Performance in cognitive tasks involves two distinct processes; acquisition of knowledge and cognitive control over knowledge already acquired. A conceptual and analytic framework is presented which allows for the disentanglement of knowledge and control, and for the quantification of each. (Author)

The concept of equivalence is shown to be an elusive one that provides difficulty for preschoolers through college students. The idea persists that the equal sign is a "do something," or operator symbol, rather than a symbol for an equivalence relation. (MP)

After an overview of several studies of cognitive instruction used with problem learners, the article describes two learning mechanisms that explain why such cognitive interventions work--prolepsis (communication that initially leaves implicit some information) and reflective abstraction (changing observables into meaningful internalized…

This paper summarizes what the author considers to be the best advice available at this time for applying Piaget's theory in the chemistry classroom to understand the difficulties that some students have. The identification of students who are operating at the concrete operational or formal operational level is discussed along with the actual…

Two phenomena related to the quality of student responses in regard to items used in a testing situation are involved in the construction of a pupil response model. The underlying phenomenon which defines the individual's cognitive limits is termed the hypothetical cognitive structure (HCS). The second phenomenon, which is a function of not only…

Reports a study of 99 twelfth graders to determine the nature and extent of misconceptions in chemical equilibirum and its relationship to achievement on tasks involving concrete and formal thought. Results indicate assessment of the student's cognitive level of development should be attempted prior to introducing formal level chemical…

This document focuses on one child's skip counting methods. The pupil, a second grade student at Steuben School, in Kankakee, Illinois, was interviewed as she made several attempts at counting twenty-five poker chips on a circular piece of paper. The interview was part of a larger study of "Children's Conceptions of Number and Numeral,"…

Three examples of teacher and student exchanges in mathematics classes are presented which typify the qualitative difference between children's thinking and adult's thinking. The cases explored also illustrate differences caused by cultural factors. (JP)

Asserts that metacognition is one of the most important developments in the contemporary study of learning. Proposes a theoretical analysis of a number of interrelated issues with regard to their importance for metacognition. Focuses on strategy selection in light of the impasse-based theories of problem solving. (CFR)

A Piagetian Task Instrument (PTI) consisting of three tasks developed by Piaget was administered to 141 preservice elementary teachers enrolled in a mathematical class, 19 preservice secondary mathematics teachers, and 11 calculus honors students. This instrument was scored by methods similar to those of Schwebel (ED 063 896) and McKinnon and…

The author seeks to clarify the difficulty and complexity of the things youngsters must do to learn mathematics, and to have teachers question their own views about children in redefining mathematics instruction. (MP)

Although many articles in the education literature recommend how to teach statistics more effectively, there is little published research on how students actually learn statistics concepts. The literature reviewed in this paper indicates a need for collaborative, cross-disciplinary research on how students come to think correctly about probability…

Begins with the assumption that by practicing something one often learns something else. A discussion is presented on the historical and social development of knowledge, the cognitive development of students, the role of teachers, and the meaning of learning situations. (PK)

This 27-item bibliography represents the variety of articles added to the ERIC database from 1983 through 1988 on left-brain/right-brain research, theory, and application as it relates to classroom incorporation. Included are conflicting opinions as to the usefulness of left-brain/right-brain studies and their application in the learning…

An intensive, naturalistic study tracked one six year old's learning for six months and more. The study was inspired by the hope that with concepts of Artificial Intelligence and sufficiently detailed observation, the path of knowledge development could be described through observing significant learning experiences. Included is a reasonably…