Spatial Associations in Numerical Cognition—From Single Digits to Arithmetic

Issues in Grounded Cognition and How to Solve Them - the Minimalist Account

The field of grounded cognition is concerned with how concepts are represented by re-activation of the bodily modalities. Considerable empirical work supports this core tenet, but the field is rife with meta-theoretical issues which prevent meaningfully progressing beyond this. We describe these issues and provide a solution: an overarching theoretical framework. The two most commonly cited grounded cognition theories are perceptual symbol systems and conceptual metaphor theory. Under perceptual symbol systems, concepts are represented by integrating fragments of multi-modal percepts in a simulator. Conceptual metaphor theory involves a limited number of image schemas, primitive structural regularities extracted from interaction with the environment, undergoing a limited number of transformations into a concept. Both theories constitute important developments to understanding mental representations, yet we argue that they currently impede progress because they are prematurely elaborate. This forces them to rely on overly specific assumptions, which generates a lack of conceptual clarity and unsystematic testing of empirical work. Our minimalist account takes grounded cognition 'back to basics' with a common-denominator framework supported by converging evidence from other fields. It postulates that concepts are represented by simulation, re-activating mental states that were active when experiencing this concept, and by metaphoric mapping, when concrete representations are sourced to represent abstract concepts. This enables incremental theory development without uncertain assumptions because it allows for descriptive research while nonetheless enabling falsification of theories. Our proposal provides the tools to resolve meta-theoretical issues and encourages a research program that integrates grounded cognition into the cognitive sciences.

The role of cognitive control in the interaction of the SNARC and MARC effects

Many studies have identified two types of spatial congruency effects in number parity judgment tasks: the SNARC effect (Spatial-Numerical Association of Response Codes), related to numerical magnitude, and the MARC effect (Linguistic Markedness Association of Response Codes), associated with parity. Although previous work has found that these effects interact, the mechanisms underlying the interaction are unclear. Previous studies have investigated the effect of linguistic connections on the activation of the SNARC and MARC effects in right-to-left readers by manipulating the time interval between tasks. We propose that a cognitive control mechanism mediates this phenomenon, with the level of cognitive conflict induced by the MARC effect under varying conditions being a critical factor in influencing spatial-numerical associations. We first performed four behavioral experiments manipulating time intervals between parity-to-response mappings. The results demonstrate that interactions between the SNARC and MARC effects are not sensitive to changes in time intervals but are primarily influenced by the congruency between the two effects. We then performed an event related potentials study. The response patterns observed in the P300 component support the hypothesis that cognitive conflict levels influence spatial-numerical associations. In conclusion, this study highlights the essential role of cognitive control in modulating the conflict between the SNARC and MARC effects, providing a new theoretical perspective on the dynamic characteristics of spatial-numerical associations.

Vertical and horizontal space-valence associations: A meta-analysis

Previous research found associations between lower vs. upper space and negative vs. positive stimuli correspondingly (vertical Space-Valence Associations, SVAs) and between the left vs. right side and negative vs. positive stimuli correspondingly (horizontal SVAs). We conducted a comprehensive meta-analysis of SVAs for both dimensions in behavioral studies. We tested the robustness of SVAs and examined factors potentially modulating them: participants' culture, handedness, gender, age, the exact valence domain under study, the experimental task, type of stimuli, publication year, and statistics used. Articles were extracted from Web of Science, PubMed, and ScienceDirect in February 2021. Overall, 91 articles with 199 experiments and 21,951 participants were included in the final analysis. We found robust evidence of SVAs in vertical (r = .440, k = 111 experiments) and horizontal dimensions (r = .310; k = 88 experiments), with little evidence for literature biases. The distribution of effect sizes was highly heterogeneous, even after subgroup analyses, which indicates unidentified factors varying across studies. Experiments on vertical SVAs explicitly asking participants to evaluate valence showed larger effect sizes than experiments where valence remained task-irrelevant. There was a robust effect of handedness on horizontal SVAs: Participants associated positive stimuli with the side of their dominant hand. There was also some evidence of cultural influences on the horizontal SVAs. Overall, our meta-analysis revealed a hierarchy of factors modulating activation of SVAs, which includes both situated and embodied factors. It is, therefore, essential to focus on specific concept categories and contexts rather than consider abstract concepts in general. PUBLIC SIGNIFICANCE STATEMENT: This meta-analysis revealed medium effects of space-valence associations: Upper/right space is associated with positive and lower/right space with negative concepts. On the vertical dimension, this effect is modulated by valence being task-relevant, e.g., directly asking people about valence results in stronger associations. For the horizontal dimension, left-handers robustly showed a reversed effect (i.e., left is good); horizontal space-valence associations might be even stronger in non-Western countries.

One and only SNARC? Spatial-Numerical Associations are not fully flexible and depend on both relative and absolute number magnitude

Numbers are associated with space, but it is unclear how flexible these associations are. We investigated whether the SNARC effect (Spatial-Numerical Association of Response Codes; Dehaene et al. 1993 J. Exp. Psychol. 122, 371-396. (doi:10.1037/0096-3445.122.3.371); i.e. faster responses to small/large number magnitude with the left/right hand, respectively) is fully flexible (depending only on relative magnitude within a stimulus set) or not (depending on absolute magnitude as well). Evidence for relative-magnitude dependency came from studies observing that numbers 4 and 5 were associated with the right in a 0-5 range but with the left in a 4-9 range (Dehaene et al. 1993; Fias et al. 1996 Math. Cogn. 2, 95-110 (doi:10.1080/135467996387552). Within this Registered Report, we conducted two online experiments running Bayesian analyses with optional recruitment stopping at moderate evidence (BF10 above 3 or below 1/3). Experiment 1 (n = 200) replicated relative-magnitude dependency using the original stimuli. However, Experiment 2 (n = 300) additionally demonstrated absolute-magnitude dependency, while considering recent advances in SNARC research using 1-5 excluding 3 and 4-8 excluding 6. In contrast to the frequently perpetuated notion of fully flexible Spatial-Numerical Associations, some fixed relation to absolute magnitude prevails. These findings have important consequences for understanding how Spatial-Numerical Associations might support numerical processing.

Implications of neural integration of math and spatial experiences for math ability and math anxiety

Mathematical and spatial abilities are positively related at both the behavioral and neural levels. Much of the evidence illuminating this relationship comes from classic laboratory-based experimental methods focused on cognitive performance despite most individuals also experiencing math and space in other contexts, such as in conversations or lectures. To broaden our understanding of math-space integration in these more commonplace situations, we used an auditory memory-encoding task with stimuli whose content evoked a range of educational and everyday settings related to math or spatial thinking. We used a multivariate approach to directly assess the extent of neural similarity between activity patterns elicited by these math and spatial stimuli. Results from whole-brain searchlight analysis revealed a highly specific positive relation between math and spatial activity patterns in bilateral anterior hippocampi. Examining individual variation in math-space similarity, we found that greater math-space similarity in bilateral anterior hippocampi was associated with poorer math skills and higher anxiety about math. Integration of neural responses to mathematical and spatial content may not always portend positive outcomes. We suggest that episodic simulation of quotidian contexts may link everyday experiences with math and spatial thinking-and the strength of this link is predictive of math in a manner that diverges from math-space associations derived from more lab-based tasks. On a methodological level, this work points to the value of considering a wider range of experimental paradigms, and of the value of combining multivariate fMRI analysis with behavioral data to better contextualize interpretations of brain data.

Where does the processing of size meet the processing of space?

Previous studies revealed an S-R compatibility effect between physical stimulus size and response location, with faster left (right) responses to small (large) stimuli, respectively, as compared to the reverse assignments. Here, we investigated the locus of interactions between the processing of size and spatial locations. In Experiment 1, we explored whether stimulus size and stimulus location interact at a perceptual level of processing when responses lack spatiality. The stimuli varied on three feature dimensions (color, size, location), and participants responded vocally to each feature in a separate task. Most importantly, we failed to observe a size-location congruency effect in the color-naming task where S-R compatibility effects were excluded. In Experiment 2, responses to color were spatial, that is, key-presses with the left and right hand. With these responses there was a congruency effect. In addition, we tested the interaction of the size-location compatibility effect with the Simon effect, which is known to originate at the stage of response selection. We observed an interaction between the two effects only with a subsample of participants with slower reaction times (RTs) and a larger size-location compatibility effect in a control condition. Together, the results suggest that the size-location compatibility effect arises at the response selection stage. An extended leaky, competing accumulator model with independent staggered impacts of stimulus size and stimulus location on response selection fits the data of Experiment 2 and specifies how the size-location compatibility effect and the Simon effect can arise during response selection.

Verbal stimuli allow for symmetrical S-R priming effects between size and space

The spatial-size association of response codes (SSARC) effect refers to the observation that left responses are faster and more accurate to small stimuli whereas right responses are faster and more accurate to large stimuli, as compared to the reverse assignment. The underlying spatial-size associations are strongly asymmetrical with physical size/location stimuli and vocal location/size responses and allow for regular but not reciprocal SSARC effects. Recent evidence, however, points towards an important role of stimulus mode in the emergence of reciprocal compatibility effects. We investigated the reciprocity of the SSARC effect with a different stimulus mode, namely with verbal size/location stimuli and vocal responses. In a size-location task, participants vocally responded to the words "small" or "large" by saying "left" or "right" according to a compatible ("small"-"left"/"large"-"right") or an incompatible mapping ("small"-"right"/"large"-"left"). In a location-size task, participants vocally responded to the words "left" or "right" by saying "small" or "large" according to a compatible ("left"-"small"/"right"-"large") or an incompatible ("left"-"large"/"right"-"small") mapping. We observed a regular and a reciprocal SSARC effect of similar size indicating symmetrical spatial-size associations. While regular SSARC effects thus emerge with verbal and physical size stimuli, reciprocal SSARC effects only emerge with verbal but not with physical location stimuli and vocal responses. Theoretical accounts of the SSARC effect differ in whether they predict reciprocal effects and whether they can account for the effect of stimulus mode on the reciprocal SSARC effect.

Different grasping experiences affect mapping effects but not correspondence effects between stimulus size and response location

The so-called spatial-size association of response codes (SSARC) effect denotes that humans respond faster and more accurately with a left response to physically small stimuli and a right response to physically large stimuli, as compared to the opposite mapping. According to an application of the CORE principle to the SSARC effect, the habit to grasp larger/heavier objects with one's dominant hand and smaller/lighter objects with one's non-dominant hand creates spatial-size associations. We investigated if grasping habits play a causal role in the formation of spatial-size associations by testing if the mapping of a preceding object-grasping task affects the size of the SSARC effect in subsequent choice-response tasks with keypress responses. In the object-grasping task, participants were instructed to grasp wooden cubes of variable size either according to a compatible (small-left; large-right) or according to an incompatible (small-right; large-left) mapping. In the choice-response tasks, participants responded with left or right keypresses to the size or color of a small or large stimulus. The results showed that participants with the compatible mapping in the object-grasping task showed a larger SSARC effect in the size discrimination task, but not in the color discrimination task, than participants with the incompatible mapping in the object-grasping task. Results suggest that a short period of practice with different size-location mappings can modulate size-location links used for controlled S-R translation, but not links underlying automatic S-R translation. In general, the results support the hypothesis that grasping habits play a causal role in the formation of spatial-size associations.

Visuospatial Perception in Prematurely Born Children Without Cerebral Palsy or Retinopathy but With Scholar Complaints

In the absence of any complaints in early childhood, preterm children remain more at risk of encountering academic difficulties, but their clinical picture remains not well characterized. We screened visuospatial perception in 70 children born preterm consulting for scholar complaints. Developmental Coordination Disorder (with or without comorbidities) was associated with high prevalence (27%) of impaired perception of spatial relationship. Prematurely born children who obtained no diagnosis of Neuro-Developmental Disorder exhibited a high prevalence (31%) of impaired perception of object magnitude. Regression revealed that low gestational age and fetal growth restriction significantly predicted the magnitude but not the spatial relationship perception.

Beyond fixed sets: boundary conditions for obtaining SNARC-like effects with continuous semantic magnitudes

Previous research has demonstrated the presence of an effect (i.e., the spatial-numerical association of response codes or SNARC) in both numerical parity and magnitude judgment tasks in which smaller numerical magnitudes are manually responded to faster on the left side and larger numerical magnitudes on the right side. Such a result has typically been attributed to a spatially based representation of numerical magnitude in long-term memory, the format of which has recently been postulated to be positional in line with learning of a canonically ordered number sequence. As a test of this view, in the current research, participants made classification judgments involving either the size (N = 88) or the living-nonliving status (N = 114) corresponding to the names of animals/objects etc. to which no learned canonical ordering of size exists. Names were taken from a very large set of 400 animals/objects etc. and each name was presented only once in an experimental session. Responses were made using left and right manual keypresses. In this work, the relation between response time and the relative sizes of the animals/objects did not differ across the left-right side of response indicating that SNARC-like effects did not occur. As such, the results suggest that space is not an inherent aspect of the long-term representation of magnitude in the brain and that some form of positional coding of magnitude is necessary for SNARC-like effects to occur.

On the embodied nature of knowledge: From neurons to numbers

Interdisciplinary investigations of the human mind through the cognitive sciences have identified a key role of the body in representing knowledge. After characterizing knowledge at grounded, embodied, and situated levels, number knowledge is analyzed from this hierarchical perspective. Lateralized cortical processing of coarse versus fine detail is identified as a grounding substrate for the population stereotype few/left, many/right, which then contributes to number-related sensory and motor biases at the embodied and situated levels. Implications of this perspective for education and rehabilitation are discussed.

Don't SNARC me now! Intraindividual variability of cognitive phenomena - Insights from the Ironman paradigm

Two implicit generalizations are often made from group-level studies in cognitive experimental psychology and their common statistical analysis in the general linear model: (1) Group-level phenomena are assumed to be present in every participant with variations between participants being often treated as random error in data analyses; (2) phenomena are assumed to be stable over time. In this preregistered study, we investigated the validity of these generalizations in the commonly used parity judgment task. In the proposed Ironman paradigm, the intraindividual presence and stability of three popular numerical cognition effects were tested in 10 participants on 30 days: the SNARC (Spatial-Numerical Association of Response Codes, i.e., faster left-/right-sided responses to small/large magnitude numbers, respectively; Dehaene, Bossini, & Giraux, 1993), MARC (Linguistic Markedness of Response Codes; i.e., faster left-/right-sided responses to odd/even numbers, respectively; Nuerk, Iversen, & Willmes, 2004), and Odd (i.e., faster responses to even numbers; Hines, 1990) effects. We replicated the group-level effects; however, they were reliably present in only four to five (SNARC), six (MARC) or five (Odd) of 10 participants. Fluctuations seemed unsystematic, although the SNARC effect decreased over time along with reaction times. No correlation between the SNARC and MARC effects and sleep duration, tiredness, daytime, and consumption of stimulants were detected in most participants. These results challenge the frequent generalizations from group-level phenomena to individual participants and from single sessions to typical behavior. The innovative Ironman paradigm combined with bootstrap analyses permits unique insights into the intraindividual presence and stability of cognitive phenomena.

Walking to a number: is there affective involvement in generating the SNARC effect in numerical cognition?

The effect known as the spatial-numerical association of response codes (SNARC) documents fast reaction to small numbers with a response at the left and to large numbers with a response at the right. The common explanation appeals to a hypothetical mental number line of a left-to-right orientation with the numerical magnitudes on the line activated in an automatic fashion. To explore the possibility of emotional involvement in processing, we employed prototypical affective behaviors for responses in lieu of the usual spatial-numerical ones (i.e., of pressing lateralized keys). In the present series of experiments, the participants walked toward a number or walked away from a number (in a physical approach-avoidance setup) or said "good" or "bad" in response to a number. We recorded strong SNARC effects with affective responding. For example, it took participants longer to say "good" than "bad" to small numbers, but it took them longer to say "bad" than "good" to larger numbers. Although each particular outcome can still be accounted for by a spatial interpretation, the cumulative results are suggestive of the possibly of affective involvement in generating the effect.

The reciprocity of spatial-numerical associations of vocal response codes depends on stimulus mode

Individuals make faster left responses to small/er numbers and faster right responses to large/r numbers than vice versa. This "spatial-numerical association of response codes" (SNARC) effect represents evidence for an overlap between the cognitive representations of number and space. Theories of the SNARC effect differ in whether they predict bidirectional S-R associations between number and space or not. We investigated the reciprocity of S-R priming effects between number and location in three experiments with vocal responses. In Experiments 1 and 2, participants completed a number-location task, with digits as stimuli and location words as responses, and a location-number task, with physical locations as stimuli and number words as responses. In addition, we varied the S-R mapping in each task. Results revealed a strong SNARC effect in the number-location task, but no reciprocal SNARC effect in the location-number task. In Experiment 3, we replaced physical location stimuli with location words and digit stimuli with number words. Results revealed a regular and a reciprocal SNARC effect of similar size. Reciprocal SNARC effects thus seem to emerge with verbal location stimuli and vocal responses, but not with physical location stimuli and vocal responses. The S-R associations underlying the SNARC effect with vocal responses thus appear bidirectional and symmetrical for some combinations of stimulus and response sets, but not for others. This has implications for theoretical accounts of the SNARC effect which need to explain how stimulus mode affects the emergence of reciprocal but not regular SNARC effects.

Horizontal mapping of time-related words in first and second language

The existence of a consistent horizontal spatial-conceptual mapping for words denoting time is a well-established phenomenon. For example, words related to the past or future (e.g., yesterday/tomorrow) facilitate respective leftward/rightward attentional shifts and responses, suggesting the visual-spatial grounding of temporal semantics, at least in the native language (L1). To examine whether similar horizontal bias also accompanies access to time-related words in a second language (L2), we tested 53 Russian-English (Experiment 1) and 48 German-English (Experiment 2) bilinguals, who classified randomly presented L1 and L2 time-related words as past- or future-related using left or right response keys. The predicted spatial congruency effect was registered in all tested languages and, furthermore, was positively associated with higher L2 proficiency in Experiment 2. Our findings (1) support the notion of horizontal spatial-conceptual mapping in diverse L1s, (2) demonstrate the existence of a similar spatial bias when processing temporal words in L2, and (3) show that the strength of time-space association in L2 may depend on individual L2 proficiency.

Hierarchical processing of feature, egocentric and relational information for spatial orientation in domestic chicks

Animals can use different types of information for navigation. Domestic chicks (Gallus gallus) prefer to use local features as a beacon over spatial relational information. However, the role of egocentric navigation strategies is less understood. Here, we tested domestic chicks' egocentric and allocentric orientation abilities in a large circular arena. In experiment 1, we investigated whether domestic chicks possess a side bias during viewpoint-dependent egocentric orientation, revealing facilitation for targets on the chicks' left side. Experiment 2 showed that local features are preferred over viewpoint-dependent egocentric information when the two conflict. Lastly, in experiment 3, we found that in a situation where there is a choice between egocentric and allocentric spatial relational information provided by free-standing objects, chicks preferentially rely on egocentric information. We conclude that chicks orient according to a hierarchy of cues, in which the use of the visual appearance of an object is the dominant strategy, followed by viewpoint-dependent egocentric information and finally by spatial relational information.

The Italian Sensorimotor Norms: Perception and action strength measures for 959 words

Neuroscience research has provided evidence that semantic information is stored in a distributed brain network involved in sensorimotor and linguistic processing. More specifically, according to the embodied cognition accounts, the representation of concepts is deemed as grounded in our bodily states. For these reasons, normative measures of words should provide relevant information about the extent to which each word embeds perceptual and action properties. In the present study, we collected ratings for 959 Italian nouns and verbs from 398 volunteers, recruited via an online platform. The words were mostly taken from the Italian adaptation of the Affective Norms for English Words (ANEW). A pool of 145 verbs was added to the original set. All the words were rated on 11 sensorimotor dimensions: six perceptual modalities (vision, audition, taste, smell, touch, and interoception) and five effectors (hand-arm, foot-leg, torso, mouth, head). The new verbs were also rated on the ANEW dimensions. Results showed good reliability and consistency with previous studies. Relations between perceptual and motor dimensions are described and interpreted, along with relations between the sensorimotor and the affective dimensions. The currently developed dataset represents an important novelty, as it includes different word classes, i.e., both nouns and verbs, and integrates ratings of both sensorimotor and affective dimensions, along with other psycholinguistic parameters; all features only partially accomplished in previous studies.

How time gets spatial: factors determining the stability and instability of the mental time line

Left-to-right readers classify faster past events with motor responses on the left side of space and future events with responses on the right side. This suggests a left-to-right spatial organization in the mental representation of time. Here, we show that the significance and reliability of this representation are linked to the joint use of temporal and spatial codes in the task at hand. In a first unimanual Go/No-Go Implicit Association Test (IAT), attending selectively to "past" or to "future" words did not activate corresponding "left" or "right" spatial concepts and vice versa. In a second IAT, attending to both temporal (i.e., "past" and "future") words and spatial targets (i.e., "left" and "right") pointing arrows produced faster responses for congruent rather than incongruent combinations of temporal and spatial concepts in task instructions (e.g., congruent = "Go with past words and left-pointing arrows"; incongruent = "Go with past words and right-pointing arrows"). This effect increased markedly in a STEARC task where spatial codes defined the selection between "left-side" and "right-side" button presses that were associated with "past" and "future" words. Two control experiments showed only partial or unreliable space-time congruency effects when (a) participants attended to superordinate semantic codes that included both spatial "left"/"right" or temporal "past/future" subordinate codes; (b) a primary speeded response was assigned to one dimension (e.g., "past vs. future") and a nonspeeded one to the other dimension (e.g., "left" vs. "right"). These results help to define the conditions that trigger a stable and reliable spatial representation of time-related concepts.

Associations between physical size and space are strongly asymmetrical

The spatial-size association of response codes (SSARC) effect describes the phenomenon that left responses are faster and more accurate to small stimuli whereas right responses are faster and more accurate to large stimuli, as compared to the opposite mapping. The effect indicates associations between the mental representations of physical size and space. Importantly, the theoretical accounts of SSARC effects make different predictions about the reciprocity and/or symmetry of spatial-size associations. To investigate the reciprocity of SSARC effects, we compared compatibility effects in two verbal choice-response tasks: a size-location (typical SSARC) task and a location-size (reciprocal SSARC) task. In the size-location task, participants responded verbally to a small/large stimulus by saying "left"/"right". In the location-size task, participants responded verbally to a left-/right-side stimulus by saying "small"/"large". Participants completed both tasks with a compatible (small-left, large-right; left-small, right-large) and an incompatible (small-right, large-left; left-large, right-small) mapping. A regular SSARC effect emerged in the size-location task. However, no reciprocal SSARC effect emerged in the location-size task if outliers were excluded. If outliers were not excluded, small reciprocal SSARC effects occurred. Associations underlying the SSARC effect are thus strongly asymmetrical: Physical (stimulus) size can prime spatial responses much more strongly than spatial (stimulus) position can prime size-related responses. The finding of asymmetrical associations between size and space is in line with some theoretical accounts of the SSARC effect but at odds with others.

Spatial-numerical associations of manual response codes are strongly asymmetrical

The spatial-numerical association of response codes (SNARC) effect denotes the observation that humans respond faster and more accurately with a left-side response to smaller numbers and a right-side response to larger numbers, as compared to the opposite mapping. Existing accounts, such as the mental number line hypothesis or the polarity correspondence principle, differ in whether they assume symmetrical associations between numerical and spatial stimulus and response codes or not. In two experiments, we investigated the reciprocity of the SNARC effect in manual choice-response tasks with two conditions. In the number-location task, participants pressed a left or right key to a number stimulus (dots in Experiment 1, digits in Experiment 2). In the location-number task, participants made one or two consecutive keypresses with one hand to a left- or right-side stimulus. Both tasks were performed with a compatible (one-left, two-right; left-one, right-two) and an incompatible (one-right, two-left; left-two, right-one) mapping. In both experiments, results showed a strong compatibility effect in the number-location task, reflecting the typical SNARC effect. In contrast, in both experiments, there was no mapping effect in the location-number task when outliers were excluded. However, when outliers were not excluded, small reciprocal SNARC effects occurred in Experiment 2. Together, the findings suggest that priming of spatial responses by numerical stimuli is much stronger than priming of numerical responses by spatial stimuli. The results are consistent with some accounts of the SNARC effect (e.g., the mental number line hypothesis), but not with others (e.g., the polarity correspondence principle).

Investigating the influence of body movements on children's mental arithmetic performance

Several lines of research have demonstrated spatial-numerical associations in both adults and children, which are thought to be based on a spatial representation of numerical information in the form of a mental number line. The acquisition of increasingly precise mental number line representations is assumed to support arithmetic learning in children. It is further suggested that sensorimotor experiences shape the development of number concepts and arithmetic learning, and that mental arithmetic can be characterized as "motion along a path" and might constitute shifts in attention along the mental number line. The present study investigated whether movements in physical space influence mental arithmetic in primary school children, and whether the expected effect depends on concurrency of body movements and mental arithmetic. After turning their body towards the left or right, 48 children aged 8 to 10 years solved simple subtraction and addition problems. Meanwhile, they either walked or stood still and looked towards the respective direction. We report a congruency effect between body orientation and operation type, i.e., higher performance for the combinations leftward orientation and subtraction and rightward orientation and addition. We found no significant difference between walking and looking conditions. The present results suggest that mental arithmetic in children is influenced by preceding sensorimotor cues and not necessarily by concurrent body movements.

Replacing vertical actions by mouse movements: a web-suited paradigm for investigating vertical spatial associations

The number of web-based studies in experimental psychology has been growing tremendously throughout the last few years. However, a straightforward web-based implementation does not exist for all types of experimental paradigms. In the current paper, we focus on how vertical response movements-which play a crucial role in spatial cognition and language research-can be translated into a web-based setup. Specifically, we introduce a web-suited counterpart of the vertical Stroop task (e.g., Fox & Shor, in Bull Psychon Soc 7:187-189, 1976; Lachmair et al., in Psychon Bull Rev 18:1180-1188, 2011; Thornton et al., in J Exp Psychol Hum Percept Perform 39:964-973, 2013). We employed nouns referring to entities typically located in lower or upper vertical space (e.g., "worm" and "bird", respectively) in Experiments 1 and 2, and emotional valence words associated with a crouched or an upward bodily posture (e.g., "sadness" and "excitement", respectively) in Experiment 3. Depending on the font color, our participants used their mouse to drag the words to the lower or upper screen location. Across all experiments, we consistently observed congruency effects analogous to those obtained with the lab paradigm using actual vertical arm movements. Consequently, we conclude that our web-suited paradigm establishes a reliable approach to examining vertical spatial associations.

The relevance of basic numerical skills for fraction processing: Evidence from cross-sectional data

Recent research indicated that fraction understanding is an important predictor of later mathematical achievement. In the current study we investigated associations between basic numerical skills and students' fraction processing. We analyzed data of 939 German secondary school students (age range = 11.92 to 18.00 years) and evaluated the determinants of fraction processing considering basic numerical skills as predictors (i.e., number line estimation, basic arithmetic operations, non-symbolic magnitude comparison, etc.). Additionally, we controlled for general cognitive ability, grade level, and sex. We found that multiplication, subtraction, conceptual knowledge, number line estimation, and basic geometry were significantly associated with fraction processing beyond significant associations of general cognitive ability and sex. Moreover, relative weight analysis revealed that addition and approximate arithmetic should also be considered as relevant predictors for fraction processing. The current results provide food for thought that further research should focus on investigating whether recapitulating basic numerical content in secondary school mathematics education can be beneficial for acquiring more complex mathematical concepts such as fractions.

Spatial metaphors and the design of everyday things

People use space (e.g., left-right, up-down) to think about a variety of non-spatial concepts like time, number, similarity, and emotional valence. These spatial metaphors can be used to inform the design of user interfaces, which visualize many of these concepts in space. Traditionally, researchers have relied on patterns in language to discover habits of metaphorical thinking. However, advances in cognitive science have revealed that many spatial metaphors remain unspoken, shaping people's preferences, memories, and actions independent of language - and even in contradiction to language. Here we argue that cognitive science can impact our everyday lives by informing the design of physical and digital objects via the spatial metaphors in people's minds. We propose a simple principle for predicting which spatial metaphors organize people's non-spatial concepts based on the structure of their linguistic, cultural, and bodily experiences. By leveraging the latent metaphorical structure of people's minds, we can design objects and interfaces that help people think.

Processing stage flexibility of the SNARC effect: Task relevance or magnitude relevance?

Previous studies have shown that the processing stage of the spatial-numerical association of response codes (SNARC) effect is flexible. Two recent studies used the same experimental paradigm to check whether the SNARC effect occurred in the semantic-representation stage but reached contradictory conclusions, showing that the SNARC effect was influenced by a magnitude Stroop effect in a magnitude comparison task but not by a parity Stroop effect in a parity judgment task. Those two studies had two distinct operational factors: the task type (magnitude comparison task or parity judgment task, with the numerical magnitude information task-relevant or task-irrelevant) and the semantic representation stage-related interference information (magnitude or parity Stroop effect, with the interference information magnitude-relevant or magnitude-irrelevant). To determine which factor influenced the SNARC effect, in the present study, the Stroop effect was switched in the two tasks based on the previous studies. The findings of four experiments consistently showed that the SNARC effect was not influenced by the parity Stroop effect in the magnitude comparison task but was influenced by the magnitude Stroop effect in the parity judgment task. Combined with the results of those two contradictory studies, the findings indicated that regardless of the task type or the task relevance of numerical magnitude information, magnitude-relevant interference information was the primary factor to affect the SNARC effect. Furthermore, a two-stage processing model that explained the observed flexibility of the SNARC effect was proposed and discussed.

Random walk: Random number generation during backward and forward walking- the role of aging

Deficits in executive function, visuospatial abilities, and cognitive embodiment may impair gait performance. This study aimed to investigate the effect of age on random number generation (RNG) performance during forward and backward locomotion to assess cognitive flexibility and cognitive embodiment during walking. Another aim was to examine the effect of age on the associations of RNG performance during walking with stride time variability (STV), the percentage of double support (DS%), and visuospatial abilities as measured by a spatial orientation test (SOT). Twenty old (age 68.8 ± 5.3, 65% female) and 20 young (age 25.2 ± 2.2, 45% female) adults generated random numbers during backward walking (BW) and forward walking (FW) over-ground and over a treadmill with an internal focus of attention and visual-attentive distraction; six walking conditions in total. To assess cognitive flexibility, sample entropy was calculated for each RNG sequence. The average of the first 5 numbers in each RNG task was calculated to assess the relationship between small/large numbers and movement direction. STV and DS% were recorded using inertial measurement units, and spatial orientation was measured using a computerized test. The older subjects had less flexibility in generating random numbers in three of the six walking conditions. A negative correlation between RNG flexibility and STV was found in older adults during treadmill BW with visual-attentive distraction and forward over-ground walking, whereas no correlations were demonstrated in the young group. The spatial orientation score (a higher value means a worse outcome) correlated positively with RNG flexibility in the older group under all walking conditions, suggesting that older adults with better visuospatial orientation have lower cognitive flexibility, and vice versa. There was no correlation between small/large numbers and direction of motion in either group. The correlation between RNG flexibility and STV may indicate similar executive control of verbal and gait rhythmicity in old adults. Conversely, our results suggest that cognitive flexibility and visuospatial ability may decline differently.

The SNARC effect: a preregistered study on the interaction of horizontal, vertical, and sagittal spatial-numerical associations

Small numbers are processed faster through left-sided than right-sided responses, whereas large numbers are processed faster through right-sided than left-sided responses [i.e., the Spatial-Numerical Association of Response Codes (SNARC) effect]. This effect suggests that small numbers are mentally represented on the left side of space, whereas large numbers are mentally represented on the right side of space, along a mental number line. The SNARC effect has been widely investigated along the horizontal Cartesian axis (i.e., left-right). Aleotti et al. (Cognition 195:104111, 2020), however, have shown that the SNARC effect could also be observed along the vertical (i.e., small numbers-down side vs. large numbers-up side) and the sagittal axis (i.e., small numbers-near side vs. large numbers-far side). Here, we investigated whether the three Cartesian axes could interact to elicit the SNARC effect. Participants were asked to decide whether a centrally presented Arabic digit was odd or even. Responses were collected through an ad hoc-made response box on which the SNARC effect could be compatible for one, two, or three Cartesian axes. The results showed that the higher the number of SNARC-compatible Cartesian axes, the stronger the SNARC effect. We suggest that numbers are represented in a three-dimensional number space defined by interacting Cartesian axes.

Catch the star! Spatial information activates the manual motor system

Previous research demonstrated a close bidirectional relationship between spatial attention and the manual motor system. However, it is unclear whether an explicit hand movement is necessary for this relationship to appear. A novel method with high temporal resolution–bimanual grip force registration–sheds light on this issue. Participants held two grip force sensors while being presented with lateralized stimuli (exogenous attentional shifts, Experiment 1), left- or right-pointing central arrows (endogenous attentional shifts, Experiment 2), or the words "left" or "right" (endogenous attentional shifts, Experiment 3). There was an early interaction between the presentation side or arrow direction and grip force: lateralized objects and central arrows led to a larger increase of the ipsilateral force and a smaller increase of the contralateral force. Surprisingly, words led to the opposite pattern: larger force increase in the contralateral hand and smaller force increase in the ipsilateral hand. The effect was stronger and appeared earlier for lateralized objects (60 ms after stimulus presentation) than for arrows (100 ms) or words (250 ms). Thus, processing visuospatial information automatically activates the manual motor system, but the timing and direction of this effect vary depending on the type of stimulus.

Influences of hand action on the processing of symbolic numbers: A special role of pointing?

Embodied and grounded cognition theories state that cognitive processing is built upon sensorimotor systems. In the context of numerical cognition, support to this framework comes from the interactions between numerical processing and the hand actions of reaching and grasping documented in skilled adults. Accordingly, mechanisms for the processing of object size and location during reach and grasp actions might scaffold the development of mental representations of numerical magnitude. The present study exploited motor adaptation to test the hypothesis of a functional overlap between neurocognitive mechanisms of hand action and numerical processing. Participants performed repetitive grasping of an object, repetitive pointing, repetitive tapping, or passive viewing. Subsequently, they performed a symbolic number comparison task. Importantly, hand action and number comparison were functionally and temporally dissociated, thereby minimizing context-based effects. Results showed that executing the action of pointing slowed down the responses in number comparison. Moreover, the typical distance effect (faster responses for numbers far from the reference as compared to close ones) was not observed for small numbers after pointing, while it was enhanced by grasping. These findings confirm the functional link between hand action and numerical processing, and suggest new hypotheses on the role of pointing as a meaningful gesture in the development and embodiment of numerical skills.

EXPRESS: How negative emotions affect young and older adults' numerosity estimation performance

In this study, we investigated the influence of negative emotions on numerosity estimation and whether this influence changes with aging during adulthood. Young and older adults were asked to estimate and compare the numerosity of collections of elements (cars or dots) with a two-digit number. Collections of elements were preceded by emotionally neutral (e.g., mushrooms) or emotionally negative (e.g., a corpse) pictures. Stimuli were easier (i.e., small-ratio) or harder (i.e., large-ratio) items. Young and older participants obtained similar numerosity estimation performance. Interestingly, participants were less accurate under negative emotions than under neutral emotions when they estimated numerosity of collections of abstract elements (i.e., dots). In contrast, participants improved their performance under negative emotions while estimating collections of non-abstract, daily-life elements (i.e., cars). These findings have important implications for furthering our understanding of the role of negative emotions in numerosity estimation and age-related differences therein.

Adding and subtracting by hand: Metaphorical representations of arithmetic in spontaneous co-speech gestures

This study investigated the spontaneous co-speech gestures produced by speakers who were talking about the concepts of addition and subtraction in a television news setting. We performed a linguistic and co-speech gesture analysis of expressions related to the concepts of addition (N plus N, addition, add) and subtraction (N minus N, subtraction, subtract). First, we compared the linguistic frequency of these structures across several corpora. Second, we performed a multimodal gesture analysis, drawing data from a television news repository. We analyzed 423 co-speech gestures (169 for subtraction and 254 for addition) in terms of their axis (e.g., lateral, sagittal) and their direction (e.g., leftwards, away from their body). Third, we examined the semantic properties of the direct object that was added or subtracted. There were two main findings. First, low-frequency linguistic expressions were more likely to be accompanied by co-speech gestures. Second, most gestures about addition and subtraction were produced along the lateral or sagittal axes. When people spoke about addition, they tended to produce lateral, rightwards movements or movements away from the body. When people spoke about subtraction, they tended to produce lateral, leftwards movements or movements towards the body. This co-speech gesture data provides evidence that people activate two different metaphors for arithmetic in spontaneous behavior: arithmetic is motion along a path and arithmetic is collecting objects.

Children perform better on left than right targets in an ordinal task

Francis Galton first reported that humans mentally organize numbers from left to right on a mental number line (1880). This spatial-numerical association was long considered to result from writing and reading habits. More recently though, newborns and animals showed a left-to-right oriented spatial numerical association challenging the primary role assigned to culture in determining the link between number and space. Despite growing evidence supporting the intrinsic association between number and space in different species, its adaptive value is still largely unknown. Here we tested for an advantage in identification of left versus right target positions in 3- to 6-year-old children. Children watched as a toy was hidden under one of 10 linearly arranged identical cups and were then asked to help a stuffed animal retrieve the toy. On each trial, the toy was hidden in the 2nd, 3rd, or 4th cup, from the left or right. To prevent children from staring at the target cup, they were asked to pick up the stuffed animal from under their chair after witnessing the hiding of the toy and then to help the stuffed animal find the toy. Older children were more accurate than younger children. Children exhibited a serial position effect, with performance higher for more exterior targets. Remarkably, children also showed a left bias: they remembered the left targets better than the right targets. Only the youngest children were dramatically influenced by the location of the experimenter during search. Additional analyses support the hypothesis that children used a left-to-right oriented searching strategy in this spatial/ordinal task.

Heterogeneity of Dyscalculia Risk Dependent on the Type of Number Line Estimation Task and the Number Magnitude

An ability that is impaired in developmental dyscalculia (DD) is related to number line estimation (NLE). However, due to variability in NLE task performance, group differences do not exemplify the real difficulty level observed in the DD population. Thirty-two of the fifty-two participants posing dyscalculia risk (DR) (mean age = 9.88) experienced difficulties in mathematics. All the children performed two number-to-position tasks and two tasks requiring a verbal estimation of a number indicated on a line, utilizing the ranges 0–100 and 0–1000. The results showed that the estimation error in the verbal task was greater in the DR group than in the typically developed (TD) group for the 0–1000 range. In the number-to-position task, group differences were found for both ranges and the variability within both groups was smaller than it was in the verbal tasks. Analyses of each of the 26 numerical magnitudes revealed a more comprehensive pattern. The majority of the group effects were related to the 0–1000 line. Therefore, considerable data variability, especially in the DD group, suggests this issue must be analyzed carefully in the case of other mathematical capacities. It also critically questions some well-established phenomena and norms in experimental and diagnostic practices.

EXPRESS: Attention does not always help: the role of expectancy, divided, and spatial attention on illusory conjunctions

Humans have the subjective impression of a rich perceptual experience, but this perception is riddled with errors that might be produced by top-down expectancies or failures in feature integration. The role of attention in feature integration is still unclear. Some studies support the importance of attention in feature integration (Paul & Schyns, 2003), whereas others suggest that feature integration does not require attention (Humphreys, 2016). Understanding attention as a heterogeneous system, in this study we explored the role of divided (as opposed to focused - Experiment 1) attention, and endogenous-exogenous spatial orienting (Experiments 2 and 3) in feature integration. We also explored the role of feature expectancy, by presenting stimulus features that were completely unexpected to the participants. Results demonstrated that both endogenous and exogenous orienting improved feature integration while divided attention did not. Moreover, a strong and consistent feature expectancy effect was observed, demonstrating perceptual completion when an unexpected perceptual feature was presented in the scene. These results support the feature confirmation account (Humphreys, 2016), which proposes that attention is important for top-down matching of stable representations.

The Effect of Verbal Task Instruction on Spatial-Numerical Associations of Response Codes Effect Coding of Spatial-Numerical Associations: Evidence From Event-Related Potential

The spatial-numerical associations of response codes (SNARC) effect reveals that individuals can represent numbers spatially. In this study, event-related potential (ERP) technology was used to probe the effect of verbal-spatial task instructions on spatial-numerical association coding by using digit parity and magnitude judgment tasks, with the numbers 1–9 (except 5) and Chinese word labels (“left” and “right”) as experimental materials. The behavioral results of Experiment 1 showed that the SNARC effect was mainly based on verbal-spatial coding and appeared when the stimulus onset asynchrony (SOA) between the presentation of the verbal labels and the target digit was 0 ms. ERP results did not reveal any significant SNARC-related effects in either the N1 or P3 components. The behavioral results of Experiment 2 again showed that the SNARC effect was dominated by verbal-spatial coding. ERP results showed that significant effects related to verbal-spatial coding were found in both the early positive deflection of the stimulus-locked lateralized readiness potential (S-LRP) and the latency of the response-locked LRP (R-LRP). Hence, in this study, the nature of the spatial coding of the digit magnitudes was influenced by the processing of the word labels and affected both the response selection and response preparation stages.

Number to me, space to you: Joint representation of spatial-numerical associations

Recent work has shown that number concepts activate both spatial and magnitude representations. According to the social co-representation literature which has shown that participants typically represent task components assigned to others together with their own, we asked whether explicit magnitude meaning and explicit spatial coding must be present in a single mind, or can be distributed across two minds, to generate a spatial-numerical congruency effect. In a shared go/no-go task that eliminated peripheral spatial codes, we assigned explicit magnitude processing to participants and spatial processing to either human or non-human co-agents. The spatial-numerical congruency effect emerged only with human co-agents. We demonstrate an inter-personal level of conceptual congruency between space and number that arises from a shared conceptual representation not contaminated by peripheral spatial codes. Theoretical implications of this finding for numerical cognition are discussed.

Grounding (fairly) complex numerical knowledge: an educational example

In this article, we contextualize and discuss an on-line contribution to this special issue in which a video-recorded lecture demonstrates the teaching of an abstract mathematical concept, namely regression to the mean. We first motivate the pertinence of this example from the perspective of embodied cognition. Then, we identify mechanisms of teaching that reflect embodied cognitive practices, such as the concreteness fading approach. Rather than a comprehensive review of multiple extensive literatures, this article provides the interested reader with several sources or entries into those literatures.

Early is left and up: Saccadic responses reveal horizontal and vertical spatial associations of serial order in working memory

Maintaining serial order in working memory is crucial for cognition. Recent theories propose that serial information is achieved by positional coding of items on a spatial frame of reference. In line with this, an early-left and late-right spatial-positional association of response code (SPoARC) effect has been established. Various theoretical accounts have been put forward to explain the SPoARC effect (the mental whiteboard hypothesis, conceptual metaphor theory, polarity correspondence, or the indirect spatial-numerical association effect). Crucially, while all these accounts predict a left-to-right orientation of the SPoARC effect, they make different predictions regarding the direction of a possible vertical SPoARC effect. In this study, we therefore investigated SPoARC effects along the horizontal and vertical spatial dimension by means of saccadic responses. We replicated the left-to-right horizontal SPoARC effect and established for the first time an up-to-down vertical SPoARC effect. The direction of the vertical SPoARC effect was in contrast to that predicted by metaphor theory, polarity correspondence, or by the indirect spatial-numerical association effect. Rather, our results support the mental whiteboard-hypothesis, according to which positions can be flexibly coded on an internal space depending on the task demands. We also found that the strengths of the horizontal and vertical SPoARC effects were correlated, showing that some people are more prone than others to use spatial references for position coding. Our results therefore suggest that context templates used for position marking are not necessarily spatial in nature but depend on individual strategy preferences.

Systematic spatial distortion of quantitative estimates

Magnitude estimation has been studied since the beginnings of scientific psychology and constitutes a fundamental aspect of human behavior. Yet, it has apparently never been noticed that estimates depend on the spatial arrangement used. We tested 167 adults in three experiments to show that the spatial layout of stimuli and responses systematically distorts number estimation, length production, and weight reproduction performance. The direction of distortion depends on the observer's counting habits, but does not seem to reflect the use of spatially associated number concepts. Our results imply that all quantitative estimates are contaminated by a "spell of space" whenever stimuli or responses are spatially distributed.

An implicit task reveals space-time associations along vertical and diagonal axes

In previous studies investigating the space-time compatibility effect, the experimental task always invites explicit spatial or temporal processing or both. In this study, we kept space and time irrelevant to the task. In a go/no-go task, participants (N = 50) were asked to either press a single button when they found the target or refrain from responding when there was no target in a search array. We manipulated the duration of the target-alone presentation that preceded a 7 × 7 search array consisting of either target plus distractors or distractors alone. The results revealed faster responses to shorter durations when the target appeared in the upper relative to the lower space. A similar effect also appeared along the diagonal axis with faster responses to shorter durations in upper-left relative to lower-right space. In contrast, no such difference was found along the horizontal axis. We hypothesize that vertical and diagonal space-time associations arise from the grounding of mental representation of time in physical experiences.

Two processing stages of the SNARC effect

The spatial-numerical association of response codes (SNARC) effect showed that small/large numbers represented in the left/right space facilitated left/right responses, respectively. However, the processing stage (semantic representation or response selection) of the SNARC effect is still controversial. To investigate this issue, we adopted a modified magnitude comparison task in which the effects of SNARC, Stroop (semantic-representation stage), and Simon (response-selection stage) could be simultaneously induced. The processing stages of the SNARC effect were investigated by examining the interactions among these effects. According to the additive factor logic, if two effects are interactive, then they occur in the same stage; if two effects are additive, then they occur in different stages. Across two experiments, the SNARC effect interacted with the Stroop effect and with the Simon effect. These results suggested that the SNARC effect occurred in both the semantic-representation and response-selection stages and provided insight into that the SNARC effect might have two originating sources.

Non-symbolic and symbolic number lines are dissociated

People use mental number lines for both symbolic numerals and numerosity, but little is known about how these two mental number lines are related. The current study investigated the association in effect size, directionality of the mental number line, and development between symbolic and non-symbolic mental number lines to determine if they were related to or independent from each other. We collected data from numerosity- and digit-matching tasks that used the following numbers: 11, 14, 17, 20, 23, 26, and 29. Tasks were performed by college undergraduates and the fifth-grade primary school students. The results showed that none of the effects for non-symbolic numbers was related to any of the effects for symbolic numbers, and vice versa, in both adults and children. Another notable finding was that the correlation between the SNARC (spatial-numerical association of response code) effect size and mathematical ability was negative in the adult group. These results are consistent with the dissociated processes hypothesis and suggest that mental number lines are notation-dependent. As shown by the SNARC effect, the mental number line might result in interference in the current task by an automatically activated spatial notation-dependent representation of numbers.

Turn the beat around: Commentary on "Slow and fast beat sequences are represented differently through space" (De Tommaso & Prpic, 2020, in Attention, Perception, & Psychophysics)

There has been increasing interest in the spatial mapping of various perceptual and cognitive magnitudes, such as expanding the spatial-numerical association of response codes (SNARC) effect into domains outside of numerical cognition. Recently, De Tommaso and Prpic (Attention, Perception, & Psychophysics, 82, 2765–2773, 2020) reported in this journal that only fast tempos over 104 beats per minute have spatial associations, with more right-sided associations and faster responses for faster tempos. After discussing the role of perceived loudness and possible response strategies, we propose and recommend methodological improvements for further research.

The Spatial-Numerical Association of Response Codes (SNARC) effect in highly math-anxious individuals: An ERP study

The Spatial-Numerical Association of Response Codes (SNARC) effect was examined in highly (HMA) and low math-anxious (LMA) individuals performing a number comparison in an ERP study. The SNARC effect consists of faster latencies when the response side is congruent with number location in the mental number line (MNL). Despite the stronger SNARC effect in the HMA group, their responses in incongruent trials were slower than in congruent trials only for the largest numerical magnitudes. Moreover, HMAs showed a less positive centroparietal P3b component in incongruent trials than in congruent ones, but only for the largest magnitudes. Since the SNARC effect arises during response selection and P3b positivity decreases with the difficulty of decision, this result suggests that HMA individuals might find it more difficult than LMAs to control the conflict between the automatically activated location of numbers in the MNL and the response side, especially in more cognitively demanding trials.

Non-magnitude sources of bias on duration judgements for blank intervals: conceptual relatedness of interval markers reduces subjective interval duration

We report three experiments in which the events flanking a temporal interval were either related or unrelated, based on overlap in the letter identity of single letters (Experiment 1), in the conceptual congruency of color words and colored rectangles (Experiment 2), or in the conceptual congruency of sentence stems and their terminal words (Experiment 3). In all cases, we observed a bias for participants to judge the duration of temporal intervals as shorter when the flanking events were related. We draw an analogy between these temporal judgement distortions and those reported elsewhere (Alards-Tomalin et al. in J Exp Psychol Learn Mem Cogn 40(2):555-566, 2014) that revealed that the similarity in the relative magnitude of flanking events generate the same type of bias on duration judgements. The observation that non-magnitude dimensions of relatedness between flanking events can also bias duration judgements raise questions about the applicability of two influential theoretical frameworks for understanding the distorting effects that non-temporal stimulus dimensions can have on duration judgments, A Theory of Magnitude (Buetl and Walsh in Philos Trans R Soc B Biol Sci 12:1831-1840, 2009, Walsh in Trends Cogn Sci 7:483-488, 2003) and the Conceptual Metaphor Theory (e.g., Lakoff and Johnson in Philosophy in the flesh: the embodied mind and its challenge to western thought. Basic Books, New York, 1999). In our general discussion, we consider a number of alternative frameworks that may account for these findings.

The Force of Numbers: Investigating Manual Signatures of Embodied Number Processing

The study has two objectives: (1) to introduce grip force recording as a new technique for studying embodied numerical processing; and (2) to demonstrate how three competing accounts of numerical magnitude representation can be tested by using this new technique: the Mental Number Line (MNL), A Theory of Magnitude (ATOM) and Embodied Cognition (finger counting-based) account. While 26 healthy adults processed visually presented single digits in a go/no-go n-back paradigm, their passive holding forces for two small sensors were recorded in both hands. Spontaneous and unconscious grip force changes related to number magnitude occurred in the left hand already 100–140 ms after stimulus presentation and continued systematically. Our results support a two-step model of number processing where an initial stage is related to the automatic activation of all stimulus properties whereas a later stage consists of deeper conscious processing of the stimulus. This interpretation generalizes previous work with linguistic stimuli and elaborates the timeline of embodied cognition. We hope that the use of grip force recording will advance the field of numerical cognition research.

The relationship between mental rotation and arithmetic: do number line estimation, working memory, or place-value concept matter?

Mental rotation is positively related to arithmetic ability; however, the mechanism underlying this relationship remains unclear. The possible roles of working memory, place-value concept, and number line estimation in the correlation between mental rotation and whole-number computation were investigated. One hundred and fifty-five first-grade students were tested to determine their mental rotation ability, arithmetic ability, and non-verbal intelligence. One year later, their working memory, place-value concept, number line estimation, and overall arithmetic ability were assessed. After controlling for age, gender, and prior arithmetic ability, we found that mental rotation uniquely predicted arithmetic ability after one year. Further mediation analyses demonstrated that number line estimation significantly mediated the relationship between mental rotation and arithmetic ability. In contrast, neither working memory nor place-value concept significantly mediated the relationship between mental rotation and arithmetic ability. This study highlights that mental number line estimation is the most important element explaining the influence of a dynamic spatial skill, that is, mental rotation, on arithmetic ability among young Chinese children.

The Brain’s Asymmetric Frequency Tuning: Asymmetric Behavior Originates from Asymmetric Perception

To construct a coherent multi-modal percept, vertebrate brains extract low-level features (such as spatial and temporal frequencies) from incoming sensory signals. However, because frequency processing is lateralized with the right hemisphere favouring low frequencies while the left favours higher frequencies, this introduces asymmetries between the hemispheres. Here, we describe how this lateralization shapes the development of several cognitive domains, ranging from visuo-spatial and numerical cognition to language, social cognition, and even aesthetic appreciation, and leads to the emergence of asymmetries in behaviour. We discuss the neuropsychological and educational implications of these emergent asymmetries and suggest future research approaches.