European Research in Mathematics Education III
Table of Contents
Maria Alessandra
Mariotti Introduction to CERME3, the Third Conference of the European society for Research in Mathematics Education 
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ERME: history, aims and current organization

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Plenary Panel
The Relationship of Theory and Practice in Mathematics Education
Barbara Jaworski Introduction to the panel 
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Barbara Jaworski The relationship of theory and practice in mathematics education (Introduction) 
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Mariolina Bartolini Bussi Theory and Practice: An Internet Project about Science and Technology 
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Christer Bergsten Theory—practice relationships in mathematics education 
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Konrad Krainer Theory and Practice: Facilitating teachers’ investigation into their own teaching 
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Barbara Jaworski Conclusive thoughts 
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Thematic Working Group 1
The Role of Metaphors and Images in Learning and Teaching Mathematics
Bernard Parzysz, Christer Bergsten, José
Manuel Matos and Angela Pesci The Role of Metaphors and Images in Learning and Teaching Mathematics (Introduction) 
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Iiris Attorps Teacher's images of the "equation" concept 
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Chris Bills Metaphor in young children's mental calculation 
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Laurie D. Edwards The nature of mathematics as viewed from cognitive science 
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Francesca Ferrara Bridging perception and theory: What role can metaphors and imagery play ? 
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Uri Leron Origins of mathematical thinking: a synthesis 
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Yves Matheron Some examples of the relationship between the use of images and metaphors and the production of memory in the teaching and learning of mathematics 
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Stavros Orfanos and Fragiskos Kalavassis The need of teaching the limits and the possibilities of the representation systems that offer the surrounding support for comprehending the concept of fraction 
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Bernard Parzysz Preservice elementary teachers and the fundamental ambiguity of diagrams in geometry problemsolving 
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Despina Potari, Kleopatra Diakogiorgi
and Helen Zanni Similes as a tool for exploring children's thinking about geometrical shape 
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Maryvonne Priolet and JeanClaude Regnier
Conversion of registers at primary school : the learner's or the teacher's responsibility ? 
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Elisabetta Robotti Functions of natural language in the resolution of a plane geometry problem 
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Roberto Tortora and Donatella Iannece
The evolution of graphic representations in a Vygotskijan perspective 
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Thematic Working Group2
Affect and Mathematical Thinking
Jeff Evans, Markku Hannula, George Philippou
and Rosetta Zan Affect and mathematical thinking (Introduction) 
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Charalambos Charalambous and George Philippou
Enhancing preservice teachers’ efficacy beliefs in mathematics 
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Jeff Evans Methods and Findings in Research on Affect and Emotion in Mathematics Education 
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Markku Hannula Affect and motivation: narratives with an attitude 
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Peter Nelmes Developing a conceptual framework for the role of the emotions in the language of teaching and learning 
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Maria Nicolaidou and George Philippou Attitudes towards mathematics, selfefficacy and achievement in problemsolving 
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Erkki Pehkonen and Anu Pietilä On Relationships between Beliefs and Knowledge in Mathematics Education 
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Päivi Perkkilä Primary School Teachers’ Mathematics Beliefs and Teaching Practices 
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Anu Pietilä Fulfilling the Criteria for a Good Mathematics Teacher  the case of one student 
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Wolfgang Schlöglmann Can neuroscience help us better to understand affective reactions in mathematics learning? 
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Rosetta Zan and Pietro Di Martino The role of affect in the research on affect: the case of 'attitude' 
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Thematic Working Group 3
Building Structures in Mathematical Knowledge
Milan Hejny, Graham. H.
Littler, Pearla Nesher and Melissa Rodd Building structures in mathematical knowledge (Introduction) 
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Rita Borromeo Ferri Mathematical thinking styles — an empirical study 
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Constantinos Christou, Andreas
Demetriou and Demetra PittaPantazi The specialized structural systems and mathematical performance 
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Milan Hejny Understanding and structure 
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Darina Jirotková and
Graham. H. Littler Insights into pupil’s structures of mathematical thinking through oral communication 
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Hartwig Meissner Constructing mathematical concepts with calculators or computers 
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Cécile OuvrierBuffet Definition construction and concept formation 
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Areti Panaoura, George Philippou
and Constantinos Christou Young pupils´ metacognitive ability in mathematics 
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Dvora Peretz, M.Gorodetsky
and T.Eisenberg A closer look into cognitive abstraction processes in the learning of abstract mathematics 
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Marios Pittalis, Constantinos
Christou and Eleni Papageorgiou Students’ ability in solving proportional problems 
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Melissa Rodd Emotion, intention and action for vital mathematical embodiment 
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Mihaela Singer How does efficient learning occur — a hypothesis 
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Nada Stehlikova Building a finite arithmetic structure: interpretation in terms of abstraction in context 
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Thematic Working Group 4
Argumentation and Proof
Rudolf vom Hofe, Christine
Knipping, Maria AlessandraMariotti and Bettina Pedemonte Argumentation and proof (Introduction) 
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Werner Blum On the Role of "Grundvorstellungen" for realityrelated proofs 
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Nadia Douek From oral to written texts in grade I and the approach to argumentation: the role of social interaction and task context 
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Viviane DurandGuerrier
Logic and mathematical reasoning from a didactical point of view 
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Aiso Heinze and Kristina Reiss Reasoning and proof: methodological knowledge as a component of proof competence 
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Christine Knipping Argumentation structures in classroom proving situations 
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Dietmar Küchemann and
Celia Hoyles The quality of students' explanations on a nonstandard geometry item 
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Christina Misailidou and Julian
Williams Children's arguments in discussion of a "difficult" ratioproblem: the role of a pistorial representation 
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Kirsti Nordström Swedish university entrants' experiences about and attitudes to proof and proving 
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Bettina Pedemonte What kind of proof can be constructed following an abductive argumentation? 
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David A. Reid Forms and uses of abduction 
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Aldo Scimone An educational experimentation on Goldbach's conjecture 
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Rudolf vom Hofe Epistemological problems with the limit concept  a case study on communication and argumentation within a computerbased learning environment 
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Oleksiy Yevdokimov The place and significance of the problems for proof in learning mathematics 
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Thematic Working Group 5
Stochastic Thinking
Dave Pratt Stochastic thinking (Introduction) 
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Carmen Batanero Curricular issues and teacher education (Introduction to Theme 1) 
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Dave Pratt Computer based tools (Introduction to Theme 2) 
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Rofl Biehler Statistical thinking (Introduction to Theme 3) 
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Michel Henry Probabilistic thinking (Introduction to Theme 4) 
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Dor Abrahamson and Uriel Wilensky
The quest of the bell curve: a constructionist designer's advocacy of learning through designing 
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J. Richard Alldredge Association of course performance with attitudes and beliefs: an analysis by gender and instructional software environment 
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Pilar Azcárate, Anna
Serradó and José Mª Cardeñoso "Hazard's treatment" in secondary school 
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Carmen Batanero, Belén
Cobo Merino and Carmen Díaz Assessing secondary school student's understanding of averages 
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Herman Callaert In search of the specificity and the identifiability of stochastic thinking and reasoning 
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M.J.Cañizares, C.Batanero,
L.Serrano and J.J.Ortiz Children's understanding of fair games 
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Carolina Carvalho Solving strategies in statistical tasks 
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Celi Aparecida Espasandin
Lopes Teachers´development and developing children's stochastic knowlegde 
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Zaven A. Karian A new approach to probability and statistics instruction 
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Maria MeletiouMavrotheris
On the formalist view of mathematics: impact on statistics instruction and learning 
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Carlos Monteiro and Janet
Ainley Developing critical sense in graphing 
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Per Nilsson Experimentation as a tool for discovering mathematical concepts of probability 
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Jenny Pange Literature survey and children's perception on risk 
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Efi Paparistodemou and Richard
Noss Fairness in a spatial computer environment 
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Irene Pitarch Andrés,
Orús Báguena Pilar Logic and treatment of data in secondary 
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Dave Pratt The emergence of probabilistic knowledge 
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Jenni Way The development of young children's notions of probability 
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Thematic Working Group 6
Algebraic Thinking
Abraham Arcavi, Luciana Bazzini, Catherine
Sackur and Pessia Tsamir Algebraic thinking (Introduction) 
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Janet Ainley, Liz Bills and Kirsty Wilson Designing tasks for purposeful algebra 
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Giorgio T. Bagni Functions, processes, properties, objects: a case study 
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Caroline Bardini The construction of meaning of algebraic symbolism at different school levels. An epistemological and didactical approach 
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Luciana Bazzini and Pessia Tsamir Connections between theory and research findings: the case of inequalities 
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Pilar Bolea, Marianna Bosch and Josep Gascón Why is modelling not included in the teaching of algebra at secondary school? 
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Sonia P. Coelho, Silvia D. A. Machado, M. Cristina
S. A. Maranhão What algebra should be taught in teachers' courses? 
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JeanPhilippe Drouhard and Mabel Panizza What do the students need to know, in order to be able to actually do algebra? The three orders of knowledge 
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Paolo Guidoni Explaining vs. understanding dynamics: The case of elementary algebraic thinking 
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Maureen Hoch Structure sense 
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Teresia JakobssonÅhl Analyzing algebraic thinking in written solutions 
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Jarmila Novotná, Sara Hershkovitz and Pearla
Nesher Cognitive factors affecting problem solving at the prealgebraic level 
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Constanta Olteanu, Barbro Grevholm and Torgny
Ottosson Algebra in upper secondary school: a study of teaches teaching and student learning 
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Catherine Sackur, Maryse Maurel and Teresa Assude Are my students actually doing mathematics? 
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Ilya Sinitsky Prealgebra combinatorial problems and algorithms in primary school mathematics 
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Anna S. Steinweg `...the partner of 4 is plus 10 of this partner'  Young children make sense of tasks on functional relations 
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Michal Tabach and Alex Friedlander The role of context in learning beginning algebra 
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Jukka Törnroos Finns and algebra in TIMSS 1999 
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Thematic Working Group 7
Geometrical Thinking
JeanLuc Dorier, Ángel
Gutiérrez and Rudolf Strässer Geometrical thinking (Introduction) 
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Claudia Margarita AcuñaSoto The role of slope and yintercept from the students perspective 
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Maria Bako Different projecting methods in teaching spatial geometry 
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Nitsa Cohen Preference of directions in 3D space 
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Ghislaine GueudetChartier
Geometric thinking in a nspace 
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Eszter Herendiné Kónya
The concept of orientation 
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Catherine Houdement, Alain
Kuzniak Elementary geometry split into different geometrical paradigms 
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Frantisek Kurina Geometry  the Resource of Opportunities 
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Nicoletta Lanciano The processes and difficulties of teachers trainees in the construction of concepts, and related didactic material, for teaching geometry 
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Victor LariosOsorio Geometrical rigidity: an obstacle in using dynamic geometry software in a geometry course 
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MarieJeanne PerrinGlorian
Studying geometric figures at primary schools  From surfaces to points 
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Magdalena Prokopová
Students' conception of a point: a comparison of phylogenesis and ontogenesis 
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Christiane Rolet Teaching and learning plane geometry in primary school: acquisition of a first geometrical thinking 
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Paola Vighi The triangle as a mathematical object 
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Thematic Group 8
Social Interactions in Mathematical Learning Situations
Alison Price Social interactions in mathematical learning situations (Introduction) 
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Andreas Andersson The discourse of engineering students constructing concept maps in Linear Algebra 
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Richard Barwell Rethorical devices in Mathematics classroom interaction: solving a word problem 
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Michele Cerulli Instruments of semiotic mediation in algebra, an example 
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Marei Fetzer Interaction in collective writing processes and early mathematical learning 
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Paola Gallopin A mathematical project realised in a non formal environment: learning as a social event 
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Bracha Kramarskiand Zemira
Mevarech Metacognitive discourse in mathematics classrooms 
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Michela Maschietto The use of perpectographs in primary school: artefacts, instruments and semiotic mediation 
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Alison Price Establishing a mathematical community of practice in the primary classroom 
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Christof Schreiber Externalization and inscription in a chatenvironment 
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Ralph Schwarzkopf Analysing processes of solving word problems in mathematical lessons interaction: framing and reference context between real world and mathematics 
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Thematic Working Group 9:
Tools and Technologies in Mathematical Didactics
Keith Jones and JeanBaptiste
Lagrange Tools and technologies in mathematical didactics (Introduction) 
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Ferdinando Arzarello and
Domingo Paola Mathematical objects and proofs within technological environments: an embodied analysis 
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Giampaolo Chiappini and Maria
Reggiani Toward a didactic practice based on mathematics laboratory activities 
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Francisco Delgado and Rubén
D. Santiago Problembased learning in sophomore and freshmen engineering students: a four year followup 
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Rossana Falcade Instruments of semiotic mediation in cabri for the notion of function 
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Franco Favilli, Laura Maffei
and Irene Venturi Traditional sand drawings: proposal for a didactical software 
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Victor Giraldo and Luiz Mariano
Carvalho Local straightness and theoreticalcomputational conflicts: computational tools on the development of the concept image of derivative and limit 
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Mariam Haspekian Between arithmetic and algebra: a space for the spreadsheet? Contribution to an instrumental approach 
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Rosalyn Hyde and Alison ClarkJeavons
MathsALIVE  Developing a technologicallyrich learning environment for secondary mathematics 
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Keith Jones Classroom implications of research on dynamic geometry software 
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JeanBaptiste Lagrange Analysing the impact of ICT on mathematics teaching practices 
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Daniela Leder An experience of the construction of particular didactical tools to learn multiplication 
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Enrica Lemut Software environments supporting and enhancing systemic thinking 
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Bibi Lins Actual meanings, possible uses: secondary mathematics teachers and Cabrigéomètre 
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Matthias Ludwig, HansGeorg
Weigand, Wolfgang Weigel and Gerald Wittmann MaDiN  a framework for internetsupported learning in mathematics teacher education 
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David Miller, Derek Glover
and Doug Averis Exposure  the introduction of interactive whiteboard technology to secondary school mathematics teachers in training 
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Ornella Robutti Real and virtual calculator: from measurements to definite integral 
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Varda Talmon and Michal Yerushalmy
Dynamic behavior in dynamic geometry environments: some questions of order 
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Menekse Seden Tapan Integration of ICT in the teaching of mathematics in situations for treatment of difficulties in proving 
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Michal Yerushalmy and Daniel
Chazan Analyzing changes in student performance: what is the role of technology? 
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Luciana Zuccheri Problems arising in teachers' education in the use of didactical tools 
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Thematic Working Group 10
Teaching and Learning Mathematics in Multicultural Classrooms
Núria Gorgorió,
Bill Barton and Philip Clarkson Teaching and learning mathematics in multicultural classrooms (Introduction) 
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Helle Alrø, Ole Skovsmose
and Paola Valero Communication, conflict and mathematics education in the multicultural classroom 
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Bill Barton and Pip NevilleBarton
Investigating the relationship between English language and mathematical learning 
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Jeff Bezemer Dealing with multilingualism in the arithmetic class. An ethnographic case study fo a Dutch primary school 
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Philip C. Clarkson Australian bilingual students and mathematics 
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Ed Elbers and Mariëtte
de Haan The construction of word meaning in a multicultural classroom. Talk and collaboration during mathematics lessons 
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Franco Favilli, M. Luisa Oliveras
and Margarida César Maths teachers in multicultural classes: finding from a southern European project 
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Núria Gorgorió
and Núria Planas Transitions: from background to foreground 
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Gabriele Kaiser Learning mathematics within the context of linguistic and cultural diversity  an empirical study 
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Carlo Marchini Different cultures of the youngest students about space (and infinity) 
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Darlinda Moreira Portuguese immigrant children and mathematics education 
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Jarmila Novotná, Hana
Moraová, and Marie Hofmannová Using original textbooks when teaching mathematics in a foreign language 
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Daniel Clark Orey The algorithm collection project (ACP): the ethnomathematics of basic number sense acquisition across cultures 
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Sarah O'Toole and Guida de
Abreu Investigating parent’s explicit and implicit home numeracy practices in multiethnic contexts 
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Filippo Spagnolo Natural language, history and the interpretation of process of learning/teaching 
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Thematic Working Group 11
Interrelating Theory and Practice in Mathematics Teacher Education
Barbara Jaworski, Lurdes
Serrazina, Andrea Peter Koop and Konrad Krainer Interrelating theory and practice in mathametics teacher education (Introduction) 
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Lucilla Cannizzaro and Marta
Menghini Geometric figures from middle school to secondary school: mediating theory and practice 
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Mercedes Garcia, Victoria
Sanchez, Isabel Escudero and Salvador Llinares The dialectic relationship between theory and practice in mathematics teacher education 
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Rossella Garuti From research in mathematics education to teachers' training through internet 
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Lucia Grugnetti and Angela
Rizza A lengthy process for the establishment of the concept of limit 
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Alena Hospesova and Marie
Ticha Selfreflection and improving mathematics classroom culture 
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Barbara Jaworski Inquiry as a pervasive pedagogic process in mathematics education development 
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Jana Kratochvilova and Ewa
Swoboda Aspects affecting pupil’s thinking in mathematics during interaction researcherpupil 
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Roza Leikin and Sarga Dinur Patterns of flexibility: teachers’ behaviour in mathematical discussion 
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Joao da Ponte, Lurdes Serrazina,
Olivia Sousa and Helena Fonseca Professionals investigate their own practice 
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Petra Scherer and Heinz The professionalisation of mathematics teachers' knowledge  Teachers commonly reflect feedbacks to their own instruction activity 
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Bernd Wollring Linking preservice and inservice teacher training: cooperative design of working environments for primary mathematics 
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Thematic Working Group 12
From a Study
of Teaching Practices to Issues in Teacher Education
Barbro Grevholm, Ruhama Even, Juliana Szendrei and José Carillo From a study of teaching practices to issues in teacher education (Introduction) 
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Jordi Deulofeu and Lourdes Figueiras Inheritance problems in arabic algebra treatises. Can they stimulate future teachers' beliefs about mathematics? 
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Ruhama Even and Tali Wallach Student assessment: issues for teacher education 
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Hagar Gal Improving teachers' ability to cope with Problematic learning situations  The case of Eti 
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Maria Goulding How do prospective primary teachers assess their own mathematical knowledge? 
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Jeremy Hodgen Reflection, identity and belief change in primary mathematics 
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M. Kaldrimidou, H. Sakonidis, M. Tzekaki Teachers' interventions in students' mathematical work: a classification 
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Boris Koichu, Abraham Berman and Michael Moore Changing teachers' beliefs about students' heuristics in problem solving 
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Nicolina A. Malara Future middle school teachers' beliefs about Algebra: Incidence of the cultural background 
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Daniela Medici and Maria Gabriella Rinaldi A teaching resource for teacher training 
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Stephanie Prestage and Pat Perks Towards a pedagogy of teacher education: from a model for teacher transformation 
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Laetitia Ravel Setting a new curriculum in a classroom: variability and space of freedom for a teacher 
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Tim Rowland, Anne Thwaites and Peter Huckstep Elementary teachers' mathematics knowledge and choice of examples 
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Leonor Santos and João Pedro da Ponte An experience in distance inservice teacher education 
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