Much problem solving and learning research in math and science has focused on formal representations. Recently researchers have documented the use of unschooled strategies for solving daily problems -- informal strategies which can be as effective, and sometimes as sophisticated, as school-taught formalisms. Our research focuses on how formal and informal strategies interact in the process of doing and learning mathematics. We found that combining informal and formal strategies is more effective than single strategies. We provide a theoretical account of (...) this multiple strategy effect and have begun to formulate this theory in an ACT-R computer model. We show why students may reach common impasses in the use of written algebra, and how subsequent or concurrent use of informal strategies leads to better problem-solving performance. Formal strategies facilitate computation because of their abstract and syntactic nature; however, abstraction can lead to nonsensical interpretations and conceptual errors. Reapplying the formal strategy will not repair such errors; switching to an informal one may. We explain the multiple strategy effect as a complementary relationship between the computational efficiency of formal strategies and the sense-making function of informal strategies. (shrink)

The relative neglect of Greek commentary by modern Aristotelian scholarship could be justified, if only the neglectors had sufficient knowledge of the material they disdain. The curt dismissal of ancient views on the active intellect by W. D. Ross is perhaps a paradigm case of misplaced condemnation, for he evidently failed to take account of what their authors were about. It would be open to those who wish to discount these commentators to argue that they were, to a greater or (...) lesser extent, influenced by their Neoplatonism, and that this impairs their judgment on Aristotelian problems. But that would not be sufficient ground for total neglect: it merely indicates the need for careful utilization. One might go so far as to ask whether it is not perfectly possible for a commentator who happened to be a Neoplatonist to offer straightforward and reasonably unbiased commentary on Aristotle. Even if the answer to that question were negative, is it not likely that such Neoplatonic views as he read into Aristotle would at least be slanted towards Aristotelianism? (shrink)

A multicomponential model of authenticity is presented which includes psychosocial, cultural, intrapsychic, personality and capacity related and neurobiological aspects of authenticity. Genetic, political and ethnic influences could also involved in authentic etiology. More research is needed into the correlates of authenticity in order to develop adequate intervention and prevention programs for individuals who demonstrate a lack of authenticity. 2012 APA, all rights reserved).

For a true Platonist the nature of the soul is, in a sense, unproblematic. So too is its status. It is an immaterial entity, with all the attributes that that entails, and it is independent of any body with which it might, from time to time, be associated. And yet this extreme dualism must be modified in some way or other, if any account is to be given of the life and activities of a man, or any other living thing, (...) at least some of which require a body for their exercise. The problems that produced are notorious. The purpose of this paper is to explore how some of them were formulated by one Platonist, John Philoponus of Alexandria, and some of the ways in which he attempted to solve them. (shrink)