Tasks based on the function concept (y = f(x)) were used in a study charting the development of anticipation in children from 5 through 7 years of age. In each task a desired outcome was a function of a combination of specific, rule-constrained, antecedent conditions. Subjects' behavior was scored according to criteria differentiating six levels…

Piaget's studies clearly highlight two qualitative advances made during the preoperational period. The first is the breakthrough of representational intelligence, beginning around 2 years of age. The second is the emergence of coordinated representational thought, beginning around 4 years of age. This paper focuses on the second advance, which…

This study investigates how students participating in the same curriculum construct understanding in elementary thermodynamics during a semester-long eighth-grade physical science class. Two questions were addressed: (1) How does the learners' understanding change during the study of elementary thermodynamics? and (2) What role do students'…

An influential proposal about aquiring mathematical knowledge is that it entails linking instruction-based concepts to intuitions derived from informal activities. In the case of non-positive numbers, informal knowledge is unlikely to emanate from observing physical objects, because non-positive objects or sets of objects do not exist. However, it…

The purpose of this study was to determine the nature of teachers' implicit in-action mental models about children's minds and learning, as inferred through the ways they teach. The work was based on the theoretical works of D. Schon, L. Shulman, and P. N. Johnson-Laird. Study participants included 24 student, novice, and experienced teachers. All…