Effect of Teachers' Stereotyping on Students' Stereotyping of Mathematics as a Male Domain

Abstract

This multilevel analysis used data from a representative sample from Grades 6, 7, and 8 in public schools in Switzerland. The data included information on (a) 6,602 students (3,307 girls, 3,295 boys) nested within 338 classes and (b) 321 mathematics teachers of these classes. The teachers and the students tended to stereotype mathematics as a male domain, and the teachers' stereotypes significantly affected the students' stereotypes after the author controlled for achievement, interest, and self-confidence in mathematics and for school grade and schooling track.     

初一学生数学学习的学科领域知识表征特点

学科领域知识由学理内容知识、认知过程知识和问题条件知识组成。本研究以529名七年级学生为被试,测查学生在数学学习中的学科领域知识表征特点,结果发现:(1)三种类型知识表征存在显著差异,学理内容知识表征水平最高,问题条件知识表征水平最低;(2)学优生的学科领域知识表征水平显著高于中等生和学困生;(3)认知过程知识表征、问题条件知识表征水平与数学学业成绩显著相关;(4)学生对学理内容知识重要性评价最高,问题条件知识最低。     

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。     

11岁和15岁儿童学习动机和数学素养的关系

选取2133名11岁和15岁学生,采用PISA测试为数学素养指标,探讨学生学习动机的不同维度与数学素养之间的关系。结果发现：（1）11岁学生的内部动机明显地强于15岁学生。（2）11岁学生内部动机中的挑战性动机与数学素养间的相关程度明显弱于15岁学生。（3）11岁高数学素养的学生组,数学素养和内、外学习动机有明显的相关,低数学素养学生组两者则不相关;对于15岁低数学素养的学生组,数学素养得分和内、外部学习动机有明显的相关,高数学素养学生组两者则不相关。     

Achievement Emotions Questionnaire-Mathematics (AEQ-M) in adolescents: Factorial structure,measurement invariance and convergent validity with personality

ABSTRACT

The Achievement Emotions Questionnaire-Mathematics (AEQ-M) is a self-report measure of emotions experienced in class, when self-studying, and during tests for the domain of mathematics. Our aim was to present a Portuguese version of this instrument for use with adolescents and to test its reliability, factorial structure, measurement invariance, and construct validity with personality dimensions. Our sample comprised 1,387 Portuguese students from the 7th, 8th and 9th grades (mean age = 13.2 years). Student responses to the AEQ-M were found to be reliable. Confirmatory factor analysis validated a seven-emotion × three-setting factorial structure. This model demonstrated measurement invariance across gender and grade. As a demonstration of construct validity, the emotions measured by the AEQ-M showed a pattern of associations with psychobiological personality dimensions that were in line with theoretical predictions. These results validate the AEQ-M as a suitable instrument for assessing adolescents’ mathematics-related achievement emotions and their associations with personality.     

Kant on Construction,Apriority, and the Moral Relevance of Universalization

This paper introduces a referential reading of Kant’s practical project, according to which maxims are made morally permissible by their correspondence to objects, though not the ontic objects of Kant’s theoretical project but deontic objects (what ought to be). It illustrates this model by showing how the content of the Formula of Universal Law might be determined by what our capacity of practical reason can stand in a referential relation to, rather than by facts about what kind of beings we are (viz., uncaused causes). This solves the neglected puzzle of why there are passages in Kant’s works suggesting robust analogies between mathematics and ethics, since to universalize a maxim is to test a priori whether a practical object with that particular content can be constructed. An apparent problem with this hypothesis is that the medium of practical sensibility (feeling) does not play a role analogous to the medium of theoretical sensibility (intuition). In response I distinguish two separate Kantian accounts of mathematical apriority. The thesis that maxim universalization is a species of construction, and thus a priori, turns out to be consistent with the account of apriority that informs Kant’s understanding of actual mathematical practice.     

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.     

Differences in Mathematical Performance,Creativity Potential,and Need for Cognitive Closure between Chinese and Australian Students

Research has shown that Chinese students outperform students from several Western countries on mathematics performance while some evidence has suggested that Western students perform more strongly on tests of creativity. One potential mechanism for these differences may be a higher need for cognitive closure among Chinese students. The current research compared performance on tests of mathematics and creativity among 50 students of Chinese background and 49 Australian students of Anglo‐Saxon background. As predicted, Chinese students performed better on mathematics while Australian students performed better on the measure of creativity. Australian students also had a lower score on one subscale of the need for cognitive closure, preference for predictability. Across the sample, preference for predictability showed small but significant negative correlations with several measures of creativity and positive correlations with several measures of mathematics. These findings were interpreted with respect to characteristic educational practices in both nations.