This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…

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,…

Discusses two strategies that provide concrete-thinking students with opportunities to develop and use formal or critical-thinking skills. Describes using task analysis and long-term investigations in the classroom. (YP)

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…

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)

Reviews research related to teaching and learning higher cognitive level objectives from a constructivist perspective. Examines several factors including the cognitive demands of academic work, classroom management, delivery of instruction, formal reasoning ability, grouping of students, and motivation to learn. Concludes that an active teaching…

Reviews recent research addressing the problem of matching students' cognitive levels to science textbooks. Suggests that most texts are written above the level of the students for whom they are written. Promotes experiential learning at the middle level and concentration on "right thinking" rather than on "right answers." (CW)

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)

Reports on a study designed to determine the effectiveness of two video programs with an audience of varied ages, grade levels, and developmental levels. Indicates that a significant difference was found between concrete, transitional, and formal operational students on pretest scores and developmental levels and results on the posttest. (RT)

This paper has two purposes: (1) to explain briefly in terms of Piaget's theory why relationships are fundamental for constructivist teachers; and (2) to show how constructivist teachers can think about relationships in classroom activities. In a nutshell, the message is that the process by which children are constructing their intelligence,…