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This proceedings of the annual conference of the International Group for the Psychology of Mathematics Education (PME) contains the following research papers: "The Construct Theory of Rational Numbers: Toward a Semantic Analysis" (M. Behr & G. Harel); "Reflections on Dealing: An Analysis of One Child's Interpretations" (G. Davis); "About Intuitional Knowledge of Density in Elementary School" (J. Gimenez); "Understanding the Multiplicative Structure: Concepts at the Undergraduate Level" (G. Harel & M. Behr); "A Contextual Approach to the Teaching and Learning of Mathematics: Outlining a Teaching Strategy that Makes Use of Pupil's Real World Experiences and Strategies, and the Results of the First Teaching Experiment of Project" (T.O. Keranto); "On Children's Mathematics Informal Method" (F.L. Lin & L.R. Booth); "A Case Study of the Role of Unitizing Operations with Natural Numbers in the Conceptualization of Fractions" (A. Ludlow); "Constructing Fractions in Computer Microworlds" (J. Olive & L.P. Steffe); "Proportional Reasoning: From Shopping to Kitchens, Laboratories, and Hopefully, Schools" (A.D. Schliemann & V.P. Magalhaes); "The Fraction Concept in Comprehensive School at Grade Levels 3-6 in Finland" (T. Strang); "Critical Decisions in the Generalization Process: A Methodology for Researching Pupil Collaboration in Computer and Non Computer Environments" (L. Healy, C. Hoyles, & R.J. Sutherland); "'Scaffolding' a Crutch or a Support for Pupils' Sense-Making in Learning Mathematics" (B. Jaworski); "The Role of Mathematical Knowledge in Children's Understanding of Geographical Concepts" (R.G. Kaplan); "Speaking Mathematically in Bilingual Classrooms: An Exploratory Study of Teacher Discourse" (L.L. Khisty, D.B. McLeod, & K. Bertilson); "The Emergence of Mathematical Argumentation in the Small Group Interaction of Second Graders" (G. Krummheuer & E. Yackel); "Potential Mathematics Learning Opportunities in Grade Three Class Discussions" (J.J. Lo, G.H. Wheatley, & A.C. Smith); "Certain Metonymic Aspects of Mathematical Discourse" (D.J. Pimm); "Inverse Relations: The Case of the Quantity of Matter" (R. Stavv & T. Rager); "The Development of Mathematical Discussion" (T. Wood); "Estrategias y Argumentos en el Estudio Descriptivo de la Asociacion Usando Microordenadores" (J.D. Godino, C. Batanero, & A.E. Castro); "Computerized Tools and the Process of Modeling" (C. Hancock & J. Kaput); "Examples of Incorrect Use of Analogy in Word Problems" (L. Bazzini); "Children's Pre-concept of Multiplication: Procedural Understanding" (C. Beattys, N. Herscovics, & N. Nantais); "The Kindergartners' Knowledge of Numerals" (J.C. Bergeron); "An Analysis of the Value and Limitations of Mathematical Representations Used by Teachers and Young Children" (G.M. Bouton-Lewis & G.S. Halford); "A Study on the Development of Second-Graders' Ability in Solving Two-Step Problems" (F. Cao); "Understanding the Division Algorithm from New Perspectives" (D.W. Carraher); "Negative Numbers Without the Minus Sign" (T.N. Carraher); "Learning Difficulties Behind the Notion of Absolute Value" (I. Chiarugi, G. Fracassina, & F. Furinghetti); "Le Role de la Representation dans la Resolution des Problemes Additifs" (R.F. Damm); "Using a Computerized Tool to Promote Students''Number Sense' and Problem Solving Strategies" (N. Hativa, V. Bill, S. Hershkovitz, & I. Machmandrow); "Children's Understanding of Compensation, Addition and Subtraction in Part/Whole Relationships" (K.C. Irwin); "Factors Affecting Children's Strategies and Success in Estimation" (C. Morgan); "Assessment in Primary Mathematics: The Effects of Item Readability" (J.A. Mousley); "Social Sense-Making in Mathematics: Children's Ideas of Negative Numbers" (S. Mukhopadhyay, L. B. Resnick, & L. Schauble); "Children's Pre-Concept of Multiplication: Logico Physical Abstraction" (N. Nantais & N. Herscovics); "Building on Young Children's Informal Arithmetical Knowledge" (A.I. Oliver, A. Murray, & P. Human); "From Protoquantities to Number Sense" (L.B. Resnick, S. Lesgold, & V. Bill); "Prospective Elementary Teachers' Knowledge of Division" (M.A. Simon); "Relative and Absolute Error in Computational Estimation" (J. Sowder, L. Sowder, & Z. Markovits); "A Child Generated Multiplying Scheme" (L. Steffe); and "Salient Aspects of Experience with Concrete Manipulatives" (P. Thompson & A.G. Thompson). Includes a listing of author addresses. (MKR)

This proceedings of the annual conference of the International Group for the Psychology of Mathematics Education (PME) includes the following research papers: "Children's Connections among Representations of Mathematical Ideas" (A. Alston & C.A. Maher); "Algebraic Syntax Errors: A Study with Secondary School Children" (A. Avila, F. Garcia, & T. Rojano); "The Development of Conceptual Structure as a Problem Solving Activity" (V. Cifarelli); "From Arithmetic to Algebra: Negotiating a Jump in the Learning Process" (A. Cortes, N. Kavafian, & G. Vergnaud); "Continuous Analysis of One Year of Science Students' Work in Linear Algebra, in First Year French University" (J.L. Dorier); "Avoidance and Acknowledgement of Negative Numbers in the Context of Linear Equations" (A. Gallardo);"Introducing Algebra: A Functional Approach in a Computer Environment" (M. Garancon, C. Kieran, & A. Boileau); "LOGO, to Teach the Concept of Function" (D. Guin & I.G. Retamal); "The Concept of Function: Continuity Image versus Discontinuity Image: Computer Experience" (F. Hitt); "Acquisition of Algebraic Grammar" (D. Kirshner); "Embedded Figures and Structures of Algebraic Expressions" (L. Linchevski & S. Vinner); "A Framework for Understanding What Algebraic Thinking Is" (R.L. Lins); "Developing Knowledge of Functions through Manipulation of a Physical Device" (L. de Lemos Meira); "Students' Interpretations of Linear Equations and Their Graphs" (J. Moschkovich); "An Experience to Improve Pupil's Performance in Inverse Problems" (A. Pesci); "Algebra Word Problems: A Numerical Approach for Its Resolution: A Teaching Experiment in the Classroom" (G. Rubio); "Children's Writing about the Idea of Variable in the Context of a Formula" (H. Sakonidis & J. Bliss); "Observations on the 'Reversal Error' in Algebra Tasks" (F. Seeger); "Generalization Process in Elementary Algebra: Interpretation and Symbolization" (S.U. Legovich); "Effects of Teaching Methods on Mathematical Abilities of Students in Secondary Education Compared by Means of a Transfer Test" (J. Meijer); "On Long Term Development of Some General Skills in Problem Solving: A Longitudinal Comparative Study" (P. Boero); "Cognitive Dissonance versus Success as the Basis for Meaningful Mathematical Learning" (N.F. Ellerton & M.A. Clements); "Time and Hypothetical Reasoning in Problem Solving" (P.L. Ferrari); "The Interplay between Student Behaviors and the Mathematical Structure of Problem Situations: Issues and Examples" (R. Herschkowitz & A. Arcavi); "Paradigm of Open-Approach Method in the Mathematics Classroom Activities: Focus on Mathematical Problem Solving" (N. Nohda); "Reflexions sur le Role du Maitre dans les Situations Didactiques a Partir du Cas de l'Enseignement a des Eleves en Difficulte" (M.J.P. Glorian); "Diagnosis and Response in Teaching Transformation Geometry" (A. Bell & D. Birks); "Children's Recognition of Right Angled Triangles in Unlearned Positions" (M. Cooper & K. Krainer); "The Role of Microworlds in the Construction of Conceptual Entities" (L.D. Edwards); "The Cognitive Challenge Involved in Escher's Potato Stamps Microworld" (R. Hadass); "Study of the Degree of Acquisition of the Van Hiele Levels by Secondary School Students" (A. Jaime & A. Gutierez); "Spatial Concepts in the Kalahari" (H. Lea); "Integrating LOGO in the Regular Maths Curriculum: A Developmental Risk or Opportunity?" (T. Lemerise); "Young Children Solving Spatial Problems" (H. Mansfield & J. Scott); "The Role of Format in Students' Achievement of Proof" (W.G. Martin); "L'influence des Aspects Figuratifs dans le Raisonnment des Eleves en Geometrie" (A. Mesquita); "Children's Understanding of Congruence According to the Van Hiele Model of Thinking" (L. Nasser); "Prospective Primary Teachers' Conceptions of Area" (C. Tierney, C. Boyd, & G. Davis); "Probability Concepts and Generative Learning Theory" (O. Bjorkqvist); "Some Considerations on the Learning of Probability" (A.M.O. Salazar); "Gambling and Ethnomathematics in Australia" (R. Peard); "Mathematization Project in Class as a Collective Higher Order Learning Process" (H.G. Steiner). Also includes a listing of author addresses. (MKR)

This proceedings of the annual conference of the International Group for the Psychology of Mathematics Education (PME) includes the following papers: "The Knowledge of Cats: Epistemological Foundations of Mathematics Education" (R.B. Davis) and "PME Algebra Research: A Working Perspective" (E. Filloy); "Some Misconceptions in Calculus: Anecdotes or the Tip of an Iceberg?" (M. Amit & S. Vinner); "Difficultes Cognitives et Didactiques dans la Construction de Relations entre Cadre Algebrique et Cadre Graphique" (M. Artigue); "Unbalance and Recovery: Categories Related to the Appropriation of a Basis of Meaning Pertaining to the Domain of Physical Thinking" (R. Cantoral); "On Difficulties with Diagrams: Theoretical Issues" (T. Dreyfus & T. Eisenberg); "The Two Faces of the Inverse Function: Prospective Teachers' Use of 'Undoing'" (R. Even); "Intuitive Processes, Mental Image, and Analytical and Graphic Representations of the Stationary State: A Case Study" (R.M. Farfan & F. Hitt); "The Role of Conceptual Entities in Learning Mathematical Concepts at the Undergraduate Level" (G. Harel & J. Kaput); "Mathematical Concept of Formation in the Individual" (L. Lindenskov); "Pupils' Interpretations of the Limit Concept: A Comparison Study between Greeks and English" (J. Mamona-Downs); "Infinity in Mathematics as a Scientific Subject for Cognitive Psychology" (R.N. Errazuriz); "Organizations Deductives et Demonstration" (L. Radford); "The Teaching Experiment 'Heuristic Mathematics Education'" (A. Van Streun); "The Understanding of Limit: Three Perspectives" (S.R. Williams);"Self Control in Analyzing Problem Solving Strategies" (G. Becker); "Influences of Teacher Cognitive/Conceptual Levels on Problem-Solving Instruction" (B.J. Dougherty); "Can Teachers Evaluate Problem Solving Ability?" (F.O. Flener & J. Reedy); "Teacher Conceptions about Problem Solving and Problem Solving Instruction" (D.A. Grouws, T.A. Good, & B.J. Dougherty); "Math Teachers and Gender Differences in Math Achievement, Math Participation and Attitudes Towards Math" (H. Kuyper & M.P.C. van der Werf); "Teaching Students to be Reflective: A Study of Two Grade Seven Classes" (F.F. Lester & D.L. Kroll); "Students' Affective Responses to Non-Routine Mathematical Problems: An Empirical Study" (D.B. McLeod, C. Craviotto, & M. Ortega); "Accommodating Curriculum Change in Mathematics: Teachers' Dilemmas" (R. Nolder); "Teachers' Characteristics and Attitudes as Mediating Variables in Computer-Based Mathematics Learning" (R. Noss, C. Hoyles, & R. Sutherland); "Teachers' Perceived Roles of the Computer in Mathematics Education" (J. Ponte); "Mathematics Process as Mathematics Content: A Course for Teachers" (D. Schifter); "Psychological/Philosophical Aspects of Mathematical Activity: Does Theory Influence Practice?" (R. Scott-Hodgetts & S. Lerman); "A Web of Beliefs: Learning to Teach in an Environment with Conflicting Messages" (R.G. Underhill). Includes 27 poster presentation abstracts and a listing of author addresses. (MKR)