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The direction of object enumeration reflects children's enculturation but previous work on the development of such spatial preferences has been inconsistent. Therefore, we documented directional preferences in finger counting, object counting, and picture naming for children (4 groups from 3 to 6 years, N = 104) and adults (N = 56). We found a right-side preference for finger counting in 3- to 6-year-olds and a left-side preference for counting objects and naming pictures by 6 years of age. Children were consistent in their special preferences when comparing object counting and picture naming, but not in other task pairings. Finally, spatial preferences were not related to cardinality comprehension. These results, together with other recent work, suggest a gradual development of spatial-numerical associations from early non-directional mappings into culturally constrained directional mappings.
Spatial-numerical associations (SNAs) have been studied extensively in the past two decades, always requiring either explicit magnitude processing or explicit spatial-directional processing. This means that the typical finding of an association of small numbers with left or bottom space and of larger numbers with right or top space could be due to these requirements and not the conceptual representation of numbers. The present study compares explicit and implicit magnitude processing in an implicit spatial-directional task and identifies SNAs as artefacts of either explicit magnitude processing or explicit spatial-directional processing; they do not reveal spatial conceptual links. This finding requires revision of current accounts of the relationship between numbers and space.
A crucial question facing cognitive science concerns the nature of conceptual representations as well as the constraints on the interactions between them. One specific question we address in this paper is what makes cross-representational interplay possible? We offer two distinct theoretical scenarios: according to the first scenario, co-activated knowledge representations interact with the help of an interface established between them via congruent activation in a mediating third-party general cognitive mechanism, e.g., attention. According to the second scenario, co-activated knowledge representations interact due to an overlap between their features, for example when they share a magnitude component. First, we make a case for cross representational interplay based on grounded and situated theories of cognition. Second, we discuss interface-based interactions between distinct (i.e., non-overlapping) knowledge representations. Third, we discuss how co-activated representations may share their architecture via partial overlap. Finally, we outline constraints regarding the flexibility of these proposed mechanisms.
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.
Previous research on the interaction between manual action and visual perception has focused on discrete movements or static postures and discovered better performance near the hands (the near-hand effect). However, in everyday behaviors, the hands are usually moving continuously between possible targets. Therefore, the current study explored the effects of continuous hand motion on the allocation of visual attention. Eleven healthy adults performed a visual discrimination task during cyclical concealed hand movements underneath a display. Both the current hand position and its movement direction systematically contributed to participants' visual sensitivity. Discrimination performance increased substantially when the hand was distant from but moving toward the visual probe location (a far-hand effect). Implications of this novel observation are discussed.
This special issue, "Concrete constraints of abstract concepts", addresses the role of concrete determinants, both external and internal to the human body, in acquisition, processing and use of abstract concepts while at the same time presenting to the readers an overview of methods used to assess their representation.
Mental arithmetic exhibits various biases. Among those is a tendency to overestimate addition and to underestimate subtraction outcomes. Does such “operational momentum” (OM) also affect multiplication and division? Twenty-six adults produced lines whose lengths corresponded to the correct outcomes of multiplication and division problems shown in symbolic format. We found a reliable tendency to over-estimate division outcomes, i.e., reverse OM. We suggest that anchoring on the first operand (a tendency to use this number as a reference for further quantitative reasoning) contributes to cognitive biases in mental arithmetic.
Mental arithmetic exhibits various biases. Among those is a tendency to overestimate addition and to underestimate subtraction outcomes. Does such “operational momentum” (OM) also affect multiplication and division? Twenty-six adults produced lines whose lengths corresponded to the correct outcomes of multiplication and division problems shown in symbolic format. We found a reliable tendency to over-estimate division outcomes, i.e., reverse OM. We suggest that anchoring on the first operand (a tendency to use this number as a reference for further quantitative reasoning) contributes to cognitive biases in mental arithmetic.
Commentary
(2020)
Commentary
(2015)
Commentary
(2020)
There is accumulating evidence suggesting an association of numbers with physical space. However, the origin of such spatial-numerical associations (SNAs) is still debated. In the present study we investigated the development of two SNAs in a cross-sectional study involving children, young and middle-aged adults as well as the elderly: (1) the SNARC (spatial-numerical association of response codes) effect, reflecting a directional SNA; and (2) the numerical bisection bias in a line bisection task with numerical flankers. Results revealed a consistent SNARC effect in all age groups that continuously increased with age. In contrast, a numerical bisection bias was only observed for children and elderly participants, implying an U-shaped distribution of this bias across age groups. Additionally, individual SNARC effects and numerical bisection biases did not correlate significantly. We argue that the SNARC effect seems to be influenced by longer-lasting experiences of cultural constraints such as reading and writing direction and may thus reflect embodied representations. Contrarily, the numerical bisection bias may originate from insufficient inhibition of the semantic influence of irrelevant numerical flankers, which should be more pronounced in children and elderly people due to development and decline of cognitive control, respectively. As there is an ongoing debate on the origins of SNAs in general and the SNARC effect in particular, the present results are discussed in light of these differing accounts in an integrative approach. However, taken together, the present pattern of results suggests that different cognitive mechanisms underlie the SNARC effect and the numerical bisection bias.
The current study explored effects of continuous hand motion on the allocation of visual attention. A concurrent paradigm was used to combine visually concealed continuous hand movements with an attentionally demanding letter discrimination task. The letter probe appeared contingent upon the moving right hand passing through one of six positions. Discrimination responses were then collected via a keyboard press with the static left hand. Both the right hand's position and its movement direction systematically contributed to participants' visual sensitivity. Discrimination performance increased substantially when the right hand was distant from, but moving toward the visual probe location (replicating the far-hand effect, Festrnan et al., 2013). However, this effect disappeared when the probe appeared close to the static left hand, supporting the view that static and dynamic features of both hands combine in modulating pragmatic maps of attention.
We investigated the mental rehearsal of complex action instructions by recording spontaneous eye movements of healthy adults as they looked at objects on a monitor. Participants heard consecutive instructions, each of the form "move [object] to [location]''. Instructions were only to be executed after a go signal, by manipulating all objects successively with a mouse. Participants re-inspected previously mentioned objects already while listening to further instructions. This rehearsal behavior broke down after 4 instructions, coincident with participants' instruction span, as determined from subsequent execution accuracy. These results suggest that spontaneous eye movements while listening to instructions predict their successful execution.
Number processing induces spatial attention shifts to the left or right side for small or large numbers, respectively. This spatial-numerical association (SNA) extends to mental calculation, such that subtractions and additions induce left or right biases, respectively. However, the time course of activating SNAs during mental calculation is unclear. Here, we addressed this issue by measuring visual position discrimination during auditory calculation. Thirty-four healthy adults listened in each trial to five successive elements of arithmetic facts (first operand, operator, second operand, equal and result) and verbally classified their correctness. After each element (except for the result), a fixation dot moved equally often to either the left or right side and participants pressed left or right buttons to discriminate its movement direction (four times per trial). First and second operand magnitude (small/large), operation (addition/subtraction), result correctness (right/wrong) and movement direction (left/right) were balanced across 128 trials. Manual reaction times of dot movement discriminations were considered in relation to previous arithmetic elements. We found no evidence of early attentional shifts after first operand and operator presentation. Discrimination performance was modulated consistent with SNAs after the second operand, suggesting that attentional shifts occur once there is access to all elements necessary to complete an arithmetic operation. Such late-occurring attention shifts may reflect a combination of multiple element-specific biases and confirm their functional role in mental calculation.
Numerical cognitions such as spatial-numerical associations have been observed to be influenced by grounded, embodied and situated factors. For the case of finger counting, grounded and embodied influences have been reported. However, situated influences, e.g., that reported counting habits change with perception and action within a given situation, have not been systematically examined. To pursue the issue of situatedness of reported finger-counting habits, 458 participants were tested in three separate groups: (1) spontaneous condition: counting with both hands available, (2) perceptual condition: counting with horizontal (left-to-right) perceptual arrangement of fingers (3) perceptual and proprioceptive condition: counting with horizontal (left-to-right) perceptual arrangement of fingers and with busy dominant hand. Report of typical counting habits differed strongly between the three conditions. 28 % reported to start counting with the left hand in the spontaneous counting condition (1), 54 % in the perceptual condition (2) and 62 % in the perceptual and proprioceptive condition (3). Additionally, all participants in the spontaneous counting group showed a symmetry-based counting pattern (with the thumb as number 6), while in the two other groups, a considerable number of participants exhibited a spatially continuous counting pattern (with the pinkie as number 6). Taken together, the study shows that reported finger-counting habits depend on the perceptual and proprioceptive situation and thus are strongly influenced by situated cognition. We suggest that this account reconciles apparently contradictory previous findings of different counting preferences regarding the starting hand in different examination situations.
Number processing evokes spatial biases, both when dealing with single digits and in more complex mental calculations. Here we investigated whether these two biases have a common origin, by examining their flexibility. Participants pointed to the locations of arithmetic results on a visually presented line with an inverted, right-to-left number arrangement. We found directionally opposite spatial biases for mental arithmetic and for a parity task administered both before and after the arithmetic task. We discuss implications of this dissociation in our results for the task-dependent cognitive representation of numbers.
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.
There is a longstanding and widely held misconception about the relative remoteness of abstract concepts from concrete experiences. This review examines the current evidence for external influences and internal constraints on the processing, representation, and use of abstract concepts, like truth, friendship, and number. We highlight the theoretical benefit of distinguishing between grounded and embodied cognition and then ask which roles do perception, action, language, and social interaction play in acquiring, representing and using abstract concepts. By reviewing several studies, we show that they are, against the accepted definition, not detached from perception and action. Focussing on magnitude-related concepts, we also discuss evidence for cultural influences on abstract knowledge and explore how internal processes such as inner speech, metacognition, and inner bodily signals (interoception) influence the acquisition and retrieval of abstract knowledge. Finally, we discuss some methodological developments. Specifically, we focus on the importance of studies that investigate the time course of conceptual processing and we argue that, because of the paramount role of sociality for abstract concepts, new methods are necessary to study concepts in interactive situations. We conclude that bodily, linguistic, and social constraints provide important theoretical limitations for our theories of conceptual knowledge.
Research in cognitive neuroscience has shown that brain structures serving perceptual, emotional, and motor processes are also recruited during the understanding of language when it refers to emotion, perception, and action. However, the exact linguistic and extralinguistic conditions under which such language-induced activity in modality-specific cortex is triggered are not yet well understood. The purpose of this study is to introduce a simple experimental technique that allows for the online measure of language-induced activity in motor structures of the brain. This technique consists in the use of a grip force sensor that captures subtle grip force variations while participants listen to words and sentences. Since grip force reflects activity in motor brain structures, the continuous monitoring of force fluctuations provides a fine-grained estimation of motor activity across time. In other terms, this method allows for both localization of the source of language-induced activity to motor brain structures and high temporal resolution of the recorded data. To facilitate comparison of the data to be collected with this tool, we present two experiments that describe in detail the technical setup, the nature of the recorded data, and the analyses (including justification about the data filtering and artifact rejection) that we applied. We also discuss how the tool could be used in other domains of behavioral research.
There is much recent interest in the idea that we represent our knowledge together with the sensory and motor features that were activated during its acquisition. This paper reviews the evidence for such "embodiment" in the domain of numerical cognition, a traditional stronghold of abstract theories of knowledge representation. The focus is on spatial-numerical associations, such as the SNARC effect (small numbers are associated with left space, larger numbers with right space). Using empirical evidence from behavioral research, I first describe sensory and motor biases induced by SNARC, thus identifying numbers as embodied concepts. Next, I propose a hierarchical relationship between grounded, embodied, and situated aspects of number knowledge. This hierarchical conceptualization helps to understand the variety of SNARC-related findings and yields testable predictions about numerical cognition. I report several such tests, ranging from cross-cultural comparisons of horizontal and vertical SNARC effects (Shaki and Fischer in J Exp Psychol Hum Percept Perform 38(3): 804-809, 2012) to motor cortical activation studies in adults with left- and right-hand counting preferences (Tschentscher et al. in NeuroImage 59: 3139-3148, 2012). It is concluded that the diagnostic features for each level of the proposed hierarchical knowledge representation, together with the spatial associations of numbers, make the domain of numerical knowledge an ideal testing ground for embodied cognition research.
"Left" and "right" coordinates control our spatial behavior and even influence abstract thoughts. For number concepts, horizontal spatial-numerical associations (SNAs) have been widely documented: we associate few with left and many with right. Importantly, increments are universally coded on the right side even in preverbal humans and nonhuman animals, thus questioning the fundamental role of directional cultural habits, such as reading or finger counting. Here, we propose a biological, nonnumerical mechanism for the origin of SNAs on the basis of asymmetric tuning of animal brains for different spatial frequencies (SFs). The resulting selective visual processing predicts both universal SNAs and their context-dependence. We support our proposal by analyzing the stimuli used to document SNAs in newborns for their SF content. As predicted, the SFs contained in visual patterns with few versus many elements preferentially engage right versus left brain hemispheres, respectively, thus predicting left-versus rightward behavioral biases. Our "brain's asymmetric frequency tuning" hypothesis explains the perceptual origin of horizontal SNAs for nonsymbolic visual numerosities and might be extensible to the auditory domain.
1 + 2 is more than 2 + 1: Violations of commutativity and identity axioms in mental arithmetic
(2015)
Over the past decade or so, a large number of studies have revealed that conceptual meaning is sensitive to situational context. More recently, similar contextual influences have been documented in the domain of number knowledge. Here we show such context dependency in a length production task. Adult participants saw single digit addition problems of the form n1 + n2 and produced the sum by changing bi-directionally the length of a horizontally extended line, using radially arranged buttons. We found that longer lines were produced when n1 < n2 compared to n1 > n2 and that unit size increased with result size. Thus, the mathematical axioms of commutativity and identity do not seem to hold in mental addition. We discuss implications of these observations for our understanding of cognitive mechanisms involved in mental arithmetic and for situated cognition generally.
"BreaThink"
(2021)
Cognition is shaped by signals from outside and within the body. Following recent evidence of interoceptive signals modulating higher-level cognition, we examined whether breathing changes the production and perception of quantities. In Experiment 1, 22 adults verbally produced on average larger random numbers after inhaling than after exhaling. In Experiment 2, 24 further adults estimated the numerosity of dot patterns that were briefly shown after either inhaling or exhaling. Again, we obtained on average larger responses following inhalation than exhalation. These converging results extend models of situated cognition according to which higher-level cognition is sensitive to transient interoceptive states.