Symbolic objects are cognitive tools children must learn to master very early in life. A crucial factor in cognitive development is the instruction or informational support children receive in social contexts. While numerous studies have investigated the relation between instruction and development in various domains, like language or symbolic…

Research on young children and their understanding and use of models indicates that they have particular difficulty understanding and using symbols that are in themselves interesting objects (have dual representation). Implications for the use of symbols for educational purposes are discussed, reviewing several commonly used symbolic objects. (SLD)

Reports research which reveals the difficulty children have in understanding (1) the real purpose of written language and (2) the abstract, technical vocabulary of language study and reading. (SW)

Four kinds of understanding of mathematics are suggested: instrumental, relational, intuitive, and formal. Each type of understanding is described and illustrated. (MN)