Teachers' knowledge of mathematical content and children's mathematical thinking have been identified as critical elements related to teachers' ability to effectively teach mathematics (Fennema & Franke, 1992; Kazemi & Franke, 2001; Ma, 1999; Peterson, Carpenter, & Fennema, 1989). Literature on teachers' knowledge…

The foundations of knowledge by tradition have been treated analytically, and knowledge has been characterized as a theoretical subject. This article introduces a steering mechanism as the prerequisite for a study of knowledge work and maintenance on empirical grounds. Knowledge is treated synthetically, that is, as something that exists only…

Presents the background, methods, and findings of a study contrasting the levels of cognitive development of community college and university students. Reveals that 48% of both student groups tested were incapable of performing at the formal-operational level (as described in Piaget's Cognitive Development Model). Discusses implications for…

Reported is a study related to diagnosing elements of propositional thinking in the cognitive functioning of 62 sixth- and seventh-grade students. The rationale is based on the work of Piaget and others. Instruments used to diagnose levels of abstract thinking involved using computer simulated experiments (CSE). The direct and indirect effects of…

Describes a study which was designed to determine the effect of a 25-hour introductory qualitative analysis course on high school students' understanding of formal concepts related to electrolytes. Suggests that introductory concrete experiences better prepare students to deal with more formal abstract concepts. (TW)

The associations among cognitive automatization, abstract problem solving, and educational performance were studied using 127 fourth to ninth grade students. A number of measures of fast, automatic, and fluent performance (FAF measures) were used: writing the alphabet; reading from a word list; and mentally performing arithmetic operations. The…

Piaget's model of children's conceptual learning and development was compared with Klausmeier's Conceptual Learning and Development (CLD) model in a longitudinal study. The CLD model suggests four successive levels of concept learning: (1) concrete--recognizing an object which has been encountered previously; (2) identity--recognizing a known…

The Conceptual Learning and Development (CLD) Model specifies four levels of concept attainment (concrete, identity, classificatory, and formal) and three uses of concepts (problem solving, subordinate-supraordinate, and principles). Longitudinal and cross-sectional studies of concept attainment may be conducted. The results of this study of 300…