The constructivist teaching experiment is used in formulating explanations of children’s mathematical behavior. Essentially, a teaching experiment consists of a series of teaching episodes and individual interviews that covers an extended period of time – anywhere from 6 weeks to 2 years. The explanations we formulate consist of models – constellations of theoretical constructs – that represent our understanding of children’s mathematical realities. However, the models must be distinguished from what might go on in children’s heads. They are formulated in the context of intensive interactions with children. Our emphasis on the researcher as teacher stems from our view that children’s construction of mathematical knowledge is greatly influenced by the experience they gain through interaction with their teacher. Although some of the researchers might not teach, all must act as model builders to ensure that the models reflect the teacher’s understanding of the children. Relevance: Constructivist teaching experiment, Model building, Clinical interview. Teaching episode, Counting scheme, Teacher as researcher

Two aspects of Vico’s constructivist epistemology are germane to contemporary cognitive developmental psychology. These aspects are Vico’s account of cognitive operations and of the limits to human knowledge of the world. Drawing on Vico’s epistemological treatise, and on contemporary commentary on Vico, it is argued that this eighteenth-century constructivist epistemology is useful in two ways. First, by being a consistent, and so radical, constructivism it may be helpful in clarifying the meaning of the environment in Piaget’s theory. Second, the description of mental operations may provide a way of overcoming objections to the overly formal quality of Piaget’s basic concrete-operational structures.

Key words: Cognitive development, Genetic epistemology, Piaget, Realism, Theory formulation, Vico

Excerpt: If the goal of the teacher’s guidance is to generate understanding, rather than train specific performance, his task will clearly be greatly facilitated if that goal can be represented by an explicit model of the concepts and operations that we assume to be the operative source of mathematical competence. More important still, if students are to taste something of the mathematician’s satisfaction in doing mathematics, they cannot be expected to find it in whatever rewards they might be given for their performance but only through becoming aware of the neatness of fit they have achieved in their own conceptual construction.

Key words: cognition, education

Like many nomina actionis, “interpretation” designates either an activity or its results. When someone says, “I’m not sure how to in-terpret what she did,” it may mean that he sees several possible in-terpretations and does not know which to choose as the most plausible; but it may also mean that he has no interpretation because he sees no way of constructing one. In the first case, the speaker’s quandary pertains to the results; in the second, to the activity. In this chapter, I shall be concerned with interpretation as activity and only incidentally with the appropriateness or choice of its results.

Key words: philosophy, language

Key words: philosophy, cognition

Key words: philosophy, mathematics, development

Key words: mathematics, cognition, development