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. II
Group 5, Group 6, Group 7

MATHEMATICAL THINKING AND LEARNING AS COGNITIVE PROCESSES
Inge Schwank, Emanuila Gelfman, Elena Nardi

• The Nature of Cognitive Structures - Introduction and Overview
  • General framework
  • Individual Preferences - Predicative versus Functional Cognitive Structures
  • Cognitive Experiences - Information Coding
• Individual Styles of Cognition
• Cognition and Emotion / Motivation
• Cognition and Language
• Cognition and New Technologies
• Mathematical Thinking in Modern Conditions - Situated Cognition
• Benefit and Outcome of the Working Group

(pdf-file, 84 skB)

COOPERATIVE PRINCIPLES AND LINGUISTIC OBSTACLES IN ADVANCED MATHEMATICS LEARNING
Pier Luigi Ferrari

• Introduction
• The Interpretation of Inequality Symbol
• A Divisibility Problem
• Terms and Objects
  • The Role of Problem Presentation in Problem Solving
  • Some Results
• Discussion
• References

(pdf-file, 77 kB)

THE ROLE OF WAYS OF INFORMATION CODING IN STUDENTS' INTELLECTUAL DEVELOPMENT
Emanuila Gelfman, Marina Kholodnaya

• Introduction
• Ways of Information Coding as One of the Conditions of Growth of Conceptual Competence
• Ways of Information Coding as One of Conditions of Individualisation of Intellectual Activity
• Conclusion
• References

(pdf-file, 108 kB)

ON TEACHING STUDENTS TO WORK WITH TEXT BOOKS
Emanuila Gelfman, Raissa Lozinskaia, Galina Remezova

• References

(pdf-file, 46 kB)

PROJECTS AND MATHEMATICAL PUZZLES - A TOOL FOR DEVELOPMENT OF MATHEMATICAL THINKING
Marie Kubinova, Jarmila Novotna, Graham H Littler

• Introduction
• Our Approach to Projects
• What Is a Project
  • Work With Projects
  • Work With Our Tasks
• Conclusions
• References

(pdf-file, 66 kB)

THREE-TERM COMPARISONS
Pearla Nesher, Sara Hershkovitz, Jarmila Novotna

• The Problems
• Analysis of the Problems
• Variables Involved in the Study
  • The Compared and the Reference
  • "More Than" or "Less Than"
  • The Underlying Scheme
  • The Variables of the Study
• The Experiment
• Findings
  • Strategies
• References

(pdf-file, 65 kB)

TEACHER STUDENTS' RESEARCHES ON COGNITIVE ACTIVITY WITH TECHNOLOGIE
Tatyana Oleinik

• Introduction
• Background
• The Experiments and Method
  • Some Remarks About Essence of Students' Researches
• Some Preliminary Results
• References

(pdf-file, 57 kB)

ON PREDICATIVE VERSUS FUNCTIONAL COGNITIVE STRUCTURES
Inge Schwank

• Introduction
• Predicative versus Functional Cognitive Structures
• Examples
  • Fitting Figures in Matrices: QuaDiPF
• EEG-Study
• Eye Movement - Reflections
• Outlook
• References

(pdf-file, 199 kB)

WINNING BELIEFS IN MATHEMATICAL PROBLEM SOLVING
Rosetta Zan, Paola Poli

• Introduction
• Method
• Results
• Conclusions
• References

(pdf-file, 51 kB)

Synthesis of the Activities of WG-6 at CERME 1
Paolo Boero

• General Information
• Methodology
• Summary of Discussions
  • The Nature of Algebra Related to the Teaching of Algebra
  • Arithmetic and Algebra 108 Tools of Research in Teaching and Learning of Algebra
  • Equations
  • Construction and Interpretation of Algebraic Expressions Related to Other Domains
• General Comments

(pdf-file, 37 kB)

ON THE CONSTRUCTION AND INTERPRETATION OF SYMBOLIC EXPRESSIONS
Luciana Bazzini

• The problem's Position
• The Teaching Experiment
  • Problem I: Analysis of the Students' Answers
  • Problem II: Analysis of the Students' Answers
  • Question I): Analysis of the Students' Answers
  • Question II): Analysis of the Students' Answers
• Final Remarks
• References

(pdf-file, 66 kB)

FROM SENSE TO SYMBOL SENSE
Christer Bergsten

• Introduction
• Mathematical Forms
• Mathematics and Image Schemata
• Mathematical Symbolism and Image Schemata
• Developmental Aspects of Understanding Forms
• Symbol Sense
• References

(pdf-file, 68 kB)

THE ROLE OF ALGEBRAIZATION IN THE STUDY OF A MATHEMATICAL ORGANIZATION
Pilar Bolea, Marianna Bosch, Josep Gascón

• Mathematics as the Study of Mathematical Works
• The Need of a Model of School Algebra
• The Algebraization of a Mathematical Work
• Characteristics of an Algebraized Mathematical Organization
• The Role of Algebraization in the Study of a Mathematical Work
• References

(pdf-file, 67 kB)

SIMULATIN OF DRAWING MACHINES ON CABRI-II AND ITS DUAL ALGEBRAIC SYMBOLISATION: DESCARTES' MACHINE & ALGEBRAIC INEQUALITY
Veronica Hoyos, Bernard Capponi, B. Geneves

• Introduction
• Class Room Context
• Theoretical Frame of our Educational Experience
• The Sources and the Techniques
• References

(pdf-file, 77 kB)

THE INTERWEAVING OF ARITHMETIC AND ALGEBRA: SOME QUESTIONS ABOUT SYNTACTIC AND STRUCTURAL ASPECTS AND THEIR TEACHING AND LEARNING
Nicolina A. Malara, Rosa Iaderosa

• Introduction
• A Few Considerations on Syntactic Difficulties in the Learning of Algebra
• The Confusion Between Additive and Multiplicative Notation: A Hypothesis of Inquiry for its Overcoming
• Considerations and Problematization of Some Arithmetical-Algebraic Activities in Middle School
• References

(pdf-file, 77 kB)

SYNTACTICAL AND SEMANTIC ASPECTS IN SOLVING EQUATIONS: A STUDY WITH 14 YEAR OLD PUPILS
Maria Reggiani

• Introduction
• Research Context
• Research Problem
• Research Method
• Summary of the Work Carried out in Class
• Verification Tests
• Analysis of the Proposed Problem
• Analysis of Results
• Analysis of Single Protocols
• Final Remarks
• References

(pdf-file, 67 kB)

FORMING ALGEBRA UNDERSTANDING IN MPI-PROJECT
Sam Rososhek

• Introduction
• Weyl-Shafarevich Conception
• Basic Elements of Algebraic Knowledge
• Algebra Propaedeutics
• Mathematical Modelling Line
• Algebraic Structures Introduction
• Computer Visualization of Algebraic Structures
• References

(pdf-file, 60 kB)

SOME TOOLS TO COMPARE STUDENTS' PERFORMANCE AND INTERPRET THEIR DIFFICULTIES IN ALGEBRAIC TASKS
Éva Szeredi, Judit Török

• Introduction
• A Priori Analysis of the Task
  • Some Possible Solutions
  • Reference Knowledge
  • Processes
  • Difficulties
  • A Priori Expectations
• Analysis of Performances
  • How the Students Exploited or not Reference Knowledge
  • Processes
• Comparison Between Hungarian and Italian Students
  • Findings
  • Possible Interpretations
• Conclusion
• References

(pdf-file, 74 kB)

Research Paradigms and Methodologies and their Relationship to Questions in Mathematics Education
Milan Hejny, Christine Shiu, Juan Diaz Godino, Herman Maier

• Theories in and of Mathematics Education
  • What is a Theory and How Do Theories Arise?
  • What Is the Role and Function of Theory in the Research Process?
  • Is It Feasible and Useful to Distinguish Different Kinds of Theory?
  • How Can Theories in Mathematics Education Be Evaluated?
• Conducting Empirical Research
  • What Can Be Learned from Empirical Research?
  • What Is the Relationship Between the Researcher and the Researched?
  • How Can Research Best Be Shared with Teachers?
  • Developing Methodologies
• Conclusions
  • Communication
  • Cooperation
  • Collaboration
• References

(pdf-file, 50 kB)

THE ROLE OF THE HISTORY OF MATHEMATICS IN MATHEMATICS EDUCATION: REFLECTIONS AND EXAMPLES
Giorgio T. Bagni

• Bombelli's Algebra (1572) and Imaginary Numbers
• Educational Problems: The Focus of Our Work
• The Group Concept from History to Mathematics Education
• History of Mathematics and Epistemology of Learning
• References

(pdf-file, 124 kB)

THE MEANINGS OF MATHEMATICAL OBJECTS AS ANALYSIS UNITS FOR DIDACTIC OF MATHEMATICES
Juan Diaz Godino, Carmen Batanero

• Introduction
• Meaning as the Content of Semiotic Functions
• Notational, Extensional and Intensional Meanings
• Elementary and Systemic Meanings
• Personal and Institutional Meanings
• Semiotic Acts and Processes in the Study of Numbers
  • Elementary Meanings: The First Encounter With Numbers
  • Systemic Meanings of Numbers
• Conclusions and Implications
• References

(pdf-file, 79 kB)

DIDACTICAL ANALYSIS: A NON EMPIRICAL QUALITATIVE METHOD FOR RESEARCH IN MATHEMATICS EDUCATION
José Luis González Marí

• Introduction
• Mathematics Education: A Field of Relationships vs. Related Fields
• Insufficiency of the Interdisciplinary Approach and Specificity
• Didactical Analysis of a Mathematical Knowledge
• References

(pdf-file, 94 kB)

INVESTIGATING TEACHERS' WORK WITH PUPILS' TEXTUAL EIGENPRODUCTIONS
Bruno D’Amore, Hermann Maier

• Pupils' Textual Eigenproductions
  • Characterisation of Textual Eigenproduction
  • Didactical Function of Textual Eigenproduction
• Teachers Interpretation of Textual Eigenproductions
  • Design of the Research
  • Some Results
• References

(pdf-file, 94 kB)

RECENT TRENDS IN THE THEORY OF DIDACTICAL SITUATIONS
André Rouchier

• Introduction
• The Classical Components of the Theory of Didactical Situations
• Knowledge and Institutions, the Particular Case of Mathematics
• New Objects, New Problems
• Conclusion
• References

(pdf-file, 60 kB)

THE RESEARCH METHODS EMPLOYED BY CONTRIBUTORS TO THE PRAGUE DIDACTICS OF MATHEMATICS
Nada Stehlíková

• Introduction and Framework
• Research Projects
  • A Student's Solution to a Word Problem
  • Ability to Construct a Mental Representation of a Structure
• Research Questions
• How to Create Models
  • Phenomena
  • Trace
  • Mechanisms
  • Models
• Inner Research
• Implementing Research Results
• Conclusion
• References

(pdf-file, 72 kB)

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