Eye gaze patterns reveal how we reason about fractions

ABSTRACT

Fractions are defined by numerical relationships, and comparing two fractions’ magnitudes requires within-fraction (holistic) and/or between-fraction (componential) relational comparisons. To better understand how individuals spontaneously reason about fractions, we collected eye-tracking data while they performed a fraction comparison task with conditions that promoted or obstructed different types of comparisons. We found evidence for both componential and holistic processing in this mixed-pairs task, consistent with the hybrid theory of fraction representation. Additionally, making within-fraction eye movements on trials that promoted a between-fraction comparison strategy was associated with slower responses. Finally, participants who performed better on a non-numerical test of reasoning took longer to respond to the most difficult fraction trials, which suggests that those who had greater facility with non-numerical reasoning attended more to numerical relationships. These findings extend prior research and support the continued investigation into the mechanistic links between numerical and non-numerical reasoning.     

Adventure based counselling,individual counselling and object relations: a critical evaluation of a qualitative study

Adventure based counselling is a short-term experiential psychotherapeutic approach, which utilises adventurous activities and being in natural environmental in order to facilitate therapeutic change in clients. The present paper critically appraises the results of a qualitative study that investigated how clients with self-reported anxiety and depression experienced participating in an innovative counselling intervention with combined individual counselling with such an adventurous outdoor transaction. Interpretative Phenomenological Analysis, as described by Smith and Osborn (2008), was used in order record and analyse the experiences of four male and six female students who were treated at the Teesside's University Counselling Service. Interviewees perceived the counselling sessions as offering a safe therapeutic space within which they could unveil their anxieties and achieve inner healing, whereas the outdoor transaction as providing an experiential venue for achieving personal change. Interviewees felt that without the outdoor transaction the therapeutic significance of the counselling process would not have reached its full potential. Likewise, without the individual counselling, the outdoor transaction would just have an entertaining event and not a venue for personal change. These findings are discussed in relation to object relations theory.     

Intergroup retaliation and intra‐group praise gain: The effect of expected cooperation from the in‐group on intergroup vicarious retribution

Intergroup vicarious retribution is the phenomenon whereby, after an out‐group member attacks an in‐group member, a member of the victim's group retaliates against a member of the perpetrator's group. This study examined the effect of expected cooperation from the in‐group on intergroup vicarious retribution through intra‐group reputation based on praise gain and exclusion avoidance. In the experiment, we conducted a one‐on‐one match in which, after participants learned that an out‐group member (as the winner) had imposed a fine on an in‐group member (as the loser) in a previous round, winning participants were allowed to impose an arbitrary fine on the other losing out‐group member. As a result, participants imposed a larger fine on their out‐group member opponent in retaliation when they were expected by in‐group members to cooperate than when such cooperation was not expected. Furthermore, participants regarded a fine as intra‐group cooperation. Since a path analysis revealed a mediating effect of praise gain, but no mediating effect of exclusion avoidance, expected cooperation from in‐group members facilitated vicarious retribution because those involved in retribution sought praise from other in‐group members. These findings suggest that the intra‐group reputation dynamics of expected cooperation and praise gain escalate intergroup conflict.     

Witnessing excellence in action: the ‘other-praising’ emotions of elevation,gratitude, and admiration

People are often profoundly moved by the virtue or skill of others, yet psychology has little to say about the ‘other-praising’ family of emotions. Here we demonstrate that emotions such as elevation, gratitude, and admiration differ from more commonly studied forms of positive affect (joy and amusement) in many ways, and from each other in a few ways. The results of studies using recall, video induction, event-contingent diary, and letter-writing methods to induce other-praising emotions suggest that: elevation (a response to moral excellence) motivates prosocial and affiliative behavior, gratitude motivates improved relationships with benefactors, and admiration motivates self-improvement. Mediation analyses highlight the role of conscious emotion between appraisals and motivations. Discussion focuses on implications for emotion research, interpersonal relationships, and morality.     

Perceptions of Self and Relationship with Parents in Aggressive and Nonaggressive Rejected Children

This study examined the perceptions of self and the attachment relationship to parents in aggressive and nonaggressive rejected children, as compared to children with an average or popular sociometric status. Participants were 216 children from grades 3 and 4. They completed peer nomination measures, the Self-Perception Profile for Children (SPPC), and the Security Scale (mother and father form). Results generally confirmed the assumption that only the nonaggressive rejected children perceive themselves as less competent and worthy as a person than the more popular children. Aggressive rejected children did not report lower feelings of global self-worth or competence, although they did report lower levels of social acceptance. Furthermore, rejected-nonaggressive children perceived the relationship with their father (but not with their mother) as less secure than did the more popular children. Logistic regression analyses suggested that the linkage between felt security with father and rejected-nonaggressive status was mediated by children's self-worth. Implications for attachment theory and for the hypothesized heterogeneity among rejected children are discussed.     

数学焦虑研究的认知取向

数学焦虑一直是心理学界研究和讨论的热点问题。本文主要从认知的角度对数学焦虑进行解释,并以此揭示数学焦虑的心理机制和思维规律。     

小学生视觉-空间表征类型和数学问题解决的研究

本研究考察并比较了四至六年级儿童的视觉－空间表征策略、数学问题解决和空间视觉化能力。结果表明：五、六年级儿童的解题正确率、使用图式表征策略的程度显著高于四年级儿童;使用图像表征策略的程度各年级无显著差异。将数学问题分成三个难度等级,发现年级差异主要表现在难度等级1的题目上。另外,六年级儿童的空间视觉化能力显著高于四年级儿童。     

儿童早期数学认知能力的结构及其特点

从北京市10所幼儿园中选取234名3、4岁的儿童为被试,采用个别测查的方法对儿童早期数学认知能力的结构及其特点进行了考察。经验证性因素分析发现：(1)儿童早期数学认知能力的结构模型是合理的,可接受的,具有较好的构想效度,具体讲,数、计算、测量、空间／几何和模式认知能力五个维度共同解释着儿童早期的数学认知能力;(2)不同年龄儿童早期数学认知能力的结构具有稳定性,但是结构模型并不完全一致,某些项目的解释率有所不同;(3)男、女儿童早期数学认知能力的结构模型具有一致性。     

Quantum Mechanics and "Song of Myself": Getting a Grip on Reality

Most recent writing linking science and literature has concerned itself with challenges to the epistemological status of scientific knowledge in an attempt to demonstrate its contingency, arguing in the more radical efforts that the structures of science are no more than useful fictions. This essay also includes an epistemological comparison between science and literature, but instead of making grand or meta–statements about the nature of knowing generally in the two fields, mine is a much narrower aim. My exploration entails two tasks. First, I provide a close–up look at a particular type of experiment, called the delayed–choice experiment, which clearly reveals the strangeness of the quantum world. In connection with this experiment, I discuss wave functions—mathematical expressions used by physicists to describe quantum behavior and predict the outcome of experiments involving quanta. Second, I look at Walt Whitman's “Song of Myself” focusing on the meaning of the “self” in the poem. My aim is to treat the object of study in each field as a “text” and to assert and demonstrate a parallel in the strategies of thought and response between physicists (“readers”) pondering the meaning and status of a wave function and poem readers pondering the meaning and status of the poem's self. In Whitman's “Song” we find an attempt to understand complex aspects of human experience that are said to transcend ordinary reality, an effort for which I believe there are parallels in the attempts of modern physicists to understand complex, nonintuitive aspects of the subatomic world. While not making the kind of broad claims eschewed above, I do suggest that this focused study has interesting implications since both the wave function and the poem's self force their respective sets of “readers” to confront questions of ultimacy—to consider, that is, epistemological and ontological issues of more than passing interest to students of science as well as those of metaphysics and theology.     

The relationship between children's self-reported recess problems, and peer acceptance and friendships

This study used three samples to investigate the nature of children's self-reported recess problems and the degree to which these were correlated with children's peer acceptance and mutual friendships. Results suggest that seven student complaints about recess can be grouped into problems with peer conflict and problems with social inclusion. Modest relations were reported between inclusion recess problems and children's mutual friendships and peer acceptance. Relations of conflict recess problems with mutual friendships and peer acceptance were less frequent. Results suggest that self-reported recess problems are a distinct construct from traditional research measures of peer acceptance and friendships.