Disentangling the Mechanisms of Symbolic Number Processing in Adults’ Mathematics and Arithmetic Achievement

A growing body of research has shown that symbolic number processing relates to individual differences in mathematics. However, it remains unclear which mechanisms of symbolic number processing are crucial—accessing underlying magnitude representation of symbols (i.e., symbol‐magnitude associations), processing relative order of symbols (i.e., symbol‐symbol associations), or processing of symbols per se. To address this question, in this study adult participants performed a dots‐number word matching task—thought to be a measure of symbol‐magnitude associations (numerical magnitude processing)—a numeral‐ordering task that focuses on symbol‐symbol associations (numerical order processing), and a digit‐number word matching task targeting symbolic processing per se. Results showed that both numerical magnitude and order processing were uniquely related to arithmetic achievement, beyond the effects of domain‐general factors (intellectual ability, working memory, inhibitory control, and non‐numerical ordering). Importantly, results were different when a general measure of mathematics achievement was considered. Those mechanisms of symbolic number processing did not contribute to math achievement. Furthermore, a path analysis revealed that numerical magnitude and order processing might draw on a common mechanism. Each process explained a portion of the relation of the other with arithmetic (but not with a general measure of math achievement). These findings are consistent with the notion that adults’ arithmetic skills build upon symbol‐magnitude associations, and they highlight the effects that different math measures have in the study of numerical cognition.     

Asymmetric prefrontal cortex functions predict asymmetries in number space

Little is known about the neuropsychological factors that contribute to individual differences in the asymmetric orientation along the mental number line. The present study documents healthy subjects’ preference for small numbers over large numbers in a random number generation task. This preference, referred to as “small-number bias” (SNB), varied with prefrontal functional lateralization: it was larger in participants with over-proportionately better performance in design fluency compared to letter fluency than in participants with over-proportionately better performance in letter fluency when compared to design fluency. Asymmetries in learning and memory tasks (verbal vs. non-verbal) were not related to direction or size of the SNB. We conclude that hemispheric asymmetries of specifically prefrontal executive functions are predictive of an individual’s lateral orientation bias along the mental number line. Therefore, the focus on parietal contributions to spatial-numerical associations may not be justified. Random number generation may be a helpful method to further explore these associations uncontaminated by the asymmetric involvement of response effectors.     

Seven-month-olds detect ordinal numerical relationships within temporal sequences

Previous evidence has shown that 11-month-olds represent ordinal relations between purely numerical values, whereas younger infants require a confluence of numerical and non-numerical cues. In this study, we show that when multiple featural cues (i.e., color and shape) are provided, 7-month-olds detect reversals in the ordinal direction of numerical sequences relying solely on number when non-numerical quantitative cues are controlled. These results provide evidence for the influence of featural information and multiple cue integration on infants’ proneness to detect ordinal numerical information.     

Spontaneous focusing on numerosity as a domain-specific predictor of arithmetical skills

The aim of this 2 year longitudinal study was to explore whether children’s individual differences in spontaneous focusing on numerosity (SFON) in kindergarten predict arithmetical and reading skills 2 years later in school. Moreover, we investigated whether the positive relationship between SFON and mathematical skills is explained by children’s individual differences in spontaneous focusing on a non-numerical aspect. The participants were 139 Finnish-speaking children. The results show that SFON tendency in kindergarten is a significant domain-specific predictor of arithmetical skills, but not reading skills, assessed at the end of Grade 2. In addition, the relationship between SFON and number sequence skills in kindergarten is not explained by children’s individual differences in their focusing on a non-numerical aspect that is, spatial locations.     

Perception of line‐up suggestiveness: effects of identification outcome knowledge

Research on the hindsight bias has shown that knowledge of an event outcome makes the observed outcome appear more predictable than it does in the absence of outcome knowledge. It was hypothesised that perceptions of the suggestiveness of a line‐up would be similarly influenced by knowledge of a witness' identification decision, with a positive identification of the suspect increasing, and a negative non‐identification decreasing, perceived suggestiveness. The ratings of undergraduate students (N = 50) in Experiment 1 showed the predicted influence of positive outcome, whereas negative outcome had no demonstrable influence. In contrast, Experiment 2, conducted with police trainees (N = 126) and with the line‐up presented in the context of a criminal investigation, partially supported the predicted influence of negative, but not positive, outcome. The discrepant findings are discussed in terms of the cognitive mechanisms underlying the hindsight bias and the implications for real‐life judgements of line‐up suggestiveness. Copyright © 2010 John Wiley & Sons, Ltd.     

分数认知的“整数偏向”研究:理论与方法

整数偏向普遍存在于分数认知中,它指儿童在应用分数知识时,常使用先前形成的有关整数的独立单元计数图式来解释分数的倾向。学者们提出了先天约束假设、未分化量假设和学习的负迁移假设分别从先天和后天角度对其成因做了解释。以往研究常采用纸笔测验或口语报告揭示它的存在,近年来有研究采用了心理数字线假设的相关效应考查了成人的整数偏向,使其研究方法和被试得以扩展。在该领域,今后应在定义、理论解释、研究方法以及教学干预方面加强研究。     

航线飞行技术性技能与航线飞行阶段任务的关系研究

通过文献、专家意见和问卷调查,构建了现代航线飞行技术性技能多维评价量表。对118名航线飞行员测评数据的验证性因素分析表明,由倾斜控制、偏航控制、平衡控制和速度控制构成的4维模型在飞行准备/滑行、起飞/爬升、巡航、下降/进近/着陆四个飞行阶段均有较好的信度和效度;多元回归分析发现,各维度对不同航线飞行阶段任务均有显著影响。航线飞行技术性技能评价量表的构建为现代航线飞行员选拔与训练、机组驾驶行为规范性评价以及飞行安全管理考核模式的设计奠定了一个良好的工作基础。     

5～9岁儿童极限概念认知发展的实验研究

皮亚杰(1985)认为儿童非要到11或12岁时才能掌握极限的概念。这个观点十分让人感兴趣,然而在众多文献中却很难发现相关研究。本研究运用实验法研究了5、6、7、9四组儿童的极限概念。结果表明:儿童在极限概念的发展存在两个快速期,即5~6岁和6~7岁;5岁儿童处于极限概念萌芽状态,6岁儿童有了部分极限概念,7岁儿童极限概念有了进一步发展但不稳定;9岁儿童开始接近有了极限概念,但仍未到达完全理解。本研究结果支持了皮亚杰的相关观点。     

Unconscious semantic categorization and mask interactions: An elaborate response to Kunde et al. (2005)

In their original report [Kunde, W., Kiesel, A., & Hoffmann, J. (2003). Conscious control over the content of unconscious cognition. Cognition, 88, 223-242] maintain that “unconscious stimuli [do not] owe their impact […] to automatic semantic categorization” (p.223), and instead propose the action-trigger theory of unconscious priming. In a reply to our paper [Kunde, W., Kiesel, A., & Hoffmann, J. (2005). On the masking and disclosure of unconscious semantic processing. A reply to Van Opstal, Reynvoet, & Verguts (2005). Cognition], the authors adopt a reconcilist position, and propose that both theories may be valid depending on the experimental situation. We discuss the evidence in favor of this position. [Kunde, W., Kiesel, A., & Hoffmann, J. (2005). On the masking and disclosure of unconscious semantic processing. A reply to Van Opstal, Reynvoet, & Verguts (2005). Cognition] also propose an alternative account of our mask-type blocking hypothesis. We report an experiment that distinguishes between our original and their alternative hypothesis.     

1 + 2 is more than 2 + 1: Violations of commutativity and identity axioms in mental arithmetic

Over the past decade or so, a large number of studies have revealed that conceptual meaning is sensitive to situational context. More recently, similar contextual influences have been documented in the domain of number knowledge. Here we show such context dependency in a length production task. Adult participants saw single digit addition problems of the form n1 + n2 and produced the sum by changing bi-directionally the length of a horizontally extended line, using radially arranged buttons. We found that longer lines were produced when n1 < n2 compared to n1 > n2 and that unit size increased with result size. Thus, the mathematical axioms of commutativity and identity do not seem to hold in mental addition. We discuss implications of these observations for our understanding of cognitive mechanisms involved in mental arithmetic and for situated cognition generally.