ABSTRACT
This chapter analyses of early mathematical competence emphasize relations between the content of the subject matter of mathematics and performance of tasks, a topic of concern for at least a decade. The postulate principles to provide a basis for defining knowledge in a domain. The fact that principles define the equivalence class of counting behaviors is relates to another characteristic they possess. The knowledge structures uses in deriving plans and meaning structures as competence, following Chomsky, who introduced the term to refer to implicitly understand rules of syntax used in deriving correctly formed sentences. The goal of the chapter is to develop and extend notions about the components of competence. Counting–linked competence is clearly domain relevant and, as will see, can even serve as a source for learning further principles. In the case of counting, additional cognitive components, including domain-linked knowledge, procedural competence, and interpretative competence, are all needed to derive competent plans for action.
