LEVELS OF UNDERSTANDING OF PATTERNS IN MULTIPLE REPRESENTATIONS

This study explores the influence of different forms of representations on pupils’ performance in complex and simple structured patterns at activities which involved continuing a pattern, predicting terms in further positions and formulating a generalization. Data were obtained from pupils in grades 5 and 6 on the basis of a test. Three levels of cognitive complexity (CC) of the understanding of mathematical relations in patterns were validated based on pupils ’ performance: empirical abstraction of mathematical relations, implicit use of a general rule and explicit use of a general rule. Findings also revealed that the initial representational form affected pupils ’ performance especially at complex patterns. Pupils dealt more efficiently with the pictorial form of representation relative to the verbal one. INTRODUCTION AND THEORETICAL FRAMEWORK Schoenfeld (1992) describes Mathematics as the science of patterns. Like patterns, which involve a series of components progressing in a clear and consistent way, mathematics involve a systematic attempt to discover the nature of the principles and laws that characterize in a rational and consistent manner different theoretica