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CERME 5

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European Research in Mathematics Education V

Originally directed to http://erme-soc.eu/ New site is now http://erme.site

Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education
Larnaca, Cyprus 22 – 26 February 2007
Editors
Demetra Pitta – Pantazi & George Philippou
Department of Education – University of Cyprus
Editorial board
Ainley J., Arcavi A., Arzarello F., Bagni G. T., Bardini C., Barzel B., Biehler R., Bills L., Blomhoj M., Bosch M., Cabassut R., Carrillo J., Cesar M., Douek N., deAbreu G., Durand-Guerrier V., Ferrari P. L., Gagatsis A., García J., Gorgorio N., Hannula M., Hejny M., Hemmi K., Jablonka E., Jaworski, B., Kadijevic D., Kadunz G., Kaiser G., Krummheuer G., Kuzniak A., Kvasz L., Kynigos C., Leikin R., Lenfant A., Littler G. H., Ludwig M., Mammona-Downs J., Marchini C., Marchive A., Marriotti M., Maschietto M., Meehan M., Meletiou-Mavrotheris M., Morgan C., Op’t Eynde P., Ottaviani M., Parzysz B., Pepin B., Perez D., Pratt D., Prediger S., Puig L., Robotti E., Rogers L., Santos L., Schöglmann W., Sriraman B., Straesser, R., Wedege T.
Editing assistance
Kallia Mattheou & Nicholas Mousoulides
© Copyright 2007 left to the authors
ISBN 978-9963-671-25-0
 
TABLE OF CONTENTS
INTRODUCTION
xvi
Rudolf Straesser, Barbara Jaworski
PLENARIES
1
Plenary 1
Balancing interest in Fundamental understanding with considerations of usefulness in mathematics education research
2
Frank K. Lester
Plenary 2
What constitutes good practice in teaching mathematics, a personal perspective
24
Naďa Stehlíková
Plenary 3
Teachers, technologies and the structures of schooling
52

Kenneth Ruthven

Plenary 4
Digital technologies: A window on theoretical issues in mathematics education
68

Michèle Artigue

WORKING GROUP 1. The role of images and metaphors in the learning and understanding mathematics
83
The role of images and metaphors in the learning and understanding mathematics (including embodied cognition)
84

Bernard Parzysz, Gert Kadunz, Elisabetta Robotti, Leo Rogers

Exploring the effects of representations on the learning of statistics in Greek primary school
90
Sofia Anastasiadou, Athanasios Gagatsis
Guess what is inside this box: Look at these opened boxes for clues
101
Roberto Araya
The number line as metaphor of the number system: A case study of a primary school
111
Maria Doritou, Eddie Gray
Ways of thinking about the uses of images in learning and teaching geometry: A more thorough investigation of the links between drawings and figures
121
Sophie Gobert
Mathematical Writing
131
Gert Kadunz
Students’ and teachers’ representations in problem solving
141
Annita Monoyiou, Pandelitsa Papageorgiou, Athanasios Gagatsis
The role of the conceptual metaphor in the development of children’s arithmetic
151
Carol Murphy
The power and perils of metaphor in making internal connections in trigonometry and geometry
161
Norma Presmeg
Metaphors and image schemata in concept formation and reasoning
171
Reinert A. Rinvold
Teaching special relativity
181
Leo Rogers, Patrick J. Caines
Metaphors and cognitive modes in the teaching-learning of mathematics
191
Jorge Soto-Andrade
WORKING GROUP 2. Affect and mathematical thinking
201
Affect and mathematical thinking
202
Markku S. Hannula, Peter Opt’Eynde, Wolfgang Schlöglmann, Tine Wedege
Evaluating the sensitivity of the refined mathematics-related beliefs questionnaire to nationality, gender and age
209
Paul Andrews, Jose Diego –Mantecón, Peter Op ‘t Eynde, Judy Sayers
Students’ motivation in mathematics and gender differences in grades 6 and 7
219
Chryso Athanasiou, George Philippou
Refining the mathematics-related beliefs questionnaire (MRBQ)
229
Jose Diego-Mantecón, Paul Andrews, Peter Op ‘t Eynde
Mathematics teachers’ desire to develop
239
Markku S. Hannula, Madis Lepik, Tiiu Kaljas
Mathematics is – favourite subject, boring or compulsory
248
Kirsti Hoskonen
Students’ beliefs and attitudes concerning mathematics and their effect on mathematical ability
258
Eleftherios Kapetanas, Theodosios Zachariades
The notion of children’s perspectives
268
Troels Lange
Belief change as conceptual change
278
Peter Liljedahl, Katrin, Rolka, Betinna Rösken
Changes in students’ motivational beliefs and performance in a self-regulated mathematical problem-solving environment
288
Andri Marcou, Stephen Lerman
About mathematical belief systems awareness
298
Manuela Moscucci
Efficacy beliefs, problem posing, and mathematics achievement
308
Aristoklis A. Nicolaou, George N. Philippou
Students’ self regulation of emotions in mathematics learning
318
Peter Op ‘t Eynde, Erik De Corte, Inge Mercken
The impact of recent metacognitive experiences on preservice teachers’ self-representation in mathematics and its teaching
329

Areti Panaoura

Is motivation analogous to cognition?
339
Marilena Pantziara, Demetra Pitta-Pantazi, GeorgePhilippou
Identifying dimensions of students’ view of mathematics
349
Bettina Rösken, Markku Hannula, Erkki Pehkonen, Raimo Kaasila, Anu Laine
Student errors in task-solving processes
359
Wolfgang Schlöglmann
Influence of didactical games on pupils’ attitudes towards mathematics and process of its teaching
369
Peter Vankúš
Intrinsic and extrinsic motivation versus social and instrumental rationale for learning mathematics
379
Kjersti Wæge
Potential for change of views in the mathematics classroom?
389
Tine Wedege, Jeppe Skott
WORKING GROUP 3. Building structures in mathematical knowledge
399
Building structures in mathematical knowledge
400
Milan Hejný, Graham Littler
Constructing Multiplication: Different strategies used by pupils
407
Joana Brocardo, Lurdes Serrazina, Isabel Rocha
Students’ thinking about fundamental real numbers properties
416
Eustathios Giannakoulias, Alkeos Souyoul, Theodossios Zachariades
Schema A ± B = C as the basis of arithmetic structure
426
Milan Hejný, Jana Slezáková
Recognising an algebraic structure
436
Maureen Hoch, Tommy Dreyfus
Creating a mental image of dice blackjack game
446
Antonín Jančařík
Classification, manipulation and communication: Work with pupils and student teachers
456
Darina Jirotková, Graham H. Littler
Investigating the processing structures of students’ inductive reasoning in mathematics
466
Eleni Papageorgiou, Constantinos Christou
Empirical Hierachy of pupils’ attainment of measurement in early primary school years
476
Alexandra Petridou, Maria Pampaka, Constantia Hadjidemetriou
How do students from primary school discovery the regularity
486
Marta Pytlak
Reflection on activity – effect relationships in solving word problems
496
Ana Isabel Roig, Salvador Llinares
Children’s perceptions on infinity: Could they be structured?
506
Mihaela Singer, Cristian Voica
The role of spatial configurations in early numeracy problems
516
Fenna Van Nes, Jan de Lange
Students’ ability in solving line symmetry tasks
526
Xenia Xistouri
WORKING GROUP 4. Argumentation and proof
536
Argumentation and proof
537
Maria Alessandra Mariotti, Kirsti Hemmi, Viviane Durrand Guerrier
Indirect proof: An interpreting model
541
Samuele Antonini, Maria Alessandra Mariotti
Mathematics learning and the development of general deductive reasoning
551
Michal Ayalon, Ruhama Even
How to decide? Students’ ways of determining the validity of mathematical statements
561
Orly Buchbinder, Orit Zaslavsky
Cabri’s role in the task of proving within the activity of building part of an axiomatic system
571
Leonor Camargo, Carmen Samper, Patricia Perry
Some remarks on the theorem about the infinity of prime numbers
581
Ercole Castagnola, Roberto Tortora
Proofs problems in elementary number theory: Analysis of trainee teachers’ productions
591
Annalisa Cusi, Nicolina A. Malara
Relationship between beginner teachers in mathematics and the mathematical concept of implication
601
Virginie Deloustal-Jorrand
Using the Van Hiele theory to analyse the teaching of geometrical proof at grade 8 in Shanghai
612
Liping Ding, Keith Jones
Analysis of conjectures and proofs produced when learning trigonometry
622
Jorge Fiallo, Angel Gutiérrez
Analysis of the teacher’s arguments used in the didactical management of a problem solving situation
633
Patrick Gibel
Structural relationships between argumentation and proof in solving open problems in algebra
643
Bettina Pedemonte
Mathematical proof: Teachers’ beliefs and practices
653
Antonis Sergis
The mental models theory of deductive reasoning: Implications for proof instruction
665
Andreas J. Stylianides, Gabriel J. Stylianides
Reviewing textbook proofs in class: A struggle between proof structure, components and details
675
Stine Timmermann
WORKING GROUP 5. Stochastic Thinking
685
Developing stochastic thinking
686
Rolf Biehler, Maria Meletiou, Maria Gabriella Ottaviani, Dave Pratt
Understanding confidence intervals
692
Herman Callaert
Conditional probability problems and contexts. The diagnostic test context
702
Marta Carles, Μ. Pedro  Huerta
A microworld to implant a germ of probability
712
Michele Cerulli, Augusto Chioccariello, Enrica Lemut
The impact of a typical classroom practice on students’ statistical knowledge
722
Andreas Eichler
The “same” problem in three presentation formats: Different percentages of success and thinking processes
732
Μ. Pedro Huerta, Μα Ángeles Lonjedo
The relationship between local and global perspectives on randomness
742
Peter Johnston-Wilder, Dave Pratt
Transparent urns and colored tinker – cubes for natural stochastics in primary school
752
Laura Martignon, Kathryn Laskey, Elke Kurz-Milcke
Constructing stochastic simulations with a computer tool – Students’ competencies and difficulties
762
Carmen Maxara, Rolf Biehler
A cross – national comparison of introductory statistics students’ prior knowledge of graphs
772
Maria Meletiou-Mavrotheris, Carl Lee
Sample space and the structure of probability combinations in preschoolers
782
Zoi Nikiforidou, Jenny Pange
Looking for randomness in tasks of prospective teachers
791
Efi Paparistodemou, Despina Potari, Demetra Pitta
Making connections between the two perspectives on distribution
801
Theodosia Prodromou
WORKING GROUP 6. Algebraic Thinking
811
Working on algebraic thinking
812
Luis Puig, Janet Ainley, Abraham Arcavi, Giorgio Bagni
Research impacting on student learning: How construction tasks influenced learners’ thinking
816
Shafia Abdul-Rahman
Elementary school students’ understanding and use of the equal sign
825
Vassiliki Alexandrou-Leonidou, George Philippou
A contribution of ancient Chinese algebra: Simultaneous equations and counting rods
835
Giorgio T. Bagni
Patterns and generalization: the influence of visual strategies
844
Ana Barbosa, Pedro Palhares, Isabel Vale
Matrices as Peircean diagrams: A hypothetical learning trajectory
852
Willibald Dörfler
Do you see what I see? Issues arising from a lesson on expressing generality
862
Helen Drury
Signs used as algebraic tools – A case study
872
Astrid Fischer
Problems of a linear kind: From Vallejo to Peacock
882
Bernardo Gómez
Developmental assessment of algebraic performance
893
Constantia Hadjidemetriou, Maria Pampaka, Alexandra Petridou, Julian Williams, Lawrence Wo
Integrating the learning of algebra with technology at the European level: Two examples in the ReMath project
903
Jean-Baptiste Lagrange, Giampaolo Chiappini
Research and practice in algebra: Interwoven influences
913
John Mason
Distinguishing approaches to solving true/false number sentences
924
Marta Molina, Encarnación Castro, John Mason
Student difficulties in understanding the difference between algebraic expressions and the concept of linear equation
934
Irini Papaieronymou
Teachers’ practices with spreadsheets and the development of algebraic activity
944
Kirsty Wilson, Janet Ainley
WORKING GROUP 7. Geometrical Thinking
954
From geometrical thinking to geometrical work
955
Alain Kuzniak, Athanasios Gagatsis, Matthias Ludwig, Carlo Marchini
The use of everyday objects and situations in mathematics teaching: The symmetry case in French geometry teaching
962
Caroline Bulf
Geometrical working space, a tool for comparison
972
Catherine Houdement
Comparison of observation of new space and its objects by sighted and non-sighted pupils
982
Iveta Kohanová
Assessing the attainment of analytic – descriptive geometrical thinking with new tools
992
George Kospentaris, Panagiotis Spyrou
Horizon as epistemological obstacle to understanding infinity
1002
Magdalena Krátká
Geometrical ridigity and the use of dragging in a dynamic geometry environment
1012
Victor Larios-Osorio
The utilisation of video enriched microworlds based on dynamic geometry environments
1022
Markus Mann, Matthias Ludwig
Geometrical tiles as a tools for revealing structures
1032
Carlo Marchini, Paola Vighi
The process of composition and decomposition of geometric figures within the frame of dynamic transformations
1042
Christos Markopoulos, Despina Potari, Eftychia Schini
Problem solving in geometry: The case of the illusion of proportionality
1052
Modestina Modestou, Iliada Elia, Athanasios Gagatsis, Giorgos Spanoudes
Spatial abilities in relation to performance in geometry tasks
1062
Georgia Panaoura, Athanasios Gagatsis, Charalambos Lemonides
Spatial ability as a predictor of students’ performance in geometry
1072
Marios Pittalis, Nicholas Mousoulides, Constantinos Christou
Computer geometry as mediator of mathematical concepts
1082
Paola Vighi
WORKING GROUP 8. Language and Mathematics
1092
Multiple perspectives on language and mathematics: Introduction and post – script
1094
Candia Morgan, Konstantinos Tatsis, Hana Moraová, Jarmila Novotná, Margarida César, Birgit Brandt, Elmar Cohors-Fresenborg, Christa Kaune
Driving spontaneous processes in mathematical tasks
1109
Rossella Ascione, Maria Mellone
Communities of practice in online mathematics discussion boards: Unpicking threads
1119
Jenni Back, Nick Pratt
Pupils’ mathematical reasoning expressed through gesture and discourse: A case study from a sixth-grade lesson
1129
Raymond Bjuland, Maria Luiza Cestari, Hans Erik Borgersen
How mathematical signs work in a class of students with special needs: Can the interpretation process become operative?
1140
Isabelle Bloch
Analyzing the constructive function of natural language in classroom discussions
1150
Paolo Boero, Valeria Consogno
Assessment in the mathematics classroom. Studies of interaction between teacher and pupil using a multimodal approach
1160
Lisa Björklund Boistrup
Certainty and uncertainty as attitudes for students’ participation in mathematical classroom interaction
1170
Birgit Brandt
Modelling classroom discussions and categorizing discursive and metacognitive activities
1180
Elmar Cohors-Fresenborg, Christa Kaune
The language of friendship: Developing sociomathematical norms in the secondary school classroom
1190
Julie-Ann Edwards
The use of a semiotic model to interpret meanings for multiplication and division
1200
Marie Therese Farrugia
“Why should I implement writing in my classes?” An empirical study on mathematical writing
1210
Marei Fetzer
Issues in analysis of individual discourse concurrent with solving a mathematical problem
1220
Boris Koichu
Authority relations in the acquisition of the mathematical register at home and at school
1230
Tamsin Meaney
Idea generation during mathematical writing: Hard work or a process of discovery?
1240
Morten Misfeldt
Students’ mathematical interactions and teachers’ reflections on their own interventions.
Part1: Epistemological analysis of students’ mathematical communication
1250
Marcus Nührenbörger, Heinz Steinbring
Students’ mathematical interactions and teachers’ reflections on their own interventions.
Part 2: Analysis of the collegial reflection on students’ mathematical communication
1260
Marcus Nührenbörger, Heinz Steinbring
Children’s talk about mathematics and mathematical talk
1270
Päivi Perkkilä, Eila Aarnos
The influence of learners’ limited language proficiency on communication obstacles in bilingual teaching/learning of mathematics
1280
Jana Petrová, Jarmila Novotná
A question of audience, a matter of address
1290
David Pimm, Ruth Beatty, Joan Moss
Selected problems in communication between the teacher and the pupil explored from the semiotic viewpoint
1300
Filip Roubíček
Obstacles in mathematical discourse during researcher – student interaction
1301
Jana Slezáková, Ewa Swoboda
Writing mathematics through dominant discourses: The case of a Greek school mathematics magazine
1311
Anastasia G. Stamou, Anna Chronaki
Investigating the influence of social and sociomathematical norms in collaborative problem solving
1321
Konstantinos Tatsis
WORKING GROUP 9. Tools and technologies in mathematical didactics
1331
Tools and technologies in mathematical didactics
1332
Chronis Kynigos, Caroline Bardini, Bärbel Barzel, Michela Maschietto
Teacher´s practices and degree of ICT integration
1339
Teresa Assude
Integration of computer algebra in an open learning environment
1349
Bärbel Barzel
Teaching analysis in dynamic geometry environments
1359
Irene Biza, Dionissis Diakoumopoulos, Alkeos  Souyoul
Online resources in mathematics: Teachers’ genesis of use
1369
Laetitia Bueno-Ravel, Ghislaine  Gueudet
Strange 3D plots
1379
Thierry Dana-Picard, Ivy Kidron, David Zeitoun
Tool use in a technology – Rich learning arrangement for the concept of function
1389
Paul Drijvers, Michiel  Doorman, Peter Boon, Sjef  van Gisbergen, Koeno Gravemeijer
Analysis of teacher education in mathematics and ICT
1399
Fabien Emprin
Developing tasks and teaching with ICT in mathematics in an inquiry community
1409
Anne Berit Fuglestad
Technology that mediates and participates in mathematical cognition
1419
Stephen Hegedus, Sara Dalton, Luis Moreno-Armella
Three dimensional constructions using an absolute frame of reference in a computer simulated 3D space
1429
Chronis Kynigos, Efi Alexopoulou, Maria Latsi
Change in perception of prospective teachers regarding the image of the teacher as a result of engagement in a computerized environment
1439
Ilana Lavy, Atara Shriki
Mathematics learning with the use of the balance, a computer programme from enciclomedia
1449
María-Dolores Lozano, María  Trigueros
Memorizing algebraic formulas: The support of a microworld
1460
Laura Maffei, Maria Alessandra Mariotti
Flexibility and cooperation: Virtual learning environments in online undergraduate mathematics
1470
Morten Misfeldt, Anders  Sanne
Algebraic modelling using a dynamically linked geometry and computer algebra system
1480
Reinhard Oldenburg
Cognitive styles, dynamic geometry and performance in area tasks
1489
Demetra Pitta-Pantazi, Constantinos Christou
Meanings for fraction as number-measure by exploring the number line
1499
Giorgos Psycharis, Maria Latsi, Chronis Kynigos
To sense and to visualize functions: The case of graph stretching
1509
Geula Sever, Michal Yerushalmy
Tools that force reflection
1519
Yianna Sirivianou, John  Threlfall
Educational software based on the theory of constructivism
1531
Mária Slavíčková
Teaching with a symbolic calculator – The first years of a long-term project
1540
Hans-Georg Weigand
WORKING GROUP 10. Mathematics education in multicultural settings
1550
Researching diversity in mathematics education
1551
Margarida César, Guida de Abreu, Núria Gorgorió
Social representations and multicultural mathematics teaching and learning
1559
Guida de Abreu, Núria Gorgorió
Landscapes of learning in a multicultural mathematics classroom
1567
Helle Alrø, Ole Skovsmose, Paola Valero
Young children’s number sense in China, England and Finland
1577
Pirjo Aunio, Carol Aubrey, Ray Godfrey, Yan Liu, Pan Yuejuan
Filling the gap between global and local mathematics
1587
Darlinda Moreira
Multiple identities in the mathematics classroom: A theoretical perspective
1597
Diana Stentoft
Storying mathematical identities with cultural models
1607
Julian Williams, Laura Black, Paul Hernandez-Martinez, Paulin Davis, Graeme Hutcheson, Su Nicholson, Maria Pampaka, Geoff Wake
WORKING GROUP 11. Different theoretical perspectives and approaches in research in mathematics education
1617
Different theoretical perspectives in research from teaching problems to research problems
1618
Ferdinando Arzarello, Marianna Bosch, Agnès Lenfant, Susanne Prediger
Ostensives through the lenses of two theoretical frameworks
1628
Ferdinando Arzarello, Ornella Robutti, Cristina Sabena
How do theories influence the research on teaching and learning limits of functions?
1638
Christer Bergsten
Integrating research teams: The TELMA approach
1648
Michele Cerulli, Jean Philippe Georget, Mirko Maracci, Giorgos Psycharis, Jana Trgalova
Construction of knowledge by primary pupils: The role of whole-class interaction
1658
Thérèse Dooley
Emergence or structure: A comparison of two sociological perspectives on mathematics classroom practice
1668
Uwe Gellert
An activity theory perspective of didacticians’ learning within a mathematics teaching development research project
1678
Simon Goodchild
Theory in developmental research in mathematics teaching and learning: Social practice theory and community of inquiry as analytical tools
1688
Barbara Jaworski
On the nature of the mathematical knowledge under construction in the classroom
1698
Maria Kaldrimidou, Haralambos Sakonidis, Marianna Tzekaki
Social interaction in learning processes as seen by three theoretical frameworks
1708
Ivy Kidron, Agnès Lenfant, Angelika Bikner-Ahsbahs, Michèle Artigue, Tommy Dreyfus
Students’ difficulties in vector spaces theory from two different theoretical perspectives
1725
Mirko Maracci
Using mixed-methods methodology to investigate Cypriot preservice teachers’ mathematics content knowledge
1735
Marilena Petrou
From teaching problems to research problems. Proposing a way of comparing theoretical approaches
1745
Susanne Prediger, Kenneth Ruthven
Towards a cultural theory of learning
1782
Luis Radford
An anthropological approach to metacognition: The “study and research courses”
1798
Esther Rodríguez, Marianna Bosch, Josep Gascón
Conditions and constraints in the teaching of statistics: The scale of levels of determination
1808
Floriane Wozniak
WORKING GROUP 12. From a study of teaching practices to issues in teacher education
1819
From a study of teaching practices to issues in teacher education
1821
José Carrillo, Leonor Santos, Liz Bills, Alain Marchive
Teachers’ activity in exercises-based lessons. Some case studies
1827
Maha Abboud-Blanchard, Claire Cazes, Fabrice Vandebrouck
Expressing generality: Focus on teachers’ use of algebraic notation
1837
Claire Vaugelade Berg
Striving to “know what is to be done”: The role of the teacher
1847
Laurinda Brown, Alf Coles
“You don’t need a tables book when you have butter beans!” Is there a need for mathematics pedagogy here?
1856
Dolores Corcoran
Facilitate research activities at the primary level: Intentional communities of practice, teaching practices, exchanges about these practices
1866
Jean-Philippe Georget
Adapting the hypothetical learning trajectory notion to secondary preservice teacher training
1876
Pedro Gómez, Maria José González, Jose Luis Lupiáñez
Formative assessment: Tools for transforming school mathematics towards a dialogic practice?
1886
Jeremy Hodgen
Developing strategies and materials impact on teacher education
1896
Marie Hofmannová, Jarmila Novotná
Differences and similarities in (qualified) pedagogical reflection
1906
Alena Hošpesová, Marie Tichá, Jana Macháčková
Pre-service teachers’ representations of division of fractions
1916
Mine Isiksal, Erdinc Cakiroglu
A task aimed at leading teachers to promoting a constructive early algebra approach
1925
Nicolina A. Malara, Giancarlo Navarra
The professional development of a novice teacher in a collaborative context: An analysis of classroom practice
1935
Maria Cinta Muñoz-Catalán, José Carrillo, Nuria Climent
From studies of cooperative learning practices towards a model of intervention on mathematics teachers
1945
Angela Pesci
Teachers’ mathematical knowledge and pedagogical practices in the teaching of derivative
1955
Despina Potari, Theodosis Zachariades, Constantinos Christou, George Kyriazis, Demetra Pitta-Pantazi
Prospective primary teachers’ use of mathematics teaching handbooks
1965
Tim Rowland
The project work and the collaboration on the initial teacher training
1974
Leonor Santos, Alexandra Bento
Primary teachers’ attitudes towards and beliefs about mathematics teaching: the collective culture of one English primary school
1984
Judy Sayers
The teaching modes: A conceptual framework for teacher education
1994
Rosa Antónia Tomás Ferreira
The mathematics content knowledge of beginning teachers: The case of Amy
2004
Fay Turner
Training mathematics teachers in a community of learners (COL)
2014
Nellie C. Verhoef, Cees Terlouw
Exemplification in the mathematics classroom: What is it like and what does it imply?
2024
Iris Zodik, Orit Zaslavsky
WORKING GROUP 13. Modelling and applications
2034
Modelling and applications – Differentiating perspectives and delineating commonalties
2035
Gabriele Kaiser, Bharath Sriraman, Morten Blomhøj, Fco. Javier Garcia
Understanding of “modelling”
2042
Mette Andresen
Using research and study courses for teaching mathematical modelling at university level
2050
Berta Barquero, Marianna Bosch, Josep Gascón
The teaching calculus with applications experiment succeeded – Why and what else?
2060
Abraham Berman, Igor M. Verner, Shuki Aroshas
Learning the integral concept through mathematical modelling
2070
Morten Blomhøj, Tinne Hoff Kjeldsen
Personal experiences and extra-mathematical knowledge as an influence factor on modelling routes of pupils
2080
Rita Borromeo Ferri
Making mathematical literacy a reality in classrooms
2090
Hugh Burkhardt
Modelling bungy jumping: Why is it so difficult?
2100
Ana Paula Canavarro
Mathematical modelling and parallel discussions
2101
Jonei Cerqueira Barbosa
Comparison of mathematization in microcomputer based laboratory (MBL) and verification – Type laboratory (VTL) in physics
2110
Murad Jurdak, Saouma BouJaoude, Norma Ghumrawi
Modelling tasks for low achieving students – First results of an empirical study
2120
Katja Maaß
Tracing students’ modelling processes in elementary and secondary school
2130
Nicholas Mousoulides, Bharath Sriraman, Marios Pittalis, Constantinos Christou
A meta-perspective on the nature of modelling and the role of mathematics
2140
Irit Peled
The role of mathematical knowledge in a practical activity: Engineering projects at university level
2150
Avenilde Romo Vázquez
Derivatives in applications: How to describe students’ understanding
2160
Gerrit Roorda, Pauline Vos, Martin Goedhart
The functional algebraic modelling at Secondary level
2170
Noemí Ruiz, Marianna Bosch, Josep Gascón
Mathematical modelling in school – Experiences from a project integrating school and university
2180
Björn Schwarz, Gabriele Kaiser
Personal meaning in relation to modelling problems
2190
Katrin Vorhölter
Interpreting velocity and stopping distance; complementarity, context and mathematics
2200
Pauline Vos, Gerrit Roorda
Measuring perceived self-efficacy in applying mathematics
2210
Geoff D. Wake, Maria Pampaka
WORKING GROUP 14. Advanced mathematical thinking
2220
Advanced mathematical thinking
2221
Joanna Mamona-Downs
Lagrange’s theorem: What does the theorem mean?
2231
Buma Abramovitz, Miryam Berezina, Abraham Berman, Ludmila Shvartsman
University students generating examples in real analysis: Where is the definition?
2241
Samuele Antonini, Fulvia Furinghetti, Francesca Morselli, Elena Tosetto
Is there equality in equation?
2250
Iiris Attorps, Timo Tossavainen
Analysis of the autonomy required from mathematics students in the French lycee
2260
Corine Castela
Local and global perspectives in problem solving
2270
Martin Downs, Joanna Mamona-Downs
The application of the abductive system to different kinds of problems
2280
Elisabetta Ferrando
University students’ difficulties with formal proving and attempts to overcome them
2290
Justyna Hawro
The interplay between syntactic and semantic knowledge in proof production: Mathematicians’ perspectives
2300
Paola Iannone, Elena Nardi
Belief bias and the study of mathematics
2310
Matthew Inglis, Adrian Simpson
Students’ concept development of limits
2320
Kristina Juter
Habits of mind associated with advanced mathematical thinking and solution spaces of mathematical tasks
2330
Roza Leikin
Mathematical background and problem solving: How does knowledge influence mental dynamics in game theory problems?
2340
Francesca Martignone
Student generated examples and the transition to advanced mathematical thinking
2349
Maria Meehan
Understanding of systems of equations in linear algebra
2359
Maria Trigueros
Students’ choices between informal and formal reasoning in a task concerning differentiability
2369
Antti Viholainen
Interplay between research and teaching from the perspective of mathematicians
2379
Carl Winsløw, Lene Møller Madsen
Advancing mathematical thinking: Looking back at one problem
2389
Rina Zazkis, Mark Applebaum
WORKING GROUP 15. Comparative studies in mathematics education
2398
Comparative Studies in mathematics education – comparing the incomparable?
2399
Birgit Pepin, Eva Jablonka, Richard Cabassut
Development of the mathematics education system in Iceland in the 1960s in comparison to three neighbouring countries
2403
Kristín Bjarnadóttir
Policy change, graphing calculators and ‘High stakes examinations: A view across three examination systems
2413
Roger G. Brown
Examples of comparative methods in the teaching of mathematics in France and in Germany
2423
Richard Cabassut
Types of algebraic activities in two classes taught by the same teacher
2433
Tammy Eisenmann, Ruhama Even
Proportion in school mathematics textbooks: A comparative study
2443
João Pedro da Ponte, Sandra Marques
Factors related to students’ mathematical literacy in Finland and Sweden
2453
Jukka Törnroos
A comparative study of assessment activity involving 8 pre-service teachers: What referent for the assessor?
2463
Marc Vantourout
The construction of personal meaning – A comparative case study in Hong Kong and Germany
2473
Maike Vollstedt

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