An investigation of the informal mathematical knowledge and competencies of reception class entrants.
Recent research on the mathematical achievement of young children prompts one to question the widely accepted views of Piaget in this regard. Researchers have begun to concentrate on assessing the development of mathematical concepts in appropriate contexts. Aubrey (1993), Hughes (1986) and Gelman and Gallistel (1978) examined the mathematical competencies of pre-school children and suggest how this knowledge could inform instruction and curriculum development. This study investigates the mathematical knowledge and competencies of 40 reception class children from English speaking, working class homes in Pietermaritzburg, Kwazulu-Natal. The assessment tasks were adapted from those of Aubrey (1993), Young-Loveridge (1989) and Wright (1991). These are compatible with the key number activities in the "Learning Through Activity Programme" used in the reception class in this province. The tasks were presented during individual interviews, using everyday objects and familiar activities. Tasks included rote counting, understanding the cardinality rule, numeral recognition, written representation of numbers, ordering numbers, addition and subtraction with concrete objects, social sharing and multiplication, estimation, patterning and an understanding of shape, space, measurement, time, and ordinal numbers. The results confirm the findings of previous studies: most children enter the pre-school year with considerable knowledge about number. Low-attaining children had some basic number knowledge but could not cope with higher numbers or more abstract tasks. Higher scoring children were already competent in most areas of the reception class mathematics curriculum. As the curriculum is suited to the low scorers, the majority of pupils are not provided with challenges to advance. Teachers may be unaware of the extent and range of children's mathematical knowledge, and the strategies used for manipulating numbers. Initial and ongoing assessment of each child's competence would enable teachers to develop and evaluate a meaningful curriculum. For every child to realise his/her potential implies instruction that is appropriate to the level and pace of learning. Further research should refine the assessment of children's mathematical knowledge and investigate the influences upon later mathematical achievements.