初中生数学家庭作业质量、控制感与作业情绪对作业努力的影响

采用问卷调查法,以 463 名初中生为被试,探讨了初中生感知到的数学家庭作业质量、控制感和家庭作业情绪影响家庭作业努力的内在作用机制。结果发现：(1)积极数学家庭作业情绪和消极数学家庭作业情绪均在数学家庭作业质量和数学家庭作业努力之间起完全中介作用;(2)数学家庭作业质量可以通过数学控制感分别经积极和消极数学家庭作业情绪的多重中介来预测数学家庭作业努力。研究表明,初中生感知到的数学家庭作业质量、控制感和家庭作业情绪均是其家庭作业努力的重要影响因素。     

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.     

An Investigation of the Relationship between Age,Achievement, and Creativity in Mathematics

In this exploratory study, I investigate the relationship between age, knowledge, and creativity in mathematics, by looking at to what extent does grade level, controlled for mathematical achievement, influence mathematical creativity and what characterizes the relationship between grade level, mathematical achievement and mathematical creativity. This was accomplished in two steps. In the first part, 301 students, 184 grade eight students and 117 grade eleven students, were given a creative mathematics test. A 3 × 2 ANOVA indicates that the older students were more creative; however, there was a significant interaction effect between grade level and achievement in mathematics on mathematical creativity. In the second part, an inductive content analysis was performed on the solutions of high achievers in grade eleven and grade eight. The results indicate that high achievers in grade eight are more creative than high achievers in grade eleven, but the nature of the task mediates the relationship between creativity and knowledge.     

高效率数学学习高中生数学成绩的影响路径

为探究高效率数学学习高中生的数学学习成绩的影响因素的不同作用效果,以及这些影响因素间存在的作用路径,通过目标抽样,选取102名高中生为被试开展调查研究。通过数据分析,并依托AMOS软件的模型界定搜寻功能进行路径分析,获得研究结论：（1）数学元认知、数学非智力因素、智力因素、数学学习策略和数学素养这5个变量对高效率数学学习高中生的数学学习成绩的作用效果值依次递减。（2）5个变量通过两条主要路径影响高效率数学学习高中生的数学学习成绩,一是智力因素与数学素养构成的影响路径,二是数学元认知、数学非智力因素以及数学学习策略构成的影响路径。     

高中生数学元认知水平调查问卷的设计与编制*

对于元认知能力的评价和测试一直以来都是研究的难点,特别是就数学学科而言,已有研究多围绕数学问题解决过程中元认知监控水平的评价以及能力的培养展开,鲜有全面评价学生数学学习元认知水平的问卷。同时,没有针对高中生编制的元认知水平调查问卷。故本研究在已有研究的基础上,对已有的问卷进行修正和完善,通过征求专家意见与样本测试和数据分析,形成《高中生数学元认知水平调查问卷》。该问卷具有较好的内容效度和结构效度。信度方面,问卷整体的内部信度为0.952,分半信度为0.931,重测信度为0.946,说明问卷具有很好的内部一致性和测量稳定性。     

The Nctm Standards and the Philosophy of Mathematics

It is argued that the philosophical and epistemological beliefs about the nature of mathematics have a significant influence on the way mathematics is taught at school. In this paper, the philosophy of mathematics of the NCTM's Standards is investigated by examining is explicit assumptions regarding the teaching and learning of school mathematics. The main conceptual tool used for this purpose is the model of two dichotomous philosophies of mathematics-absolutist versus- fallibilist and their relation to mathematics pedagogy. The main conclusion is that a fallibilist view of mathematics is assumed in the Standards and that most of its pedagogical assumptions and approaches are based on this philosophy.     

Empiricism,probability, and knowledge of arithmetic: A preliminary defense

The topic of this paper is our knowledge of the natural numbers, and in particular, our knowledge of the basic axioms for the natural numbers, namely the Peano axioms. The thesis defended in this paper is that knowledge of these axioms may be gained by recourse to judgments of probability. While considerations of probability have come to the forefront in recent epistemology, it seems safe to say that the thesis defended here is heterodox from the vantage point of traditional philosophy of mathematics. So this paper focuses on providing a preliminary defense of this thesis, in that it focuses on responding to several objections. Some of these objections are from the classical literature, such as Frege's concern about indiscernibility and circularity (Section 2.1), while other are more recent, such as Baker's concern about the unreliability of small samplings in the setting of arithmetic (Section 2.2). Another family of objections suggests that we simply do not have access to probability assignments in the setting of arithmetic, either due to issues related to the ω-rule (Section 3.1) or to the non-computability and non-continuity of probability assignments (Section 3.2). Articulating these objections and the responses to them involves developing some non-trivial results on probability assignments (Appendix A–Appendix C), such as a forcing argument to establish the existence of continuous probability assignments that may be computably approximated (Theorem 4 Appendix B). In the concluding section, two problems for future work are discussed: developing the source of arithmetical confirmation and responding to the probabilistic liar.     

Ideas and processes in mathematics: A course on history and philosophy of mathematics

This paper describes an attempt to develop a program for teaching history and philosophy of mathematics to inservice mathematics teachers. I argue briefly for the view that philosophical positions and epistemological accounts related to mathematics have a significant influence and a powerful impact on the way mathematics is taught. But since philosophy of mathematics without history of mathematics does not exist, both philosophy and history of mathematics are necessary components of programs for the training of preservice as well as inservice mathematics teachers.     

初中生感知到的同伴支持与数学学习投入—基于变量为中心和个体为中心的分析

为考察同伴支持对初中生数学学习投入的影响机制,采用问卷法对1177名七、八年级学生感知到的同伴支持、数学认同、数学焦虑和数学学习投入进行测查。结果发现：同伴支持不仅能直接预测初中生的数学学习投入,还通过数学认同经数学焦虑的链式中介作用来预测数学学习投入;对数学认同和数学焦虑的得分进行潜剖面分析,可将学生分为高认同-低焦虑、中认同-中焦虑和低认同-高焦虑三组,同伴支持可预测学生的不同亚组,三组学生的数学学习投入得分存在显著差异。上述发现为促进基础教育阶段学生数学学习投入的教育实践提供了理论依据。     

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.     

An Examination of Implicitly Activated,Explicitly Activated,and Nullified Stereotypes on Mathematical Performance: It's Not Just a Woman's Issue

This study was designed to examine the different ways that stereotypes might become activated in testing situations and the effects this activation has on task performance. In Experiment 1, women undergraduates exposed to an explicitly activated stereotype (i.e., told men outperform women in mathematics) performed worse than women exposed to a nullified stereotype (i.e., told men and women perform at the same level in mathematics). The stereotype threat also was activated implicitly under normal conditions (i.e., just given the test with nothing else stated) such that performance in this condition was at the same (low) level as the explicitly activated threat. In Experiment 2, the results were replicated with White male undergraduates using the stereotype that Asians are better than Whites in mathematics. In addition, in a small field survey we found that this belief about ethnicity did occur spontaneously for White men in college calculus courses. Taken together, the results of these studies suggest that even under normal circumstances, math test situations may lead to nonoptimal performance for both stigmatized (women) and traditionally nonstigmatized (White men) group members. Implications for threat nullification techniques are discussed.     

Behavioral fluency and mathematics intervention research: A review of the last 20 years

Behavioral fluency refers to the relationship between the achievement of performance standards, or frequency ranges of behavior, and critical learning outcomes. Over the past 20 years, Precision Teaching and related research have contributed a number of studies examining behavioral fluency. The subsequent review investigates the empirical evidence from mathematics intervention research. Several studies suggest numerical markers that best support behavioral fluency. Results indicate that fluency interventions set to performance standards increased behavioral fluency and associated critical learning outcomes; however, more research is warranted to operationalize and standardize each outcome to the principles of behavior and numerical markers that constitute behavioral fluency.     

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.     

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。     

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.     

Self-Concept,Motivational Orientation,and Help-Seeking Behavior in Mathematics: A Study of Adults Returning to High School

The purpose of this study was to explore relations between mathematics achievement, self-concept, goal orientation, intrinsic motivation, and help-seeking behavior among adults studying for a high school diploma. Participants in this study were 145 adults (55 males and 90 females) enrolled in nine first year high school classes for adult students at five high schools in three cities in Norway. The age of the students varied from 18 to 52 years. Data were analyzed by means of structural equation modeling. The results indicate that mathematics self-concept in adult years build strongly on achievement in school years and that it is predictive of adult students’ goal orientation, intrinsic motivation, and learning strategies. Three weakly correlated dimensions of goal orientation predicted interest and help-seeking behavior in mathematics lessons differently.     

The Interplay among Stereotypes, Performance-Avoidance Goals, and Women's Math Performance Expectations

This project was designed to examine whether and how achievement goals contribute to the effect of gender stereotypes on women's low expectancies for success on math tasks. Study 1 confirmed predictions from the Stereotyped Task Engagement Process (STEP) model (Smith, 2004) by demonstrating that, compared to a counter-stereotype situation, women reminded of the gender-stereotype endorsed performance-avoidance goals. Study 2 tested whether performance-goal adoption differed between men and women. Results showed that, compared to men, women in a stereotype salient math situation were more likely to endorse performance-avoidance achievement goals. This performance-avoidance goal adoption in turn, accounted for the negative relationship between participants' gender and performance expectations for a standardized math test.     

个体自我监控能力、思维品质与数学学业成绩的关系研究

对197个高三生施测《中学生数学学科自我监控能力问卷》和《高三学生数学思维品质问卷》,以探讨个体自我监控能力、思维品质对数学学业成绩的影响模式。结果:(1)自我监控能力与思维品质、数学学业成绩均呈显著正相关。(2)在自我监控能力、思维品质对数学学业成绩的影响模型中,自我监控能力直接影响数学学业成绩,并通过思维品质这一中介变量作用于数学学业成绩。思维品质直接影响数学学业成绩。(3)女生组与男生组的自我监控能力、思维品质与数学学业成绩的结构系数的模型无显著差异。     

小学生数学学习观:结构与特点的研究

采用问卷法,本研究探讨了小学生数学学习观的结构与表现特点。研究表明:小学生数学学习观的四个因素,即数学学习兴趣、课堂参与性、数学学科观与数学交流的素养,能够较好地解释数学学习观的心理结构;小学生的数学学习兴趣与课堂参与性,随着年级升高显著下降,而在数学学科观与数学交流的素养方面则表现出相反的趋势,即随着年级升高而提升;男生的学习兴趣与课堂参与性明显高于女生,但在数学学科观与数学交流的素养方面,女生则明显好于男生。