Coding strategies in number space: memory requirements influence spatial-numerical associations

The tendency to respond faster with the left hand to relatively small numbers and faster with the right hand to relatively large numbers (spatial numerical association of response codes, SNARC effect) has been interpreted as an automatic association of spatial and numerical information. We investigated in two experiments the impact of task-irrelevant memory representations on this effect. Participants memorized three Arabic digits describing a left-to-right ascending number sequence (e.g., 3-4-5), a descending sequence (e.g., 5-4-3), or a disordered sequence (e.g., 5-3-4) and indicated afterwards the parity status of a centrally presented digit (i.e., 1, 2, 8, or 9) with a left/right keypress response. As indicated by the reaction times, the SNARC effect in the parity task was mediated by the coding requirements of the memory tasks. That is, a SNARC effect was only present after memorizing ascending or disordered number sequences but disappeared after processing descending sequences. Interestingly, the effects of the second task were only present if all sequences within one experimental block had the same type of order. Taken together, our findings are inconsistent with the idea that spatial-numerical associations are the result of an automatic and obligatory cognitive process but do suggest that coding strategies might be responsible for the cognitive link between numbers and space.     

不同数字线下儿童与成人分数估计的表征模式

以44名小学六年级儿童与40名大学生为被试,通过0~1和1/100~1/10两种数字线的NP（数字位置）和PN（位置数字）估计任务系统考察儿童与成人的分数估计的表征方式。结果显示：（1）儿童和成人在0~1数字线的NP和PN任务上都呈线性表征,但在1/100~1/10数字线下,两组被试在NP任务上却呈对数表征,在PN任务上呈指数表征;（2）NP任务的错误百分比均高于PN任务,且儿童在两数字线下的准确性均明显低于成人。     

Mapping numerical magnitudes onto symbols: the numerical distance effect and individual differences in children's mathematics achievement

Although it is often assumed that abilities that reflect basic numerical understanding, such as numerical comparison, are related to children’s mathematical abilities, this relationship has not been tested rigorously. In addition, the extent to which symbolic and nonsymbolic number processing play differential roles in this relationship is not yet understood. To address these questions, we collected mathematics achievement measures from 6- to 8-year-olds as well as reaction times from a numerical comparison task. Using the reaction times, we calculated the size of the numerical distance effect exhibited by each child. In a correlational analysis, we found that the individual differences in the distance effect were related to mathematics achievement but not to reading achievement. This relationship was found to be specific to symbolic numerical comparison. Implications for the role of basic numerical competency and the role of accessing numerical magnitude information from Arabic numerals for the development of mathematical skills and their impairment are discussed.     

数字加工的认知神经基础

数学作为人类最重要的发明,越来越引起认知神经科学家的重视与关注,究竟什么才是人类数学知识的脑基础？脑成像的研究已经证实了一个参与数学运算加工的神经网络,包括顶叶皮质、侧前额叶皮质、内前额叶皮质、和小脑。实验证明：人脑对于数字具有一种模拟表达,类似于将数量在脑内部作为一种内心的数字线上的点来操作。神经心理学的研究证实数字加工的这种数量表达分布于两半球,其优势区位于下顶叶皮质区。     

Mistakes on display: Incorrect examples refine equation solving and algebraic feature knowledge

Although findings from cognitive science have suggested learning benefits of confronting errors (Metcalfe, 2017), they are not often capitalized on in many mathematics classrooms (Tulis, 2013). The current study assessed the effects of examples focused on either common mathematical misconceptions and errors or correct concepts and procedures on algebraic feature knowledge and solving quadratic equations. Middle school algebra students (N = 206) were randomly assigned to four conditions. Two errorful conditions either displayed errors and asked students to explain or displayed correct solutions and primed students to reflect on potential errors by problem type. A correct example condition and problem-solving control group were also included. Studying and explaining common errors displayed in incorrect examples improved equation-solving ability. An aptitude-by-treatment interaction revealed that learners with limited understandings of algebraic features demonstrated greater benefits. Theoretical implications about using examples to promote learning from errors are considered in addition to suggestions for educational practice.     

Logic Without Contraction as Based on Inclusion and Unrestricted Abstraction

On the one hand, the absence of contraction is a safeguard against the logical (property theoretic) paradoxes; but on the other hand, it also disables inductive and recursive definitions, in its most basic form the definition of the series of natural numbers, for instance. The reason for this is simply that the effectiveness of a recursion clause depends on its being available after application, something that is usually assured by contraction. This paper presents a way of overcoming this problem within the framework of a logic based on inclusion and unrestricted abstraction, without any form of extensionality. This revised version was published online in June 2006 with corrections to the Cover Date.     

Number Use at Home by Children and Their Parents and Its Relationship to Early Mathematical Performance

The purpose of this research was to measure the frequency and variety of number activities occurring in the homes of pre-school and kindergarten children and to determine if there was a relationship between those activities and the children's mathematical performance. In two studies, parents were interviewed over the telephone and asked how often their child or they and their child had engaged in each of 33 number-related activities over the last week. Both studies found considerable variability in the frequency and type of number activities that children participated in at home. There was a positive correlation between the frequency of number activities that parents reported for their children and parental participation in the same activities. In addition, in study 2, parental reports of children's number activities at home were predictive of children's performance on a standardized test of early mathematical ability.     

An expert–novice comparison of feature choice

Perceptual experts have learned to rapidly and accurately perceive the structural regularities that define categories and identities within a domain. They extract important features and their relations more efficiently than novices. We used fingerprint examination to investigate expert–novice differences in feature choice. On each fingerprint within our set, experts and novices selected one feature they thought was most useful for distinguishing a particular print and one feature they thought was least useful. We found that experts and novices often differed in the features they chose, and experts tended to agree more with each other. However, any such expert–novice difference appeared to depend on the image at hand typically emerging when salient or more conspicuous features of a fingerprint were unclear. We suggest that perceptual training ought to direct attention to useful features with the understanding that what is useful may change depending on the clarity of the stimuli.     

视觉工作记忆中的特征捆绑

特征捆绑是认知科学和神经科学研究的前沿问题,近来已经成为研究者们关于意识问题争论的焦点所在。很多心理活动涉及复杂对象各种特征的捆绑,在工作记忆中保持这些捆绑的机制是心理加工得以有效进行的基础。视觉工作记忆中的特征捆绑近来成为研究热点之一,有关研究大多凭借变化检测范式和单刺激探测范式,探讨了视觉工作记忆中捆绑特征的保持是否需要注意参与,以及分离特征存储和捆绑特征存储的关系等问题,但目前这些问题仍都没有明确的答案。     

“All I remember is the black eye”: A distinctive facial feature harms eyewitness identification

Many crimes occur in which a perpetrator has a distinctive facial feature, such as a tattoo or black eye, but few eyewitness identification (ID) studies have involved such a feature. We conducted an experiment to determine how eyewitness ID performance is impacted by a distinctive facial feature, and how police could deal with this issue. Participants (N = 4,218) studied a target face with or without a black eye, and later viewed a simultaneous photo lineup either containing the target or not. For those who saw a target with a black eye, this feature was either replicated among all lineup members or was removed. The black eye harmed empirical discriminability regardless of replication or removal, which did not differ. However, participants responded more conservatively when the black eye was removed, compared to replication. Lastly, immediate confidence was consistently indicative of accuracy.