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CERME 3 Proceedings

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CERME 3: Third Conference of the European Society for Research in Mathematics Education

28 February – 3 March 2003 in Bellaria, Italy

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

All Plenary Papers
Barbara Jaworski
  The relationship of theory and practice in mathematics education (Introduction)



Mariolina Bartolini Bussi
  Theory and Practice: An Internet Project about Science and Technology



Christer Bergsten
  Theory—practice relationships in mathematics education



Konrad Krainer
  Theory and Practice: Facilitating teachers’ investigation into their own teaching



Barbara Jaworski
  Conclusive thoughts


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) 

All TG1 papers
Iiris Attorps
   Teacher’s images of the “equation” concept

Chris Bills
   Metaphor in young children’s mental calculation


Laurie D. Edwards
   The nature of mathematics as viewed from cognitive science


Francesca Ferrara
    Bridging perception and theory: What role can metaphors and imagery play ?


Uri Leron
    Origins of mathematical thinking: a synthesis


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


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



Bernard Parzysz
    Pre-service elementary teachers and the fundamental ambiguity of diagrams in geometry problem-solving


Despina Potari,  Kleopatra Diakogiorgi and Helen Zanni
    Similes as a tool for exploring children’s thinking about geometrical shape


Maryvonne Priolet and Jean-Claude Regnier
    Conversion of registers at primary school : the learner’s or the teacher’s responsibility ?



Elisabetta Robotti
    Functions of natural language in the resolution of a plane geometry problem


Roberto Tortora and Donatella Iannece
    The evolution of graphic representations in a Vygotskijan perspective


Thematic Working Group2

Affect and Mathematical Thinking

Jeff Evans, Markku Hannula, George Philippou and Rosetta Zan
    Affect and mathematical thinking (Introduction)

All TG2 papers
Charalambos Charalambous and George Philippou
    Enhancing preservice teachers’ efficacy beliefs in mathematics


Jeff Evans
    Methods and Findings in Research on Affect and Emotion in Mathematics Education


Markku Hannula
    Affect and motivation: narratives with an attitude


Peter Nelmes
   Developing a conceptual framework for the role of the emotions in the language of teaching and learning


Maria Nicolaidou and George Philippou
   Attitudes towards mathematics, self-efficacy and achievement in problem-solving

Erkki Pehkonen and Anu Pietilä
    On Relationships between Beliefs and Knowledge in Mathematics Education


Päivi Perkkilä
    Primary School Teachers’ Mathematics Beliefs and Teaching Practices

Anu Pietilä
    Fulfilling the Criteria for a Good Mathematics Teacher – the case of one student


Wolfgang Schlöglmann
    Can neuroscience help us better to understand affective reactions in mathematics learning?

Rosetta Zan and Pietro Di Martino
    The role of affect in the research on affect: the case of ‘attitude’


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)

All TG3 papers
Rita Borromeo Ferri
    Mathematical thinking styles — an empirical study


Constantinos Christou, Andreas Demetriou and Demetra Pitta-Pantazi
    The specialized structural systems and mathematical performance


Milan Hejny
    Understanding and structure


Darina Jirotková and Graham. H. Littler
    Insights into pupil’s structures of mathematical thinking through oral communication


Hartwig Meissner
    Constructing mathematical concepts with calculators or computers


Cécile Ouvrier-Buffet
    Definition construction and concept formation


Areti Panaoura, George Philippou and Constantinos Christou
    Young pupils´ metacognitive ability in mathematics


Dvora Peretz, M.Gorodetsky and T.Eisenberg
    A closer look into cognitive abstraction processes in the learning of abstract mathematics


Marios Pittalis, Constantinos Christou and Eleni Papageorgiou
    Students’ ability in solving proportional problems


Melissa Rodd
    Emotion, intention and action for vital mathematical embodiment


Mihaela Singer
    How does efficient learning occur — a hypothesis


Nada Stehlikova
    Building a finite arithmetic structure: interpretation in terms of abstraction in context


Thematic Working Group 4

Argumentation and Proof

Rudolf vom Hofe, Christine Knipping, Maria AlessandraMariotti and Bettina Pedemonte
Argumentation and proof (Introduction)

All TG4 papers
Werner Blum
On the Role of “Grundvorstellungen” for reality-related proofs


Nadia Douek
From oral to written texts in grade I and the approach to argumentation: the role of social interaction and task context


Viviane Durand-Guerrier
Logic and mathematical reasoning from a didactical point of view


Aiso Heinze and Kristina Reiss
Reasoning and proof: methodological knowledge as a component of proof competence


Christine Knipping
Argumentation structures in classroom proving situations


Dietmar Küchemann and Celia Hoyles
The quality of students’ explanations on a non-standard geometry item


Christina Misailidou and Julian Williams
Children’s arguments in discussion of a “difficult” ratioproblem: the role of a pistorial representation


Kirsti Nordström
Swedish university entrants’ experiences about and attitudes to proof and proving


Bettina Pedemonte
What kind of proof can be constructed following an abductive argumentation?


David A. Reid
Forms and uses of abduction


Aldo Scimone
An educational experimentation on Goldbach’s conjecture


Rudolf vom Hofe
Epistemological problems with the limit concept – a case study on communication and argumentation within a computer-based learning environment


Oleksiy Yevdokimov
The place and significance of the problems for proof in learning mathematics


Thematic Working Group 5

Stochastic Thinking

Dave Pratt
    Stochastic thinking (Introduction)

All TG5 papers
Carmen Batanero
    Curricular issues and teacher education (Introduction to Theme 1)


Dave Pratt
    Computer based tools (Introduction to Theme 2)


Rofl Biehler
    Statistical thinking (Introduction to Theme 3)


Michel Henry
    Probabilistic thinking (Introduction to Theme 4)


Dor Abrahamson and Uriel Wilensky
    The quest of the bell curve: a constructionist designer’s advocacy of learning through designing


J. Richard Alldredge
    Association of course performance with attitudes and beliefs: an analysis by gender and instructional software environment


Pilar Azcárate, Anna Serradó and José Mª Cardeñoso
    “Hazard’s treatment” in secondary school


Carmen Batanero, Belén Cobo Merino and Carmen Díaz
    Assessing secondary school student’s understanding of averages


Herman Callaert
    In search of the specificity and the identifiability of stochastic thinking and reasoning


M.J.Cañizares, C.Batanero, L.Serrano and J.J.Ortiz
    Children’s understanding of fair games


Carolina Carvalho
    Solving strategies in statistical tasks


Celi Aparecida Espasandin Lopes
    Teachers´development and developing children’s stochastic knowlegde


Zaven A. Karian
    A new approach to probability and statistics instruction


Maria Meletiou-Mavrotheris
    On the formalist view of mathematics: impact on statistics instruction and learning


Carlos Monteiro and Janet Ainley
    Developing critical sense in graphing


Per Nilsson
    Experimentation as a tool for discovering mathematical concepts of probability


Jenny Pange
    Literature survey and children’s perception on risk


Efi Paparistodemou and Richard Noss
    Fairness in a spatial computer environment


Irene Pitarch Andrés, Orús Báguena Pilar
    Logic and treatment of data in secondary


Dave Pratt
    The emergence of probabilistic knowledge


Jenni Way
    The development of young children’s notions of probability


Thematic Working Group 6

Algebraic Thinking

Abraham Arcavi, Luciana Bazzini, Catherine Sackur and Pessia Tsamir
    Algebraic thinking (Introduction)


All TG6 papers
Janet Ainley, Liz Bills and Kirsty Wilson
    Designing tasks for purposeful algebra


Giorgio T. Bagni
    Functions, processes, properties, objects: a case study


Caroline Bardini
    The construction of meaning of algebraic symbolism at different school levels. An epistemological and didactical approach


Luciana Bazzini and Pessia Tsamir
    Connections between theory and research findings: the case of inequalities


Pilar Bolea, Marianna Bosch and Josep Gascón
    Why is modelling not included in the teaching of algebra at secondary school?


Sonia P. Coelho, Silvia D. A. Machado, M. Cristina S. A. Maranhão
    What algebra should be taught in teachers’ courses?


Jean-Philippe 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

Paolo Guidoni
    Explaining vs. understanding dynamics: The case of elementary algebraic thinking


Maureen Hoch
    Structure sense


Teresia Jakobsson-Åhl
    Analyzing algebraic thinking in written solutions



Jarmila Novotná, Sara Hershkovitz and Pearla Nesher
    Cognitive factors affecting problem solving at the pre-algebraic level


Constanta Olteanu, Barbro Grevholm and Torgny Ottosson
    Algebra in upper secondary school: a study of teaches teaching and student learning


Catherine Sackur, Maryse Maurel and Teresa Assude
    Are my students actually doing mathematics?


Ilya Sinitsky
    Pre-algebra combinatorial problems and algorithms in primary school mathematics


Anna S. Steinweg
    `…the partner of 4 is plus 10 of this partner’ – Young children make sense of tasks on functional relations


Michal Tabach and Alex Friedlander
    The role of context in learning beginning algebra


Jukka Törnroos
    Finns and algebra in TIMSS 1999


Thematic Working Group 7

Geometrical Thinking

Jean-Luc Dorier, Ángel Gutiérrez and Rudolf Strässer
Geometrical thinking (Introduction)

All TG7 papers
Claudia Margarita Acuña-Soto
The role of slope and y-intercept from the students perspective


Maria Bako
Different projecting methods in teaching spatial geometry


Nitsa Cohen
Preference of directions in 3-D space


Ghislaine Gueudet-Chartier
Geometric thinking in a n-space


Eszter Herendiné Kónya
The concept of orientation


Catherine Houdement, Alain Kuzniak
Elementary geometry split into different geometrical paradigms


Frantisek Kurina
Geometry – the Resource of Opportunities


Nicoletta Lanciano
The processes and difficulties of teachers trainees in the construction of concepts, and related didactic material, for teaching geometry


Victor Larios-Osorio
Geometrical rigidity: an obstacle in using dynamic geometry software in a geometry course


Marie-Jeanne Perrin-Glorian
Studying geometric figures at primary schools – From surfaces to points


Magdalena Prokopová
Students’ conception of a point: a comparison of phylogenesis and ontogenesis


Christiane Rolet
Teaching and learning plane geometry in primary school: acquisition of a first geometrical thinking


Paola Vighi
The triangle as a mathematical object


Thematic Group 8

Social Interactions in Mathematical Learning Situations

Alison Price
    Social interactions in mathematical learning situations (Introduction)

All TG8 papers
Andreas Andersson
    The discourse of engineering students constructing concept maps in Linear Algebra


Richard Barwell
    Rethorical devices in Mathematics classroom interaction: solving a word problem


Michele Cerulli
    Instruments of semiotic mediation in algebra, an example


Marei Fetzer
    Interaction in collective writing processes and early mathematical learning


Paola Gallopin
    A mathematical project realised in a non formal environment: learning as a social event



Bracha Kramarskiand Zemira Mevarech
    Metacognitive discourse in mathematics classrooms


Michela Maschietto
    The use of perpectographs in primary school: artefacts, instruments and semiotic mediation


Alison Price
    Establishing a mathematical community of practice in the primary classroom


Christof Schreiber
    Externalization and inscription in a chat-environment


Ralph Schwarzkopf
    Analysing processes of solving word problems in mathematical lessons interaction: framing and reference context between real world and mathematics



Thematic Working Group 9:

Tools and Technologies in Mathematical Didactics

Keith Jones and Jean-Baptiste Lagrange
    Tools and technologies in mathematical didactics (Introduction)

All TG9 papers
Ferdinando Arzarello andDomingo Paola
    Mathematical objects and proofs within technological environments: an embodied analysis


Giampaolo Chiappini and Maria Reggiani
    Toward a didactic practice based on mathematics laboratory activities


Francisco Delgado and Rubén D. Santiago
    Problem-based learning in sophomore and freshmen engineering students: a four year follow-up


Rossana Falcade
    Instruments of semiotic mediation in cabri for the notion of function


Franco Favilli, Laura Maffei and Irene Venturi
    Traditional sand drawings: proposal for a didactical software


Victor Giraldo and Luiz Mariano Carvalho
    Local straightness and theoretical-computational conflicts: computational tools on the development of the concept image of derivative and limit


Mariam Haspekian
    Between arithmetic and algebra: a space for the spreadsheet? Contribution to an instrumental approach


Rosalyn Hyde and Alison Clark-Jeavons
    MathsALIVE – Developing a technologically-rich learning environment for secondary mathematics


Keith Jones
    Classroom implications of research on dynamic geometry software


Jean-Baptiste Lagrange
    Analysing the impact of ICT on mathematics teaching practices



Daniela Leder
    An experience of the construction of particular didactical tools to learn multiplication



Enrica Lemut
    Software environments supporting and enhancing systemic thinking

Bibi Lins
    Actual meanings, possible uses: secondary mathematics teachers and Cabri-géomètre


Matthias Ludwig, Hans-Georg Weigand, Wolfgang Weigel and Gerald Wittmann
    MaDiN – a framework for internet-supported learning in mathematics teacher education


David Miller, Derek Glover and Doug Averis
    Exposure – the introduction of interactive whiteboard technology to secondary school mathematics teachers in training


Ornella Robutti
    Real and virtual calculator: from measurements to definite integral

Varda Talmon and Michal Yerushalmy
    Dynamic behavior in dynamic geometry environments: some questions of order


Menekse Seden Tapan
    Integration of ICT in the teaching of mathematics in situations for treatment of difficulties in proving


Michal Yerushalmy and Daniel Chazan
    Analyzing changes in student performance: what is the role of technology?


Luciana Zuccheri
    Problems arising in teachers’ education in the use of didactical tools


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)

All TG10 papers
Helle Alrø, Ole Skovsmose and Paola Valero
    Communication, conflict and mathematics education in the multicultural classroom


Bill Barton and Pip Neville-Barton
    Investigating the relationship between English language and mathematical learning


Jeff Bezemer
    Dealing with multilingualism in the arithmetic class. An ethnographic case study fo a Dutch primary school


Philip C. Clarkson
    Australian bilingual students and mathematics


Ed Elbers and Mariëtte de Haan
    The construction of word meaning in a multicultural classroom. Talk and collaboration during mathematics lessons

Franco Favilli, M. Luisa Oliveras and Margarida César
    Maths teachers in multicultural classes: finding from a southern European project


Núria Gorgorió and Núria Planas
    Transitions: from background to foreground

Gabriele Kaiser
    Learning mathematics within the context of linguistic and cultural diversity – an empirical study


Carlo Marchini
    Different cultures of the youngest students about space (and infinity)


Darlinda Moreira
    Portuguese immigrant children and mathematics education

Jarmila Novotná, Hana Moraová, and Marie Hofmannová
    Using original textbooks when teaching mathematics in a foreign language


Daniel Clark Orey
    The algorithm collection project (ACP): the ethnomathematics of basic number sense acquisition across cultures


Sarah O’Toole and Guida de Abreu
    Investigating parent’s explicit and implicit home numeracy practices in multiethnic contexts


Filippo Spagnolo
    Natural language, history and the interpretation of process of learning/teaching


Thematic Working Group 11

Inter-relating Theory and Practice in Mathematics Teacher Education

Barbara Jaworski, Lurdes Serrazina, Andrea Peter Koop and Konrad Krainer
    Inter-relating theory and practice in mathametics teacher education (Introduction)

All TG11 papers
Lucilla Cannizzaro and Marta Menghini
    Geometric figures from middle school to secondary school: mediating theory and practice


Mercedes Garcia, Victoria Sanchez, Isabel Escudero and Salvador Llinares
    The dialectic relationship between theory and practice in mathematics teacher education


Rossella Garuti
    From research in mathematics education to teachers’ training through internet


Lucia Grugnetti and Angela Rizza
    A lengthy process for the establishment of the concept of limit


Alena Hospesova and Marie Ticha
    Self-reflection and improving mathematics classroom culture


Barbara Jaworski
    Inquiry as a pervasive pedagogic process in mathematics education development


Jana Kratochvilova and Ewa Swoboda
    Aspects affecting pupil’s thinking in mathematics during interaction researcher-pupil


Roza Leikin and Sarga Dinur
    Patterns of flexibility: teachers’ behaviour in mathematical discussion


Joao da Ponte, Lurdes Serrazina, Olivia Sousa and Helena Fonseca
    Professionals investigate their own practice


Petra Scherer and Heinz
    The professionalisation of mathematics teachers’ knowledge – Teachers commonly reflect feedbacks to their own instruction activity

Bernd Wollring
    Linking pre-service and in-service teacher training: co-operative design of working environments for primary mathematics


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)

All TG12 papers
Jordi Deulofeu and Lourdes Figueiras
    Inheritance problems in arabic algebra treatises. Can they stimulate future teachers’ beliefs about mathematics?


Ruhama Even and Tali Wallach
    Student assessment: issues for teacher education


Hagar Gal
    Improving teachers’ ability to cope with Problematic learning situations – The case of Eti


Maria Goulding
   How do prospective primary teachers assess their own mathematical knowledge?


Jeremy Hodgen
   Reflection, identity and belief change in primary mathematics


M. Kaldrimidou, H. Sakonidis, M. Tzekaki
   Teachers’ interventions in students’ mathematical work: a classification


Boris Koichu, Abraham Berman and Michael Moore
   Changing teachers’ beliefs about students’ heuristics in problem solving


Nicolina A. Malara
   Future middle school teachers’ beliefs about Algebra: Incidence of the cultural background


Daniela Medici and Maria Gabriella Rinaldi
   A teaching resource for teacher training


Stephanie Prestage and Pat Perks
   Towards a pedagogy of teacher education: from a model for teacher transformation


Laetitia Ravel
   Setting a new curriculum in a classroom: variability and space of freedom for a teacher

Tim Rowland, Anne Thwaites and Peter Huckstep
   Elementary teachers’ mathematics knowledge and choice of examples


Leonor Santos and João Pedro da Ponte
   An experience in distance in-service teacher education


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