This document, the first of three volumes, reports on the 15th annual conference of the International Group for the Psychology of Mathematics Education (PME) held in Italy 1991. Plenary addresses and speakers are: "Social Interaction and Mathematical Knowledge" (B. M. Bartolini); "Meaning: Image Schemata and Protocols" (W. Dorfler); "On the Status of Visual Reasoning in Mathematics and Mathematics Education" (T. Dreyfus); "The Activity Theory of Learning and Mathematics Education in the USSR" (T. Gabay). Research reports in this volume include: "Applications of R-Rules as Exhibited in Calculus Problem Solving" (Amit, M.; Movshovitz-Hadar N.); "Effects of Diagrams on the Solution of Problems Concerning the Estimation of Differences" (Antonietti, A.; Angelini, C.); "Le probleme de statut du "millieu" dans un enseignement de la geometric avec support logiciel" (Artigue, M.; Belloc, J.; Kargiotakis, G.); "Procedural and Relational Aspects of Algebraic Thinking" (Arzarello, F.); "Hegemony in the Mathematics Curricula the Effect of Gender and Social Class on the Organisation of Mathematics Teaching for Year 9 Students" (Atweh, B.; Cooper, T.); "Instantaneous Speed: Concept Images at College Students' Level and its Evolution in a Learning Experience" (Azcarate, C.); "Students' Mental Prototypes for Functions and Graphs" (Bakar, M.; Tall, D.); "Illustrations de problemes mathematiques complexes mettant en jeu un changement au une sequence de changements par des enfants du primaire (Bednarz, N.; Janvier, B.); "The Operator Construct of Rational Number: A Refinement of the Concept" (Behr, M.; Harel, G.; Post, T.; Lesh, R.); "Children's Use of Outside-School Knowledge to Solve Mathematics Problems In-School" (Bishop, A. J.; De Abreu, G.); "Influences of an Ethnomathematical Approach on Teacher Attitudes to Mathematics Education" (Bishop, A. J.; Pompeu, G., Jr.); "Gender and the Versatile Learning of Trigonometry Using Computer Software" (Blackett, N.; Tall, D.); "La dimension du travail psychique dans la formation continue des enseignant(e)s de mathematiques" (Blanchard-Laville, C.); "Drawing a Diagram: Observing a Partially-Developed Heuristic Process in College Students" (Bodner, B. L.; Goldin, G. A.); "The Active Comparison of Strategies in Problem-Solving: an Exploratory Study" (Bondesan, M. G.; Ferrari, P. L.); "Teachers' Conceptions of Students' Mathematical Errors and Conceived Treatment of Them" (Boufi, A.; Kafoussi, S.); "Children's Understanding of Fractions as Expressions of Relative Magnitude" (Carraher, D. W.; Dias, Schliemann A.); "Dificultad en problemas de estructura multiplicative de comparacion" (Castro, Martinez E.; Rico, Romero L.; Batanero, Bernabeu C.); "Construction and Interpretation of Algebraic Models" (Chiappini G., Lemut E.); "Analysis of the Behaviour of Mathematics Teachers in Problem Solving Situations with the Computer" (Chiappini, G.; Lemut E., Parenti, L.); "Analysis of the Accompanying Discourse of Mathematics Teachers in the Classroom" (Chiocca, C.; Josse, E.; Robert, A.); "Van Hiele Levels of Learning Geometry" (Clements, D. H.; Battista, M. T.); "Some Thoughts about Individual Learning Group Development, and Social Interaction" (Cobb, P.); "Une analyse des brouillons de calcul d'eleves confrontes a des items de divisions ecrites" (Conne, F.; Brun, J.); "Brian's Number Line Representation of Fractions" (Davis, R. B.; Alston, A.; Maher, C.); and "Pupils' Needs for Conviction and Explanation within the Context of Geometry" (De Villiers, M.). This volume contains the addresses of research report authors. (MKR)