In this paper, a focus is made on defining processes at stake in an unfamiliar situation coming from discrete mathematics which brings surprising mathematical results. The epistemological framework of Lakatos is questioned and used for the design and the analysis of the situation. The cognitive background of Vergnaud's approach enriches the study…

An elementary analysis of a common textbook airplane problem is given, and then, as an illustrative example, the possibilities of this mechanism for animal navigation are briefly considered. (Author/MA)

This paper provides an up-to-date review of the relationship between item response theory (IRT) and (nonlinear) common factor theory and draws out of this relationship some implications for current and future research in IRT. Nonlinear common factor analysis yields a natural embodiment of the weak principle of local independence in appropriate…

Criticizes methodological tendencies of economics and sociological researchers who do not ask "how large is large?" Reliance on statistical significance and existence theorems shows the limits of formalistic rather than humanistic research approaches. Argues that serious scholars develop whole arguments and understand the rhetoric of…

This book, one of a series prepared in connection with the Behavioral and Social Sciences Survey (BASS) conducted between 1967 and 1969, deals with problems of statistics, mathematics, and computation as they related to the social sciences. Chapter 1 shows how these subjects help in their own ways for studying learning behavior with irregular…