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Fischer MH, Felisatti A, Li X, Shaki S. A cross-cultural comparison of finger-based and symbolic number representations. J Exp Child Psychol 2024; 246:105979. [PMID: 38861807 DOI: 10.1016/j.jecp.2024.105979] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2023] [Revised: 04/29/2024] [Accepted: 04/30/2024] [Indexed: 06/13/2024]
Abstract
The current study examined predictions from embodied cognition for effects of finger counting on number processing. Although finger counting is spontaneous and nearly universal, counting habits reflect learning and culture. European cultures use a sub-base-five system, requiring a full hand plus additional fingers to express numbers exceeding 5. Chinese culture requires only one hand to express such numbers. We investigated the differential impact of early-acquired finger-based number representations on adult symbolic number processing. In total, 53 European and 56 Chinese adults performed two versions of the magnitude classification task, where numbers were presented either as Arabic symbols or as finger configurations consistent with respective cultural finger-counting habits. Participants classified numbers as smaller/larger than 5 with horizontally aligned buttons. Finger-based size and distance effects were larger in Chinese compared with Europeans. These differences did not, however, induce reliably different symbol processing signatures. This dissociation challenges the idea that sensory and motor habits shape our conceptual representations and implies notation-specific processing patterns.
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Affiliation(s)
- Martin H Fischer
- Department of Psychology, University of Potsdam, 14476 Potsdam, Germany
| | - Arianna Felisatti
- Department of Psychology, University of Potsdam, 14476 Potsdam, Germany; Department of General Psychology, University of Padua, 35131 Padova, Italy.
| | - Xin Li
- Department of Psychology, University of Potsdam, 14476 Potsdam, Germany
| | - Samuel Shaki
- Department of Psychology, Ariel University, Ariel 44837, Israel
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2
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Marlair C, Guillon A, Vynckier M, Crollen V. Enhancing mathematics learning through finger-counting: A study investigating tactile strategies in 2 visually impaired cases. APPLIED NEUROPSYCHOLOGY. CHILD 2024; 13:269-281. [PMID: 38569167 DOI: 10.1080/21622965.2024.2333832] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/05/2024]
Abstract
Finger-counting plays a crucial role in grounding and establishing mathematics, one of the most abstract domains of human cognition. While the combination of visual and proprioceptive information enables the coordination of finger movements, it was recently suggested that the emergence of finger-counting primarily relies on visual cues. In this study, we aimed to directly test this assumption by examining whether explicit finger-counting training (through tactile stimulation) may assist visually impaired children in overcoming their difficulties in learning mathematics. Two visually impaired participants (2 boys of 8.5 and 7.5 years) were therefore trained to use their fingers to calculate. Their pre- and post-training performance were compared to two control groups of sighted children who underwent either the same finger counting training (8 boys, 10 girls, Mage = 5.9 years; 10 kindergarteners and eight 1st graders) or another control vocabulary training (10 boys, 8 girls, Mage = 5.9 years; 11 kindergarteners and seven 1st graders). Results demonstrated that sighted children's arithmetic performance improved much more after the finger training than after the vocabulary training. Importantly, the positive impact of the finger training was also observed in both visually impaired participants (for addition and subtraction in one child; only for addition in the other child). These results are discussed in relation to the sensory compensation hypothesis and emphasize the importance of early and appropriate instruction of finger-based representations in both sighted and visually impaired children.
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Affiliation(s)
- Cathy Marlair
- Psychological Sciences Research Institute (IPSY), Université catholique de Louvain, Louvain-la-Neuve, Belgium
| | - Aude Guillon
- Psychological Sciences Research Institute (IPSY), Université catholique de Louvain, Louvain-la-Neuve, Belgium
| | - Menik Vynckier
- Psychological Sciences Research Institute (IPSY), Université catholique de Louvain, Louvain-la-Neuve, Belgium
| | - Virginie Crollen
- Psychological Sciences Research Institute (IPSY), Université catholique de Louvain, Louvain-la-Neuve, Belgium
- Institute of NeuroScience (IoNS), Université catholique de Louvain, Louvain-la-Neuve, Belgium
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3
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Sixtus E, Lindner N, Lohse K, Lonnemann J. Investigating the influence of body movements on children's mental arithmetic performance. Acta Psychol (Amst) 2023; 239:104003. [PMID: 37567051 DOI: 10.1016/j.actpsy.2023.104003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2021] [Revised: 04/04/2023] [Accepted: 08/03/2023] [Indexed: 08/13/2023] Open
Abstract
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.
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Affiliation(s)
- Elena Sixtus
- Empirical Childhood Research, University of Potsdam, Germany.
| | - Nadja Lindner
- Empirical Childhood Research, University of Potsdam, Germany
| | - Karoline Lohse
- Empirical Childhood Research, University of Potsdam, Germany
| | - Jan Lonnemann
- Empirical Childhood Research, University of Potsdam, Germany
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4
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Salehzadeh R, Soylu F, Jalili N. A comparative study of machine learning methods for classifying ERP scalp distribution. Biomed Phys Eng Express 2023; 9:045027. [PMID: 37279711 DOI: 10.1088/2057-1976/acdbd0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2023] [Accepted: 06/06/2023] [Indexed: 06/08/2023]
Abstract
Objective. Machine learning (ML) methods are used in different fields for classification and regression purposes with different applications. These methods are also used with various non-invasive brain signals, including Electroencephalography (EEG) signals to detect some patterns in the brain signals. ML methods are considered critical tools for EEG analysis since could overcome some of the limitations in the traditional methods of EEG analysis such as Event-related potentials (ERPs) analysis. The goal of this paper was to apply ML classification methods on ERP scalp distribution to investigate the performance of these methods in identifying numerical information carried in different finger-numeral configurations (FNCs). FNCs in their three forms of montring, counting, and non-canonical counting are used for communication, counting, and doing arithmetic across the world between children and even adults. Studies have shown the relationship between perceptual and semantic processing of FNCs, and neural differences in visually identifying different types of FNCs.Approach.A publicly available 32-channel EEG dataset recorded for 38 participants while they were shown a picture of an FNC (i.e., three categories and four numbers of 1,2,3, and 4) was used. EEG data were pre-processed and ERP scalp distribution of different FNCs was classified across time by six ML methods, including support vector machine, linear discriminant analysis, naïve Bayes, decision tree, K-nearest neighbor, and neural network. The classification was conducted in two conditions: classifying all FNCs together (i.e., 12 classes) and classifying FNCs of each category separately (i.e., 4 classes).Results.The support vector machine had the highest classification accuracy for both conditions. For classifying all FNCs together, the K-nearest neighbor was the next in line; however, the neural network could retrieve numerical information from the FNCs for category-specific classification.Significance.The significance of this study is in exploring the application of multiple ML methods in recognizing numerical information contained in ERP scalp distribution of different finger-numeral configurations.
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Affiliation(s)
- Roya Salehzadeh
- Department of Mechanical Engineering, The University of Alabama, Tuscaloosa, AL 35487, United States of America
| | - Firat Soylu
- Department of Educational Studies, The University of Alabama, Tuscaloosa, AL 35487, United States of America
| | - Nader Jalili
- Department of Mechanical Engineering, The University of Alabama, Tuscaloosa, AL 35487, United States of America
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5
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Sixtus E, Krause F, Lindemann O, Fischer MH. A sensorimotor perspective on numerical cognition. Trends Cogn Sci 2023; 27:367-378. [PMID: 36764902 DOI: 10.1016/j.tics.2023.01.002] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2021] [Revised: 01/10/2023] [Accepted: 01/10/2023] [Indexed: 02/11/2023]
Abstract
Numbers are present in every part of modern society and the human capacity to use numbers is unparalleled in other species. Understanding the mental and neural representations supporting this capacity is of central interest to cognitive psychology, neuroscience, and education. Embodied numerical cognition theory suggests that beyond the seemingly abstract symbols used to refer to numbers, their underlying meaning is deeply grounded in sensorimotor experiences, and that our specific understanding of numerical information is shaped by actions related to our fingers, egocentric space, and experiences with magnitudes in everyday life. We propose a sensorimotor perspective on numerical cognition in which number comprehension and numerical proficiency emerge from grounding three distinct numerical core concepts: magnitude, ordinality, and cardinality.
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Affiliation(s)
- Elena Sixtus
- Empirical Childhood Research, University of Potsdam, Potsdam, Germany.
| | - Florian Krause
- Donders Institute for Brain, Cognition and Behaviour, Radboud University Medical Center, Nijmegen, The Netherlands.
| | - Oliver Lindemann
- Department of Psychology, Education and Child Studies, Erasmus University Rotterdam, The Netherlands
| | - Martin H Fischer
- Department of Psychology, University of Potsdam, Potsdam, Germany
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6
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Czarnecka M, Rączy K, Szewczyk J, Paplińska M, Jednoróg K, Marchewka A, Hesselmann G, Knops A, Szwed M. Overlapping but separate number representations in the intraparietal sulcus – probing format- and modality-independence in sighted Braille readers. Cortex 2023; 162:65-80. [PMID: 37003099 DOI: 10.1016/j.cortex.2023.01.011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2022] [Revised: 06/20/2022] [Accepted: 01/22/2023] [Indexed: 03/06/2023]
Abstract
The Triple-Code Model stipulates that numerical information from different formats and modalities converges on a common magnitude representation in the Intraparietal Sulcus (IPS). To what extent the representations of all numerosity forms overlap remains unsolved. It has been postulated that the representation of symbolic numerosities (for example, Arabic digits) is sparser and grounded in an existing representation that codes for non-symbolic numerosity information (i.e., sets of objects). Other theories argue that numerical symbols represent a separate number category that emerges only during education. Here, we tested a unique group of sighted tactile Braille readers with numerosities 2, 4, 6 and 8 in three number notations: Arabic digits, sets of dots, tactile Braille numbers. Using univariate methods, we showed a consistent overlap in activations evoked by these three number notations. This result shows that all three used notations are represented in the IPS, which may suggest at least a partial overlap between the representations of the three notations used in this experiment. Using MVPA, we found that only non-automatized number information (Braille and sets of dots) allowed successful number classification. However, the numerosity of one notation could not be predicted above chance from the brain activation patterns evoked by another notation (no cross-classification). These results show that the IPS may host independent number codes in overlapping cortical circuits. In addition, they suggest that the level of training in encoding a given type of number information is an important factor that determines the amount of exploitable information and needs to be controlled for in order to identify the neural code underlying numerical information per se.
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Sabaghypour S, Moghaddam HS, Farkhondeh Tale Navi F, Nazari MA, Soltanlou M. Do numbers make us handy? Behavioral and electrophysiological evidence for number-hand congruency effect. Acta Psychol (Amst) 2023; 233:103841. [PMID: 36709688 DOI: 10.1016/j.actpsy.2023.103841] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2021] [Revised: 08/26/2022] [Accepted: 01/19/2023] [Indexed: 01/30/2023] Open
Abstract
Finger counting facilitates numerical representations and mathematical processing. The current study investigated the association between finger counting habits and number processing by employing behavioral and electrophysiological measures. We explored whether small and large numerical primes influence the recognition of embodied target hand stimuli. Twenty-four right-handed participants that were grouped into right-starters (n = 13) and left-starters (n = 11) for finger counting performed a hand recognition task that consisted of numerical magnitudes as prime and hand recognition as targets. Based on the finger counting habits, congruent (i.e., left-starters: small number/left hand or large number/right hand; right-starters: small number/right hand or large number/left hand) and incongruent (i.e., left-starters: large number/left hand or small number/right hand; right-starters: large number/right hand or small number/left hand) conditions were presented to the participants. The participants were required to indicate whether the targets were left or right hand by simply pressing the left or the right key, respectively. Results indicated faster reaction times (RTs) for congruent as opposed to incongruent trials for all participants. The mean amplitude of the centro-parietal P300 component was significantly increased for the incongruent compared to congruent condition, indicating increased mental effort. Also, analysis of the latency of the P300 in terms of congruency effect in all participants revealed significant results. These combined results provide behavioral and electrophysiological evidence indicating the embodied nature of numbers. The results are interpreted in light of the general findings related to the P300 component. This research supports the association of number-hand representations and corroborates the idea of embodied numerosity.
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Affiliation(s)
- Saied Sabaghypour
- Department of Cognitive Neuroscience, Faculty of Education and Psychology, University of Tabriz, Tabriz, Iran.
| | - Hassan Sabouri Moghaddam
- Department of Cognitive Neuroscience, Faculty of Education and Psychology, University of Tabriz, Tabriz, Iran
| | - Farhad Farkhondeh Tale Navi
- Department of Cognitive Neuroscience, Faculty of Education and Psychology, University of Tabriz, Tabriz, Iran
| | - Mohammad Ali Nazari
- Department of Neuroscience, Faculty of Advanced Technologies in Medicine, Iran University of Medical Sciences, Tehran, Iran
| | - Mojtaba Soltanlou
- Department of Cognitive Neuroscience, Faculty of Education and Psychology, University of Tabriz, Tabriz, Iran; School of Psychology, University of Surrey, Guildford, UK
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8
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de Carvalho Souza AM, Barrocas R, Fischer MH, Arnaud E, Moeller K, Rennó-Costa C. Combining virtual reality and tactile stimulation to investigate embodied finger-based numerical representations. Front Psychol 2023; 14:1119561. [PMID: 37179854 PMCID: PMC10174462 DOI: 10.3389/fpsyg.2023.1119561] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2022] [Accepted: 03/31/2023] [Indexed: 05/15/2023] Open
Abstract
Finger-based representation of numbers is a high-level cognitive strategy to assist numerical and arithmetic processing in children and adults. It is unclear whether this paradigm builds on simple perceptual features or comprises several attributes through embodiment. Here we describe the development and initial testing of an experimental setup to study embodiment during a finger-based numerical task using Virtual Reality (VR) and a low-cost tactile stimulator that is easy to build. Using VR allows us to create new ways to study finger-based numerical representation using a virtual hand that can be manipulated in ways our hand cannot, such as decoupling tactile and visual stimuli. The goal is to present a new methodology that can allow researchers to study embodiment through this new approach, maybe shedding new light on the cognitive strategy behind the finger-based representation of numbers. In this case, a critical methodological requirement is delivering precisely targeted sensory stimuli to specific effectors while simultaneously recording their behavior and engaging the participant in a simulated experience. We tested the device's capability by stimulating users in different experimental configurations. Results indicate that our device delivers reliable tactile stimulation to all fingers of a participant's hand without losing motion tracking quality during an ongoing task. This is reflected by an accuracy of over 95% in participants detecting stimulation of a single finger or multiple fingers in sequential stimulation as indicated by experiments with sixteen participants. We discuss possible application scenarios, explain how to apply our methodology to study the embodiment of finger-based numerical representations and other high-level cognitive functions, and discuss potential further developments of the device based on the data obtained in our testing.
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Affiliation(s)
- Alyson Matheus de Carvalho Souza
- Digital Metropolis Institute, Federal University of Rio Grande do Norte, Natal, Brazil
- Leibniz-Institut für Wissensmedien, Tübingen, Germany
| | | | - Martin H. Fischer
- Department of Psychology, University of Potsdam, Potsdam, Germany
- *Correspondence: Martin H. Fischer,
| | - Emanuel Arnaud
- Digital Metropolis Institute, Federal University of Rio Grande do Norte, Natal, Brazil
| | - Korbinian Moeller
- Leibniz-Institut für Wissensmedien, Tübingen, Germany
- Centre for Mathematical Cognition, School of Science, Loughborough University, Loughborough, United Kingdom
- LEAD Graduate School and Research Network, University of Tuebingen, Tübingen, Germany
| | - César Rennó-Costa
- Digital Metropolis Institute, Federal University of Rio Grande do Norte, Natal, Brazil
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9
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Khatin-Zadeh O, Farsani D, Eskandari Z, Marmolejo-Ramos F. The roles of motion, gesture, and embodied action in the processing of mathematical concepts. Front Psychol 2022; 13:969341. [PMID: 36312053 PMCID: PMC9616004 DOI: 10.3389/fpsyg.2022.969341] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2022] [Accepted: 09/20/2022] [Indexed: 08/26/2023] Open
Abstract
This article discusses perspective and frame of reference in the metaphorical description of mathematical concepts in terms of motions, gestures, and embodied actions. When a mathematical concept is described metaphorically in terms of gestures, embodied actions, or fictive motions, the motor system comes into play to ground and understand that concept. Every motion, gesture, or embodied action involves a perspective and a frame of reference. The flexibility in taking perspective and frame of reference allows people to embody a mathematical concept or idea in various ways. Based on the findings of past studies, it is suggested that the graphical representation of a mathematical concept may activate those areas of the motor system that are involved in the production of that graphical representation. This is supported by studies showing that when observers look at a painting or handwritten letters, they simulate the painter's or writer's hand movements during painting or writing. Likewise, the motor system can contribute to the grounding of abstract mathematical concepts, such as functions, numbers, and arithmetic operations.
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Affiliation(s)
- Omid Khatin-Zadeh
- School of Foreign Languages, University of Electronic Science and Technology of China, Chengdu, China
| | - Danyal Farsani
- Department of Teacher Education, Norwegian University of Science and Technology, Trondheim, Norway
- Facultad de Educación, Psicología y Familia, Universidad Finis Terrae, Santiago, Chile
- Programa de Pós-Graduação em Educação Matemática, State University of São Paulo (UNESP), Rio Claro, Brasil
| | - Zahra Eskandari
- Department of English, Chabahar Maritime University, Chabahar, Sistan and Baluchestan, Iran
| | - Fernando Marmolejo-Ramos
- Center for Change and Complexity in Learning, The University of South Australia, Adelaide, SA, Australia
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10
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Fischer MH, Glenberg AM, Moeller K, Shaki S. Grounding (fairly) complex numerical knowledge: an educational example. PSYCHOLOGICAL RESEARCH 2021; 86:2389-2397. [PMID: 34757438 DOI: 10.1007/s00426-021-01577-4] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Abstract
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.
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Affiliation(s)
| | - Arthur M Glenberg
- Department of Psychology, Arizona State University, Tempe, AZ, 85287-1104, USA.
- University of Wisconsin-Madison, Madison, WI, USA.
- Universidad de Salamanca, INICO, Salamanca, Spain.
| | - Korbinian Moeller
- Loughborough University, Loughborough, UK
- Leibniz-Institut Für Wissensmedien, Tübingen, Germany
- LEAD Graduate School and Research Network, University of Tübingen, Tübingen, Germany
- Individual Development and Adaptive Education for Children at Risk Center, Frankfurt am Main, Germany
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11
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Miklashevsky A, Lindemann O, Fischer MH. The Force of Numbers: Investigating Manual Signatures of Embodied Number Processing. Front Hum Neurosci 2021; 14:590508. [PMID: 33505256 PMCID: PMC7829181 DOI: 10.3389/fnhum.2020.590508] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2020] [Accepted: 12/08/2020] [Indexed: 11/17/2022] Open
Abstract
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.
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Affiliation(s)
- Alex Miklashevsky
- Potsdam Embodied Cognition Group, Cognitive Sciences, University of Potsdam, Potsdam, Germany
| | - Oliver Lindemann
- Department of Psychology, Education and Child Studies, School of Social and Behavioural Sciences, Erasmus University Rotterdam, Rotterdam, Netherlands
| | - Martin H Fischer
- Potsdam Embodied Cognition Group, Cognitive Sciences, University of Potsdam, Potsdam, Germany
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12
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Winter B, Yoshimi J. Metaphor and the Philosophical Implications of Embodied Mathematics. Front Psychol 2020; 11:569487. [PMID: 33224063 PMCID: PMC7667247 DOI: 10.3389/fpsyg.2020.569487] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2020] [Accepted: 09/28/2020] [Indexed: 11/13/2022] Open
Abstract
Embodied approaches to cognition see abstract thought and language as grounded in interactions between mind, body, and world. A particularly important challenge for embodied approaches to cognition is mathematics, perhaps the most abstract domain of human knowledge. Conceptual metaphor theory, a branch of cognitive linguistics, describes how abstract mathematical concepts are grounded in concrete physical representations. In this paper, we consider the implications of this research for the metaphysics and epistemology of mathematics. In the case of metaphysics, we argue that embodied mathematics is neutral in the sense of being compatible with all existing accounts of what mathematical entities really are. However, embodied mathematics may be able to revive an older position known as psychologism and overcome the difficulties it faces. In the case of epistemology, we argue that the evidence collected in the embodied mathematics literature is inconclusive: It does not show that abstract mathematical thinking is constituted by metaphor; it may simply show that abstract thinking is facilitated by metaphor. Our arguments suggest that closer interaction between the philosophy and cognitive science of mathematics could yield a more precise, empirically informed account of what mathematics is and how we come to have knowledge of it.
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Affiliation(s)
- Bodo Winter
- Department of English Language and Linguistics, University of Birmingham, Birmingham, United Kingdom
| | - Jeff Yoshimi
- Cognitive and Information Sciences, University of California, Merced, Merced, CA, United States
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13
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Vanstavel S, Coello Y, Mejias S. Processing of numerical representation of fingers depends on their location in space. PSYCHOLOGICAL RESEARCH 2020; 85:2566-2577. [PMID: 33125507 DOI: 10.1007/s00426-020-01436-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2020] [Accepted: 10/08/2020] [Indexed: 01/29/2023]
Abstract
Fingers can express quantities and thus contribute to the acquisition and manipulation of numbers as well as the development of arithmetical skills. As embodied entities, the processing of finger numerical configurations should, therefore, be facilitated when they match shared cultural representations and are presented close to the body. To investigate these issues, the present study investigated whether canonical finger configurations are processed faster than noncanonical configurations or spatially matched dot configurations, taking into account their location in the peripersonal or the extrapersonal space. Analysis of verbal responses to the enumeration of small and large numerosities showed that participants (N = 30) processed small numerosities faster than large ones and dots faster than finger configurations despite visuo-spatial matching. Canonical configurations were also processed faster than noncanonical configurations but for finger numerical stimuli only. Furthermore, the difference in response time between dots and fingers processing was greater when the stimuli were located in the peripersonal space than in the extrapersonal space. As a whole, the data suggest that, due to their motor nature, finger numerical configurations are not processed as simple visual stimuli but in relation to corporal and cultural counting habits, in agreement with the embodied framework of numerical cognition.
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Affiliation(s)
- Sébastien Vanstavel
- University of Lille, CNRS, UMR 9193-SCALab-Sciences Cognitives et Sciences Affectives, F-59000, Lille, France
| | - Yann Coello
- University of Lille, CNRS, UMR 9193-SCALab-Sciences Cognitives et Sciences Affectives, F-59000, Lille, France
| | - Sandrine Mejias
- University of Lille, CNRS, UMR 9193-SCALab-Sciences Cognitives et Sciences Affectives, F-59000, Lille, France.
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14
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Zhang L, Wang W, Zhang X. Effect of Finger Gnosis on Young Chinese Children's Addition Skills. Front Psychol 2020; 11:544543. [PMID: 33101118 PMCID: PMC7554299 DOI: 10.3389/fpsyg.2020.544543] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2020] [Accepted: 09/03/2020] [Indexed: 11/21/2022] Open
Abstract
Evidence has revealed an association between finger gnosis and arithmetic skills in young Western children, however, it is unknown whether such an association can be generalized to Chinese children and what mechanism may underlie this relationship. This study examines whether finger gnosis is associated with addition skills in young Chinese children and, if so, what numerical skills could explain this correlation. A total of 102 Chinese children aged 5–6 years were asked to complete finger gnosis and addition tasks in Study 1. Results showed that finger gnosis was significantly associated with addition performance. However, no significant correlation was found between finger gnosis and the use of finger counting in solving addition problems. Moreover, girls’ finger gnosis was better than boys’, and children with musical training demonstrated better finger gnosis than those without. In Study 2, 16 children with high finger gnosis and 20 children with low finger gnosis were selected from the children in Study 1 and asked to perform enumeration, order judgment, number sense, and number line estimation. Children with high finger gnosis performed better in number line estimation than their counterparts with low finger gnosis. Moreover, the number line estimation fully mediated the relationship between finger gnosis and addition performance. Together, these studies provide evidence of a correlation between finger gnosis and addition skills. They also highlight the importance of number line estimation in bridging this association.
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Affiliation(s)
- Li Zhang
- School of Sociology and Psychology, Central University of Finance and Economics, Beijing, China
| | - Wei Wang
- School of Sociology and Psychology, Central University of Finance and Economics, Beijing, China
| | - Xiao Zhang
- Faculty of Education, The University of Hong Kong, Hong Kong, China
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15
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Felisatti A, Laubrock J, Shaki S, Fischer MH. A biological foundation for spatial-numerical associations: the brain's asymmetric frequency tuning. Ann N Y Acad Sci 2020; 1477:44-53. [PMID: 32645221 DOI: 10.1111/nyas.14418] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2020] [Revised: 05/22/2020] [Accepted: 06/03/2020] [Indexed: 11/29/2022]
Abstract
"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.
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Affiliation(s)
| | - Jochen Laubrock
- Department of Psychology, University of Potsdam, Potsdam, Germany.,Department of Psychology, Brandenburg Medical School Theodor Fontane, Neuruppin, Germany
| | - Samuel Shaki
- Department of Behavioral Sciences and Psychology, Ariel University, Ariel, Israel
| | - Martin H Fischer
- Department of Psychology, University of Potsdam, Potsdam, Germany
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16
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Barrocas R, Roesch S, Gawrilow C, Moeller K. Putting a Finger on Numerical Development - Reviewing the Contributions of Kindergarten Finger Gnosis and Fine Motor Skills to Numerical Abilities. Front Psychol 2020; 11:1012. [PMID: 32528379 PMCID: PMC7264267 DOI: 10.3389/fpsyg.2020.01012] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2019] [Accepted: 04/22/2020] [Indexed: 01/29/2023] Open
Abstract
The well-documented association between fingers and numbers is not only based on the observation that most children use their fingers for counting and initial calculation, but also on extensive behavioral and neuro-functional evidence. In this article, we critically review developmental studies evaluating the association between finger sensorimotor skills (i.e., finger gnosis and fine motor skills) and numerical abilities. In sum, reviewed studies were found to provide evidential value and indicated that both finger gnosis and fine motor skills predict measures of counting, number system knowledge, number magnitude processing, and calculation ability. Therefore, specific and unique contributions of both finger gnosis and fine motor skills to the development of numerical skills seem to be substantiated. Through critical consideration of the reviewed evidence, we suggest that the association of finger gnosis and fine motor skills with numerical abilities may emerge from a combination of functional and redeployment mechanisms, in which the early use of finger-based numerical strategies during childhood might be the developmental process by which number representations become intertwined with the finger sensorimotor system, which carries an innate predisposition for said association to unfold. Further research is nonetheless necessary to clarify the causal mechanisms underlying this association.
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Affiliation(s)
| | | | - Caterina Gawrilow
- Department of Psychology, LEAD Graduate School & Research Network, Eberhard Karls University Tuebingen, Tuebingen, Germany
| | - Korbinian Moeller
- Leibniz-Institut fuer Wissensmedien, Tuebingen, Germany
- Department of Psychology, LEAD Graduate School & Research Network, Eberhard Karls University Tuebingen, Tuebingen, Germany
- Centre for Mathematical Cognition, Loughborough University, Loughborough, United Kingdom
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17
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Abstract
The first steps in numerical cognition are usually done in conjunction with fingers. Following the assumption that abstract concepts stay associated with the sensory-motor information that was present during their acquisition and consolidation, mental number representations should always be associated with the respective finger counting components. We tested whether finger movements that imply finger counting actually prime the corresponding number concepts in adults. All participants counted number 1 with their thumb and incremented sequentially to number 5 with their pinky. In the experiment, participants sequentially and repeatedly pressed five buttons from thumb to pinky. Each button press triggered the visual presentation of a random number between 1 and 5 that had to be named aloud, resulting in 20% counting-congruent and 80% counting-incongruent finger-number mappings. Average naming latencies were significantly shorter for congruent than incongruent finger-number combinations. Furthermore, there was a distance effect where primes partly co-activated numerically close target numbers and with decreasing priming for more distant prime-target pairs. Overall, these results provide further evidence that number representations are strongly associated with finger counting experience, making fingers an effective tool for number comprehension.
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