E uropean Society for
R esearch in
M athematics
E ducation
Institute for
Cognitive Mathematics

Contents Vol. I
.


European Research in Mathematics Education I.I + I.II
Proceedings of the First Conference
of the
European Society for Research in Mathematics Education, Vol. I + II

Editor: Inge Schwank, 1999
Publishing House: Forschungsinstitut fuer Mathematikdidaktik, Osnabrueck.

 
Internet-Versions Vol. I: ISBN 3-925386-50-5
pdf-file, 2.706 kB, V1.01
  Vol. II: ISBN 3-925386-51-3
pdf-file, 1.321 kB, V1.0
Paper-Versions Vol. I: ISBN: 3-925386-53-X
how to order
  Vol. II: ISBN: 3-925386-54-8
how to order
Overview
including direct link
to complete single
contributions
in pdf-format 		Vol. I: Table of contents I html-file
Abstracts I html-file
Vol. II: Table of contents II html-file
Abstracts II html-file
Contents - Sketch Vol. I: Contents,
Preface, Introduction,
Keynote Addresses,
Group 1 "Nature of Mathematics",
Group 2 "New Technologies",
Group 3 "Teaching Practices",
Group 4 "Social Interactions",
Keywords, Author Index
  Vol. II:

Contents,
Group 5 "Cognition",
Group 6 "School Algebra",
Group 7 "Methodologies",
Keywords, Author Index

 

Contents Vol. I

Preface, Introduction, Keynote Addresses,
Group 1, Group 2, Group 3, Group 4
PREFACE
Inge Schwank
(pdf-file, 51kB)
INTRODUCTION: A NEW EUROPEAN SOCIETY AND ITS FIRST CONFERENCE
Babara Jaworski on behalf of the CERME 1 Programm Committee
  • The Development of the Scientific Programme of CERME1
    • Setting up the groups
    • The Organisation of Group Working
    • Plenary Presentations from Groups
    • Other Sessions at the Conference
  • Constituting ERME
  • Participation in CERME1
  • Publications from the conference
  • Evaluation of CERME1
  • Conference Programme Committee

(pdf-file, 54kB)

Keynote Addresses

RESEARCH IN MATHEMATICS EDUCATION OBSERVATION AND ... MATHEMATICS
Guy Brousseau

  • Introduction
  • Subject of research
  • Forms of Observation
    • The Subject of Observation
    • Passive observation
    • The educative action, research - action
    • A form of research in didactics: « participatory observation »
  • Relationship between the didactics of mathematics and mathematicians
    • Difficulties and failures of didactic activities
  • Conclusion

(pdf-file, 66kB)

ICH BIN EUROPÄISCH
Jeremy Kilpatrick

  • Retrospect
  • Prospect
  • Science and Doubt
  • Solidarity
  • References

Note:
"ICH BIN EUROPÄISCH": I AM EUROPEAN
In allusion to the famous event:
« Thirty-five years ago this summer, on 26 June 1963, John F. Kennedy came to Germany to speak on the fifteenth anniversary of the Berlin airlift and said, “I am a Berliner.” . . . » (Jeremy Kilpatrick)

(pdf-file, 84 kB)

Group 1:
The Nature and Content of Mathematics and its Relationship to Teaching and Learning

MATHEMATICS AS A CULTURAL PRODUCT
Ferdinando Arzarello (Group-Coordinator), Jean-Luc Dorier, Lisa Hefendehl-Hebeker, StefanTurnau

  • The main issue: mathematics as a cultural product
  • An example
  • The game of Mathematics: knowing and coming to know
  • Some research problems
    • A list of questions
    • An immediate agenda for Working Group 1
  • References

(pdf-file, 53 kB)

SUCCESS AND FAILURE: FINDINGS FROM THE THIRD INTERNATIONAL MATHEMATICS AND SCIENCE STUDY (TIMSS) IN BULGARIA
Kiril Bankov

  • Study and test design
  • Student Achievement
    • Proportionality
    • Algebra
    • Data representation, analysis and probability
  • Summary
  • References    

(pdf-file, 59 kB)

MATHEMATICIANS AND THEIR EPISTEMOLOGIES - AND THE LEARNING OF MATHEMATICS
Leone Burton

  • Introduction
  • The person- and cultural/social relatedness of mathematics
  • The aesthetics of mathematical thinking
  • The nurturing of intuition and insight
  • Styles of thinking
  • Connectivities
  • Conclusions
  • References   

(pdf-file, 72 kB)

TEACHING AND LEARNING LINEAR ALGEBRA IN FIRST YEAR OF FRENCH SCIENCE UNIVERSITY
Jean-Luc Dorier, Aline Robert, Jacqueline Robinet, Marc Rogalski

  • General Presentation of the research
  • The case of linear dependence
    • Introduction
    • Historical background
    • Didactical implications
    • A proposition
    • Conclusions
  • References

(pdf-file, 59 kB)

RELATION FUNCTION/ALGEBRA: AN EXAMPLE IN HIGH SCHOOL (AGE 15-16)
Régine Douady

  • Problematic and methodology of the research
  • Successive steps of the engineering
    • Study of polynomial functions (age 15-16)
    • The teaching tradition
    • An epistemological difficulty
    • A didactical hypothesis
    • The role of the cartesian graphical representation
    • A didactical engineering based on frameworks interplay: algebraic-graphical-functions
    • Statements: choices and reasons for the choices
    • Statement given in 2 times
    • Organization of the class and unfolding
    • Statement 2
    • Realization and comments
    • Conclusion, reinvestment
  • References  

(pdf-file, 69 kB)

SOME REMARKS ABOUT ARGUMENTATION AND MATHEMATICAL PROOF AND THEIR EDUCATIONAL IMPLICATIONS
Nadia Douek

  • Introduction
  • About argumentation and proof
    • What argumentation are we talking about?
    • Formal proof
    • Mathematical proof
    • Argumentation in mathematics
    • Reference corpus
    • Tools of analysis and comparison of argumentation and proof
  • Analysis and comparison of argumentation and proof as products
    • About  the reference corpus
    • How to dispel doubts about a statement and the form of reasoning
  • The processes of argumentation and construction of proof
  • Some educational implications
  • References

(pdf-file, 72 kB)

DISCRETE MATHEMATICS IN RELATION TO LEARNING AND TEACHING PROOF AND MODELLING
Denise Grenier, Charles Payan

  • What are discrete mathematics?
  • Didactical transposition of discrete mathematics in France
  • Global research questions
  • Proof and Modelization in Discrete Mathematics
    • An example of proof method : induction
    • Two examples of modelization
    • A particular tool : the Pigeonholes principle
  • Conclusion
  • References

(pdf-file, 641 kB)

STUDENT’S PERFORMANCE IN PROVING: COMPETENCE OR CURRICULUM?
Lulu Healy, Celia Hoyles

  • Aims
  • Method
  • Results
  • Some contrasting views of proof
  • Discussion
  • References 

(pdf-file, 103 kB)

INTERACTION IN THE MATHEMATICS CLASSROOM: SOME EPISTEMOLOGICAL ASPECTS
Andreas Ikonomou, Maria Kaldrimidou, Charalambos Sakonidis, Marianna Tzekaki

  • Introduction
  • Theoretical framework
  • Methodology
  • Presentation of data and discussion
    • Elements of mathematical content
    • Elements of mathematical activity
  • Conclusion
  • References  

(pdf-file, 65 kB)

Group 2:
Tools and Technologies

TOOLS AND TECHNOLOGIES
Angel Gutiérrez, Colette Laborde (Group Coordinator), Richard Noss, Sergei Rakov

  • Tools and Technologies in the Didactics of Mathematics
  • Tools and knowledge
  • Interactions between tool and learner
  • Tools and technologies in the curriculum
  • The papers   

(pdf-file, 45 kB)

CONSTRUCTING MEANING FOR FORMAL NOTATION IN ACTIVE GRAPHING
Janet Ainley, Elena Nardi, Dave Pratt

  • Background
  • Method
  • Analysis
  • Connecting a pattern based on the data with the experiment
  • Connecting patterns based on the data with a rule
  • Connecting a rule based on the data with a formula
  • Constructing meaning for trend and for formal notation
  • References   

(pdf-file, 94 kB)

TRAINING EXPLORATIONS ON NUMERICAL METHODS COURSE USING TECHNOLOGY
Ludmila Belousova, Tatyana Byelyavtseva

  • Introduction
  • Design issues
  • A Course for Numerical Methods
  • Plan Reports
  • Conclusion
  • References 

(pdf-file, 55kB)

CABRI BASED LINEAR ALGEBRA: TRANSFORMATIONS
Tommy Dreyfus, Joel Hillel, Anna Sierpinska

  • A geometric approach to beginning linear algebra
  • The Cabri model for the 2-d vector space: The notion of vector
  • Transformations
  • The students’ conception of transformations
  • Possible sources of the students’ conceptions of transformation
  • Conclusion
  • References  

(pdf-file, 70 kB)

INTEGRATION OF LEARNING CAPABILITIES INTO A CAS: THE SUITES ENVIRONMENT AS EXAMPLE
 Jean-Michel Gélis, Dominique Lenne

  • Preliminary study
    • Domain and methods
    • Identification of difficulties to use a CAS
  • The SUITES environment
    • Functions
    • Basic help
    • Contextual help
  • Evaluation and future work
    • Granularity
    • Integration
  • Conclusion
  • References

(pdf-file, 65 kB)

THE TEACHING OF TRADITIONAL STANDARD ALGORITHMS FOR THE FOUR ARITHMETIC OPERATIONS VERSUS THE USE OF PUPILS’ OWN METHODS
 Rolf Hedrén

  • Introduction
  • Background
  • Previous research
  • My Own Research
  • Some Results
  • Discussion
    • Introduction
    • Advantages of the pupils’ own methods of computation
    • Advantages of the traditional standard algorithms
  • A Final Word
  • References 

(pdf-file, 61 kB)

STUDENT INTERPRETATIONS OF A DYNAMIC GEOMETRY ENVIRONMENT
 Keith Jones

  • Introduction
  • Theoretical Framework
  • Empirical study
  • Examples of student interpretations
    • Example 1
    • Example 2
    • Example 3
    • Example 4
  • Some observations on the examples
  • Concluding remarks
  • References

(pdf-file, 80 kB)

USING PLACE-VALUE BLOCKS OR A COMPUTER TO TEACH PLACE-VALUE CONCEPTS
Peter Price

  • Introduction
  • Physical Materials as Models for Numbers
    • Research Design
    • Research Questions
    • Method
    • Participants
    • The Software
    • Results
  • Discussion
  • References 

(pdf-file, 78 kB)

COURSEWARE IN GEOMETRY (ELEMENTARY, ANALYTIC, DIFFERENTIAL)
Sergei Rakov, V. Gorokh

  • Introduction
  • Examples
  • References

(pdf-file, 242 kB)

SEMITRANSPARENT MIRRORS AS TOOLS FOR GEOMETRY TEACHING
Luciana Zuccheri

  • Laboratory Activities And Didactic Tools
  • A Didactic Tool For Geometry Teaching: The Simmetroscopio
  • The Exhibition “Oltre Lo Specchio” (“Beyond The Mirror”)
  • Some Examples
    • An exercise that mathematicians like
    • A path for describing the composition of
      two planar axial symmetries with parallel axes
  • Conclusion
  • References

(pdf-file, 112 kB)

Group 3:
From a Study of Teaching Practices to Issues in Teacher Education

ON RESEARCH IN MATHEMATICS TEACHER EDUCATION
Konrad Krainer, Fred Goffree

  • Some remarks on “practice”, “teacher education”, and “research in teacher education”
  • Some remarks on the work of Thematic Group 3
  • Short preview of the chapters 1 to 6

(pdf-file, 810kB, CERME 1 - Proceedings, Special Volume)

Group 4:
Social Interactions in
Mathematical Learning Situations

INTRODUCTION
Götz Krummheuer (Group Coordinator)

(pdf-file, 34 kB)

RECIPIENTS IN ELEMENTARY MATHEMATICS CLASSROOM INTERACTION
Birgit Brandt

  • The research project
  • Participation in multi-party-interaction
    • Partnerwork in a multi-party-interaction: an empirical example
  • Participation framework
    • Recipients’ roles in focussed talks
    • Interaction lines
    • Participants competence
  • References

(pdf-file, 530 kB)

NECESSARY MATHEMATICAL STATEMENTS AND ASPECTS OF KNOWLEDGE IN THE CLASSROOM
Jean-Philippe Drouhard, Catherine Sackur, Maryse Maurel, Yves Paquelier, Teresa Assude

  • Introduction
  • The CESAME research group
  • Necessary statements
    • Institutionalisation in Mathematical Discussions
    • Resistance
    • Wittgenstein
    • Awareness
  • Aspects of knowledge
  • Teaching and learning
  • Provisional conclusion
  • References 

(pdf-file, 70 kB)    

THE NARRATIVE CHARACTER OF ARGUMENTATIVE MATHEMATICS CLASSROOM INTERACTION IN PRIMARY EDUCATION
Götz Krummheuer

  • Introduction
  • The social constitution of learning
  • The narrativity of classroom culture
  • An example
  • Social learning conditions in classroom interaction and an implication for enhancing the classroom culture
  • References    

(pdf-file, 66 kB)

HOW SOCIAL INTERACTIONS WITHIN A CLASS DEPEND ON THE TEACHER’S ASSESSMENT OF THE PUPILS VARIOUS MATHEMATICAL CAPABILITIES: A CASE STUDY
Alain Mercier, Gérard Sensevy, Maria-Luisa Schubauer-Leoni

  • Framework
  • Social interactions and acquisition of knowledge within the class of mathematics: the case of Jerome and Louis
  • The mathematical work in didactical game and classroom game
  • References

(pdf-file, 70 kB)

HELP, METAHELPING, AND FOLK PSYCHOLOGY IN ELEMENTARY MATHEMATICS CLASSROOM INTERACTION
Natalie Naujok

  • Working context and project
  • Help and metahelping as forms of student cooperation
  • An empirical example of metahelping
  • Folk psychology and folk pedagogy
  • Summarizing considerations
  • References

(pdf-file, 63 kB)

IT IS NOT JUST ABOUT MATHEMATICS, IT IS ABOUT LIFE: ADDITION IN A PRIMARY CLASSROOM
Alison J. Price

  • Theoretical Background
  • Data collection and analysis
  • The Bus Lesson
  • Conclusion and implications
  • References

(pdf-file, 65 kB)

CESAME: THE PERSONAL HISTORY OF LEARNING MATHEMATICS IN THE CLASSROOM: AN ANALYSIS OF SOME STUDENTS NARRATIVES
Catherine Sackur, Teresa Assude, Maryse Maurel

  • First step
  • Time and Narratives
  • Typology of memories
  • Some examples of narratives
  • Conclusion
  • References    

(pdf-file, 68 kB)

MATHEMATICAL INTERACTION AS AN AUTOPOIETIC SYSTEM: SOCIAL AND EPISTEMOLOGICAL INTERRELATIONS
Heinz Steinbring

  • Mathematics teaching as a social process of communication
  • The characterization of mathematical interaction as an autopoietic system
    • Analysis of the 4. phase: The mathematical interaction with Tarik
    • Analysis of the 5. phase: The mathematical interaction with Svenja
  • Comparing the two interactions from an epistemological perspective
  • Specific issues of mathematical communication processes
  • References

(pdf-file, 83 kB)

ON THE ACTIVATING ROLE OF PROJECTS IN THE CLASSROOM
Marie Tichá, Marie Kubínová

  • Introduction
  • Backgrounds
  • Work on projects
  • Two samples from the work on projects
  • Current experience with projects
  • Intentions for further research
  • References

(pdf-file, 77 kB)

Cerme 1 - Proceedings - Homepage

 
Last modified: 2001 Feb 15.
This site is managed and maintained by Inge Schwank (schwank@mathematik.uni-osnabrueck.de),
who is pleased to get your questions, comments and/or suggestions.
Copyright: Forschungsinstitut fuer Mathematikdidaktik (Research Institute for Mathematics Education), Osnabrueck

 

Statistics: