ICMI

Bulletin No. 45

December 1998

Efraim Fischbein died on Wednesday, 22 July 1998. His death is a great loss to his family, to his students and colleagues at Tel Aviv University and to the entire community of mathematics educators.

Fischbein was born in Romania, in 1920. He taught mathematics and philosophy in high school. In 1949 he was offered the position of lecturer at the department of Department of Educational Psychology at the University of Bucharest, and from 1959 to 1975 he served as the head of the Educational Psychology department at the Institute of Psychology in Bucharest. His work on child development, cognitive psychology, and mathematics education during that period is characterized by the originality of the questions he asked, his systematic methods of exploration and the insights he provided in the interpretation of the data. His many books and articles created international interest, and he was frequently invited, from behind the Iron Curtain, to conferences and meetings in western countries.

By 1975, Efraim Fischbein was internationally known as one of the leading researchers in mathematics education. After leaving Romania for Israel, he was offered an appointment as professor of mathematics education at Tel Aviv University where he founded the Department of Science Education and continued to teach, to be active and creative in research, and to supervise many research students until his last moments.

Efraim Fischbein is best known for his creative, systematic, coherent and influential contribution to the knowledge about, and the understanding of the role of intuition in learning and teaching mathematics and science. His first contributions in this area concerned intuitions of probability and combinatorics; they established a strong bridge between psychology and education and were published internationally in journals from both domains, including Educational Studies in Mathematics and The British Journal of Educational Psychology. In the preface to Fischbein's book "The intuitive sources of probabilistic thinking in children" (Reidel, 1975), Hans Freudenthal related in warm words to the contribution of Fischbein's approach and wrote: "I interpret and welcome Fischbein's work as a major breakthrough in mentality of research in the field of developmental psychology. ... I consider Fischbein's shifting the stress from concepts to intuitions as a cognitive advance which may benefit teaching mathematics."

Fischbein's desire to understand the nature of intuitive thinking and the relationship between intuitive and other forms of thinking is evidenced in his further work on infinity, on implicit models of multiplication and division, on irrational numbers, on the relationship between intuitions and proofs, on the interaction between the formal, the algorithmic and the intuitive components in mathematical activities, and other topics. In "Intuition in Science and Mathematics" (Reidel, 1987) Fischbein proposed a theoretical, comprehensive view of the domain of intuition, identified and organized the related experimental findings, and described and discussed their educational and didactic implications. In this book, like in other publications, he coined new, useful terminology (e.g., primary intuitions, secondary intuitions), raised problematic issues (e.g., the educational dilemma) and stimulated further related research, thus leading the field of mathematics education ahead. It is not surprising that his articles were published in four languages and translated into many others.

Another major contribution of Efraim Fischbein to the domain of mathematics education relates to the creation and the organization of PME, The International Group for the Psychology of Mathematics Education. He was the organizer, the first president and an honorary member of PME. He actively participated in almost all the annual meetings of PME, and contributed a great deal to the ongoing development of the organization. His imprint on this important constituent of our field will be felt for many years to come.

At the beginning of 1998, Efraim Fischbein started working on a third book entitled "Intuitions, Schemata and Models in Mathematical and Scientific Reasoning". Unfortunately, he was unable to finish this work. But his books, his articles, and mainly his ideas will stay with us forever, and his contribution to mathematics education will serve as a permanent memorial to him, and as a never-ending source of inspiration for us all.

**Dina Tirosh** and **Tommy Dreyfus**