Reports observations of the use of mental aerobics with 48 adults whose median age was 70. Provides examples of the group puzzles and logic, math, and word problems used to enhance cognitive functioning and creative thinking. (SK)

Assessed the effectiveness of instruction in promoting sixth-grade students' conceptual understanding of the concept of averages using a leveling model and an open-ended problem-solving approach. Found that students were more capable of using the leveling approach and applying formal averaging algorithm to solve problems than using the open-ended…

Makes a case for presenting humanistic mathematics and science to elementary school children. Introduces a theoretical yet practical framework for teaching these subjects in K-6 classrooms. Describes components of the humanistic curriculum: interactive/collaborative, holistic/relevant, interdisciplinary, and problem-based. (Contains 43…

Joins an affective system of representation with several cognitive representational systems to try to construct a realistic model for problem solving competence. Discusses two major affective pathways, one favorable and one unfavorable, together with conjectured relationships between affective states and useful or counterproductive heuristic…

Learners' choices of problem solving tools and techniques are influenced by the context in which the problem is encountered, and methods utilized in one context may not be recognized as natural ways to proceed in another. Explores the process of fostering learner-initiated applications of technology to address the wide range of problems outside of…

Reports on a mathematical investigation of fractals and highlights the thinking involved, problem solving strategies used, generalizing skills required, the role of technology, and the role of mathematics. (ASK)

Presents the results of a study that aimed to incorporate a wide range of problem posing situations into students' problem solving in a classroom project with mathematically-able students in the first two years of secondary school. (Contains 15 references.) (ASK)

Analyzed the role of explanations students provide themselves (self-explanation) in solving word problems. Results from six female ninth graders show how students' categorical self-explanations mediate their transfer from the sequential representation of the problem to the tabular one. (SLD)

Presents an activity to integrate literature into the mathematics curriculum that is an interesting springboard to problem solving, an opportunity to research famous mathematicians, and a vehicle to enhance the understanding of mathematics concepts. (ASK)

Considers the circumstances surrounding instances where help is sought and/or provided in a collaborative problem-solving situation. Analyzed videotaped observations of nine groups of three grade 5-6 students working over three 45-minute periods on an open-ended task. Defines hierarchical levels for questions, answers, and outcomes. Indicates some…

Investigates whether high school Algebra I students' (n=29) writing about their mathematical problem solving processes showed evidence of a metacognitive framework. Indicates that various metacognitive behaviors were present in students' writings. Describes the more predominant metacognitive behaviors. (Contains 36 references.) (Author/ASK)

Discusses planning instruction on the basis of children's thinking. First, individualize instruction by adjusting the value of the numbers used for individual children. Second, base problem presentation on the types of thinking prevalent in the class. Third, conduct some instruction in small groups. Fourth, suggest alternative strategies. Finally,…

Presents four card games that can teach arithmetic concepts, reinforce skills, and develop problem-solving techniques. (MKR)

Discusses reasons why problem solving has failed. Offers an alternative approach--the use of investigations in mathematics instruction. Lists the characteristics of an idealized classroom. (ASK)

Describes the mathematical processes that occur during problem solving, reasoning, and communication. Provides examples from mathematics education research with preschoolers. (ASK)