流畅体验、内/外动机、数学焦虑及数学成绩的路径分析

目的：研究旨在考察数学学习中的流畅体验,探讨流畅体验、内/外动机、数学焦虑及数学成绩的关系。方法：招募296名高中生,在数学月考后完成自编考试流畅体验量表、学习动机量表、数学焦虑量表。结果：路径分析表明,存在四条显著路径,即内部动机→流畅状态→数学成绩;数学焦虑→流畅状态→数学成绩;外部动机→流畅状态→数学成绩;外部动机→数学成绩。结论：只有通过考试过程中的流畅体验,内部动机和数学焦虑才能影响考试成绩。     

Mathematics,science and ontology

According to quasi-empiricism, mathematics is very like a branch of natural science. But if mathematics is like a branch of science, and science studies real objects, then mathematics should study real objects. Thus a quasi-empirical account of mathematics must answer the old epistemological question: How is knowledge of abstract objects possible? This paper attempts to show how it is possible. The second section examines the problem as it was posed by Benacerraf in ‘Mathematical Truth’ and the next section presents a way of looking at abstract objects that purports to demythologize them. In particular, it shows how we can have empirical knowledge of various abstract objects and even how we might causally interact with them. Finally, I argue that all objects are abstract objects. Abstract objects should be viewed as the most general class of objects. The arguments derive from Quine. If all objects are abstract, and if we can have knowledge of any objects, then we can have knowledge of abstract objects and the question of mathematical knowledge is solved. A strict adherence to Quine's philosophy leads to a curious combination of the Platonism of Frege with the empiricism of Mill.     

Quine, Analyticity and Philosophy of Mathematics

Quine correctly argues that Carnap's distinction between internal and external questions rests on a distinction between analytic and synthetic, which Quine rejects. I argue that Quine needs something like Carnap's distinction to enable him to explain the obviousness of elementary mathematics, while at the same time continuing to maintain as he does that the ultimate ground for holding mathematics to be a body of truths lies in the contribution that mathematics makes to our overall scientific theory of the world. Quine's arguments against the analytic/synthetic distinction, even if fully accepted, still leave room for a notion of pragmatic analyticity sufficient for the indicated purpose.     

Making Sense of Groups,Computers, and Mathematics

In this article, we report the findings of research that was designed to identify factors associated with learning mathematics in groups with computers. The study was influenced by different theoretical perspectives on social interaction and learning mathematics, and we describe how we attempted to integrate these approaches into the research design. To cope with complex data based on eight groups of six students (aged 9-12 years), we developed a methodology that involved moving between quantitative and qualitative approaches in an iterative spiral. In this article, we focus on the patterns of learning associated with two group tasks incorporating the use of Logo. Quantitative analysis of learning measures indicated positive learning gains as a result of the groupwork, with no differences across gender or ability; qualitative and quantitative analysis of process factors pointed to explanations for the differing profiles of success across groups. Although balanced coconstruction at the computer, coupled with the coordination of others' perspectives, was most advantageous for learning conceptually based mathematics, this was not the case with "technology-driven" mathematics, where fragmentation and concentrated work at the computer proved to be more efficient. These findings suggest that detailed specification of the learning goal is crucial when evaluating groupwork within educational settings.     

Foundations of Mathematics: Metaphysics, Epistemology, Structure

Since virtually every mathematical theory can be interpreted in set theory, the latter is a foundation for mathematics. Whether set theory, as opposed to any of its rivals, is the right foundation for mathematics depends on what a foundation is for. One purpose is philosophical, to provide the metaphysical basis for mathematics. Another is epistemic, to provide the basis of all mathematical knowledge. Another is to serve mathematics, by lending insight into the various fields. Another is to provide an arena for exploring relations and interactions between mathematical fields, their relative strengths, etc. Given the different goals, there is little point to determining a single foundation for all of mathematics.     

Process Ontology: Conversations and Argumentations,Controversies in Mathematics and Mathematics as Socialisation

To better conceive the socializing and pragmatic aspects of mathematics, it can be useful to use a process ontology, which allows, starting from an analysis of the processes of conversations, to compare their recourse, from degree to degree, to supposedly common “virtualities”, in particular in argumentative conversations, with the construction of more complex mathematical entities that allow new symmetries, but also with controversies between mathematicians on the use of these entities.

     

Mathematics,Morality, and Self‐Effacement

I argue that certain species of belief, such as mathematical, logical, and normative beliefs, are insulated from a form of Harman‐style debunking argument whereas moral beliefs, the primary target of such arguments, are not. Harman‐style arguments have been misunderstood as attempts to directly undermine our moral beliefs. They are rather best given as burden‐shifting arguments, concluding that we need additional reasons to maintain our moral beliefs. If we understand them this way, then we can see why moral beliefs are vulnerable to such arguments while mathematical, logical, and normative beliefs are not—the very construction of Harman‐style skeptical arguments requires the truth of significant fragments of our mathematical, logical, and normative beliefs, but requires no such thing of our moral beliefs. Given this property, Harman‐style skeptical arguments against logical, mathematical, and normative beliefs are self‐effacing; doubting these beliefs on the basis of such arguments results in the loss of our reasons for doubt. But we can cleanly doubt the truth of morality.     

Mathematics and Mysticism,Name Worshipping,Then and Now

The author's purpose is to put together three different mystical approaches to mathematics which are located in different contexts and periods of recent times but can be compared and may enrich one another: (1) the name-worshipping movement in the Russia of the beginning of the twentieth century, which gave birth to the famous Moscow School of Mathematics; (2) the deep mystical approach to mathematics of the important French philosopher Simone Weil; and (3) the recent autobiographical thoughts of the very important French mathematician Alexander Grothendieck. All three instances give a central role to the act of naming, and the author suggests further theological and mathematical investigations of the naming process.     

The Relations Between Patterning,Executive Function,and Mathematics

Patterning, or the ability to understand patterns, is a skill commonly taught to young children as part of school mathematics curricula. It seems likely that some aspects of executive function, such as cognitive flexibility, inhibition, and working memory, may be expressed in the patterning abilities of children. The primary objective of the present study was to examine the relationship between patterning and executive functioning for first grade children. In addition, the relations between patterning, executive functioning, mathematics, and reading were examined. The results showed that patterning was significantly related to cognitive flexibility and working memory, but not to inhibition. Patterning, cognitive flexibility, and working memory were significantly related to mathematical skills. Only patterning and working memory were significantly related to reading. Regression analyses and structural equation modeling both showed that patterning had effects on both reading and mathematics measures, and that the effects of cognitive flexibility were entirely mediated by patterning. Working memory had independent effects on reading and mathematics, and also effects moderated by patterning. In sum, these findings suggest that cognitive flexibility and working memory are related to patterning and express their effects on reading and mathematics in whole or in part through patterning.     

God,Truth and Mathematics in Nineteenth-century England

In his Essay Concerning Human Understanding, John Locke created a special epistemological category for mathematical and religious knowing. This category of knowledge was quickly brushed to the side in the French Enlightenment, but the English preserved it well into the nineteenth century. This article considers the ways that the neo-Lockian joining of mathematics and theology fundamentally affected both mathematical and theological thinking in the first half of the English nineteenth century. It argues that these developments set the stage for the post-Darwinian conflicts between science—including mathematics—and religion.     

Mathematics of forgiveness

This study was aimed at determining the integration rule--summation or averaging--underlying the forgiveness schema. The main reason for distinguishing between these structures is that they have very different practical implications regarding the influence of various factors specific to each case on the propensity to forgive. In a summative model, the impact of the different factors and the direction of the effects are constant. For example, the presence of apologies always is a positive element even when these apologies assume a very weak form. By contrast, in an averaging model, the apologies can be a positive or a negative element depending on the current level of propensity to forgive and the form of the apologies. Two experiments were conducted using the functional theory of cognition framework. Experiment 1 applied the missing information test. Experiment 2 applied the credibility of information test. In both experiments, clear evidence favored a summative rule for judging willingness to forgive from circumstantial information such as presence or absence of intent, presence of absence of apologies, and degree of cancellation of consequences.     

Experimental Mathematics

The rise of the field of “experimental mathematics” poses an apparent challenge to traditional philosophical accounts of mathematics as an a priori, non-empirical endeavor. This paper surveys different attempts to characterize experimental mathematics. One suggestion is that experimental mathematics makes essential use of electronic computers. A second suggestion is that experimental mathematics involves support being gathered for an hypothesis which is inductive rather than deductive. Each of these options turns out to be inadequate, and instead a third suggestion is considered according to which experimental mathematics involves calculating instances of some general hypothesis. The paper concludes with the examination of some philosophical implications of this characterization.

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Women,Education, Mathematics,and Computers: An Instance of Vocational Incongruence

A course in computer literacy was taken by 16 female elementary education majors specializing in mathematics. Results indicated that the students were dissimilar to the typical female college sample and to predicted occupational groups.