical terminology and the verbal expressions of pupils / Rose Vogel, Melanie Huth

Technologies and resources in mathematical education

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Introduction / 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 / Silke Ladel, Ulrich Kortenkamp

The impact of technological tools in the teaching and learning of integral calculus / Alejandro Lois, Liliana Milevicich

Using technology in the teaching and learning of box plots / Ulrich Kortenkamp, Katrin Rolka

Dynamical exploration of two-variable functions using virtual reality / Thierry Dana-Picard, Yehuda Badihi, David Zeitoun, Oren David Israeli

Designing a simulator in building trades and using it in vocational education / Annie Bessot, Colette Laborde

Collaborative design of mathematical activities for learning in an outdoor setting / Per Nilsson, Håkan Sollervall, Marcelo Milrad

Student development process of designing and implementing exploratory and learning objects / Chantal Buteau, Eric Muller

How can digital artefacts enhance mathematical analysis teaching and learning / Dionysis I. Diakoumopoulos

A learning environment to support mathematical generalisation in the classroom / Eirini Geraniou, Manolis Mavrikis, Celia Hoyles, Richard Noss

Establishing a longitudinal efficacy study using SimCalc MathWorlds / 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 / Ulrich Kortenkamp, Axel M. Blessing, Christian Dohrmann, Yves Kreis, Paul Libbrecht, Christian Mercat

Quality process for dynamic geometry resources: the Intergeo project / Jana Trgalova, Ana Paula Jahn, Sophie Soury-Lavergne

New didactical phenomena prompted by TI-Nspire specificities The mathematical component of the instrumentation process / Michèle Artigue, Caroline Bardini

Issues in integrating cas in post-secondary education: a literature review / Chantal Buteau, Zsolt Lavicza, Daniel Jarvis, Neil Marshall

The long-term project “Integration of symbolic calculator in mathematics lessons”. The case of calculus / Hans-Georg Weigand, Ewald Bichler

Enhancing functional thinking using the computer for representational transfer / Andrea Hoffkamp

The Robot Race: understanding proportionality as a function with robots in mathematics class / Elsa Fernandes, Eduardo Fermé, Rui Oliveira

Internet and mathematical activity within the frame of “Sub14” / Hélia Jacinto, Nélia Amado, Susana Carreira

A resource to spread math research problems in the classroom / Gilles Aldon, Viviane Durand-Guerrier

The synergy of students’ use of paper-and-pencil techniques and dynamic geometry software: a case study / Núria Iranzo, Josep Maria Fortuny

Students’ utilization schemes of pantographs for geometrical transformations: a first classification / Francesca Martignone, Samuele Antonini

The utilization of mathematics textbooks as instruments for learning / Sebastian Rezat

Teachers’ beliefs about the adoption of new technologies in the mathematics curriculum / Marilena Chrysostomou, Nicholas Mousoulides

Systemic innovations of mathematics education with dynamic worksheets as catalysts / Volker Ulm

A didactic engineering for teachers education courses in mathematics using ICT / Fabien Emprin

Geometers’ sketchpad software for non-thesis graduate students: a case study in Turkey / Berna Cantürk-Günhan, Deniz Özen

Leading teachers to perceive and use technologies as resources for the construction of mathematical meanings / Eleonora Faggiano

The teacher’s use of ICT tools in the classroom after a semiotic mediation approach / Mirko Maracci, Maria Alessandra Mariotti

Establishing didactical praxeologies: teachers using digital tools in upper secondary mathematics classrooms / Mary Billington

Dynamic geometry software: the teacher’s role in facilitating instrumental genesis / Nicola Bretscher

Instrumental orchestration: theory and practice / Paul Drijvers, Michiel Doorman, Peter Boon, Sjef van Gisbergen

Teaching Resources and teachers’ professional development: towards a documentational apProach of didactics / Ghislaine Gueudet, Luc Trouche

An investigative lesson with dynamic geometry: a case study of key structuring features of technology integration in classroom practice / Kenneth Ruthven

Methods and tools to face research fragmentation in technology enhanched mathematics education / 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 / Giampaolo Chiappini, Bettina Pedemonte

Casyopée in the classroom: two different theory-driven pedagogical approaches / Mirko Maracci, Claire Cazes, Fabrice Vandebrouck, Maria Alessandra Mariotti

Navigation in geographical space / Christos Markopoulos, Chronis Kynigos, Efi Alexopoulou, Alexandra Koukiou

Making sense of structural aspects of equations by using algebraic-like formalism / Foteini Moustaki, Giorgos Psycharis, Chronis Kynigos

Relationship between design and usage of educational software: the case of Aplusix / Jana Trgalova, Hamid Chaachoua

Questions and thoughts for researching cultural diversity and mathematics education

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Introduction / Guida de Abreu, Sarah Crafter, Núria Gorgorió

A survey of research on the mathematics teaching and learning of immigrant students / Marta Civil

Parental resources for understanding mathematical achievement in multiethnic settings / Sarah Crafter

Discussing a case study of family training in terms of communities of practices and adult education / Javier Díez-Palomar, Montserrat Prat Moratonas

Understanding Ethnomathematics from its criticisms and contradictions / Maria do Carmo Domite, Alexandre Santos Pais

Using mathematics as a tool in Rwandan workplace settings: the case of taxi drivers / Marcel Gahamanyi, Ingrid Andersson, Christer Bergsten

Parents’ experiences as mediators of their children’s learning: the impact of being a parent-teacher / Rachael McMullen, Guida de Abreu

Batiks: another way of learning mathematics / Lucília Teles, Margarida César

The role of Ethnomathematics within mathematics education / Karen François

Different theoretical perspectives and approaches in mathematics education research

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

Research problems emerging from a teaching episode: a dialogue between TDS and ATD / Michèle Artigue, Marianna Bosch, Joseph Gascón, Agnès Lenfant

Complementary networking: enriching understanding / Ferdinando Arzarello, Angelika Bikner-Ahsbahs, Cristina Sabena

Interpreting students’ reasoning through the lens of two different languages of description: integration or juxtaposition? / Christer Bergsten, Eva Jablonka

Coordinating multimodal social semiotics and institutional perspective in studying assessment actions in mathematics classrooms / Lisa Björklund-Boistrup, Staffan Selander

Integrating different perspectives to see the front and the back: The case of explicitness / Uwe Gellert

The practice of (university) mathematics teaching: mediational inquiry in a community of practice or an activity system / Barbara Jaworski

An interplay of theories in the context of computer-based mathematics teaching: how it works and why / Helga Jungwirth

On the adoption of a model to interpret teachers’ use of technology in mathematics lessons / Jean-Baptiste Lagrange, John Monaghan

The joint action theory in didactics: why do we need it in the case of teaching and learning mathematics? / Florence Ligozat, Maria-Luisa Schubauer-Leoni

Teacher’s didactical variability and its role in mathematics education / Jarmila Novotná, Bernard Sarrazy

The potential to act for low achieving students as an example of combining use of different theories / Ingolf Schäfer

Outline of a joint action theory in didactics / Gérard Sensevy

The transition between mathematics studies at secondary and tertiary levels; individual and social perspectives / Erika Stadler

Combining and Coordinating theoretical perspectives in mathematics education research / Tine Wedege

Comparing theoretical frameworks in didactics of mathematics: the GOA-model / Carl Winslow

Mathematical curriculum and practice

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Introduction / Leonor Santos, José Carrillo, Alena Hospesova, Maha Abboud-Blanchard

Effective ‘blended’ professional development for teachers of mathematics: Design and evaluation of the “UPOLA” Program / Lutz Hellmig

Teachers’ efficacy beliefs and perceptions regarding the implementation of new primary mathematics curriculum / Isil Isler, Erdine Cakiroglu

Curriculum management in the context of a mathematics subject group / Cláudia Canha Nunes, João Pedro da Ponte

Gestures and styles of communication: are they intertwined? / Chiara Andrá

Teachers’ subject knowledge: the number line representation / Maria Doritou, Eddie Gray

Communication as social interaction. Primary School Teacher Practices / Antonio Guerreiro, Lurdes Serrazina

Experimental devices in mathematics and physics standards in lower and upper secondary school, and their consequences on teacher’s practices / Fabrice Vandebrouck, Cecile de Hosson, Aline Robert

Professional development for teachers of mathematics: opportunities and change / Marie Joubert, Jenni Back, Els De Geest, Christine Hirst, Rosamund Sutherland

Teachers’ perception about infinity: a process or an object? / Maria Kattou, Michael Thanasia, Katerina Kontoyianni, Constantinos Christou, George Philippou

Perceptions on teaching the mathematically gifted / Katerina Kontoyianni, Maria Kattou, Polina Ioannou, Maria Erodotou, Constantinos Christou, Marios Pittalis

The nature on the numbers in grade 10: A professional problem / 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 / Nicolina A. Malara, Roberto Tortora

Why is there not enough fuss about affect and meta-affect among mathematics teachers? / Manuela Moscucci

The role of subject knowledge in Primary Student teachers’ approaches to teaching the topic of area / Carol Murphy

Developing of mathematics teachers’ community: five groups, five different ways / Regina Reinup

Foundation knowledge for teaching: contrasting elementary and secondary mathematics / Tim Rowland

Results of a comparative study of future teachers from Australia, Germany and Hong Kong with regard to competences in argumentation and proof / Björn Schwarz, Gabriele Kaiser

Kate’s conceptions of mathematics teaching: Influences in the first three years / Fay Turner

Pre-service teacher-generated analogies for function concepts / Behiye Ubuz, Ayşegül Eryılmaz, Utkun Aydın, Ibrahim Bayazit

Technology and mathematics teaching practices: about in-service and pre-service teachers / Maha Abboud-Blanchard

Teachers and triangles / Sylvia Alatorre, Mariana Saíz

Mathematics teacher education research and practice: researching inside the MICA program / Joyce Mgombelo, Chantal Buteau

Cognitive transformation in professional development: some case studies / Jorge Soto-Andrade

What do student teachers attend to? / Nad’a Stehlíková

The mathematical preparation of teachers: A focus on tasks / Gabriel J. Stylianides, Andreas J. Stylianides

Problem posing and development of pedagogical content knowledge in pre-service teacher training / Marie Tichá, Alena Hospesová

Sustainability of professional development / Stefan Zehetmeier

A collaborative project as a learning opportunity for mathematics teachers / Maria Helena Martinho, João Pedro da Ponte

Reflection on Practice: content and depth / Christina Martins, Leonor Santos

Developing mathematics teachers’ education through personal reflection and collaborative inquiry: which kinds of tasks? / Angela Pesci

The learning of mathematics teachers working in a peer group / Martha Witterholt, Martin Goedhart

Use of focus groups interviews in mathematics educational research / Bodil Kleve

Analyses of interactions in a collaborative context of professional development / Maria Cinta Muñoz-Catalán, José Carrillo, Nuria Climent

Adapting the knowledge quarter in the Cypriot mathematics classroom / Marilena Petrou

Professional knowledge in an improvisation episode: the importance of a cognitive model / C. Miguel Ribeiro, Rute Monteiro, José Carrillo

Applications and modelling

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Introduction / Morten Blomhøj

Mathematical modelling in teacher education – Experiences from a modelling seminar / Rita Borromeo Ferri, Werner Blum

Designing a teacher questionnaire to evaluate professional development in modelling / Katja Maaß, Johannes Gurlitt

Modeling in the classroom – Motives and obstacles from the teacher’s perspective / Barbara Schmidt

Modelling in mathematics teachers’ professional development / Jeroen Spandaw, Bert Zwaneveld

Towards understanding teachers’ beliefs and affects about mathematical modelling / Jonas Bergman Ärlebäck

The use of motion sensor can lead the students to understanding the cartesian graph / Maria Lucia Lo Cicero, Filippo Spagnolo

Interacing populations in a restricted habitat – Modelling, simulation and mathematical analysis in class / Christina Roeckerath

Aspects of visualization during the exploration of “quadratic world” via the ICT. Problem “fireworks” / Mária Lalinská, Janka Majherová

Mathematical modelling in class with and without technology / Hans-Stefan Siller, Gilbert Greefrath

The ‘ecology’ of mathematical modelling: constraints to its teaching at university level / Berta Barquero, Marianna Bosch, Josep Gascón

The double transposition in mathematisation at primary school / Richard Cabassut

Exploring the use of theoretical frameworks for modelling-oriented instructional design / F.J. García, L. Ruiz-Higueras

Study of a practical activity: engineering projects and their training context / Avenilde Romo Vázquez

Fitting models to data: the mathematising step in the modelling process / Lídia Serrano, Marianna Bosch, Josep Gascón

What roles can modelling play in multidisciplinary teaching / Mette Andresen

Modelling in environments without numbers – A case study / Roxana Grigoras

Modelling activities while doing experiments to discover the concept of variable / Simon Zell, Astrid Beckmann

Modeling with technology in elementary classrooms / N. Mousoulides, M. Chrysostomou, M. Pittalis, C. Christou

Advanced mathematical thinking

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

A theoretical model for visual-spatial thinking / Conceição Costa, José Manuel Matos, Jaime Carvalho e Silva

Secondary-tertiary transition and students’ difficulties: the example of duality / Martine De Vleeschouwer

Learning advanced mathematical concepts: the concept of limit / António Domingos

Conceptual change and connections in analysis / Kristina Juter

Using the onto-semiotic approach to identify and analyze mathematical meaning in a multivariate context / Mariana Montiel, Miguel R. Wilhelmi, Draga Vidakovic, Iwan Elstak

Derivatives and applications; development of one student’s understanding / Gerrit Roorda, Pauline Vos, Martin Goedhart

Finding the shortest path on a spherical surface: “academics” and “reactors” in a mathematics dialogue / Maria Kaisari, Tasos Patronis

Number theory in the national compulsory examination at the end of the French secondary level: between organising and operative dimensions / Véronique Battie

Defining, proving and modelling: a background for the advanced mathematical thinking / Mercedes García, Victoria Sánchez, Isabel Escudero

Necessary realignments from mental argumentation to proof presentation / Joanna Mamona-Downs, Martin Downs

An introduction to defining processes / Cécile Ouvrier-Buffet

Problem posing by novice and experts: comparison between students and teachers / Cristian Voica, Ildikó Pelczer

Advanced mathematical knowledge: how is it used in teaching? / Rina Zazkis, Roza Leikin

Urging calculus students to be active learners: what works and what doesn't / Buma Abramovitz, Miryam Berezina, Boris Koichu, Ludmila Shvartsman

From numbers to limits: situations as a way to a process of abstraction / Isabelle Bloch, Imène Ghedamsi

From historical analysis to classroom work: function variation and long-term development of functional thinking / Renaud Chorlay

Experimental and mathematical control in mathematics / Nicolas Giroud

Introduction of the notions of limit and derivative of a function at a point / Ján Gunčaga

Factors influencing teacher’s design of assessment material at tertiary level / Marie-Pierre Lebaud

Design of a system of teaching elements of group theory / Ildar Safuanov

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Introduction / Eva Jablonka, Paul Andrews, Birgit Pepin

Comparing Hungarian and English mathematics teachers’ professional motivations / Paul Andrews

Spoken mathematics as a distinguishing characteristic of mathematics classrooms in different countries / David Clarke, Xu Li Hua

Mathematical behaviours of successful students from a challenged ethnic minority / Tiruwork Mulat, Abraham Arcavi

A problem posed by J. Mason as a starting point for a Hungarian-Italian Teaching Experiment within a European project / Giancarlo Navarra, Nicolina A. Malara, András Ambrus

A comparison of teachers’ beliefs and practices in mathematics teaching at lower secondary and upper secondary school / Hans Kristian Nilsen

Mathematical tasks and learner dispositions: A comparative perspective / Birgit Pepin

Elite mathematics students in Finland and Washington: Access, collaboration, and hierarchy / Jennifer von Reis Saari

International comparative research on mathematical problem solving: Suggestions for new research directions / Constantinos Xenofontos

Early years mathematics

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Introduction / Patti Barber

Girls and boys in “the land of mathematics”. 6 to 8 years old children’s relationship to mathematics interpreted from their drawings / Päivi Perkkilä, Eila Aarnos

“Numbers are actually not bad”. Attitudes of people working in German kindergarten about mathematics in kindergarten / Christiane Benz

Learning mathematics within family discourses / Birgit Brandt, Kerstin Tiedemann

Orchestration of mathematical activities in the kindergarten: the role of questions / Martin Carlsen, Ingvald Erfjord, Per Sigurd Hundeland

Didactical analysis of a dice game / Jean-Luc Dorier, Céline Maréchal

“Tell them that we like to decide for ourselves” – Children’s agency in mathematics education / Troels Lange

Exploring the relationship between justification and monitoring among kindergarten children / Pessia Tsamir, Dina Tirosh, Esther Levenson

Early years mathematics – The case of fractions / Ema Mamede

Only two more sleeps until the school holidays: referring to quantities of things at home / Tamsin Meaney

Supporting children potentially at risk in learning mathematics Findings of an early intervention study / Andrea Peter-Koop

The structure of prospective kindergarten teachers’ proportional reasoning / Demetra Pitta-Pantazi, Constantinos Christou

How can games contribute to early mathematics education? – A video-based study / Stephanie Schuler, Gerald Wittmann

Natural differentiation in a pattern environment (4 year old children make patterns) / Ewa Swoboda

Can you do it in a different way? / Dina Tirosh, Pessia Tsamir, Michal Tabach

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Introduction / 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 / Cissé Ba, Jean-Luc Dorier

Geometry teaching in Iceland in the late 1800s and the van Hiele theory / Kristín Bjarnadóttir

Introducing the normal distribution by following a teaching approach inspired by history: an example for classroom implementation in engineering education / Mónica Blanco, Marta Ginovart

Arithmetic in primary school in Brazil: end of the nineteenth century / David Antonio Da Costa

Historical pictures for acting on the view of mathematics / Adriano Demattè, Fulvia Furinghetti

Students’ beliefs about the evolution and development of mathematics / Uffe Thomas Jankvist

Using history as a means for the learning of mathematics without losing sight of history: the case of differential equations / Tinne Hoff Kjeldsen

What works in the classroom. Project on the history of mathematics and the collaborative teaching practice / Snezana Lawrence

Intuitive geometry in early 1900s Italian middle school / Marta Menghini

The appropriation of the New Math on the Technical Federal School of Parana in 1960 and 1970 decades / Bárbara Winiarski Diesel Novaes, Neuza Bertoni Pinto

History, heritage, and the UK mathematics classroom / Leo Rogers

Introduction of an historical and anthropological perspective in mathematics: an example in secondary school in France / Claire Tardy, Vivianne Durand-Guerrier

The implementation of the history of mathematics in the new curriculum and textbooks in Greek secondary education / Yannis Thomaidis, Constantinos Tzanakis