This paper theoretically characterizes number sense as a set of cognitive capabilities for constructing and reasoning within mental models. This perspective provides support for viewing various aspects of number sense as features of students' general condition of knowing about numbers and magnitude, rather than as skills needing specific…

Identifies and describes the problems students have with the concept of neutralization. Analysis of over 7,500 students' answers to test questions over neutralization showed that many students understand the concept in its original meaning. Students assumed that in any neutralization reaction a neutral solution is formed, even if a weak acid or…

Examines seventh grade life science students, tenth grade biology students, and college zoology students for understanding of the concept of diffusion. Describes the differences among the grade levels in sound or partial understanding, misconceptions, and no understanding. Discusses the effect of developmental level on understanding. (KR)

Analyzes the nature and growth of students' algebraic knowledge and thinking from an epistemological perspective supported by historical observations. Focuses on two crucial transitions: from the purely operational algebra to the structural algebra of a fixed value of an unknown and then to the functional algebra of a variable. (Contains 58…

Discusses a teaching experiment with (n=19) senior and graduate mathematics students. Analysis suggests that students' difficulties with the Fundamental Theorem of Calculus stem from impoverished concepts of rate of change and from poorly developed and coordinated images of functional covariation and multiplicatively constructed quantities.…

Eighteen children (mean age 10.2 years) with mild mental retardation were pretested on a variety of measures and then instructed on Piagetian concepts twice per week for 4 months via a learning set technique. When posttested at semester's end, the children had, with few exceptions, mastered the concepts and made significant gains on the Peabody…

The constructivist hypothesis that the acquisition of domain-specific conceptual knowledge (declarative) requires the use of general procedural knowledge was tested. Students (n=314) were classified as reflective, transitional, or intuitive thinkers and presented with four concept-acquisition tasks. Skill in hypothetico-deductive reasoning…

The complex interactions between picture, text, and learner are examined, based on a 3-D model which describes the context of the learning task. The different strategies that children of various ability levels use in reading from illustrated texts are described. (KR)

The author shows some causes of failure in the creation of mathematical concepts. One is the stiffening of concept cores, which prevents identification of atypical exemplars and solution of atypical problems and causes a bifurcation between the natural system of everyday concepts and the formal system of school concepts. (Author/MDH)

Argues that the cognitive mechanisms in human creativity are, for the most part, sighted rather than blind. Reviews attempts to apply evolutionary ideas to psychology and argues that these ideas do not apply to the psychology of human creativity. An alternative sighted-variation framework is then proposed. (Author/CR)

Students, ages 12, 15, 18, and 23 (n=60 per group), wrote definitions for 16 abstract nouns. Responses were analyzed for Aristotelian style. There was an increasing tendency for students to mention the appropriate category to which a word belongs, core features of the word, and subtle aspects of meaning. (DB)

Demonstrates the need for a process-oriented, constructivist approach to understanding infants' categorization abilities. Suggests that emphasizing the distinction between perceptual and conceptual categorization has been an obstacle to forging an approach. Proposes a more microanalytic consideration of features available to infants at different…

Three longitudinal studies examined means-ends behavior of 6- to 8-month olds. Found that intentional means-end behavior increased between 6 and 7 months, with 7-month olds' performance influenced by the presence of a toy on the cloth. Performance was the same when cloth was attached to or separate from the toy. By 8 months, infants adjusted…

Investigates children's development of causal explanations of success and failure. Compares two measures of causal attribution to show that the use of unipolar scales best depicts differences in causal factors used by children. Explores two hypotheses about the impact of normative context on the development of causal differentiation. (DSK)

Explores the notion that some social interactions are more conducive to the construction of knowledge than others. Describes the use of argumentation as a learning tool during play by analyzing transcripts of the interactions of four-and-a-half year olds. Derives implications for early childhood education from these examples and from a theoretical…