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。     

关于数字卦与六十四卦符号体系之形成问题

将见于商周器物上的数字卦与传逝文献的有关记载结合起来分析,商周时期应已存在用两个符号记写的六十四卦体系;周初陶拍所见易卦与传本《周易》相同的非覆即反的排列方法,也表明当时的筮书应是用两个确定的符号记写的;六十四卦应如文献所记是由八卦重合而成的,而这种八卦形成的前提同样是将其记写符号确定为两个;构成八卦的阴阳爻应是按阴阳观念将偶数记成“一一”,将奇数记戚“—”的产物。     

纯小数加工的心理机制:选择通达还是平行通达?

采用数字线索提示的目标觉察范式,以60名在校大学生与研究生为被试,设计3个实验探讨纯小数(整数部分是零的小数,例如0.2)的加工及其与空间表征的联系。实验1探讨纯小数作为线索时是否能引起空间注意的空间-数字反应编码联合效应(Spatial Numerical Association of Response Codes,SNARC),结果发现,纯小数数量大小的加工可以引起空间注意的SNARC效应;实验2探讨纯小数的加工是否会同时激活小数点后对应的自然数,结果发现,对纯小数数量大小相同、小数点后对应的自然数是否有0(例如0.2和0.20,0.4和0.40)的加工能引起空间注意的转移;实验3比较纯小数的加工对纯小数本身及小数点后对应的自然数激活强度,结果发现,在纯小数数量大小判断和纯小数小数点后对应的自然数数量大小判断冲突的条件下,纯小数的加工未能引起注意的SNARC效应。该研究结果表明,在目标觉察范式中,纯小数的加工采取了平行通达的方式,引发了注意的SNARC效应,并且纯小数空间注意的转移受到纯小数本身以及对应的自然数的影响。     

Beyond quantity: Individual differences in working memory and the ordinal understanding of numerical symbols

In two different contexts, we examined the hypothesis that individual differences in working memory (WM) capacity are related to the tendency to infer complex, ordinal relationships between numerical symbols. In Experiment 1, we assessed whether this tendency arises in a learning context that involves mapping novel symbols to quantities by training adult participants to associate dot-quantities with novel symbols, the overall relative order of which had to be inferred. Performance was best for participants who were higher in WM capacity (HWMs). HWMs also learned ordinal information about the symbols that lower WM individuals (LWMs) did not. In Experiment 2, we examined whether WM relates to performance when participants are explicitly instructed to make numerical order judgments about highly enculturated numerical symbols by having participants indicate whether sets of three Arabic numerals were in increasing order. All participants responded faster when sequential sets (3-4-5) were in order than when they were not. However, only HWMs responded faster when non-sequential, patterned sets (1-3-5) were in order, suggesting they were accessing ordinal associations that LWMs were not. Taken together, these experiments indicate that WM capacity plays a key role in extending symbolic number representations beyond their quantity referents to include symbol-symbol ordinal associations, both in a learning context and in terms of explicitly accessing ordinal relationships in highly enculturated stimuli.     

The SNARC effect in the processing of second-language number words: Further evidence for strong lexico-semantic connections

We present new evidence that word translation involves semantic mediation. It has been shown that participants react faster to small numbers with their left hand and to large numbers with their right hand. This SNARC (spatial-numerical association of response codes) effect is due to the fact that in Western cultures the semantic number line is oriented from left (small) to right (large). We obtained a SNARC effect when participants had to indicate the parity of second-language (L2) number words, but not when they had to indicate whether L2 number words contained a particular sound. Crucially, the SNARC effect was also obtained in a translation verification task, indicating that this task involved the activation of number magnitude.     

Who can escape the natural number bias in rational number tasks? A study involving students and experts

Many learners have difficulties with rational number tasks because they persistently rely on their natural number knowledge, which is not always applicable. Studies show that such a natural number bias can mislead not only children but also educated adults. It is still unclear whether and under what conditions mathematical expertise enables people to be completely unaffected by such a bias on tasks in which people with less expertise are clearly biased. We compared the performance of eighth‐grade students and expert mathematicians on the same set of algebraic expression problems that addressed the effect of arithmetic operations (multiplication and division). Using accuracy and response time measures, we found clear evidence for a natural number bias in students but no traces of a bias in experts. The data suggested that whereas students based their answers on their intuitions about natural numbers, expert mathematicians relied on their skilled intuitions about algebraic expressions. We conclude that it is possible for experts to be unaffected by the natural number bias on rational number tasks when they use strategies that do not involve natural numbers.     

Numerical comparison of two-digit numbers: How differences at encoding can involve differences in processing

The study of two-digit numbers processing has recently gathered a growing interest. Here, we examine whether differences at encoding of two-digit oral verbal numerals induce differences in the type of processing involved. Twenty-four participants were submitted to a comparison task to 55. Differences at encoding were introduced by the use of dichotic listening and synchronous (synchronous condition) or asynchronous presentation (tens-first and units-first conditions) of the two-digit numerals' components. Our results showed that differences at the encoding stage of two-digit numerals involve: (1) different comparison processes (tens-first and units-first conditions: parallel comparison; synchronous condition: parallel and holistic comparison); and (2) differences in the weight of the tens- and units-effects. Therefore, attentional mechanisms determining at the encoding stage how much attention is paid to the two-digit numerals' components might account for the different types of processing found with two-digit numbers.