CERME 3 Proceedings

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