Development of the Japanese Version of the Achievement Emotions Questionnaire – Elementary School (AEQ-ES-J)1,2

The purpose of this study was to develop and validate a Japanese version of the Achievement Emotions Questionnaire – Elementary School (AEQ-ES), which assesses enjoyment, anxiety, and boredom experienced by elementary school students within the settings of attending class, doing homework, and taking tests. Japanese elementary school students (n = 863 for the first survey; n = 332 for the second survey) participated in the questionnaire survey. The results showed that the psychometric properties of the Japanese AEQ-ES were comparable to those of the original version. Moreover, the results showed that students' achievement emotions were associated with their control and value appraisals, as well as their academic motivation, learning strategies, academic performance, and support from teachers. These results indicated that the Japanese version of the AEQ-ES was a good measure of elementary school students' emotions and supported the propositions of the control–value theory of achievement emotions.     

Learning Abilities and Disabilities: Generalist Genes, Specialist Environments

ABSTRACT— Twin studies comparing identical and fraternal twins consistently show substantial genetic influence on individual differences in learning abilities such as reading and mathematics, as well as in other cognitive abilities such as spatial ability and memory. Multivariate genetic research has shown that the same set of genes is largely responsible for genetic influence on these diverse cognitive areas. We call these "generalist genes." What differentiates these abilities is largely the environment, especially nonshared environments that make children growing up in the same family different from one another. These multivariate genetic findings of generalist genes and specialist environments have far-reaching implications for diagnosis and treatment of learning disabilities and for understanding the brain mechanisms that mediate these effects.     

两类数学学习困难小学儿童抑制控制水平的实验研究

为考察单纯型数学困难与混合型数学困难小学儿童的抑制控制水平及特点,使用Stroop色词命名测验和颜色匹配反转作业,对各30名的单纯型困难、混合型困难和对照组小学儿童的优势反应抑制能力进行测试、分析。结果发现:单纯型数学困难儿童抑制优势反应的能力显著低于对照组,但其对事物初次学习的能力与对照组相当;混合型数学困难儿童在对事物初次学习能力及对优势反应的抑制能力方面均显著低于对照组儿童,其中对事物的初次学习能力也显著低于单纯型数学困难儿童。     

On three arguments against categorical structuralism

Some mathematicians and philosophers contend that set theory plays a foundational role in mathematics. However, the development of category theory during the second half of the twentieth century has encouraged the view that this theory can provide a structuralist alternative to set-theoretical foundations. Against this tendency, criticisms have been made that category theory depends on set-theoretical notions and, because of this, category theory fails to show that set-theoretical foundations are dispensable. The goal of this paper is to show that these criticisms are misguided by arguing that category theory is entirely autonomous from set theory.     

THE EFFECTS OF TEACHING PRECURRENT BEHAVIORS ON CHILDREN'S SOLUTION OF MULTIPLICATION AND DIVISION WORD PROBLEMS

We examined the effects of teaching overt precurrent behaviors on the current operant of solving multiplication and division word problems. Two students were taught four precurrent behaviors (identification of label, operation, larger numbers, and smaller numbers) in a different order, in the context of a multiple baseline design. After meeting criterion on three of the four precurrent skills, the students demonstrated the current operant of correct problem solutions. These skills generalized to novel problems. Correct current operant responses (solutions that matched answers revealed by coloring over the space with a special marker) maintained the precurrent behaviors in the absence of any other programmed reinforcement.     

"不可或缺性论证"与反实在论数学哲学

The indispensability argument for abstract mathematical entities has been an important issue in the philosophy of mathematics. The argument relies on several assumptions. Some objections have been made against these assumptions, but there are several serious defects in these objections. Ameliorating these defects leads to a new anti-realistic philosophy of mathematics, mainly: first, in mathematical applications, what really exist and can be used as tools are not abstract mathematical entities, but our inner representations that we create in imagining abstract mathematical entities; second, the thoughts that we create in imagining infinite mathematical entities are bounded by external conditions. __________ Translated from Zhexue Yanjiu 哲学研究 (Philosophical Researches), 2006, (8): 74–83     

Erkenntnistheorie der Zahldefinition und philosophische Grundlegung der Arithmetik unter Bezugnahme auf einen Vergleich von Gottlob Freges Logizismus und platonischer Philosophie (Syrian, Theon von Smyrna u.a.)

The epistomology of the definition of number and the philosophical foundation of arithmetic based on a comparison between Gottlob Frege's logicism and Platonic philosophy (Syrianus, Theo Smyrnaeus, and others). The intention of this article is to provide arithmetic with a logically and methodologically valid definition of number for construing a consistent philosophical foundation of arithmetic. The – surely astonishing – main thesis is that instead of the modern and contemporary attempts, especially in Gottlob Frege's Foundations of Arithmetic, such a definition is found in the arithmetic in Euclid's Elements. To draw this conclusion a profound reflection on the role of epistemology for the foundation of mathematics, especially for the method of definition of number, is indispensable; a reflection not to be found in the contemporary debate (the predominate ‘pragmaticformalism’ in current mathematics just shirks from trying to solve the epistemological problems raised by the debate between logicism, intuitionism, and formalism). Frege's definition of number, ‘The number of the concept F is the extension of the concept ‘numerically equal to the concept F”, which is still substantial for contemporary mathematics, does not fulfil the requirements of logical and methodological correctness because the definiens in a double way (in the concepts ‘extension of a concept’ and ‘numerically equal’) implicitly presupposes the definiendum, i.e. number itself. Number itself, on the contrary, is defined adequately by Euclid as ‘multitude composed of units’, a definition which is even, though never mentioned, an implicit presupposition of the modern concept ofset. But Frege rejects this definition and construes his own - for epistemological reasons: Frege's definition exactly fits the needs of modern epistemology, namely that for to know something like the number of a concept one must become conscious of a multitude of acts of producing units of ‘given’ representations under the condition of a 1:1 relationship to obtain between the acts of counting and the counted ‘objects’. According to this view, which has existed at least since the Renaissance stoicism and is maintained not only by Frege but also by Descartes, Kant, Husserl, Dummett, and others, there is no such thing as a number of pure units itself because the intellect or pure reason, by itself empty, must become conscious of different units of representation in order to know a multitude, a condition not fulfilled by Euclid's conception. As this is Frege's main reason to reject Euclid's definition of number (others are discussed in detail), the paper shows that the epistemological reflection in Neoplatonic mathematical philosophy, which agrees with Euclid's definition of number, provides a consistent basement for it. Therefore it is not progress in the history of science which hasled to the a poretic contemporary state of affairs but an arbitrary change of epistemology in early modern times, which is of great influence even today. This revised version was published online in August 2006 with corrections to the Cover Date.     

Anxiety-induced miscalculations,more than differential inhibition of intuition,explain the gender gap in cognitive reflection

The Cognitive Reflection Test (CRT) is among the most common and well-known instruments for measuring the propensity to engage reflective processing, in the context of the dual-process theory of high-level cognition. There is robust evidence that men perform better than women on this test—but we should be wary to conclude that men are more likely to engage in reflective processing than women. We consider several possible loci for the gender difference in CRT performance, and use mathematical modeling to show, across two studies, that the gender difference in CRT performance is more likely due to women making more mathematical mistakes (partially explained by their greater mathematics anxiety) than due to women being less likely to engage reflective processing. As a result, we argue that we need to use gender-equivalent variants of the CRT, both to improve the quality of our instruments and to fulfill our social responsibility as scientists.     

EFFECTS OF HIGH-PREFERENCE SINGLE-DIGIT MATHEMATICS PROBLEM COMPLETION ON MULTIPLE-DIGIT MATHEMATICS PROBLEM PERFORMANCE

The purpose of this study was to examine the effects of a sequence of three single-digit (1 digit × 1 digit) multiplication problems on the latency to initiate multiple-digit (3 digit × 3 digit) multiplication problems for 2 students in an alternative education school. Data showed that (a) during the preference assessment, both students selected the single-digit problems in a majority of the sessions, and (b) intervention resulted in a decrease in latency between problems for both students. Results are discussed in relation to using high-preference sequences to promote behavioral momentum in academic content areas.