Proposes analogy as the central mechanism of knowledge acquisition in formal domains. Discusses experimental data on preschoolers' knowledge of one-to-one correspondence and college students' understanding of force decomposition. Suggests that a knowledge base domain is a thematically organized knowledge structure and that thematic relations in a…

Presents a three-phase process that connects writing and cooperative problem solving to each other and to mathematical skills and concepts. The three phases are: (1) writing to communicate mathematics; (2) cooperative learning; and (3) problem solving. Provides examples illustrating each phase. (MDH)

Evaluation of a schoolwide enrichment and resource room enrichment program on problem solving/problem finding for gifted children in grades 3-5 found that the gifted students involved made significantly greater gains than did average ability students receiving the special treatment and significantly greater gains than did gifted students receiving…

Discusses problem-solving evaluation methods and describes the development of an instrument to evaluate an individual's problem-solving processes. Provides an example of the instrument. (MDH)

This paper comments on EC 603 157, which discusses cognitive and metacognitive strategy instruction on mathematical problem solving of middle school students with learning disabilities. The commentary analyzes the separability of cognition and metacognition and raises questions about the identifiable components that contribute to the effectiveness…

A study asked 24 first grade children from 3 different classes to write number sentences and select appropriate alternative number sentences for addition and subtraction word problems. Results indicated that children could be characterized into five clusters according to their flexibility in accepting alternative number sentences and that…

Proposes helping students understand fractions by establishing connections between students' informal knowledge of fractions and the mathematical symbols used to represent fractions. Sample dialogues demonstrate how these connections can be made. (MDH)

Describes the current state of knowledge about human decision-making and problem-solving processes, explaining recent developments and their implications for management and management training. Rational goal-setting is the key to effective decision making and accomplishment. Bounded rationality is a realistic orientation, because the world is too…

A cognitive education program applicable across many classroom settings was evaluated with 147 Australian students in grades 4 through 7 who were or were not exposed to the Process-Based Instruction (PBI) approach. Results indicate the positive effects of PBI on student achievement and student and teacher attitudes. (SLD)

Presents examples that recognize young children's technological prowess and support the case for including two significant curriculum perspectives: an intellectual-processes perspective and a social-expression perspective. Contains 34 references. (Author/PVD)

This study analyzed relations between student achievement in the domain of fractions and the extent to which classroom practices are aligned with principles recommended by current reform frameworks. Hierarchical linear-model analyses revealed that alignment of classroom practices with reform principles was related to student achievement in problem…

Investigated the effects of student working-memory capacity, preference for amount of instruction, spatial problem-solving ability, and school mathematics grades on eighth graders' recall of factual information and conceptual understanding. Pairs of students worked through 16 activities using a dynamic, computer-based geometry program. Presents…

Unique associations between three families of mathematical knowledge and individual differences in the mathematics skills of 103 seventh and eighth graders were studied. Conceptual and procedural knowledge adequately explained individual differences in fraction solving and problem set-up accuracy, but only conceptual knowledge adequately expressed…

Four computer-based training strategies for geometrical problem solving in the domain of computer numerically controlled machinery programming were studied with 60 Dutch secondary technical school students for effects on training performance, transfer of performance, and cognitive load. Results support the utility of worked examples for transfer…

Argues that the unit operations laboratory provides an ideal setting to help chemical engineering students become better engineering practitioners. Describes a summer program at the Colorado School of Mines that incorporates experience into a unit operations laboratory. (DDR)