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We examined the spontaneous association between numbers and space by documenting attention deployment and the time course of associated spatial-numerical mapping with and without overt oculomotor responses. In Experiment 1, participants maintained central fixation while listening to number names. In Experiment 2, they made horizontal target-direct saccades following auditory number presentation. In both experiments, we continuously measured spontaneous ocular drift in horizontal space during and after number presentation. Experiment 2 also measured visual-probe-directed saccades following number presentation. Reliable ocular drift congruent with a horizontal mental number line emerged during and after number presentation in both experiments. Our results provide new evidence for the implicit and automatic nature of the oculomotor resonance effect associated with the horizontal spatial-numerical mapping mechanism.
Spatial-numerical associations (small numbers-left/lower space and large numbers-right/upper space) are regularly found in simple number categorization tasks. These associations were taken as evidence for a spatially oriented mental number line. However, the role of spatial-numerical associations during more complex number processing, such as counting or mental arithmetic is less clear. Here, we investigated whether counting is associated with a movement along the mental number line. Participants counted aloud upward or downward in steps of 3 for 45 s while looking at a blank screen. Gaze position during upward counting shifted rightward and upward, while the pattern for downward counting was less clear. Our results, therefore, confirm the hypothesis of a movement along the mental number line for addition. We conclude that space is not only used to represent number magnitudes but also to actively operate on numbers in more complex tasks such as counting, and that the eyes reflect this spatial mental operation.
Our study addresses the following research questions: Are there differences between handwriting movements on paper and on a tablet computer? Can experienced writers, such as most adults, adapt their graphomotor execution during writing to a rather unfamiliar surface for instance a tablet computer? We examined the handwriting performance of adults in three tasks with different complexity: (a) graphomotor abilities, (b) visuomotor abilities and (c) handwriting. Each participant performed each task twice, once on paper and once on a tablet computer with a pen. We tested 25 participants by measuring their writing duration, in air time, number of pen lifts, writing velocity and number of inversions in velocity. The data were analyzed using linear mixed-effects modeling with repeated measures. Our results reveal differences between writing on paper and on a tablet computer which were partly task-dependent. Our findings also show that participants were able to adapt their graphomotor execution to the smoother surface of the tablet computer during the tasks. (C) 2016 Elsevier B.V. All rights reserved.
Apraxia typically results from left-hemispheric (LH), but also from right-hemispheric (RH) stroke, and often impairs gesture imitation. Especially in LH stroke, it is important to differentiate apraxia-induced gesture imitation deficits from those due to co-morbid aphasia and associated semantic deficits, possibly influencing the imitation of meaningful (MF) gestures. To explore this issue, we first investigated if the 10 supposedly meaningless (ML) gestures of a widely used finger imitation test really carry no meaning, or if the test also contains MF gestures, by asking healthy subjects (n=45) to classify these gestures as MF or ML. Most healthy subjects (98%) classified three of the 10 gestures as clearly MF. Only two gestures were considered predominantly ML. We next assessed how imitation in stroke patients (255 LH, 113 RH stroke) is influenced by gesture meaning and how aphasia influences imitation of LH stroke patients (n=208). All patients and especially patients with imitation deficits (17% of LH, 27% of RH stroke patients) imitated MF gestures significantly better than ML gestures. Importantly, meaningfulness-scores of all 10 gestures significantly predicted imitation scores of patients with imitation deficits. Furthermore, especially in LH stroke patients with imitation deficits, the severity of aphasia significantly influenced the imitation of MF, but not ML gestures. Our findings in a large patient cohort support current cognitive models of imitation and strongly suggest that ML gestures are particularly sensitive to detect imitation deficits while minimising confounding effects of aphasia which affect the imitation of MF gestures in LH stroke patients. (C) 2015 Elsevier Ltd. All rights reserved.
Previous work on spatial-numerical association (SNAs) included either spatially distributed stimuli or responses. This raises the possibility that the inferred spatial nature of number concepts was a methodological artifact. We present results from a novel task that involves two categories (spatially oriented objects and number magnitudes) and dissociates spatial classification from number classification. The results reveal SNAs without inferential limitations of previous work and point to a working memory mechanism that transfers spatial coding across categories.
Commentary
(2020)
While the influence of spatial-numerical associations in number categorization tasks has been well established, their role in mental arithmetic is less clear. It has been hypothesized that mental addition leads to rightward and upward shifts of spatial attention (along the "mental number line"), whereas subtraction leads to leftward and downward shifts. We addressed this hypothesis by analyzing spontaneous eye movements during mental arithmetic. Participants solved verbally presented arithmetic problems (e.g., 2 + 7, 8-3) aloud while looking at a blank screen. We found that eye movements reflected spatial biases in the ongoing mental operation: Gaze position shifted more upward when participants solved addition compared to subtraction problems, and the horizontal gaze position was partly determined by the magnitude of the operands. Interestingly, the difference between addition and subtraction trials was driven by the operator (plus vs. minus) but was not influenced by the computational process. Thus, our results do not support the idea of a mental movement toward the solution during arithmetic but indicate a semantic association between operation and space.
Language and Arithmetic
(2018)
We examined cross-domain semantic priming effects between arithmetic and language. We paired subtractions with their linguistic equivalent, exception phrases (EPs) with positive quantifiers (e.g., “everybody except John”) while pairing additions with their own linguistic equivalent, EPs with negative quantifiers (e.g., “nobody except John”; Moltmann, 1995). We hypothesized that EPs with positive quantifiers prime subtractions and inhibit additions while EPs with negative quantifiers prime additions and inhibit subtractions. Furthermore, we expected similar priming and inhibition effects from arithmetic into semantics. Our design allowed for a bidirectional analysis by using one trial's target as the prime for the next trial. Two experiments failed to show significant priming effects in either direction. Implications and possible shortcomings are explored in the general discussion.
Idioms in the World
(2019)
It has been debated whether negative number concepts are cognitively represented on the same mental number line as positive number concepts. The present study reviews this debate and identifies limitations of previous studies. A method with nonspatial stimuli and responses is applied to overcome these limitations and to document a systematic implicit association of negative numbers with left space, thus indicating a leftward extension of the mental number line. Importantly, this result only held for left-to-right counting adults. Implications for the experiential basis of abstract conceptual knowledge are discussed.
Number to me, space to you
(2022)
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.
Spinal muscular atrophy (SMA) and Duchenne muscular dystrophy (DMD) both are rare genetic neuromuscular diseases with progressive loss of motor ability. The neuromotor developmental course of those diseases is well documented. In contrast, there is only little evidence about characteristics of general and specific cognitive development. In both conditions the final motor outcome is characterized by an inability to move autonomously: children with SMA never accomplish independent motoric exploration of their environment, while children with DMD do but later lose this ability again. These profound differences in developmental pathways might affect cognitive development of SMA vs. DMD children, as cognition is shaped by individual motor experiences. DMD patients show impaired executive functions, working memory, and verbal IQ, whereas only motor ability seems to be impaired in SMA. Advanced cognitive capacity in SMA may serve as a compensatory mechanism for achieving in education, career progression, and social satisfaction. This study aimed to relate differences in basic numerical concepts and arithmetic achievement in SMA and DMD patients to differences in their motor development and resulting sensorimotor and environmental experiences. Horizontal and vertical spatial-numerical associations were explored in SMA/DMD children ranging between 6 and 12 years through the random number generation task. Furthermore, arithmetic skills as well as general cognitive ability were assessed. Groups differed in spatial number processing as well as in arithmetic and domain-general cognitive functions. Children with SMA showed no horizontal and even reversed vertical spatial-numerical associations. Children with DMD on the other hand revealed patterns in spatial numerical associations comparable to healthy developing children. From the embodied Cognition perspective, early sensorimotor experience does play a role in development of mental number representations. However, it remains open whether and how this becomes relevant for the acquisition of higher order cognitive and arithmetic skills.
There is a debate about whether and why we overestimate addition and underestimate subtraction results (Operational Momentum or OM effect). Spatial-attentional accounts of OM compete with a model which postulates that OM reflects a weighted combination of multiple arithmetic heuristics and biases (AHAB). This study addressed this debate with the theoretically diagnostic distinction between zero problems (e.g., 3 + 0, 3 - 0) and non-zero problems (e.g., 2 + 1, 4 - 1) because AHAB, in contrast to all other accounts, uniquely predicts reverse OM for the latter problem type. In two tests (line-length production and time production), participants indeed produced shorter lines and under-estimated time intervals in non-zero additions compared with subtractions. This predicted interaction between operation and problem type extends OM to non-spatial magnitudes and highlights the strength of AHAB regarding different problem types and modalities during the mental manipulation of magnitudes. They also suggest that OM reflects methodological details, whereas reverse OM is the more representative behavioural signature of mental arithmetic.
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.