Teachers who are experts in certain subjects, such as science and mathematics, use the child's everyday knowledge and associations to create a new basis of knowledge and open the possibilities of critical thinking. Particularly, Renshaw shows how Davydov applied these concepts to the mathematics curriculum.

According to Davydov, and indeed as Vygotsky notes, children do not acquire specialized, organized, or scientific knowledge in an automatic manner. In this, the latter rejects the transmission model of learning, which "allows" children to assimilate knowledge by exposing them to it rather than consciously imparting it to them. Instead, a child needs specialized guidance via a social process that combines everyday experience with more abstract notions. Basing his views on this, Davydov holds that a mathematics curriculum, particularly at the elementary level, is to follow a logical, psychological, and didactic procedure. In this way, children are led towards greater knowledge in steps that focus...
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