小学儿童数学态度与数学成就的纵向联系：学业拖延和数学元认知的作用

为深入探讨小学儿童的数学态度、学业拖延、数学元认知与数学成就之间的纵向联系及内在作用机制,对515名三、五年级小学生进行为期半年的追踪研究。结果表明:(1)学业拖延在儿童的数学态度与数学成就之间发挥着即时和纵向中介作用;(2)不同水平数学元认知个体在纵向中介模型中“数学态度→数学成就”这一路径上存在差异。这意味着较积极的数学态度有利于减少小学儿童的学业拖延行为,进而提高其数学成就,而高数学元认知则能够监控和调节个体的数学态度,使其发挥积极作用,从而提高数学成就。该发现为有效促进儿童的数学学习提供了重要实践启示。     

动态测验对“数学学习困难”儿童的进一步甄别

本研究意在考查动态测验对数学学习困难儿童作进一步程度区分的有效性。以传统且常用的数学学习困难鉴别方式和标准选取30名四年级数学学习困难儿童为实验组,30名同年级智力匹配儿童为对照组,以Swanson认知加工测验(S-CPT)的4个子测验为测量工具对被试进行动态测验。结果发现：(1)在传统数学学习困难鉴别方式的基础上,动态测验的“潜在认知能力”指标可以对儿童数学成绩增加19%的预测力;(2)以“潜在认知能力”指标为依据能够将数学学习困难儿童进一步区分为“发展落后”和“发展缺陷”两个水平;(3)“发展落后”儿童一年内数学成绩发生了增长性变化,与正常儿童水平相当,而“发展缺陷”儿童的数学成绩没有变化。研究证实关注潜能指标的动态测验范式在快速、准确甄别数学学习困难儿童上具有独特效用。     

An Evolutionary Topological Theory of Participatory Socioeconomic Development

The epistemological foundation of unity of knowledge is used to formulate a system-model of participatory socioeconomic development. The micro-properties of such a participatory development approach are deeply ethical in nature. In order to bring out the endogenous role of ethics derived from the moral law in reference to the epistemic foundation, and thereby explain their impact on the socioeconomic development experience, the methods of topological space and topological mappings are found to be appropriate for formalizing the complex nature of participatory dynamics. They emerge in the midst of institutional and organic interaction, integration, and evolution. The application of topological methods to participatory socioeconomic development thus opens up a field that is rarely used by mathematical economists. In this sense this article is an original contribution to the area of ethical development theory and its topological explanation and application.     

Early Education in Plato's Republic

In this paper, I reconsider the commonly held position that the early moral education of the Republic is arational since the youths of the Kallipolis do not yet have the capacity for reason. I argue that, because they receive an extensive mathematical education alongside their moral education, the youths not only have a capacity for reason but that capacity is being developed in their early education. If this is so, though, then we must rethink why the early moral education is arational. I argue that the reason is rooted in the nature of moral explanations. These sorts of explanations are rooted in the Forms and thus one can only understand those explanations when they have knowledge of the Forms. But this requires preparation – the very sort of preparation that is provided by both the mathematical and moral educations.     

Mereology and mathematics: Christian Wolff's foundational programme

ABSTRACT

How did the traditional doctrine of parts and wholes evolve into contemporary formal mereology? This paper argues that a crucial missing link may lie in the early modern and especially Wolffian transformation of mereology into a systematic sub-discipline of ontology devoted to quantity. After some remarks on the traditional scholastic approach to parts and wholes (Sect. 1), Wolff's mature mereology is reconstructed as an attempt to provide an ontological foundation for mathematics (Sects. 2–3). On the basis of Wolff's earlier mereologies (Sect. 4), the origin of this foundational project is traced back to one of Wolff's private conversations with Leibniz (Sect. 5) and especially to the former's appropriation of the latter's notion of similarity as a means to define quantity (Sect. 6). Despite some hesitancy concerning the ultimate characterization of quantity (Sect. 7), Wolff's contribution was historically significant and influential. By developing a quantitative, extensional account of mereological relations, Wolff departed from the received doctrine and paved the way for the later revival of mereology at the intersection of ontology and mathematics.     

Plotinus: towards an ontology of likeness (On the One and Nous)

Plotinus’ thesis of the relationship between the One and Nous (Intellect) is central to his thought. In dealing with this relationship, he concentrates far more on what makes the One and Nous alike than on what makes them different. This is because by preference he envisages the One as the ‘causal principle () of everything’, in what might be termed a ‘top‐down’ model of metaphysics in which first cause (the One) leads downwards to second cause (Nous). Plotinus is obliged to present the distinction between the One and Nous as relative, not as absolute, precisely because he wants to show that Nous is firmly grounded in the One. The One differs from Nous to no more than the degree, and in no more than the manner, that are necessary for there to be created a Nous which is as like as possible to the One Itself.     

Traces of Identity In Deleuze’s Differential Ontology

Abstract

Deleuze’s differential ontology is a sustained attempt to think and affirm difference as opposed to the unity of identity he insists philosophical thought has tended to privilege. However, by distinguishing between three senses of identity, termed identity of the identical, same, and common, I show that, while Deleuze’s differential ontology offers a powerful critique of identity in the senses of the identical and same, at numerous points in his analysis, such as the virtual-actual movement, the transcendental conditions defining different forms of thinking, and the relationship between the forms of thinking, it appears Deleuze’s affirmation of difference depends on identity in the sense of the common. Rather than using these instances to offer a critique of Deleuze’s differential ontology, I follow his exhortation to read a philosopher creatively and suggest that distinguishing between three senses of identity reveals the complexity of the difference-identity relationship and acts as a stimulus to rethinking this relationship.     

高考数学试卷多维项目反应理论的分析及应用

高考数学学科试卷的试题综合性较强,一道试题通常考查多种能力属性,而基于单维性假设下的经典测量理论和传统的项目反应理论无法完成该种情形下试卷测量性能分析和考生作答表现分析.本文以MIRT理论为基础,使用CONQUEST软件为工具进行分析,可以获得试卷内部不同能力维度之间的相关以及考生不同维度的能力参数,为提升命题质量和改进教学提供了依据,表明MIRT具有很好的应用前景.由于MIRT理论的复杂性以至于目前分析软件的不足制约其进一步的深入应用,这是今后应该深入研究的问题.     

No time for powers

In this paper, I will investigate the compatibility of different metaphysics of time with the powers view. At first sight, it seems natural to combine some sort of powers ontology with a dynamical view of time, since the dynamic character of powers appears to account for the progression of time. Accordingly, it has been argued that a powers ontology, which is supposed to be inherently dynamic and productive, is incompatible with eternalism, which does not allow for any sort of real productivity. After having reviewed these arguments, I will argue that the powers view is not only incompatible with eternalism but also with the moving spotlight view and growing block theory. I will go on to argue that the specific notion of activity that the powers ontology provides is not straightforwardly compatible with presentism either.     

The Red and The Real

It is often claimed that principles of individuation imply essential properties of the things individuated. For example, sets are individuated by their members, hence sets have their members essentially. But how does this inference work? First I discuss the form of such inferences, and conclude that the essentialist inference is not a purely formal matter: although there is a form which all principles of individuation have in common, it is not true that any statement of that form is a principle of individuation, and hence there is no valid inference based purely on that form. However, I argue that there is a viable version of the essentialist inference nonetheless. The resources for a proper reconstruction of this type of inference can be gathered from reflections upon the role principles of individuation play in the project of the ontologist: such principles turn out to carry a modal weight similar to that of definitions or conceptual truths. It follows that, no matter how austere the ontology, some portion of essentialist modality is inevitable.