Differences in mathematical reasoning between typically achieving and gifted children

Mathematical giftedness refers to mastery in a specific mathematical domain at an earlier than expected age. The present study examined which cognitive processes accounted for differences in mathematical reasoning between gifted children (MRG) and their typically achieving peers (TA). Naming speed, phonological awareness, short-term memory, executive functioning, and working memory were examined in 51 children aged approximately 7 years. A series of stepwise regression models, using a contrast variable to capture differences in mathematical reasoning between MRG and TA children, were created to examine which cognitive domains accounted for differences in mathematical reasoning. Short-term memory (r²?=?.08) and visual-spatial working memory (r²?=?.39) emerged as the only cognitive predictors within a model that included gender, age, and fluid intelligence. This model captured all of the variance distinguishing mathematics reasoning between MRG and TA children, explaining an overall contribution of 70% of the variance in mathematical reasoning.     

Penrose's New Argument

It has been argued, by Penrose and others, that Gödel's proof of his first incompleteness theorem shows that human mathematics cannot be captured by a formal system F: the Gödel sentence G(F) of F can be proved by a (human) mathematician but is not provable in F. To this argment it has been objected that the mathematician can prove G(F) only if (s)he can prove that F is consistent, which is unlikely if F is complicated. Penrose has invented a new argument intended to avoid this objection. In the paper I try to show that Penrose's new argument is inconclusive.     

初中数学学习中教师归因与学生自我归因的比较研究

本文研究了初中数学学习中教师的信念与归因．学生自我的信念与归因以及师生归因的比较,得出如下几点结论：(1)在教师和学生的信念中男生在数学学习中更占优势。但在归因领域里却没有发现显著的性别差异。(2)对最好的学生,教师倾向于努力归因;对最差的学生,教师倾向于基础归囚。(3)最好的学生自我归因时倾向于基础和方法归因,最差的学生倾向于努力和方法归因。(4)师生归因维度上的一般趋势：造成数学学习成功的原因比较稳定、内源、可控;造成数学学习失败的原因也倾向于内源,但比较不稳定,不可控。(5)师生特定归因中的差异广泛存在,建议采取相应的教育对策。     

Are People Naïve Probability Theorists? A Further Examination of the Probability Theory + Variation Model

Two experiments tested predictions derived from the Probability Theory + Variation (PTV) model. PTV model assumes that judgments follow probability theory, but systematic errors arise from noise in the judgments. Experiment 1 compared the PTV model to a configural weighted averaging model in joint probability judgment and found more support for the PTV model in diagnostic cases. Specifically, noise was negatively correlated with semantic coherence and conjunction and disjunction fallacies increased when order effects produced more noise in conjunctions and disjunctions. Consistent with both models, judgments adhered stochastically to the addition law. Contrary to the integration rules of the PTV model, we failed to find increased noise in disjunctions compared to conjunctions. Experiment 2 tested predictions of the PTV model for conditional probability judgment. Consistent with the PTV model, noise was negatively correlated with semantic coherence in conditional probabilities and judgments adhered stochastically to Bayes' theorem. Conversion errors were generally more prevalent than conditional reversals, a finding that is not fully consistent with the PTV model. In general, the quantitative fit of the PTV model was relatively better for overlapping and subset problems compared to identical, independent and mutually exclusive problems, especially for semantic coherence. Copyright © 2014 John Wiley & Sons, Ltd.     

GORDON KAUFMAN,FLAT ONTOLOGY,AND VALUE: TOWARD AN ECOLOGICAL THEOCENTRISM

Gordon Kaufman's theology is characterized by a heightened tension between transcendence, expressed as theocentrism, and immanence, expressed as theological naturalism. The interplay between these two motifs leads to a contradiction between an austerity created by the conjunction of naturalism and theocentrism, on the one hand, and a humanized cosmos which is characterized by a pivotal and unique role for human moral agency, on the other. This paper tracks some of the influences behind Kaufman's program (primarily H. Richard Niebuhr and Henry Nelson Wieman) and then utilizes the flat ontology that emerges in the work of philosopher/sociologist of science Bruno Latour and of environmental philosopher Timothy Morton in order to point toward a reconstructed immanent theocentrism that no longer stakes meaning and value on the unique place of the human. Such a theology remains theocentric, but is now fully ecological.     

Deleuze’s Difference

Abstract

This article delineates the core concerns and motivations of the ontological work of Gilles Deleuze, and is intended as a programmatic statement for a general philosophical audience. The article consists of two main parts. In the first, two early writings by Deleuze are analysed in order to clarify his understanding of ontology broadly, and to specify the precise aim of his understanding of being in terms of difference. The second part of the article looks at the work of Heidegger and Derrida in order to distinguish Deleuze’s conceptions of ontology and difference from theirs. A final section clarifies Deleuze’s efforts to undertake the construction of an ontology divergent from the dominant tradition and in contrast to the emphasis on the closure of metaphysics in the thought of Heidegger and Derrida.     

Thoughts,Processive Character and the Stream of Consciousness

Abstract

This paper explores the relation of thought and the stream of consciousness in the light of an ontological argument raised against cognitive phenomenology views. I argue that the ontological argument relies on a notion of ‘processive character’ that does not stand up to scrutiny and therefore it is insufficient for the argument to go through. I then analyse two more views on what ‘processive character’ means and argue that the process-part account best captures the intuition behind the argument. Following this view, I reconstruct the ontological argument and argue that it succeeds in establishing that some mental episodes like judging, understanding and occurrent states of thought do not enter into the stream but fails to exclude episodes like entertaining. Contrary to what it might seem, this conclusion fits well with cognitive phenomenology views, given that, as I show, there is a way for non-processive mental episodes to be fundamentally related to processive ones, such that they cannot be excluded from the phenomenal domain. This paper sheds light on the nature of different kinds of thoughts and questions a fundamental asymmetry between the perceptual and the cognitive domain when it comes to their ontology and temporal character.     

Mathematics and Theology: A Stroll through the Garden of Mathaphors

Mathematics has long been considered the language of science and has even been acknowledged as the universal language of the future. Yet mathematics also plays a less-recognized religious role in that metaphors drawn from mathematics (mathaphors) can influence our spiritual perspectives by helping us to entertain new religious ideas and to challenge old ones. Mathaphors are therefore useful tools in matheology (the study of mathematics and theology). This essay explores ten ways in which contemporary mathaphors affect our spiritual lives. Specifically, mathaphors are: changing our metaphors for God; challenging our human role in the universe; helping us accept ambiguity; revamping our understanding of the one and the many; revising our thoughts about free will and determinism; moving us toward pluralistic, multi-world views; pushing the envelope on what consciousness is; altering our expectations for afterlife; offering the hope of a more compassionate future; encouraging faith perspectives that are always incomplete and in process.     

Scientific Philosophy,Mathematical Philosophy,and All That

This article suggests that scientific philosophy, especially mathematical philosophy, might be one important way of doing philosophy in the future. Along the way, the article distinguishes between different types of scientific philosophy; it mentions some of the scientific methods that can serve philosophers; it aims to undermine some worries about mathematical philosophy; and it tries to make clear why in certain cases the application of mathematical methods is necessary for philosophical progress.     

Good and Bad Years: An Index of American Social,Economic, and Political Threat (1920–1986)

Information provided by 196 U.S. history professors, indicating the degree to which they considered each of the years from 1920 to 1986 threatening to the established order and way of life in America, was pooled to form a social, economic, and political threat (SEPT) index. Interrater reliability was high, and substantial test-retest reliability was evident for a selected subsample over a 6-month period. The index significantly correlated with 11 objective indices of threat, including the suicide rate, unemployment rate, rise and fall of common stocks, and number of military men on active duty. Several studies involving threat and authoritarianism were replicated and in some instances extended with the SEPT index (McCann & Stewin, 1984; Sales, 1972, 1973). The pseudo-archival SEPT index has utility when relatively global estimates of prevailing threat are required for historiometric research testing a diversity of hypotheses gleaned from psychological, sociological, historical, and political science theories.