Studied 100 adolescents' approaches to problem-solving proofs and reasoning competence tasks. Found that a formal level of reasoning competence is associated with a deductive approach. Results support the notion of a cognitive development progression from an inductive approach to a deductive approach. (ETB)

Protocols of people attempting to solve syllogistic problems and explaining how they reached their conclusions were examined. Two main groups of subjects were identified. One group represented the relationship between classes in a spatial manner supplemented by verbal representation. The other group used a primarily verbal representation. A…

The effectiveness of coaching active reasoning of students with learning disabilities was studied with 63 grade 4 and 5 students. Students in the coaching condition outperformed students in the two comparison conditions on immediate and one-week delayed tests of factual information and explanations. (Author/SW)

Described are how students (n=2,000) reduce the complexity of multivariable problems. Tendencies toward "functional reduction" in common reasoning are shown to range from a simple reduction in the number of variables considered, to a more elaborate procedure where all variables are taken into account, but in a simplified way involving…

This article describes a 16-session training program to improve analogical reasoning skills in school-age children with language disorders, patterned after R. Sternberg's componential theory of analogical reasoning. Phase I consists of mediated learning experiences in which the instructor focuses on the direct instruction of the component…

College students were assigned to either dyadic or individual problem-solving conditions and were given a series of formal operational tasks. Dyadic subjects solved more problems during the interaction phase than did individual subjects. Among dyadic subjects, interactions were associated with problem solving and pre-to-posttest gain scores. (BC)

Discusses the growing interest in "ethnomathematics," an effort to embrace non-European methods of math in college courses, especially in teacher education courses. Proponents claim they are teaching the same concepts as in traditional math but adding new culturally sensitive reasoning skills. Critics suggest dangers in teaching "politically…

Comparison of the comprehension of proverbs of 200 students (50 each in Grades 6, 8, 10, and 12) found growth in proverb comprehension was most pronounced at two transitional points in development: when students move from late childhood into early adolescence, and again when they move from late adolescence into adulthood. Implications for…

Suggests an elementary school activity and questions to promote five types of mathematical thinking including modeling, logical analysis, inference, optimization, and abstraction. Discusses evaluating activities for mathematical reasoning opportunities. (ASK)

Explores strategies to encourage students' understanding of proportional reasoning. Conducts a study to compare the proportional reasoning of students studying one of the new standards-based curricula with that of students from a control group. (ASK)

Clarifies how students' mathematical reasoning as acts of participation are analyzed in the mathematical practices established by the classroom community. Presents episodes from a recently completed classroom teaching experiment that focused on statistics. Discusses change, diversity, and equity. (Contains 66 references.) (Author/ASK)

To study the developmental interrelationships among various aspects of logico-mathematical knowledge, 80 one- to 4-year-olds were individually asked to build "something tall" with 20 blocks. Percentages of new and significant behaviors increased with age and were analyzed in terms of the development of logico-mathematical relationships. It was…

One of the most basic theoretical areas in the study of visual communication and visual literacy is the nature of representation. Some of the important research in this area is reviewed in this paper, and a model of representation is developed that satisfies many of the philosophical concerns. The paper begins with a discussion on the relationship…

Staff developers who have worked intensively with teachers to promote higher order thinking tend to emphasize similar types of training activities, especially involving teachers in higher order thinking and authentic problem solving in their subjects and translating ideas about the teaching of thinking into specific lessons for students.…

This paper reports on methods of students' justifications of their solution to a problem in the area of combinatorics. From the analysis of the problem solving of 150 students in a variety of settings from high-school to graduate study, four major forms of reasoning evolved: (1) Justification by Cases, (2) Inductive Argument, (3) Elimination…