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Early Links Between Psychology and Mathematics Education Research

From at least as early as the 1950s, theoretical commentaries on elementary school mathematics pointed to the need to involve learners in activities which would enable them to link the language and ideas of mathematics with physical materials and the personal worlds of the learners. The work of Cuisenaire and of Gattegno in the 1950s, and of Dienes and Bruner in the 1960s, is particularly noteworthy in this regard. In the background, justifying such approaches, were the writings of the Genevan developmental psychologist Jean Piaget, and the Soviet psychologist and linguist, Lev Vygotsky. While Piaget was fundamentally a psychologist, and not an educator, he did write about the implication of his ideas for education (see, for example, Piaget, 1975), and there can be no doubt that not only did Piaget influence Dienes and Bruner, but also his own original writings were often cited as the main justification for introducing activity-based elementary school mathematics courses.

In the 1970s, mathematics educators in the United States as well as in many other countries, began to accept and extol the developmental principles of Piaget, and the associated ideas of Dienes and Bruner. Elementary school mathematics programs (such as the Nuffield Program in the United Kingdom) made it clear that their programs were based on readiness ideas directly associated with the Piagetian notion of stages whereby learners could be classified as sensorimotor, pre-operational, concrete operational, or formal operational. Certain ways of thinking were linked to each stage, and marker tasks (such as conservation of number) were defined by Piaget as being capable of distinguishing learners who were about to or who had already moved from one stage to another. Trainee teachers were taught the Piagetian stages in their teacher education courses, and were expected to be able to see evidence of the stages when they were on teaching practice rounds. In a similar way, Zoltan Dienes's six stages of learning (Dienes, 1964) were thought to provide an important framework for understanding how children developed mathematics concepts.

Psychological theory, then, came to be acknowledged as important, both for explaining children's mathematical behaviour and for guiding those responsible for developing elementary school mathematics curricula or writing elementary school mathematics textbooks. Furthermore, as mentioned earlier in this paper, from the 1960s on, psychological theory provided an important base for framing curriculum development and classroom behaviour in secondary school mathematics. However, the behaviourism of Skinner, Gagné, Carroll, Bloom and Block were an altogether different thing from developmental notions of Bruner, Dienes, Gattegno and Piaget.

The Establishment of PME

Given that psychological theories were so highly regarded by mathematics educators of the 1960s and early 1970s, it was hardly surprising when, in 1976, Professor Efraim Fischbein of Tel Aviv University instituted a study group which brought together researchers working in the area of the psychology of mathematics education. The International Group for the Psychology of Mathematics Education (PME) was formed, with the following three-fold mission:

1. To promote international contacts and the exchange of scientific information in the psychology of mathematics education;

2. To promote and stimulate interdisciplinary research in the aforesaid area with the cooperation of psychologists, mathematicians, and mathematics teachers;

3. To further a deeper and better understanding of the psychological aspects of teaching and learning mathematics and the implications thereof.

Since 1976, many different countries have hosted annual PME conferences, and in 1993, the 17th Annual Conference was held in Tsukuba Japan. Usually between 200 and 500 mathematics educators and psychologists attend the annual conferences, which have become an annual meeting ground for the world's leading mathematics educators.

Thus, in the 1970s, the emerging discipline of mathematics education seemed to link itself formally with the established social science of psychology. The message was clear: not only should mathematics educators draw from the discipline of mathematics, but they should draw from various literatures in psychology to inform them not only on how children learn, but also on what mathematics learners of various ages might reasonably be expected to learn.

This link with psychology carried at least one important implication for the fledgling group of mathematics education researchers scattered around the world - it appeared to be reasonable to assume that if psychology had so many insights to offer mathematics education, then it made sense for research methodologies commonly used by psychologists to be adopted by mathematics educators for their research. The two most common methodologies used by psychologists were (a) experimental designs, in which inferential statistical analyses were employed, and (b) developmental studies in which small samples were intensively studied in largely qualitative ways. One only has to examine papers published in the major mathematics education research journals (for example, Journal for Research in Mathematics Education, and Education Studies in Mathematics) between 1975 and 1985 to be convinced that these two research paradigms, borrowed from psychology, steered the thinking of mathematics educators on what constituted acceptable research in their domain. The two approaches became standard for masters and doctoral dissertations written in the 1970s and early 1980s in almost every country around the world where mathematics education research was carried out.

Behaviourism New paradigms

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