This paper reports results related to the development of a consistent descriptive language for research on mathematical reasoning. Ways of reasoning deductively are highlighted, using examples drawn from observations of young students. One-step deductions versus multi-step deductions, known versus hypothetical premises, and single versus multiple…

This research evaluates the effectiveness of computer-mediated support for students' individual and collaborative argumentation. "Convince Me" is a "reasoner's workbench" program that aids students in generating and analyzing arguments, providing feedback on argument coherence from a general computational model. Laboratory studies indicate that…

A cross-sectional study examined age differences in children's conceptions of early U.S. history. Students in grades 2, 3, 6, and 8 (n=281) were asked to respond to a question about how the United States became a country. Their essays show significant changes with age. Older students were more likely to include errors of historical fact in their…

Specific illustrations are given of questions and problems designed to lead students in introductory physics courses into visualizing and reasoning qualitatively about physical phenomena. Examples include phenomena related to mechanics, electrostatic/magnetic interactions, resistive direct-current circuits, and Thompson's experiments marking the…

Four experiments compared three alternative models of linear syllogistic reasoning: (1) linguistic; (2) spatial; and (3) mixed linguistic-spatial. The mixed model, indicating the importance of both verbal and spatial ability, was supported by all four experiments, and for about three-fourths of the undergraduate students studied. (Author/GDC)

Depression has been linked to cognitive deficits and learned helplessness models in various theories. To examine depression effects on abstract problem solving ability and the relationship between intelligence and anxiety, 66 of 303 college students (23 male, 43 female), evidencing least and most depressed states as assessed by the Beck Depression…

Studies exploring the transition from early to middle adolescence have found a significant increase in formal-operational thinking, but it is questionable whether the typical adolescent is capable of consistently applying formal operational logic. To examine the relationship between Piagetian-based training techniques and formal-operational…

The study examined the relationship between language and mathematics with 11 classes of deaf students taking Algebra 1 or Algebra 2 at the Gallaudet University School of Preparatory Studies. Specifically, the study attempted to predict the difficulty of a variety of relatively simple algebra problems based on the abstractness of the math and the…

Students and instructors may be frustrated with students' lack of understanding of sociological concepts. We suggest that the difficulty of teaching and learning sociology is that sociological concepts and relationships require the use of abstract reasoning patterns. Many students are unaccustomed to using these abstract reasoning patterns. We use…

The effect of verbal contextual information on junior high school students' categorization of differences among photographic art was examined. Photographs of varying levels of abstraction were presented to the viewers both with and without correct and erroneous titles that referred to descriptive or interpretive information. Twelve students…

This study compared the performance of 51 gifted Caucasian children on the Stanford Binet LM and the Stanford Binet Fourth Edition (SB4) to determine whether significantly different scores would be obtained. The 33 male and 18 female subjects were from middle and upper-middle class families in a western urban area. Their developmental histories,…

An inservice model was developed to assist teachers in asking students the kinds of questions that facilitate higher order thinking. Higher order thinking involves problem identification and definition, hypothesizing, collecting, analyzing and synthesizing data, and formulating conclusions that upon application will prove valid. Based on this…

Students (N=22) enrolled in secondary school biology were evaluated for their abilities to use: combinatorial logic; correlational reasoning; separation and control of variables; exclusion of irrelevant variables; proportional reasoning; and probabilistic reasoning. Each student responded individually to six Piagetian tasks designed to measure…

A study of the development of abstract noun definitions in children and adolescents had as its subjects 120 students evenly divided into age groups of 10-, 14-, and 18-year-olds, randomly selected from students scoring in the 40th to 88th percentiles on the Iowa Test of Basic Skills (for 10-year-olds) and the Tests of Achievement and Proficiency…

An experiment concerning children's conceptions of price was conducted to investigate the influence of the context of a problem on its apprehension. A total of 120 children of several age groups (nursery school, grades 2, 4, and 6) were interviewed individually. An initial question was asked ("Why does a bun cost about one Swedish…