to enter into the child’s experience and enable him to move toward developing higher mental processes is called the zone of proximal development (ZPD). “The lower level of the ZPD is defined by the child’s independent performance and its upper level is defined by the most a child can do with assistance” (Bodrova, 1997:20). As long as the child’s knowledge remains where improvement is still possible with adult assistance, the child is said to be within the ZPD. With adult help, the child may advance toward independent and autonomous thinking.

One important strategy that the adult employs is called scaffolding, in which questions or discussion are used to help the child advance incrementally to a higher level of thinking. In a way, this is analogous to Piaget’s notion of the child moving from stage to stage. The difference is that in Vygotsky’s approach the movement upward is possible with appropriate guidance; it is not as dependent on the unfolding of an endogenous developmental process. Vygotsky thus gives instruction a more central role in development than does Piaget.

Another critical concept in the Vygotskyan perspective is that of mental tools. For a child to acquire these tools en route to higher-order mental function like abstract reasoning, the child has to be helped by knowing individuals, teachers, or parents. This can occur in school or at home. Mental tools come in various forms including the development of strategies to remember and to solve problems (such as trial-and-error and counting-on strategies), developing analogies, or reviewing related information or ideas. Their common characteristic is that they help the child restructure his thinking. Gelman, in discussing the teaching of arithmetic to young children, emphasizes the importance of recognizing that even the young child develops some knowledge and concepts of mathematics that can be built on (Gelman, 2000). The use of questions and demonstrations can help draw out existing knowledge and build on it, contributing to a restructuring of the child’s understanding.

The last 30 years have witnessed a considerable growth in evidence of strategic and metacognitive competence at an early age, especially when children are asked about topics or problems they understand (Brown and DeLoache, 1978; DeLoache et al., 1998). Children can think about their own thinking and the think-

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