Many students encounter difficulty in their transition to advanced mathematical thinking. Such difficulty may be explained by a lack of understanding of many concepts taught in early school years, especially multiplicative reasoning. Advanced mathematical thinking depends on the development of multiplicative reasoning. The purpose of this study…

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)

This report describes a program for developing and improving critical thinking skills in adolescents in order to prepare them for life-long learning. The targeted population consisted of high school math and social studies students from two middle-class communities located in northern Illinois. The students' lack of critical thinking skills was…

Presented is a study in which students' intellectual reasoning development was evaluated following instruction that emphasized formal operations in a traditional lecture format. Results indicated that formal-operational students had significantly more success in the three reasoning areas than transitional students and transitional students had…

Students (n=46) were assigned to one of three instructional groups (descriptive, question design, and hypothesis testing) to test the hypothesis that descriptive learning cycles are not sufficient to stimulate students to reason at a formal operational level. Analyses indicated that the hypothesis-testing group exhibited a significant increase on…

Presents a discussion on the significance of questioning techniques in the development of critical thinking skills. Stresses that teachers can increase a student's mental engagement by using appropriate wait time, increasing nonevaluative responses, avoiding rephrasing a question, and avoiding questions requiring a yes or no response. (RT)

This paper provides an introduction to the Alberta Education Developmental Framework, and describes the provincial department's position on curriculum and the cognitive domain. Intended for use in designing and implementing instruction, the developmental framework delineates the developmental stages and processes through which students progress,…

Developmental assumptions that are frequently regarded as constraints on elementary school science curricula are analyzed. The argument that elementary school children cannot function as experimentalists because they have not yet attained formal operational thought is not supported by the Piagetian or non-Piagetian research reviewed. (SLD)

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)

Presents study findings which explored the effect of teacher reasoning level and teaching style preference on improvement in student-reasoning ability. Reports that students of concrete operational teachers and of inquiry teachers showed greater gains in reasoning ability than students of formal operational teachers and of expository teachers. (ML)

Investigated were gender-related differences in the relationship between the development of formal reasoning skills and learning interests during the early adolescent stage. Results indicated that adolescent boys appeared to develop patterns of formal reasoning before their female classmates. Differences in subject preferences were also found. (CW)

Analogies and examples from student's experiences are frequently cited as important to teaching conceptual material. This study was conducted in order to explore the effectiveness of an analogical teaching technique, which uses a connected sequence of "bridging" analogies, compared with a more standard teaching-by-example technique. The…

A teaching procedure and a curriculum construction model known as the learning cycle is described in this paper and research findings are discussed. Questions investigated include: (1) would students achieve more content understanding if taught with the learning cycle or exposition?; (2) would more content retention be evident if measurements were…

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…