University students' answers to a "Minds on Physics" problem revealed six distinct approaches to the solution. Discusses implications for teaching and assessment. (Author/WRM)

Discusses and presents examples of alternative styles of transmitting mathematical knowledge at the tertiary level, with a view to promoting debate on the issue. Emphasizes processes rather than skills, and considers problem solving and peer tutoring. (Author/ASK)

Investigated relationships among different types of errors occurring during probability problem solving by 50 graduate students without mathematical sophistication. Categorized errors as text comprehension, conceptual, procedural, and arithmetic/computation errors. Discusses implications for the teaching and learning of probability problem…

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…

Presents three classification activities in which students work in cooperative small groups using physical materials to foster flexible thinking in doing mathematics. Concludes that attribute blocks are useful physical manipulatives for promoting classification activities and problem-solving skills. (ASK)

Describes a fifth-grade student solving the "Food for Thought" problem featured in the February 1998 issue. (ASK)

Clarifies how the relationship between macro and micro social contexts has been addressed in the Vygotskian and Neo-Piagetian approaches to learning. Discusses how these insights can be used to broaden the basis for studying interactions in mathematics classrooms and concludes with ideas for new developments in socio-cultural theory. (Contains 92…

Aims to find the influence of overcoming fixation in mathematical problem-solving towards divergent thinking in open-ended mathematics problems. Presents findings from an investigation of Japanese junior high school students. Reports that students who can overcome fixation in mathematics can contribute varied and original ideas in open-ended…

Compares a teaching program designed to enhance schema acquisition with one of worked examples, traditionally used to teach geometry. Shows that both groups of subjects had improvements in the number of problems solved, with those exposed to non-goal-specific procedures demonstrating greater rates of improvement and greater efficacy in…

The author's experiences with short-term interventions show that students with identified learning disabilities exhibit no problem-solving difficulties when problems are interesting and engaging. In fact, studies show that adolescents with suspected learning disabilities can match nondisabled students' performance on complex math problems.…

Analyzes a didactical sequence for the teaching of addition and subtraction procedures and algorithms. Uses didactical procedures by children in problem solving activities in order to gain a better understanding of the interaction between numbers, numeration, and operations knowledge which are involved in the construction of addition and…

Jinfa Cai's study comparing Chinese and American sixth-grade students' mathematics performance found that American students did better on simple and complex problems than on computation. One reason might be Asian countries' stress on rote learning. Paul George's 1995 monograph "Japanese Schools: A Closer Look" found instruction…

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)

Develops and tests a learning environment for teaching and learning how to model and solve mathematical application problems using four classes of fifth graders. Indicates that the intervention had a positive effect on different aspects of pupils' mathematical modeling and problem solving abilities. (Contains 62 references.) (Author/ASK)

Discusses findings from a research study designed to characterize students' development of significant mathematical models by examining the shifts in their thinking that occur during problem investigations. Reveals four sources of mismatches that were significant in bringing about the occurrence of shifts in students' thinking. (Contains 16…