The 16 units of this book are designed as textbook supplements to encourage students to think mathematically and as mathematicians. Each unit begins with an orientation session which raises general concerns that always occur within mathematical exploration. This is followed by a short, original text in which a mathematician creates a particular…

This paper introduces successive and coordinate intellectual thinking skills, using concepts as a best case example. The attributes and optimal presentation requirements of successive and coordinate concepts are reviewed, and types of errors commonly associated with successive and coordinate skills are delineated. The effects of both of these…

The purpose of this paper is to review literature on analogical reasoning, to work out the implications of Polya's model of analogical problem solving, and to propose an alternative model of instructional design based on the use of analogical reasoning. Justification of the model is based on research on the nature of analogical thought and an…

A study involving 120 undergraduate students attending the University of St. Thomas in St. Paul (Minnesota) was undertaken to test the interactive effect of instructional strategy (structured versus constructed) with learner's prior domain knowledge in concept acquisition. Previous instructional design research on concept learning has focused on…

A research project explored the idea that reasoning develops in distinct phases of thinking as individuals journey from simplistic learning of facts to highly proficient consequence predicting of integrated relationships. These results were derived from a study that examined the thinking processes and problem-solving actions of 13 students and…

Working on the hypothesis that if readers had several alternative correct meanings of a given text set before them they would select the one in accordance with their abstract abilities and intellectual maturity, a study investigated the measurement of levels of meaning as illustrated in taxonomies and focused on the applicability of the taxonomies…

Two questions arise in examining the implications of physical education: Is physical education an education of the physical? and Is physical education an education through the physical? In these two questions there are two distinct points of view, two different ways of understanding the meaning, scope, and aim of education, two conceptions of man,…

The field of education has largely ignored the concept of the dialectic, except in the Socratic teaching method, and even there bipolar meaning or reasoning has not been recognized. Mainstream educational psychology bases its assumptions about human reasoning and learning on current demonstrative concepts of information processing and levels of…

To determine the impact of causal relationships and shared features in the use of analogy, subjects in two separate studies were informed of the behavior of six members of a little known primitive tribe and asked to make predictions on the behavior of additional tribe members based on their perceived similarities with the original group. Results…

Sixty adolescents, stratified by sex and grade level (i.e., 9th, 12th, and college sophomore) participated in an examination of Piaget's suggestion that the formal operations are prerequisite to the development of political idealism, abstract thought and future time perspective in adolescence. Analysis of the cognition data revealed that the…

The author discusses the therapeutic mechanisms in group therapy. After considering the views of three authors, the following four mechanisms seem to be accepted generally: ventilation, acceptance, spectator therapy and intellectualization. (SE)

This study investigated the emergence of combinatorial competence in early adolescence and the effectiveness of a programmed discovery training procedure. Significant increases in combinatorial skill with age were shown; it was found that the expression of this skill was significantly facilitated if problems involved concrete material of low…

Intended for college instructors interested in promoting and developing intellectual abilities in their students, this publication details the Perry and Toulmin models of cognitive development. The first section explains the Perry model of dualistic students, who are comfortable in a framework of absolute knowledge and unquestionable right and…

A technique to teach cognitive skills to directly facilitate abstract and rational thinking is described. Based on George Kelly's theory of personal constructs, his Role Construct Repertory Test has students construe similarities and differences among important course concepts rather than provide individual definitions or examples of those…

The foundations of knowledge by tradition have been treated analytically, and knowledge has been characterized as a theoretical subject. This article introduces a steering mechanism as the prerequisite for a study of knowledge work and maintenance on empirical grounds. Knowledge is treated synthetically, that is, as something that exists only…