Presented preschoolers and first graders with 3-term inversion problems such as 3 + 2 - 2 and similar standard problems to examine whether children used the inversion principle and if use was based on qualitative identity, length, or quantity. Found that both age groups showed evidence of using inversion in a fully quantitative manner, indicating…

Examines the balance model and identifies the issues that divide scientists. Describes learning situations that were the subject of the empirical study which involved 40 students in two 8th-grade classes. Shows the presence of negative numbers gave rise to many errors. Discusses the relevance of the balance model and analyzes the arguments put…

Studies the role of context in students' uses of alternative conceptual models by using Newton's third law. Identifies four contextual features that are frequently used by students in their reasoning. Probes the effects of specific contextual features on student reasoning using a multiple-choice survey. (Contains 39 references.) (Author/YDS)

Compares two laboratory treatments: (1) Constructing and Applying the Concepts of Physics (CACP) which is guided-inquiry; and (2) Toys in Motion (TIM) which focuses on problem solving skills and design work. Discusses the two laboratory courses and assessment procedures. (YDS)

Focuses on children making sense of multiplication. In an activity called "Silent Multiplication," students use what they know about easier multiplication problems to solve increasingly difficult, related problems mentally. (Author/NB)

Develops computational fluency using a game format. Activities involve a standard deck of playing cards. (Author/NB)

Explains big ideas in algebra that help students connect ideas with procedures in different mathematical topics to build a relational understanding of algebra. (Contains 10 references.) (YDS)

Investigates the efficacy of promoting 8th grade students' problem-solving ability through history of science teaching. After one year of teaching, with the statistical procedure of the analysis of covariance, finds that the experimental group students outperformed their counterparts in the chemistry conceptual problem-solving ability. Initial…

Examines 250 sixth-grade students' understanding of arithmetic average by assessing their understanding of the computational algorithm. Results indicate that the majority of the students knew the "add-them-all-up-and-divide" averaging algorithm, but only half of the students were able to correctly apply the algorithm to solve a…

Describes a study in which concept maps drawn by high school students (n=12) were evaluated using quantitative measures. Results indicate that the concept maps are useful in assessing the understanding of relationships between the concepts required for multiple step problem solving in physics. Contains 12 references. (DDR)

Assesses the ability of university students enrolled in an introductory calculus course to solve related-rates problems set in geometric contexts. Indicates that overall performance on the geometric related-rates problems was poor and the poorest performance was on steps linked to conceptual understanding. (Contains 34 references.) (Author/ASK)

Investigates the metacognitive development of students in a second year chemical engineering course which had such development as an explicit goal. Concludes, among other results, that there is a shift in student approach from a focus on solving problems towards a stronger valuing of conceptual understanding. (Author/MM)

Effective teaching should focus on representational change, which is fundamental to learning and education, rather than conceptual change, which involves transformation of theories in science rather than the gradual building of knowledge that occurs in students. This article addresses the question about how to develop more efficient strategies for…

This study examines a series of children's drawings ("Draw for Math" tasks) to determine the relationship of students' spatial understanding and mathematical problem solving. Level of spatial understanding was assessed by applying the framework of central conceptual structures suggested by Case (1996), a cognitive developmental researcher.…

This study examines Indonesian students' understanding of conservation of matter, balancing of equations and stoichiometry. Eight hundred and sixty-seven Grade 12 students from 22 schools across four different cities in two developed provinces in Indonesia participated in the study. Nineteen teachers also participated in order to validate the…