What Do Preschool Children Know About Number?

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What Do Preschool Children Know About Number?

By | May 2008
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Over the last few decades, developmental researchers have attempted to study mathematical cognition as they seek to understand cognitive changes from infancy to aging since mathematics poses a very interesting set of questions in terms of the fact that mathematical knowledge takes on several forms and its concepts tend to be abstract, complex and sophisticated. Studies of counting, conservation, quantitative comparison, arithmetic, and other aspects of mathematical thinking now provide a rich insight on cognitive development, one in which the development of problem solving, reasoning, memory, perception, and motivation is examined in the context of acquiring knowledge and skills that are culturally relevant and important in the daily lives of children. By exploring differences related to gender, disability, brain injury, and genius, as well as probing the effects of schooling and other characteristics of culture as they have strived to develop tools for educational assessment and for instructional intervention. Before reaching this stage however, one of the primary points of debate has been whether this abstract knowledge of mathematics is an innate quality that infants are born with or whether babies start out with a conceptual blank slate and mathematical abilities are progressively developed in the their minds by observing, internalizing and abstracting regularities about the world. According to the “constructivism” theory of renowned researcher Jean Piaget, the latter seems to be true and he posited that children evolve gradually through characteristic stages of thinking, known familiarly as the sensorimotor, pre-operational, concrete operations, and formal stages of thinking (Piaget, 1952). He examined how cognitive growth takes place, a proposed a model that allows for a continual “folding in” of more complex understandings. Keeping this in mind, Piaget and his many collaborators seemed to believe that young children were unable to grasp or understand...

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