This thesis considers some aspects of equivalence relations, especially in areas outside mathematics end in the development of children's thinking.
The aim of Section 1 is to show that equivalence classes (and by implication equivalence relations) are an essential mode of thinking for adult English speakers in a variety of activities.
As children have their own patterns of thinking which are developing toward adult form. Section 2 is devoted to establishing a framework within which observations about the development of the concept of equivalence relation can be organised.
The relevant factors of Piaget's work are taken as the starting point. These are reviewed alongside more recent American studies. Some recent reformulations of Piaget's theory of groupings by Gorman writers ere also considered.
This review Identifies difficulties arising from
(a) diversity of interpretation of (i) Piaget's work (ii) terminology used,
(b) gaps between the psychological models and the behavioural counterparts which they were designed to represent,
(c) lock of agreed criterion for concept attainment.
Points arising from (a) and (c) have been considered in greater detail in the context of
- the identification and modification of points of weakness in the hypothesis that soristion implies transitivity,
- an attempt to specify the characteristics of a test of conservation of a quantitative relation.
The review also shows gaps in the research, notably, in the study of the growth of the understanding of symmetric relations; proposals for further tests to clarify the stages in the development of the concept of symmetry are put forward. The feasibility of these tests has been studied in the classroom
