Experimental studies of mathematical concept formation in young children

Abstract

URING the last three years we have performed a series of experiments in the area of children’s mathematical concept formation, a number of which we present in this report. One of our most urgent concerns during this period and one which will probably be of close interest to our readers, has been to try to bring to this somewhat amorphous area precise quantative analysis. To achieve this we have made use of a quantitative theory of psychology, mathematical learning theory [ l], which in one form or another has had considerable success in dealing with other behavioral areas [Z]. To familiarize the reader with this approach we present, in the following pages, an intuitive description of the assumptions, implications and outcomes of the particular mathematical model employed and have tried to give enough of the theoretical analysis to give the reader some feeling for the possibilities of this kind of approach. At the same time the empirical variables introduced in these experiments have not been arbitrarily chosen. This experimental project has been run concurrently with the development of a program of primary grade mathematics “Sets and Numbers ” [3] which makes use of simple set theoretical notions to introduce the child at the outset to concepts and operations in arithmetic. Consequently the concepts to be learned in each experiment and the experimental variables introduced have some bearing on problems which have arisen through the development of the S & and Numbers program. Because of shortness of space *Based on paper presented lat meeting of Section Q, American Association for the Atdvancement