Challenges Smolensky's theory that human intuitive/nonconscious cognitive processes can only be accurately explained in terms of subsymbolic computations in artificial neural networks. Symbolic learning models of two cognitive tasks involving nonconscious acquisition of information are presented: learning production rules and artificial finite…

A new field of children's learning is emerging. This new field differs from the old in recognizing that children's learning includes active as well as passive mechanisms and qualitative as well as quantitative changes. Children's learning involves substantial variability of representations and strategies within individual children as well as…

Discussion about the nature and varieties of mathematical understanding is presented. Symbolic understanding is defined as a mutual assimilation between a symbol system and a conceptual structure, that is dominated by the conceptual structure. (MP)