The Structure of Creativity in Primary Education: An Empirical Confirmation of the Amusement Park Theory

In this study, we explored the structure of pupils’ creativity in primary education following the Amusement Park Theory, by investigating undiscovered linkages between the domains of writing, mathematics, and drawing. More specifically, we examined: (a) whether some domains and general thematic areas are more closely related to each other than to others, (b) whether literacy and mathematical ability are specific underlying traits of creativity in writing and mathematics, respectively, and (c) whether intelligence and divergent thinking are related to creativity in all domains. The sample consisted of 331 Dutch 4th grade pupils. For each research question, a model was analyzed using structural equation modeling. We found creativity in mathematics and creativity in writing to be most similar, followed by creativity in mathematics and creativity in drawing, with creativity in writing and creativity in drawing being least similar. Additionally, we found evidence for several underlying traits (i.e., literacy ability and mathematical ability) and initial requirements of creativity (i.e., intelligence and divergent thinking), none of which were important for creativity in only one domain, and of which only intelligence was important for creativity in all domains. Herewith, our study provides insights regarding the complexity of the structure of creativity in primary education.     

Making Numbers Come to Life: Two Scoring Methods for Creativity in Aurora's Cartoon Numbers

Although creativity has long been recognized as an important aspect of mathematical thinking, both for the advancement of the field and in students' developing expertise in mathematics, assessments of student creativity in that domain have been limited in number and focus. This article presents an assessment developed for creativity that provides a score for mathematical creativity (MaC) in addition to a score for general creativity in the numeric domain, or what we might call numerical creativity (NuC). We developed different rating scales for each and then explored how each scoring method accounts for the students' mathematical/numerical and creative skills. The psychometric properties for both scoring approaches were examined. Each method was shown to reflect different relationships with other performance tests. In addition, it is proposed that MaC may provide useful insight into students' levels of adaptive expertise in mathematics, as reflected by their ability to apply mathematical knowledge (i.e., language, operations, concepts) to novel situations, representing an informative supplement to performance indicators of math achievement.     

The Search for Mathematical Creativity: Identifying Creative Potential in Middle School Students

The identification of creative potential in mathematics poses many challenges. Much of the research into the identification of mathematical creativity has focused on the development of measurement instruments. Scoring of these instruments is time consuming and subject to scorer interpretation, limiting their use. This study sought a simpler means to obtain indicators of creative potential in mathematics. Existing instruments were used to explore the relationship between mathematical creativity and mathematical achievement, attitude towards mathematics, self-perception of creative ability, gender, and teacher perception of mathematical talent and creative ability. Data were gathered from 89 7th graders in a suburban Connecticut school. The regression model predicted 35% of the variance in mathematical creativity scores. Mathematical achievement was the strongest predictor accounting for 23% of the variance. Student attitudes towards mathematics, self-perception of their own creative abilities, and gender contributed the remaining 12% of variance. Interpretation of the relative importance of the independent variables was complicated by correlations among them.     

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.     

Mathematical Intelligence and Mathematical Creativity: A Causal Relationship

This study investigated the causal relationship between mathematical creativity and mathematical intelligence. Four hundred thirty-nine 8th-grade students, age ranged from 11 to 14 years, were included in the sample of this study by random cluster technique on which mathematical creativity and Hindi adaptation of mathematical intelligence test were administered with 4-month time lag. Cross-lagged panel analysis was used to analyze the data. The uncorrected cross-lagged correlations appeared to show no causal relation between mathematical creativity and mathematical intelligence. But after the correction the difference in the cross-lagged correlations was found to be small and does not give guarantee of unidirectional causal relation between these two constructs. It revealed that there is a mutually reinforcing (symmetric) relationship between mathematical intelligence and mathematical creativity, i.e., mathematical intelligence causes mathematical creativity and vice-versa.     

小学生近似数量系统敏锐度的发展趋势及其与数学能力的关系：抑制控制的中介作用

采用测量法和问卷法考察了172名小学生近似数量系统敏锐度的发展,以及抑制控制在近似数量系统敏锐度与数学能力关系中的中介效应。结果表明：(1)随着年龄增长,小学生的近似数量系统敏锐度逐渐提高;(2)近似数量系统敏锐度(负相关序列中的韦伯系数)和抑制控制均能显著正向预测小学生的数学能力;(3)抑制控制在小学生近似数量系统敏锐度(负相关序列中的韦伯系数)与数学能力的关系中起部分中介作用。     

早期儿童数学学习与执行功能的关系

执行功能是个体对复杂的认知活动的自我调节和以明确目标为导向的活动过程, 对早期儿童的数学学习起着重要的作用。早期儿童数学学习与执行功能呈显著正相关, 执行功能是儿童数学学习的重要认知加工机制。早期儿童执行功能和数学学习之间存在着相互预测的关系, 执行功能可以预测数学成绩, 数学成绩可以预测执行功能。高质量的早期数学教育可能具有发展儿童执行功能和数学能力的双重价值。未来研究可以明确执行功能的界定和统一测量工具, 提供更可靠的证据证明早期儿童执行功能与数学能力的因果关系, 以及进一步探究语言、数学以及执行功能三者之间的关系。     

Mathematical models and the experimental analysis of behavior

The use of mathematical models in the experimental analysis of behavior has increased over the years, and they offer several advantages. Mathematical models require theorists to be precise and unambiguous, often allowing comparisons of competing theories that sound similar when stated in words. Sometimes different mathematical models may make equally accurate predictions for a large body of data. In such cases, it is important to find and investigate situations for which the competing models make different predictions because, unless two models are actually mathematically equivalent, they are based on different assumptions about the psychological processes that underlie an observed behavior. Mathematical models developed in basic behavioral research have been used to predict and control behavior in applied settings, and they have guided research in other areas of psychology. A good mathematical model can provide a common framework for understanding what might otherwise appear to be diverse and unrelated behavioral phenomena. Because psychologists vary in their quantitative skills and in their tolerance for mathematical equations, it is important for those who develop mathematical models of behavior to find ways (such as verbal analogies, pictorial representations, or concrete examples) to communicate the key premises of their models to nonspecialists.     

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.     

乡镇小学生的数学焦虑与数学成绩:数学自我效能感和数学元认知的链式中介作用

采用儿童数学焦虑量表、小学生数学学习自我效能感量表和小学生数学元认知问卷,对508名乡镇中、高年级小学生进行测量,并运用结构方程模型探讨数学焦虑影响数学成绩的内在作用机制。结果发现：（1）数学焦虑显著负向预测数学自我效能感、数学元认知和数学成绩,数学自我效能感显著正向预测数学元认知和数学成绩,数学元认知显著正向预测数学成绩;（2）在数学焦虑对数学成绩的预测中,数学自我效能感和数学元认知均发挥了部分中介作用;（3）数学自我效能感和数学元认知在数学焦虑和数学成绩之间起链式多重中介的作用。因此,数学焦虑除了直接作用于小学生的数学成绩,还可通过数学自我效能感或数学元认知间接影响数学成绩,而且可通过数学自我效能感进而通过数学元认知间接影响数学成绩。文章讨论了上述发现的理论及教育实践含义。     

The Relationship between Emotional Intelligence and Domain-Specific and Domain-General Creativity

The Amusement Park Theory of Creativity, which represents both domain-specific and domain-general perspectives of creativity, calls for more research on how individual difference constructs are related to creativity at all ends of the domain-specificity and general spectrum. Toward this goal, this study examined emotional intelligence (using the Emotional Intelligence Scale) in relationship with both a domain-general measure (the Abbreviated Torrance Test for Adults) and a domain-specific measure (Kaufman Domains of Creativity Scale) in a sample of 281 Chinese undergraduates. Although emotional intelligence demonstrated no relationship with divergent thinking, it did positively predict all five domains of creativity on the self-report measure (ranging from .52 to .77). These findings add to the nuanced relationship between emotional intelligence and creativity and serve as a call for more work of this nature.     

绩效薪酬对员工突破性创造力和渐进性创造力的影响

研究分别从认知评价理论和习得性努力理论视角考察了绩效薪酬对员工突破性创造力和渐进性创造力的影响及其作用机制, 并检验了变革型领导和交易型领导对上述两条路径的调节效应。基于24家企业的364对上下级匹配数据的研究结果表明：绩效薪酬对内在动机和突破性创造力没有显著的影响, 对外在动机和渐进性创造力有显著的正向影响。变革型领导调节绩效薪酬与突破性创造力的关系：高变革领导情境下, 绩效薪酬通过正向影响内在动机间接对突破性创造力产生正向影响; 低变革领导情境下, 绩效薪酬通过负向影响内在动机间接对突破性创造力产生负向影响。交易型领导调节绩效薪酬与渐进性创造力的关系：交易型领导通过强化绩效薪酬对外在动机的影响进而放大了绩效薪酬对渐进性创造力的正向效应。针对上述结果, 讨论了本文的理论与实践意义。     

心理旋转训练对5~6岁儿童空间能力和数学能力的影响

采用2（时间：前测/后测）×2（分组：实验组/控制组）的两因素混合实验设计,考察心理旋转游戏训练对5~6岁儿童空间及数学能力的影响。基于心理旋转的可塑性以及空间能力与数学能力之间的密切关系设计心理旋转干预方案,将36名被试分为实验组和控制组进行为期8周共24次的干预研究。研究结果表明：（1）空间能力与数学能力之间显著正相关;（2）心理旋转游戏有效地提高了5~6岁儿童的空间能力和数学能力,该训练方案具有良好的即时效果。     

Mathematical Spandrels

The aim of this paper is to open a new front in the debate between platonism and nominalism by arguing that the degree of explanatory entanglement of mathematics in science is much more extensive than has been hitherto acknowledged. Even standard examples, such as the prime life cycles of periodical cicadas, involve a penumbra of mathematical features whose presence can only be explained using relatively sophisticated mathematics. I introduce the term ‘mathematical spandrel’ to describe these penumbral properties, and focus on the property that cicada period lengths are expressible as the sum of two perfect squares. I argue that mathematical spandrels pose a particular problem for nominalism because of the way in which they are entangled with scientific explanations.     

母亲评价与幼儿数学认知发展的关系

母亲对幼儿数学能力的评价是母亲教育观念的重要组成部分。研究运用问卷法与个别测查法,考察母亲对子女数学能力的评价与幼儿数学认知能力,并通过二者的一致程度揭示母亲评价其子女数学能力的准确性。研究发现,母亲对子女数学能力的评价存在明显的高估倾向;与母亲受教育水平及子女性别等因素不同,子女前期的数学成绩对母亲评价其数学能力的准确性存在显著影响;母亲对子女数学能力评价的准确性与子女数学认知发展水平存在显著的正相关,适当的高估对子女未来数学认知的发展最为有利     

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。     

The Contribution of Personality Traits,Motivation, Academic Risk-Taking and Metacognition to the Creative Ability in Mathematics

The purpose of this study was to investigate the extent to which personality traits, motivation, academic risk-taking, and metacognition explain the mathematical creative ability of high school students. The participants were 217 9th-grade students that were exceptionally high achievers. The participants responded to a set of measures about personality traits, motivation, academic risk-taking, metacognition, and creative ability in mathematics. The results revealed that although openness to experience and consciousness were significantly correlated with creative ability in mathematics, extraversion, agreeableness, and neuroticism were not correlated with the creativity scores. Moreover, intrinsic goal orientation followed by openness to experience was the most significant predictor of mathematical creative ability. Academic risk-taking was not significantly correlated with creative ability. Although knowledge of cognition and regulation of cognition showed moderate correlations with creative ability in mathematics, they failed to predict creative ability.     

TPH2基因rs4570625多态性和母亲权威教养对创造力的交互作用

采用基因分型技术、自我报告及表现性评价对409名健康的中国汉族大学生的基因型、母亲教养方式、一般智力和创造力进行测量,综合运用分层回归分析和显著性区域分析（regions of significance, RoS）方法探讨了TPH2基因rs4570625多态性与母亲权威教养对创造力的交互作用及其交互作用模式。结果发现：（1）在创造力的流畅性和独创性维度上,rs4570625多态性和母亲权威存在显著的交互作用。（2）RoS分析结果均支持差别易感模型,T等位基因是母亲权威的“可塑性”基因。这些发现将有助于从遗传和环境相互作用的角度解释个体创造力差异的起源。     

数学能力与决策的关系：个体差异的视角

即便在相同的情形中, 每个人所做的决策也有千差万别, 导致决策个体差异的因素之一就是数学能力。文章综述了算术能力、数量表征、概率推理能力以及数学认知启发式对各种决策的影响。目前这方面的研究或者采用相关范式将数学能力作为决策的外部关联因素, 或者采用成分范式确定决策过程所需要的特定数学认知成分; 观点上的主要争论在于是一般认知能力还是数学能力在预测决策表现, 以及数学能力是否总是对决策有积极作用; 此外, 双系统模型和模糊痕迹理论有望为决策的个体差异提供理论解释。今后研究应该澄清上述争论, 确定合适的研究范式和结果解释框架, 并探讨更多提高决策能力的措施。     

创造性与初级思维过程

创造性是当今心理学研究的热点问题,从精神分析学的角度来探讨创造性的内部发生机制将是一个有益的尝试。随着脑科学的发展,越来越多的研究表明初级思维过程与创造性有着极为密切的关系。本文通过对该领域相关研究的简单回顾,提出了有关创造性源事件激活能力的假说,并对未来的研究做出了展望,以期能最终揭示出创造性的内部机制。