# Table of contents

## GENERAL INTRODUCTION

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## PLENARY 1

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

Luis Radford, Université Laurentienne, Ontario, Canada

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the Heinz Steinbring's reaction

## PLENARY 2

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the Margarida Cesar's reaction

## SPECIAL PLENARY SESSION

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- Introduction / Tommy Dreyfus
- Networking of theories: why and how? / Angelika Bikner-Ahsbahs
- People and theories / John Monaghan
- Discussion

## WORKING GROUP 1

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

## WORKING GROUP 2

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

## WORKING GROUP 3

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

## WORKING GROUP 4

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
- Interrelation between anticipating thought and interpretative aspects in the use of algebraic language for the construction of proofs in elementary number theory / Annalisa Cusi
- 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

## WORKING GROUP 5

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

## WORKING GROUP 6

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

## WORKING GROUP 7

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

## WORKING GROUP 8

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

## WORKING GROUP 9

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

## WORKING GROUP 10

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

## WORKING GROUP 11

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
- Modelling and formative assessment pedagogies mediating change in actions of teachers and learners in mathematics classrooms / Geoff Wake
- 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

## WORKING GROUP 12

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

## WORKING GROUP 13

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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

## WORKING GROUP 14

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

## WORKING GROUP 15

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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