Key words: science

Key words: mathematics, education

Excerpt: The topic of this paper arises in research into developmental psychology in the form of the problem of the relative importance of external conditions and the subjective orientation attainments of individuals. However, it also represents a general philosophical problem, transcending not only questions of the philosophy of science but even problems of epistemology. […] In the first part of this paper I shall describe and criticize various possibilities with respect to preliminary methodological decisions con-||cerning the collection of data in order, in the second part, to delineate an alternative which avoids the errors which have come to light, in the hope that my criticism in the first part is not understood as a general methodological condemnation of a sub-discipline of psychology.

George Kelly’s theory of personal construct psychology is introduced in the context of comparisons with the radical constructivism theory of Ernst von Glasersfeld and the autopoietic theory of Humberto Maturana. Personal construct theory, although written in the decade up to 1955, anticipates in detail many of the epistemological and praxis issues currently concerning practitioners of psychotherapy. Following the comparative introduction, the formal aspects of Kelly’s theory, namely, the Fundamental Postulate and elaborative Corollaries, are explicated within the framework provided by Maturana’s theory. In this the chapter focusses upon the themes of change and stability within self-organizing systems. Finally, specific comments are addressed to the implementation of these theoretical prescriptions in the therapeutic relationship.

This chapter introduces the central concerns of Humberto Maturana’s theory of autopoiesis as they relate to the domain of psychotherapy. Several common terms which are redefined within his theory in an unusual manner are unpacked as to their idiosyncratic significance including the expressions, ‘linguistic behavior’, ‘languaging’, ‘structure determinism’, ‘organization’, ‘structure’ and others. The source material used for this exposition include not only the cited texts but also several workshops from which verbatim transcripts are often used in the form of brief quotations. I have attempted to stay as close to the original material as possible in order to convey both the meaning and the texture of Maturana’s work. This is not an easy theory to grasp, ranging as it does across several specialist fields from the neurophysiology of perception through social communication to epistemology. Nor are the implicative transitions from a theory of biology to the praxis of psychotherapy without complexity and controversy. Nonetheless, Maturana offers a novel theory of conversations which could form the basis of a much needed new paradigm for personal change.

A large number of students enter college each year not knowing basic mathematical concepts such as fractions, decimals and percents. Although many students take mathematics for twelve years in elementary school, junior high school and high school they lack the fundamental processes necessary to be successful in college level mathematics courses. In this paper a teaching model is outlined that will benefit those students in the learning of mathematics and mathematical processes. This model is based on the tenets of constructivism as put forth by von Glasersfeld (1983).