Teachers across all grade levels agree that problem solving and reasoning are areas of weakness in students. Assessments among U.S. students indicate that these weaknesses persist (NCTM 2014) in spite of repeated calls that date back more than thirty years for increased problem solving, reasoning, and sense making in our schools. The NCTM is…

Cognitively demanding tasks (CDT) (Stein et al. 2000) are necessary for the development of students' mathematical reasoning skills. Research is unequivocal on the importance of giving students opportunities to engage in such tasks. Although current reform efforts call for mathematics learning for "all" students, learners who…

John Dewey discussed the dry school curriculum a century ago. One of the "evils" was a simplified curriculum having an outward appearance of mathematics. Dewey posited that such a simplified curriculum deprived students of opportunities to experience the thought-provoking character of the accumulated wisdom found in human knowledge. Dewey's…

Can middle-grades students determine which of two rectangular prisms has a larger volume? Can they do so without using a formula? Geometry, and particularly the concept of volume, is important in many subjects, such as physics and chemistry. Students greatly enhance their mathematics knowledge when they make generalizations and construct arguments…

A study found gifted middle schoolers (n=60) solved analogous problems better when presented in verbal form, but improved skills in both modalities once exposed to the solution of analogous problems in the visual-humorous modality. Average children (n=60) tended to solve cartoons better, but working with cartoons increased verbal problem-solving…

Outlines four solution methods for the Mangoes Problem, discusses how middle school students have approached the problem, suggests generalizations of the problem, and gives an example of a related problem that can be used as an extension to explore the four strategies discussed. (MKR)

Thirty-eight sixth graders were trained in fraction calculation through progressive transformation dialectics (PT) whereas a control group of 38 was taught through a traditional mathematics education framework. The PT group, encouraged to form network-type knowledge representations, performed better on problems that required more than mere…

Describes a study to determine middle school children's representational strategies to form part-whole or part-part relationships for relational numbers such as proportions, ratios, or fractions. Quantitative and qualitative analysis revealed that children prefer a part-part representation to solve relational quantity problems. (15 references)…

Reports on the design and study of a new computerized environment enabling a variety of metacognitive supports in different phases of the problem-solving process and designed to influence students' metacognition during word problem-solving. Results indicate that learning environments that provide metacognitive support during the solution process…

A testing procedure used by J. W. Getzels and M. Csikszentmihalyi (1964) to gauge the relationship between problem finding and creativity in art students was employed in a study designed to determine if the same relationship existed in writers. Subjects were middle school students identified as either creative or noncreative by two separate…

A study designed to test the Piagetian theory that distinct stages in the organization of memory relating to horizontality correspond to successive stages in operative level was conducted with 154 twelve- to fourteen-year-old subjects. Loglinear and path analysis models were used to describe the association between operative level and spatial…

This study assessed use of five computerized analogy problems as a measure of mental speed with 62 children (ages 3-13) with mild/moderate mental retardation. Results found medium to high correlation between scores on the tasks and other cognitive measures and the adaptive behavior scale. The value of assessing cognitive speed in the cognitive…

Described is a model for planning and conducting an investigation designed to teach science process skills. Use of this model illustrates the generalizability of process skills and facilitates their inclusion in novel curriculum areas and beyond the classroom. (DS)

Discussed are science activities appropriate for middle school students. Considerations include the degree of abstractness of the concepts and the need for increased class time for explaining, discussing, and integrating students' activity experiences. (DS)

Middle school and college students were assessed on percentage. Better students in each group were given word problems involving percentage and asked to think aloud as they solved problems. College students made more use of strategies for control and monitoring of their own procedures. A three-stage model for problem solving is then hypothesized.…