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,…

Investigates the effects of two context variables on the performance of seventh-grade students on a qualitative and numerical proportional reasoning test. Explores the nature of the relationships between rational number skills, qualitative reasoning about ratios, and numerical proportional reasoning. (Author/YP)

Investigates the effect of cognitive style on the performance of college students on proportional reasoning tasks. Reports that students having proportional reasoning can be misled by the presence of field effects and that there was a significant correlation between the test of field independence and the items of proportional reasoning. (Author/YP)

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)

Research involving cognitive modification and using intervention instruction in general prerequisite cognitive processes has shown that significant and long-term results are possible. Use of intervention instruction involving prerequisite data gathering skills with teachers has been successful in improving ability to use probing questions in…

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…

Assesses the ability of tenth grade students (n=364) to acquire meanings of graphs that are frequently used in their biology textbooks. Indicates that the main source of failure to process information equally well from tables and graphs was not a lack of basic analytical skills but rather a lack of understanding of the relationship between…

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…

One formal operational schema, hypothetical-deductive reasoning, is seen as most important to effective decisionmaking in planning and carrying out classroom lessons. While it is clear that formal thought schema are widely used in teaching, it is also understood that these reasoning schema are themselves dependent upon the more fundamental…

Two years after the end of a two-year intervention program set within the context of science learning intended to promote formal operational thinking, achievement of students (n=234) was tested by their results on British National examinations taken at age 16. Male experimental subjects achieved an average of 40 percent more grades of C or above…

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)