In this paper epistemological, ontological and sociological questions concerning the statistical significance of sharp hypotheses in scientific research are investigated within the framework provided by Cognitive Constructivism and the FBST (Full Bayesian Significance Test). The constructivist framework is contrasted with the traditional epistemological settings for orthodox Bayesian and frequentist statistics provided by Decision Theory and Falsificationism.

This article explores the metaphor of Science as provider of sharp images of our environment, using the epistemological framework of Objective Cognitive Constructivism. These sharp images are conveyed by precise scientific hypotheses that, in turn, are encoded by mathematical equations. Furthermore, this article describes how such knowledge is pro-duced by a cyclic and recursive development, perfection and reinforcement process, leading to the emergence of eigen-solutions characterized by the four essential properties of precision, stability, separability and composability. Finally, this article discusses (...) the role played by ontology and metaphysics in the scientific production process, and in which sense the resulting knowledge can be considered objective. (shrink)

The current literature suggests that the use of Husserl’s and Heidegger’s approaches to phenomenology is still practiced. However, a clear gap exists on how these approaches are viewed in the context of constructivism, particularly with non-traditional female students’ study of mathematics. The dissertation attempts to clarify the constructivist role of phenomenology within a transcendental framework from the first-hand meanings associated with the expression of the relevancy as expressed by interviews of six nontraditional female students who have studied undergraduate mathematics. Comparisons (...) also illustrate how the views associated with Husserl’s stance on phenomenology inadvertently relate to the stances of the participants interviewed as part of the study. The research questions focus on the emotional association with studying mathematics and how pre-conceived opinions regarding the study of mathematics may have influenced the essences of the experiences of the participants who have studied collegiate-level mathematics. The essences of the experiences of the participants are analyzed using bracketing and epoché to ensure personal biases of the researcher do not affect the interpretation of the expressed essences of the participants. Data collection is accomplished through two series of qualitative interviews seeking the participants’ firsthand impressions of how they view the way instructional design is oriented with regard to mathematics. Additional questions seek to illuminate the participants’ point of view regarding their emotional association with mathematics as well as their opinions and theoretical perspectives on the study of mathematics. (shrink)

Constructivism is at the heart of a pedagogical philosophy going back to Vico, whose view of the interrelationship of the arts and sciences sought to reconstitute the classical paideia. The Vichian idea that human beings can only know the truth of what they themselves have made has theoretical and practical consequences for Vico's pedagogy and view of the university. Vico's ideas on education are extended in the modern period by such thinkers as Cassirer, Piaget and Bateson. At the basis of (...) Cassirer's pedagogical philosophy is his theory of the symbol, the symbol being a universal and transcendent modality in culture. The result of this unifying theory is that symbolism, which is pervasive across the disciplines, provides a moral and ethical means for integrating communication about teaching. Cassirer's thought is compatible with Piaget's, which emphasizes the pluralism of experience and the role of dynamic learning in the construction of meaningful order. Piaget's constructivism assumes that an operational bridge exists to link together the hard sciences, the human sciences, and the historical disciplines. This systems view of epistemological matters is similar in many respects to the one advanced by Gregory Bateson, which is explored in the paper's final section. (shrink)