Symbolic representation of the number three: a study with three-year-old children from contrasting socioeconomic environments

The goal of the present study was to compare a range of aspects in children’s symbolic knowledge about the number three among two groups of three-year-olds from contrasting socioeconomic backgrounds. Every child was presented with five tasks that focused on the number three and that had cognitive demands of different complexity: expressing their age, reciting the conventional number series up to three, quantifying a collection of three, and two tasks requiring the use of visually presented quantitative information.The results showed the same order of difficulty of the tasks in both socioeconomic groups and a clear performance difference depending on socioeconomic background. These findings show that symbolic knowledge about the number three does not come in an all or none fashion. Rather, different aspects of this symbolic competence become apparent in response to different tasks, and seem to depend largely on the socioeconomic environment in which children develop.     

非参数认知诊断方法下诊断结果的概率化表征

非参数认知诊断分类方法非常适合课堂评估,其诊断结果采用0-1形式而缺乏概率化表征,不能精细地区分被试属性掌握程度的差异或变化,还缺乏可用于评价真实测验分类结果的信度和效度指标。要刻画被试属性掌握程度的差异,首要的问题是要为非参数认知诊断方法提供一种可以量化属性掌握概率的方法。针对此问题,基于二项分布和玻尔兹曼分布提出非参数认知诊断方法下诊断结果的概率化表征方法,并用于构建分类准确性和分类一致性指标。模拟研究与实测数据分析结果显示：概率化表征方法与非参数认知诊断方法的分类结果高度一致;概率化表征方法与认知诊断模型所得的属性掌握概率十分接近;概率化表征方法所得的属性（模式）掌握概率可用于计算属性（模式）分类准确性和分类一致性指标,在实际测验情景下可作为信度和效度指标,评价诊断结果的重测一致率和判准率。     

How the Abstract Becomes Concrete: Irrational Numbers Are Understood Relative to Natural Numbers and Perfect Squares

Mathematical cognition research has largely emphasized concepts that can be directly perceived or grounded in visuospatial referents. These include concrete number systems like natural numbers, integers, and rational numbers. Here, we investigate how a more abstract number system, the irrationals denoted by radical expressions like , is understood across three tasks. Performance on a magnitude comparison task suggests that people interpret irrational numbers (specifically, the radicands of radical expressions) as natural numbers. Strategy self‐reports during a number line estimation task reveal that the spatial locations of irrationals are determined by referencing neighboring perfect squares. Finally, perfect squares facilitate the evaluation of arithmetic expressions. These converging results align with a constellation of related phenomena spanning tasks and number systems of varying complexity. Accordingly, we propose that the task‐specific recruitment of more concrete representations to make sense of more abstract concepts (referential processing) is an important mechanism for teaching and learning mathematics.     

数字空间表征的在线建构：来自干扰情境中数字SNARC效应的证据

尽管已有研究发现数字以空间方式表征在人类记忆系统, 但是人脑如何完成数字的空间表征尚存争议。本研究两个实验在不同比例的数字字母(实验1)和不同比例的数字汉字(实验2)混合情境中考察了数字空间表征特点及其机制, 对上述争议进行了深入研究。结果发现：(1)当数字字母比例为“1 : 1”时, 数字加工中不出现SNARC效应。当数字字母比例为“1 : 6”和“6 : 1”时, 数字加工中均出现SNARC效应。即数字字母比例与数字SNARC效应之间呈倒“U”型关系。(2)数字汉字混合情境中数字汉字比例与数字SNARC效应之间同样呈倒“U”型关系。结果说明：(1)干扰刺激与数字混合呈现会影响数字SNARC效应。(2)干扰刺激加工对数字SNARC效应的影响受到数字与干扰刺激比例的调节, 且具有跨干扰材料的稳定性。研究结果意味着数字的空间表征是人类通过统计学习在线建构的, 支持了工作记忆理论。     

The left digit effect in a complex judgment task: Evaluating hypothetical college applicants

A left digit effect has been broadly observed across judgment and decision-making contexts ranging from product evaluation to medical treatment decisions to number line estimation. For example, $3.00 is judged to be a much greater cost than $2.99, and “801” is estimated strikingly too far to the right of “798” on a number line. Although the consequences of the effects for judgment and decision behavior have been documented, the sources of the effects are not well established. The goal of the current work is to extend investigations of the left digit effect to a new complex judgment activity and to assess whether the magnitude of the effect at the individual level can be predicted from performance on a simpler number skills task on which the left digit effect has also recently been observed. In three experiments (N = 434), adults completed a judgment task in which they rated the strength of hypothetical applicants for college admission and a self-paced number line estimation task. In all experiments, a small or medium left digit effect was found in the college admissions task, and a large effect was found in number line estimation. Individual-level variation was observed, but there was no relationship between the magnitudes of the effects in the two tasks. These findings provide evidence of a left digit effect in a novel multiattribute judgment task but offer no evidence that such performance can be predicted from a simple number skills task such as number line estimation.     

Body weight, not facial width-to-height ratio, predicts aggression in pro hockey players

Studies indicate that facial characteristics may predict behavior, but it is unclear if this will hold within highly selective populations. One relevant characteristic is the face’s width-to-height ratio (FWHR), a sexually dimorphic trait that has been shown to predict aggression. That FWHR may predict aggression within highly selective populations was suggested by Carré and McCormick’s (2008) finding that professional hockey players with greater FWHRs accrued more penalties. We attempted to replicate this result using all NHL players. We also explored fighting penalties as another aggression measure and height and weight as additional aggression predictors. We found that body weight predicted substantial variance in aggression but FWHR did not. Thus, in highly selective populations, inferences based on faces may be inaccurate.     

听觉通道下负数的低水平加工引起注意的SNARC效应

采用刺激探测任务,探讨了听觉通道下负数的低水平加工能否引起注意的SNARC效应。结果表明:(1)负数的低水平加工能够产生注意的SNARC效应,即线索为绝对值小的负数时,被试对左耳目标反应更快;线索为绝对值大的负数时,被试对右耳目标反应更快。(2)负数的加工所引起听觉空间注意的转移并不依赖于负数所在的情境,而仅通过其绝对值大小与空间表征发生关联。这一结论与视觉条件下所得到的结论不一致,并支持了系统发生论假说。