This paper discusses ways to use worked examples in teaching mathematics. It is argued that neither investigative teaching such as discovery learning nor lecturing and starting from the abstract are helpful as they are based on emotive associations with general labels rather than precise details of pedagogic strategies. (KHR)

One of the most challenging daily experiences of teaching young adolescents is helping them transition from Piaget's concrete to the formal operational stage of cognitive development during the middle school years. Students who have reached formal operations can design and test hypotheses, engage in deductive reasoning, use flexible thinking,…

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)

Previous investigations on Piagetian cognitive levels among college students both within and across academic disciplines have not addressed the issue of possible differences in cognitive levels between traditional undergraduates and older returning students. Piagetian cognitive levels were studied among traditional- and nontraditional-age college…

Twenty-nine children with learning disabilities (LD) in grades 2 and 4 through 7 were compared with children without LD for their development of proportional structures of thought. Significantly fewer children with LD had constructed second-order logical structures necessary to act on problems using multiplicative and preproportional reasoning.…

As an introduction to exploring the possibilities of an inservice plan to facilitate teacher cognitive development, the theories of educational philosophers and developmental psychologists are cited in arriving at a broad definition of the cognitive development of adults. From these theories it is surmised that teachers do operate at different…

Considers the period of adolescence and describes how cognitive-developmental concerns might apply to the understanding of adolescent problems in interpersonal and affective adaptation. Also investigates ways in which intervention practices with adolescents might be placed within a cognitive-developmental context. (PCB)

This paper reviews some literature on the emergence of formal reasoning and reports a study of reasoning performance of 213 middle grade students in relationship to grade level and chronological age. While a number of large-scale studies have indicated that formal reasoning emerges in a regular progression across age ranges and grade levels, few…

A study in which Logo programming was used to teach problem-solving skills to fourth to eighth grade students is described. The results, and their implications for further use of the computer to teach higher order thinking skills, are discussed. The possible use of Prolog programming to teach reasoning skills is described. (JL)

Attempts to show that not only can density be taught to lower ability pupils but that by doing so, there is the possibility of assisting pupils to develop their reasoning powers. Lists teaching activities that help in this process. (CW)

The reasoning abilities to be expected of the concrete operational and formal operational student, the percentage of secondary science students that are capable of each type of reasoning pattern, and effective strategies to teach science to concrete reasoners are described. Implications for curriculum development are discussed. (KR)

Effective teaching strategies must be developed to help students bridge the gap between concrete operational thinking and full formal thinking in the content areas. Reading for meaning requires readers to categorize subjects, recognize relationships, develop and maintain a sequence of thought, recognize and understand inferences, and draw…

Describes a study which was designed to determine the effect of a 25-hour introductory qualitative analysis course on high school students' understanding of formal concepts related to electrolytes. Suggests that introductory concrete experiences better prepare students to deal with more formal abstract concepts. (TW)

The purpose of this study was to investigate the relationship between the achievement of some abstract concepts in "molecular genetics" and prior knowledge, formal reasoning ability, and sex. The major findings of the study were: (1) prior knowledge had a high significant correlation with the achievement of abstract concepts; (2) the…

Studies 94 undergraduate students in introductory statistics and computer science courses. Applies Formal Operations Reasoning Test (FORT) and Kolb's Learning Style Inventory (LSI). Finds that substantial numbers of students have not achieved the formal operation level of cognitive maturity. Emphasizes need to examine students learning style and…