The third volume of this proceedings contains more of the research reports begun in Volume 2. Papers include: (1) "A Semiotic Model for Analyzing the Relationships between Thought, Language and Context in Mathematics Education" (Juan D. Godino and Angel M. Recio); (2) "Conceptions as Articulated in Different Microworlds Exploring Functions" (Veronica Gitirana Gomes-Ferreira); (3) "The Nature and Role of Discussion in Mathematics: Three Elementary Teachers' Beliefs and Practice" (Susie Groves and Brian Doig); (4) "Proof in Geometry as an Explanatory and Convincing Tool" (Nurit Hadas and Rina Hershkowitz); (5) "The Case of Rita: 'Maybe I Started To Like Math More'" (Markku Hannula); (6) "On Teaching Early Number through Language" (Dave Hewitt and Emma Brown); (7) "Relating Culture and Mathematical Activity: An Analysis of Sociomathematical Norms" (Lynn Liao Hodge and Michelle Stephan); (8) "'Automatism' in Finding a 'Solution' among Junior High School Students" (Bat-Sheva Ilany and Nurit Shmueli); (9) "The Role of Context in Collaboration in Mathematics" (Kathryn C. Irwin); (10) "Design and Evaluation on Teaching Unit: Focusing on the Process of Generalization" (Hideki Iwasaki, Takeshi Yamaguchi, and Kaori Tagashira); (11) "The Teaching-Research Dialectic in a Mathematics Course in Pakistan" (Barbara Jaworski and Elena Nardi); (12) "Characterizing Mathematics Teaching Using the Teaching Triad" (Barbara Jaworski and Despina Potari); (13) "The Mediation of Learning within a Dynamic Geometry Environment" (Keith Jones); (14) "Using Information Systems for Mathematical Problem-Solving: A New Philosophical Perspective" (C. Jotin Khisty and Lena Licon Khisty); (15) "Collaborative versus Individual Problem Solving: Entering Another's Universe of Thought" (Carolyn Kieran and Tommy Dreyfus); (16) "Increasing Teachers' Awareness of Students' Conceptions of Operations with Rational Numbers" (Ronith Klein, Ruthi Barkai, Dina Tirosh, and Pessia Tsamir); (17) "Inflexibility in Teachers' Ratio Conceptions" (Anat Klemer and Irit Peled); (18) "Preservice Teachers' Conceptions of Probability in Relation to Its History" (Hari Prasad Koirala); (19) "Team Teaching and Preservice Teachers' Classroom Practice with Innovative Methods of Instruction--The Case of Computers" (Bilha Kutscher); (20) "Professional Influences on Teachers' Perceptions of Teaching and Assessment in Mathematics" (Leonidas Kyriakides); (21) "Student Motivation and Attitudes in Learning College Mathematics through Interdisciplinary Courses" (Diana V. Lambdin and Rajee Amarasinghe); (22) "Algebra: Meaning through Modeling" (Susan J. Lamon); (23) "An Alternative Assessment: The Gutiemez, Jaime and Fortuny Technique" (Christine Lawrie); (24) "Who Persists with Mathematics at the Tertiary Level: A New Reality?" (Gilah C. Leder, Helen J. Forgasz, and Christine Brew); (25) "Re-Starting Algebra in High School: The Role of Systematic Thinking and of Representation Systems Command" (E. Lemut and S. Greco); (26) "In Pursuit of Practical Wisdom in Mathematics Education Research" (Frank K. Lester, Jr.); (27) "More Games for Integers" (Patricia Rosana Linardi and Roberto Ribeiro Baldino); (28)"Moments of Conflict and Moments of Conviction in Generalizing" (Liora Linchevski, Alwyn Olivier, Rolene Liebenberg, and Marlene Sasman); (29) "Students' Reasoning on Qualitative Changes in Ratio: A Comparison of Fraction and Division Representations" (Francis Lopez-Real); (30) "Non-Elementary Mathematics in a Work Setting" (Zlatan Magajna and John Monaghan); (31) "On the Difficulties of Visualization and Representation of 3D Objects in Middle School Teachers" (Nicolina A. Malara); (32) "From Drawing to Construction: Teachers' Mediation within the Cabri Environment" (M.A. Mariotti and M.G. Bartolini Bussi); (33) "'She Says We've Got to Think Back': Effective Folding Back for Growth in Understanding" (Lyndon Martin and Susan Pirie); (34) "Young Children's Beliefs about the Nature of Mathematics" (Andrea McDonough); (35) "Recognition of Angular Similarities between Familiar Physical Situations" (Michael Mitchelmore and Paul White); (36) "Culture, Games and Mathematics Education: An Exploration Based on String Games" (Mogege David Mosimege); (37) "Enlarging Mathematical Activity from Modeling Phenomena to Generating Phenomena" (Ricardo Nemirovsky, James J. Kaput, and Jeremy Roschelle); (38) "Young Students' Constructions of Fractions" (Karen Newstead and Hanlie Murray); (39) "Development of the Concept of Conservation of Mass, Weight and Volume in Children of Mezam Division, Cameroon." (Rosemary Kongla Ngwa); (40) "Subtraction Strategies in Developmental Perspective: A Comparison of Mathematically Normal and Mathematically Disabled Children" (Snorre A. Ostad); (41)"Representing Problems in the First Year of School" (Lynne Outhred and Sarah Sardelich); (42) "Operational and Conceptual Abilities in the Learning of Algebraic Language. A Case Study" (M.M. Palarea and M.M. Socas); (43) "Widening the Interpretation of van Hiele's Levels 2 and 3" (John Pegg and Penelope Currie); and (44) "Class Discussion as an Opportunity for Proportional Reasoning" (Angela Pesci). (ASK)