Cultural Differences in Mathematical Concept Learning

Abstract

THE purposes of this paper are two. The first is to examine the acquisition of certain mathematical concepts by young children in two different cultures. The data from a concept formation experiment performed with children in California will be compared with data from the same type of experiment performed with children of the same age level in Accra, Ghana.' The concepts to be acquired in these experiments are two fundamental concepts in mathematics, identity of sets and identity of ordered sets. The second purpose is to apply mathematical learning theory, and in particular a learning model, to the data from both experiments. The model has proved to be a reasonably good first approximation to actual response behavior in a variety of experimental situations. One objective here is a further application of the theoretical model in a widely different cultural context. Specifically,. my interest is in a comparison of the fit of the model to data from two experimental situations which are, with one major exception, almost identical. The cultural backgrounds of the subjects are widely disparate. The two purposes are in a sense complementary: On the one hand, we can identify differences or similarities across cultures in children's formation of mathematical concepts. From the standpoint of the teaching of mathematics these culturally determined differences are of utmost significance. On the other hand, we assume that the basic behavioral processes involved in learning are the same, and a general learning theory should deal with, represent, or analyze these fundamental processes. We should expect a theoretical model to go beyond what are perhaps adventitious differences in its prediction of actual response behavior. Therefore, we should expect the model to fit the data from two dissimilar cultures equally well when the experimental situations are in other respects comparable. Before going on to a description of various aspects of the experiments, I should like to comment on the immediate relevance of comparisons of children's concept learning in different cultures. The revolution in the teaching of mathematics or in curriculum in mathematics is spreading throughout the world. In particular, many new programs and methods developed in one country are being adopted or adapted in other countries. With this exchange of ideas, materials, curricula, methods, etc., in mathematics teaching, any evidence concerning cultural differences in the concepts, children already possess, or their manner of acquiring new concepts, or the background of experience and language necessary to the formation of fundamental mathematical ideas is essential. The experiments to be described were performed primarily to provide evidence for just such a purpose. They were carried out in connec-