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 | html format | |
| ERME: history, aims and current organization | html format |
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 |
