Although it is commonly assumed that increases in mathematical knowledge and problem-solving skill alter one's understanding of mathematical problems, little research exists to support this assumption. The present study investigated the relationship between mathematical background and problem perception in two experiments. Experiment 1 employed…

Experts' perceptions of mathematical problem structures were compared with students' perceptions before and after a course on mathematical problem solving. After the course the students perceived problem relatedness more like the experts, indicating that criteria for problem perception shift as a person's knowledge bases become more richly…

Describes a study which concluded that, to restructure the mathematics curriculum, modification of existing teaching practices is required. Recommends that practices be modified to enable students to construct effective knowledge bases and become active learners. Contains 38 references. (DDR)

Investigates reasoning strategies students use in solving stoichiometric problems and explores the relation between these strategies and alternative conceptions, prior knowledge, and cognitive variables. Results show how stoichiometric relations produce conflicting situations for students leading to conceptual misunderstanding of certain concepts.…

Students' strategies for solving long division problems under a realistic mathematics approach (RME) at Dutch primary schools were categorized in two ways: (a) according to the level of how students created multiples of the divisor (chunking) to be subtracted from the dividend; and (b) according to their use, or nonuse, of schematic notation.…

The curriculum for eleven-year old students in the United Kingdom, currently adopted by most schools, includes solving linear equations with the unknown on one side only before moving onto those with the unknown on both sides in later years. School textbooks struggle with the balance between developing algebraic understanding and training…

Although the distinction between verbal ability and spatial ability is fundamental in all models of human abilities, differences in the relative strengths of verbal and spatial abilities have failed to show consistent interactions with instructional treatments. This study investigated the hypothesis that spatial tests measure different abilities…

This study investigated patterns and effects of cognitive tools usage during engagement with an open-ended hypermedia learning environment. Seven technical institute students engaged in problem-solving tasks concerning anatomy and physiology. They used 16 cognitive tools embedded in a hypermedia system and their tool use patterns and corresponding…

Third grade children (n=24) who were administered the standard, simultaneous version of the Matching Familiar Figures test committed fewer errors when administered a sequential version of the same test than did subjects (n=24) who took the more difficult sequential version first. (PN)

Comparison of performance in 3 practical problem-solving tasks by eighth graders in Singapore (170 boys, 107 girls matched for aptitude, attitude, and prior knowledge) indicated that girls distinctly preferred content familiarity and outperformed boys in several processes/skills when familiar with content. (SK)

Explores high school students' collaborative efforts in solving qualitative physics problems and investigates how and whether confronting students with varying views improves problem solving skills. (Contains 22 references.) (DDR)

Four experiments were conducted to determine the source of difficulty of Wason's THOG problem. The THOG problem permits examination of the way people tackle a novel hypothetico-deductive problem. The results are interpreted as demonstrating the importance of problem presentation in problem solving. (Author/PN)

Presents strategies for encouraging dialog with students from eliciting preconceptions to bringing closure to a unit. Includes the general structure of an instructional unit that employs dialog, strategies for teachers to use, and strategies for students which include active listening. (DDR)

Tested the effects of prior knowledge and two instructional models--structured problem solving and guided generation (GG)--on mathematical problem solving and transfer to an analogous task. Data on students with high and low prior knowledge highlighted significant main effects for prior knowledge, significant differences on transfer to analogous…

Analyzed 1.5- and 2.5-year-olds' problem solving and learning. Found that changes in toddlers' strategies could be assessed reliably on a trial-by-trial basis, that changes followed the basic form predicted by the overlapping waves model, and that analyses could reveal information about the qualitative and quantitative aspects of their learning.…