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)

In this autoethnographic essay, I reflect on my brief personal experiences of conducting field research on ways in which way a small group of Tibetan Buddhist monks enact a monastic total institution in Ladakh, India. More specifically, I analyze my experiences in view of the relationship between dual and nondual mind, as discussed by Henry Vyner (2002) in Anthropology of Consciousness, and use this analysis to develop preliminary insights into the ways in which a Tibetan Buddhist monastery is constituted.

J. M. M. H. Thijssen - Nicolas d'Autrécourt et la Faculté des Arts de Paris - Journal of the History of Philosophy 46:1 Journal of the History of Philosophy 46.1 172-173 Muse Search Journals This Journal Contents Reviewed by Johannes M. M. H. Thijssen Radboud University Nijmegen Stefano Caroti and Christophe Grellard, editors. Nicolas d'Autrécourt et la Faculté des Arts de Paris . Quaderni di Paideia, 4. Cesena: Stilgraf Editrice, 2006. Pp. 329. e32.00. This book is a coherent set of (...) papers resulting from a conference organized by its editors, Stefano Caroti and Christophe Grellard. In the opening paper, William Courtenay rightly observes that the 1330s are an understudied period in the intellectual history of the University of Paris, especially with respect to its.. (shrink)

The aim of this paper is to contribute to the clarification of concepts usually found in books on quantum mechanics, aided by knowledge from the field of the theory of operators in Hilbert space. Frequently the basic distinction between bounded and unbounded operators is not established in books on quantum mechanics. It is repeatedly overlooked that the condition for an unbounded operator to be symmetric (Hermitian) is not sufficient to make it self-adjoint. To make things worse, nearly all operators in (...) quantum mechanics are unbounded. Often one finds statements such as: For any linear operator A we can write a Hermitian operator HA=(A+A+)/2, where Hermitian is thought to mean self-adjoint. Along these lines, self-adjointness of the momentum operator in generalized coordinates, taken from that expression, is questioned. In particular, the redescription in terms of spherical polar coordinates and its implications for the eventual loss of self-adjointness of the momenta conjugate to them are studied. (shrink)

Topic of this paper is the way in which the structure of events features in discourse. We focus on the structure as introduced by verbs that express some sense of progress. First it is shown by means of examples that this structure is anaphorically available in discourse. Then we go on to discuss the different ways in which the same event may be structured within one discourse situation. We give formal representations of the crucial examples in many-sorted dynamic logic.

About one third of patients with epilepsy have seizures refractory to the medical treatment. Electrical stimulation mapping is the gold standard for the identification of “eloquent” areas prior to resection of epileptogenic tissue. However, it is time-consuming and may cause undesired side effects. Broadband gamma activity recorded with extraoperative electrocorticography during cognitive tasks may be an alternative to ESM but until now has not proven of definitive clinical value. Considering their role in cognition, the alpha and beta bands could further (...) improve the identification of eloquent cortex. We compared gamma, alpha and beta activity, and their combinations for the identification of eloquent cortical areas defined by ESM. Ten patients with intractable focal epilepsy participated in a delayed-match-to-sample task, where syllable sounds were compared to visually presented letters. We used a generalized linear model approach to find the optimal weighting of each band for predicting ESM-defined categories and estimated the diagnostic ability by calculating the area under the receiver operating characteristic curve. Gamma activity increased more in eloquent than in non-eloquent areas, whereas alpha and beta power decreased more in eloquent areas. Diagnostic ability of each band was close to 0.7 for all bands but depended on multiple factors including the time period of the cognitive task, the location of the electrodes and the patient’s degree of attention to the stimulus. We show that diagnostic ability can be increased by 3–5% by combining gamma and alpha and by 7.5–11% when gamma and beta were combined. We then show how ECoG power modulation from cognitive testing can be used to map the probability of eloquence in individual patients and how this probability map can be used in clinical settings to optimize ESM planning. We conclude that the combination of gamma and beta power modulation during cognitive testing can contribute to the identification of eloquent areas prior to ESM in patients with refractory focal epilepsy. (shrink)

Supreme Audit Institutions (SAIs) investigate the regularity (conformity to legislation) and performance (economy, efficiency, and effectiveness) of central government policies and administration through the instrument of accountability. Both types of audit have their own research process and set of standards. This article deals with the question of whether this distinction inhibits a proper appraisal of policy and administration and investigates the possibilities for SAIs to attain more integrated assessment procedures. This question is of vital importance, not only to SAIs but (...) to any controlling and inspecting body, whether political or administrative. (shrink)