SNARC for numerosities is modulated by comparative instruction (and resembles some non-numerical effects)

The spatial–numerical association of response codes (SNARC) effect is observed for both numerical (Arabic digits) and non-numerical stimuli (size, duration, height). However, in a context of comparative judgment, Arabic numbers are mapped onto space differently from sizes and heights: SNARC for Arabic digits is formed consistently in a certain cultural reading direction, whereas SNARC for sizes and heights is additionally modulated by comparative instruction (it reverses when participants choose larger magnitudes). In the present study, we test whether the spatial characteristic of magnitude processing revealed in a context of comparison is determined by a presence or lack of numerical content of the processed information, or it depends on specific directional experience (e.g., left-to-right ordering) associated with the processed magnitude format. We examine the SNARC effect with the pairwise comparison design, by using non-symbolic numerical stimuli (objects’ collections), for which the left-to-right spatial structure is not as exceedingly overlearned as for Arabic numbers. We asked participants from two reading cultures (left-to-right vs. mixed reading culture) to compare numerosities of two sets, choosing either a larger or smaller one. SNARC emerged in both groups. Additionally, it was modulated by comparative instruction: It appeared in a left-to-right direction when participants selected a smaller set, but it tended to reverse when participants selected a larger set. We conclude that spatial processing of numerosities is dissociated from spatial processing of Arabic numbers, at least in a context of comparative judgment. This dissociation could reflect differences in spatial ordering experience specific to a certain numerical input.     

Musical space synesthesia: Automatic,explicit and conceptual connections between musical stimuli and space

In musical–space synesthesia, musical pitches are perceived as having a spatially defined array. Previous studies showed that symbolic inducers (e.g., numbers, months) can modulate response according to the inducer’s relative position on the synesthetic spatial form. In the current study we tested two musical–space synesthetes and a group of matched controls on three different tasks: musical–space mapping, spatial cue detection and a spatial Stroop-like task. In the free mapping task, both synesthetes exhibited a diagonal organization of musical pitch tones rising from bottom left to the top right. This organization was found to be consistent over time. In the subsequent tasks, synesthetes were asked to ignore an auditory or visually presented musical pitch (irrelevant information) and respond to a visual target (i.e., an asterisk) on the screen (relevant information). Compatibility between musical pitch and the target’s spatial location was manipulated to be compatible or incompatible with the synesthetes’ spatial representations. In the spatial cue detection task participants had to press the space key immediately upon detecting the target. In the Stroop-like task, they had to reach the target by using a mouse cursor. In both tasks, synesthetes’ performance was modulated by the compatibility between irrelevant and relevant spatial information. Specifically, the target’s spatial location conflicted with the spatial information triggered by the irrelevant musical stimulus. These results reveal that for musical–space synesthetes, musical information automatically orients attention according to their specific spatial musical-forms. The present study demonstrates the genuineness of musical–space synesthesia by revealing its two hallmarks—automaticity and consistency. In addition, our results challenge previous findings regarding an implicit vertical representation for pitch tones in non-synesthete musicians.     

Basic numerical skills in children with mathematics learning disabilities: a comparison of symbolic vs non-symbolic number magnitude processing

Forty-five children with mathematics learning disabilities, with and without comorbid reading disabilities, were compared to 45 normally achieving peers in tasks assessing basic numerical skills. Children with mathematics disabilities were only impaired when comparing Arabic digits (i.e., symbolic number magnitude) but not when comparing collections (i.e., non-symbolic number magnitude). Moreover, they automatically processed number magnitude when comparing the physical size of Arabic digits in an Stroop paradigm adapted for processing speed differences. Finally, no evidence was found for differential patterns of performance between MD and MD/RD children in these tasks. These findings suggest that children with mathematics learning disabilities have difficulty in accessing number magnitude from symbols rather than in processing numerosity per se.     

不同加工深度非符号数量信息的SNARC效应：眼动证据

通过两项眼动实验考察了个体在水平和垂直方向上对点阵数量进行较浅(浏览)和较深(数字比较)程度加工时的数量空间表征联系。结果显示：点阵在水平方向上出现了SNARC效应, 且SNARC效应的大小不受加工深浅的影响, 而在垂直方向上没有出现SNARC效应。表明(1)点阵数量SNARC效应的稳定性不如阿拉伯数字; (2)方向对点阵SNARC效应的影响更大, 加工程度的影响则不明显。结合加工程度、空间方向和点阵数量的自身特征等对研究发现进行了讨论, 认为数字的空间表征在多个因素的共同影响下可能呈现出多样性。     

数量对时间知觉的影响-来自抽象数量和实际数量的证据

本研究采用抽象数量和实际数量叠加的方式呈现刺激,进一步探讨数量对时间知觉的影响。两个实验都运用时间的系列比较任务,以抽象数量和实际数量这两种数量的一致和不一致为条件,将阿拉伯数字和其字体大小叠加及阿拉伯数字和其呈现个数叠加的方式系列呈现在屏幕中央,要求被试比较判断刺激呈现的时间长短。结果显示被试均依靠实际数量的大小判断时间长短,而似乎忽略了抽象数量的存在。这一结果表明实际数量对时间知觉的影响要比抽象数量大,支持并扩展了数量理论。     

Two plus blue equals green: Grapheme-color synesthesia allows cognitive access to numerical information via color

In grapheme-color synesthesia, graphemes (e.g., numbers or letters) evoke color experiences. It is generally reported that the opposite is not true: colors will not generate experiences of graphemes or their associated information. However, recent research has provided evidence that colors can implicitly elicit symbolic representations of associated graphemes. Here, we examine if these representations can be cognitively accessed. Using a mathematical verification task replacing graphemes with color patches, we find that synesthetes can verify such problems with colors as accurately as with graphemes. Doing so, however, takes time: ～250 ms per color. Moreover, we find minimal reaction time switch-costs for switching between computing with graphemes and colors. This demonstrates that given specific task demands, synesthetes can cognitively access numerical information elicited by physical colors, and they do so as accurately as with graphemes. We discuss these results in the context of possible cognitive strategies used to access the information.     

Automatic quantity processing in 5-year olds and adults

In this study adults performed numerical and physical size judgments on a symbolic (Arabic numerals) and non-symbolic (groups of dots) size congruity task. The outcomes would reveal whether a size congruity effect (SCE) can be obtained irrespective of notation. Subsequently, 5-year-old children performed a physical size judgment on both tasks. The outcomes will give a better insight in the ability of 5-year-olds to automatically process symbolic and non-symbolic numerosities. Adult performance on the symbolic and non-symbolic size congruity tasks revealed a SCE for numerical and physical size judgments, indicating that the non-symbolic size congruity task is a valid indicator for automatic processing of non-symbolic numerosities. Physical size judgments on both tasks by children revealed a SCE only for non-symbolic notation, indicating that the lack of a symbolic SCE is not related to the mathematical or cognitive abilities required for the task but instead to an immature association between the number symbol and its meaning.     

非符号数量表征和符号分数表征的关系

个体学习符号分数的一个关键是能对其数值形成准确表征。现有研究假设符号分数表征的认知基础是人类自婴幼儿期就具有的非符号数量表征(如表征两个集合各自的数量, 或两个数量的比例)。其证据包括表征非符号数量(尤其是非符号数量比例关系)和表征符号分数在行为和大脑神经活动层面上都表现出相关性。然而要说明非符号数量表征是符号分数表征的认知基础, 还需更多研究表明两者在数量概念上的独特相关和因果联系, 并阐明符号分数表征形成的认知机制。     

Synesthetic colors are elicited by sound quality in Japanese synesthetes

Determinants of synesthetic color choice for Japanese phonetic characters were studied in six Japanese synesthetes. The study used Hiragana and Katakana characters, which represent the same set of syllables although their visual forms are dissimilar. From a palette of 138 colors, synesthetes selected a color corresponding to each character. Results revealed that synesthetic color choices for Hiragana characters and those for their Katakana counterparts were remarkably consistent, indicating that color selection depended on character-related sounds and not visual form. This Hiragana–Katakana invariance cannot be regarded as the same phenomenon as letter case invariance, usually reported for English grapheme-color synesthesia, because Hiragana and Katakana characters have different identities whereas upper and lower case letters have the same identity. This involvement of phonology suggests that cross-activation between an inducer (i.e., letter/character) brain region and that of the concurrent (i.e., color) area in grapheme-color synesthesia is mediated by higher order cortical processing areas.     

Preschoolers prior formal mathematics education engage numerical magnitude representation rather than counting principles in symbolic ±1 arithmetic: Evidence from the operational momentum effect

In numerical cognition research, the operational momentum (OM) phenomenon (tendency to overestimate the results of addition and/or binding addition to the right side and underestimating subtraction and/or binding it to the left side) can help illuminate the most basic representations and processes of mental arithmetic and their development. This study is the first to demonstrate OM in symbolic arithmetic in preschoolers. It was modeled on Haman and Lipowska's (2021) non-symbolic arithmetic task, using Arabic numerals instead of visual sets. Seventy-seven children (4–7 years old) who know Arabic numerals and counting principles (CP), but without prior school math education, solved addition and subtraction problems presented as videos with one as the second operand. In principle, such problems may be difficult when involving a non-symbolic approximate number processing system, whereas in symbolic format they can be solved based solely on the successor/predecessor functions and knowledge of numerical orders, without reference to representation of numerical magnitudes. Nevertheless, participants made systematic errors, in particular, overestimating results of addition in line with the typical OM tendency. Moreover, subtraction and addition induced longer response times when primed with left- and right-directed movement, respectively, which corresponds to the reversed spatial form of OM. These results largely replicate those of non-symbolic task and show that children at early stages of mastering symbolic arithmetic may rely on numerical magnitude processing and spatial-numerical associations rather than newly-mastered CP and the concept of an exact number.     

Database of synesthetic color associations for Japanese kanji

Synesthesia is a neurological phenomenon in which certain types of stimuli elicit involuntary perceptions in an unrelated pathway. A common type of synesthesia is grapheme–color synesthesia, in which the visual perception of letters and numbers stimulates the perception of a specific color. Previous studies have often collected relatively small numbers of grapheme–color associations per synesthete, but the accumulation of a large quantity of data has greater promise for uncovering the mechanisms underlying synesthetic association. In this study, we therefore collected large samples of data from a total of eight synesthetes. All told, we obtained over 1000 synesthetic colors associated with Japanese kanji characters from each of two synesthetes, over 100 synesthetic colors form each of three synesthetes, and about 80 synesthetic colors associated with Japanese hiragana, Latin letters, and Arabic numerals from each of three synesthetes. We then compiled the data into a database, called the KANJI-Synesthetic Colors Database (K-SCD), which has a total of 5122 colors for 483, 46, and 46 Japanese kanji, hiragana, and katakana characters, respectively, as well as for 26 Latin letters and ten Arabic numerals. In addition to introducing the K-SCD, this article demonstrates the database’s merits by using two examples, in which two new rules for synesthetic association, “shape similarity” and “synesthetic color clustering,” were found. The K-SCD is publicly accessible (www.cv.jinkan.kyoto-u.ac.jp/site/uploads/K-SCD.xlsm) and will be a valuable resource for those who wish to conduct statistical analyses using a rich dataset in order to uncover the rules governing synesthetic association and to understand its mechanisms.     

Synesthesia and memory: color congruency, von Restorff, and false memory effects

In the current study, we explored the influence of synesthesia on memory for word lists. We tested 10 grapheme-color synesthetes who reported an experience of color when reading letters or words. We replicated a previous finding that memory is compromised when synesthetic color is incongruent with perceptual color. Beyond this, we found that, although their memory for word lists was superior overall, synesthetes did not exhibit typical color- or semantic-defined von Restorff isolation effects (von Restorff, 1933) compared with control participants. Moreover, our synesthetes exhibited a reduced Deese-Roediger-McDermott false memory effect (Deese, 1959; Roediger & McDermott, 1995). Taken as a whole, these findings are consistent with the idea that color-grapheme synesthesia can lead people to place a greater emphasis on item-specific processing and surface form characteristics of words in a list (e.g., the letters that make them up) relative to relational processing and more meaning-based processes. (PsycINFO Database Record (c) 2010 APA, all rights reserved).     

Modality and variability of synesthetic experience

In synesthesia, stimulation of one sensory or cognitive pathway leads to additional, involuntary experiences in a second sensory or cognitive pathway. We here review previous surveys on this neurologically based phenomenon and report the results of 63 synesthetes who completed our Internet and paper questionnaire on synesthesia. In addition to asking for personal data and information on the participant's synesthesia, the questionnaire focused on the components of the inducer that elicit or modulate synesthesia. Synesthesia was most often developmental (92%) and of the grapheme-color type (86%). Sixty-two percent of the participants perceived time-related words in a spatial configuration. Music-color synesthesia was common (41%), and synesthesia for natural and artificial sounds (33%) was higher than in previous estimates. Eighty-one percent of participants experienced more than one form of synesthesia. Multimodal synesthesia, in which inducer and concurrent belong to 2 different sensory modalities, occurred in 92% of the participants. Overall, auditory stimuli were most often reported as inducers, and visual concurrents were most common. Modulations of the synesthetic experiences such as changes of the concurrent color, expansion within the same or to a different sensory modality, or reduction of the number of inducers over time were reported by 17% of participants. This challenges the presumed consistency of synesthesia and the adequacy of the test-retest consistency score still most commonly used to assess the veracity of reported synesthesia. Implications of the high prevalence of cross-modal synesthesia and the variability of synesthesia are discussed.     

Consistency and strength of grapheme-color associations are separable aspects of synesthetic experience

Consistency of synesthetic associations over time is a widely used test of synesthesia. Since many studies suggest that consistency is not a completely reliable feature, we compared the consistency and strength of synesthetes’ grapheme-color associations. Consistency was measured by scores on the Synesthesia Battery and by the Euclidean distance in color space for the specific graphemes tested for each participant. Strength was measured by congruency magnitudes on the Implicit Association Test. The strength of associations was substantially greater for synesthetes than non-synesthetes, suggesting that this is a novel, objective marker of synesthesia. Although, intuitively, strong associations should also be consistent, consistency and strength were uncorrelated, indicating that they are likely independent, at least for grapheme-color synesthesia. These findings have implications for our understanding of synesthesia and for estimates of its prevalence since synesthetes who experience strong, but inconsistent, associations may not be identified by tests that focus solely on consistency.     

发展性计算障碍儿童的数量转换缺陷

本研究拟考察发展性计算障碍儿童的认知缺陷成因。实验1要求被试在三种形式(点/点,数/数,点/数)下进行数量比较,实验2仅将点集替换为汉字数字词。结果表明障碍组和正常组在数/数、点/数和汉字/汉字比较任务上的成绩存在显著差异,而在点/点和汉字/汉字比较上没有差异。据此推论,计算障碍儿童符号加工能力受到损伤,符号与非符号数量转换能力存在缺陷,但非符号加工能力和不同符号间数量转换没有缺陷,支持语义提取缺陷假设。     

非符号分数与整数计算能力的发展及其与数字记忆的关系

幼儿数学能力可以使用符号（如数字）和非符号（如图形）两种材料进行测量,但有研究发现符号材料会对幼儿真实数学能力的测量产生干扰。本研究使用动画序列设计范式,考察了94名55-75个月幼儿的非符号分数和整数计算能力。研究结果表明：在避开数学符号的影响后,幼儿在分数计算任务上的表现稍弱于整数计算任务,但两者随年龄增长表现出相似的发展模式。同时使用基于故事情景的数字记忆任务测查了幼儿的数字工作记忆能力,发现幼儿的数字回忆能力稍弱于数字再认。随着年龄增长,幼儿数字工作记忆与计算能力均不断发展,且二者相关显著。     

Metacontrast masking is processed before grapheme–color synesthesia

We investigated the physiological mechanism of grapheme–color synesthesia using metacontrast masking. A metacontrast target is rendered invisible by a mask that is delayed by about 60 ms; the target and mask do not overlap in space or time. Little masking occurs, however, if the target and mask are simultaneous. This effect must be cortical, because it can be obtained dichoptically. To compare the data for synesthetes and controls, we developed a metacontrast design in which nonsynesthete controls showed weaker dichromatic masking (i.e., the target and mask were in different colors) than monochromatic masking. We accomplished this with an equiluminant target, mask, and background for each observer. If synesthetic color affected metacontrast, synesthetes should show monochromatic masking more similar to the weak dichromatic masking among controls, because synesthetes could add their synesthetic color to the monochromatic condition. The target–mask pairs used for each synesthete were graphemes that elicited strong synesthetic colors. We found stronger monochromatic than dichromatic U-shaped metacontrast for both synesthetes and controls, with optimal masking at an asynchrony of 66 ms. The difference in performance between the monochromatic and dichromatic conditions in the synesthetes indicates that synesthesia occurs at a later processing stage than does metacontrast masking.     

The relationship between numerical mapping abilities,maths achievement and socioeconomic status in 4- and 5-year-old children

Background

Early numeracy skills are associated with academic and life-long outcomes. Children from low-income backgrounds typically have poorer maths outcomes, and their learning can already be disadvantaged before they begin formal schooling. Understanding the relationship between the skills that support the acquisition of early maths skills could scaffold maths learning and improve life chances.

Aims

The present study aimed to examine how the ability of children from different SES backgrounds to map between symbolic (Arabic numerals) and non-symbolic (dot arrays) at two difficulty ratios related to their math performance.

Sample

Participants were 398 children in their first year of formal schooling (Mean age = 60 months), and 75% were from low SES backgrounds.

Method

The children completed symbolic to non-symbolic and non-symbolic to symbolic mapping tasks at two difficulty ratios (1:2; 2:3) plus standardized maths tasks.

Results

The results showed that all the children performed better for symbolic to non-symbolic mapping and when the ratio was 1:2. Mapping task performance was significantly related to maths task achievement, but low-SES children showed significantly lower performance on all tasks.

Conclusion

The results suggest that mapping tasks could be a useful way to identify children at risk of low maths attainment.     

What can the same–different task tell us about the development of magnitude representations?

We examined the development of magnitude representations in children (Exp 1: kindergartners, first-, second- and sixth graders, Exp 2: kindergartners, first-, second- and third graders) using a numerical same-different task with symbolic (i.e. digits) and non-symbolic (i.e. arrays of dots) stimuli. We investigated whether judgments in a same-different task with digits are based upon the numerical value or upon the physical similarity of the digits. In addition, we investigated whether the numerical distance effect decreases with increasing age. Finally, we examined whether the performance in this task is related to general mathematics achievement. Our results reveal that a same-different task with digits is not an appropriate task to study magnitude representations, because already late kindergarteners base their responses on the physical similarity instead of the numerical value of the digits. When decisions cannot be made on the basis of physical similarity, a similar numerical distance effect is present over all age groups. This suggests that the magnitude representation is stable from late kindergarten onwards. The size of the numerical distance effect was not related to mathematical achievement. However, children with a poorer mathematics achievement score seemed to have more difficulties to link a symbol with its corresponding magnitude.     

When 9 is not on the right: Implications from number-form synesthesia

Number-form synesthetes consciously experience numbers in spatially-defined locations. For non-synesthete individuals, a similar association of numbers and space appears in the form of an implicit mental number line as signified by the distance effect–reaction time decreases as the numerical distance between compared numbers increases. In the current experiment, three number-form synesthetes and two different non-synesthete control groups (Hebrew speaking and English speaking) performed a number comparison task. Synesthete participants exhibited a sizeable distance effect only when presented numbers were congruent with their number-form. In contrast, the controls exhibited a distance effect regardless of congruency or presentation type. The findings suggest that: (a) number-form synesthesia impairs the ability to represent numbers in a flexible manner according to task demands; (b) number-form synesthesia is a genuine tangible experience, triggered involuntarily; and (c) the classic mental number line can be more pliable than previously thought and appears to be independent of cultural-lingo direction.