Examines the relationship between development of logical processes required in deductive reasoning and their use by preschoolers, also considering possible explanations for children's deductive reasoning. The relationship of problem content to real-world knowledge and the sequence of presentation of problem types were found to affect the display…

Experiment 1 examined the position that mirror-image confusions reflect an inability among three- to five-year-olds to determine whether their performance level differences reflect differences among nonreaders already attending and those not yet attending to reading cues. Experiment 2 examined the Experiment 1 four- and five-year-olds, identified…

The goal of this study was to find a way to quantify three criteria of representational quality, described by Greeno, so that it would be possible to examine statistically the relationship between representational quality and other variables related to problem solution. The sample consisted of 18 college students, 84 percent of whom had…

Explored are various aspects of drawing graphs on surfaces. The Euler's formula, Kuratowski's theorem and the drawing of graphs in the plane with as few crossings as possible are discussed. Some applications including embedding of graphs and coloring of maps are included. (YP)

Examines the students' understanding of mathematical structure and the relationship between problem solving and the identification of the structure in 13 word problems. Multidimensional scaling and hierarchical cluster analysis were used to assess how subjects organized word problems in their minds. (YP)

Reviewed are 15 studies on cognitive style and problem solving in science education. The effects of problem context, problem type, and three kinds of cognitive style on subjects' abilities to encounter and solve problems are investigated. Three protocols of the subjects' encountering activities are provided. (YP)

From 1984 through 1988, the authors worked with teachers using an inquiry approach to teach high school geometry courses with the aid of the "Geometric Supposers." Problems are a critical component of the approach because they focus attention and energy and guide students in the application, integration, and extension of knowledge.…

Explored are responses of students aged 9 to 13 to linear generalizing problems from both a technical and strategic point of view. The methods commonly used were the same in all age groups and across all three questions, although some students choosing each model varied. (YP)

This project was designed to: (1) assess 7th-graders' metacognitive beliefs and processes and investigate how they affect problem-solving behaviors; and (2) explore the extent to which these students can be taught to be more strategic and aware of their own problem-solving behaviors. The primary assessment was conducted by analyzing video tapes of…

Describes an exploratory investigation of how children reacted to problems with missing, surplus or contradictory data. It was found that the majority of children gave unsatisfactory answers to such problems. (PK)

This investigation focuses upon the question of: (1) how naive subjects organize and represent knowledge when solving problems; (2) how previous experience of a novice is used in solving a problem; (3) what kinds of information and knowledge are sought as well as overlooked by novices when solving problems; (4) what kinds of strategies novices…

The effect on performance of different formats for typical mathematics story problems was studied, along with the relationship of certain learner variables. More than 1200 children in grades 3-8, including over 220 learning-disabled students, were tested and/or interviewed. Story problems were in the usual format found in textbooks, an abbreviated…

This project was based on recent interview research which suggested that in choosing operations for story problems in mathematics many students are guided by computational considerations rather than meanings for the operations. This project aimed to refine the catalogue of strategies used by students and to design and test instructional materials…

In 1986 the United States (U.S.)-Japan Seminar on Mathematical Problem Solving convened to compare the state of problem solving in the classroom and in research in the two countries. The data and results given in this paper are the results of research conducted in the United States in response to the 1986 seminar. The U.S. and Japanese research…