1
|
Qu C, Clarke S, Luzzi F, Brannon E. Rational number representation by the approximate number system. Cognition 2024; 250:105839. [PMID: 38870562 DOI: 10.1016/j.cognition.2024.105839] [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: 06/14/2023] [Revised: 03/03/2024] [Accepted: 05/27/2024] [Indexed: 06/15/2024]
Abstract
The approximate number system (ANS) enables organisms to represent the approximate number of items in an observed collection, quickly and independently of natural language. Recently, it has been proposed that the ANS goes beyond representing natural numbers by extracting and representing rational numbers (Clarke & Beck, 2021a). Prior work demonstrates that adults and children discriminate ratios in an approximate and ratio-dependent manner, consistent with the hallmarks of the ANS. Here, we use a well-known "connectedness illusion" to provide evidence that these ratio-dependent ratio discriminations are (a) based on the perceived number of items in seen displays (and not just non-numerical confounds), (b) are not dependent on verbal working memory, or explicit counting routines, and (c) involve representations with a part-whole (or subset-superset) format, like a fraction, rather than a part-part format, like a ratio. These results vindicate key predictions of the hypothesis that the ANS represents rational numbers.
Collapse
Affiliation(s)
- Chuyan Qu
- Department of Psychology, University of Pennsylvania, United States of America.
| | - Sam Clarke
- Department of Psychology, University of Pennsylvania, United States of America; Department of Philosophy, University of Southern California, United States of America
| | - Francesca Luzzi
- Department of Psychology, University of Pennsylvania, United States of America
| | - Elizabeth Brannon
- Department of Psychology, University of Pennsylvania, United States of America
| |
Collapse
|
2
|
Szczygieł M, Sarı MH. The relationship between numerical magnitude processing and math anxiety, and their joint effect on adult math performance, varied by indicators of numerical tasks. Cogn Process 2024; 25:421-442. [PMID: 38644404 DOI: 10.1007/s10339-024-01186-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2022] [Accepted: 03/21/2024] [Indexed: 04/23/2024]
Abstract
According to the hypothesis of Maloney et al. (Cognition 114(2):293-297, 2010. https://doi.org/10.1016/j.cognition.2009.09.013), math anxiety is related to deficits in numerical magnitude processing, which in turn compromises the development of advanced math skills. Because previous studies on this topic are contradictory, which may be due to methodological differences in the measurement of numerical magnitude processing, we tested Maloney et al.'s hypothesis using different tasks and their indicators: numerical magnitude processing (symbolic and non-symbolic comparison tasks: accuracy, reaction time, numerical ratio, distance and size effects, and Weber fraction; number line estimation task: estimation error), math anxiety (combined scores of learning, testing, math problem solving, and general math anxiety), and math performance. The results of our study conducted on 119 young adults mostly support the hypothesis proposed by Maloney et al. that deficiency in symbolic magnitude processing is related to math anxiety, but the relationship between non-symbolic processes and math anxiety was opposite to the assumptions. Moreover, the results indicate that estimation processes (but not comparison processes) and math anxiety are related to math performance in adults. Finally, high math anxiety moderated the relationship between reaction time in the symbolic comparison task, reaction time in the non-symbolic comparison task, numerical ratio effect in the symbolic comparison task, and math performance. Because the results of the joint effect of numerical magnitude processing and math anxiety on math performance were inconsistent, this part of the hypothesis is called into question.
Collapse
Affiliation(s)
- Monika Szczygieł
- Institute of Psychology, Jagiellonian University in Kraków, Kraków, Poland.
| | - Mehmet Hayri Sarı
- Faculty of Education, Nevşehir Hacı Bektaş Veli University, Nevşehir, Türkiye
| |
Collapse
|
3
|
Ma M, Likhanov M, Zhou X. Number sense-arithmetic link in Grade 1 and Grade 2: A case of fluency. BRITISH JOURNAL OF EDUCATIONAL PSYCHOLOGY 2024. [PMID: 38802998 DOI: 10.1111/bjep.12693] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2023] [Revised: 05/10/2024] [Accepted: 05/13/2024] [Indexed: 05/29/2024]
Abstract
BACKGROUND Recent research suggested fluent processing as an explanation on why number sense contributes to simple arithmetic tasks-'Fluency hypothesis'. AIMS The current study investigates whether number sense contributes to such arithmetic tasks when other cognitive factors are controlled for (including those that mediate the link); and whether this contribution varies as a function of participants' individual maths fluency levels. SAMPLE Four hundred and thirty-seven Chinese schoolchildren (186 females; Mage = 83.49 months) completed a range of cognitive measures in Grade 1 (no previous classroom training) and in Grade 2 (a year later). METHODS Number sense, arithmetic (addition and subtraction), spatial ability, visuo-spatial working memory, perception, reaction time, character reading and general intelligence were measured. RESULTS Our data showed that the link between number sense and arithmetic was weaker in Grade 1 (Beta = .15 for addition and .06 (ns) for subtraction) compared to Grade 2 (.23-.28), but still persisted in children with no previous maths training. Further, math's performance in Grade 1 did not affect the link between number sense and maths performance in Grade 2. CONCLUSION Our data extended previous findings by showing that number sense is linked with simple maths task performance even after controlling for multiple cognitive factors. Our results brought some evidence that number sense-arithmetic link is somewhat sensitive to previous formal maths education. Further research is needed, as the differences in effects between grades were quite small, and arithmetic in Grade 1 did not moderate the link at question in Grade 2.
Collapse
Affiliation(s)
- Mei Ma
- State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing, China
| | - Maxim Likhanov
- State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing, China
| | - Xinlin Zhou
- State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing, China
| |
Collapse
|
4
|
Henrich J, Muthukrishna M. What Makes Us Smart? Top Cogn Sci 2024; 16:322-342. [PMID: 37086053 DOI: 10.1111/tops.12656] [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: 07/12/2022] [Revised: 04/04/2023] [Accepted: 04/05/2023] [Indexed: 04/23/2023]
Abstract
How did humans become clever enough to live in nearly every major ecosystem on earth, create vaccines against deadly plagues, explore the oceans depths, and routinely traverse the globe at 30,000 feet in aluminum tubes while nibbling on roasted almonds? Drawing on recent developments in our understanding of human evolution, we consider what makes us distinctively smarter than other animals. Contrary to conventional wisdom, human brilliance emerges not from our innate brainpower or raw computational capacities, but from the sharing of information in communities and networks over generations. We review how larger, more diverse, and more optimally interconnected networks of minds give rise to faster innovation and how the cognitive products of this cumulative cultural evolutionary process feedback to make us individually "smarter"-in the sense of being better at meeting the challenges and problems posed by our societies and socioecologies. Here, we consider not only how cultural evolution supplies us with "thinking tools" (like counting systems and fractions) but also how it has shaped our ontologies (e.g., do germs and witches exist?) and epistemologies, including our notions of what constitutes a "good reason" or "good evidence" (e.g., are dreams a source of evidence?). Building on this, we consider how cultural evolution has organized and distributed cultural knowledge and cognitive tasks among subpopulations, effectively shifting both thinking and production to the level of the community, population, or network, resulting in collective information processing and group decisions. Cultural evolution can turn mindless mobs into wise crowds by facilitating and constraining cognition through a wide variety of epistemic institutions-political, legal, and scientific. These institutions process information and aid better decision-making by suppressing or encouraging the use of different cultural epistemologies and ontologies.
Collapse
Affiliation(s)
- Joseph Henrich
- Department of Human Evolutionary Biology, Harvard University
| | - Michael Muthukrishna
- Department of Psychological and Behavioral Science, London School of Economics and Political Science
| |
Collapse
|
5
|
Okuyama S, Kuki T, Mushiake H. Recruitment of the premotor cortex during arithmetic operations by the monkey. Sci Rep 2024; 14:6450. [PMID: 38548764 PMCID: PMC10978941 DOI: 10.1038/s41598-024-56755-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2023] [Accepted: 03/11/2024] [Indexed: 04/01/2024] Open
Abstract
Arithmetic operations are complex mental processes rooted in the abstract concept of numerosity. Despite the significance, the neural architecture responsible for these operations has remained largely uncharted. In this study, we explored the presence of specific neuronal activity in the dorsal premotor cortex of the monkey dedicated to numerical addition and subtraction. Our findings reveal that many of these neural activities undergo a transformation, shifting their coding from arithmetic to motor representations. These motor representations include information about which hand to use and the number of steps involved in the action. We consistently observed that cells related to the right-hand encoded addition, while those linked to the left-hand encoded subtraction, suggesting that arithmetic operations and motor commands are intertwining with each other. Furthermore, we used a multivariate decoding technique to predict the monkey's behaviour based on the activity of these arithmetic-related cells. The classifier trained to discern arithmetic operations, including addition and subtraction, not only predicted the arithmetic decisions but also the subsequent motor actions of the right and left-hand. These findings imply a cognitive extension of the motor cortex's function, where inherent neural systems are repurposed to facilitate arithmetic operations.
Collapse
Affiliation(s)
- Sumito Okuyama
- Department of Physiology, Tohoku University School of Medicine, Sendai, 980-8575, Japan
- Department of Neurosurgery, Southern Tohoku General Hospital, Miyagi, 989-2483, Japan
| | - Toshinobu Kuki
- Department of Physiology, Tohoku University School of Medicine, Sendai, 980-8575, Japan
| | - Hajime Mushiake
- Department of Physiology, Tohoku University School of Medicine, Sendai, 980-8575, Japan.
| |
Collapse
|
6
|
Kondapaneni N, Perona P. A number sense as an emergent property of the manipulating brain. Sci Rep 2024; 14:6858. [PMID: 38514690 PMCID: PMC10958013 DOI: 10.1038/s41598-024-56828-2] [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: 07/10/2023] [Accepted: 03/12/2024] [Indexed: 03/23/2024] Open
Abstract
The ability to understand and manipulate numbers and quantities emerges during childhood, but the mechanism through which humans acquire and develop this ability is still poorly understood. We explore this question through a model, assuming that the learner is able to pick up and place small objects from, and to, locations of its choosing, and will spontaneously engage in such undirected manipulation. We further assume that the learner's visual system will monitor the changing arrangements of objects in the scene and will learn to predict the effects of each action by comparing perception with a supervisory signal from the motor system. We model perception using standard deep networks for feature extraction and classification. Our main finding is that, from learning the task of action prediction, an unexpected image representation emerges exhibiting regularities that foreshadow the perception and representation of numbers and quantity. These include distinct categories for zero and the first few natural numbers, a strict ordering of the numbers, and a one-dimensional signal that correlates with numerical quantity. As a result, our model acquires the ability to estimate numerosity, i.e. the number of objects in the scene, as well as subitization, i.e. the ability to recognize at a glance the exact number of objects in small scenes. Remarkably, subitization and numerosity estimation extrapolate to scenes containing many objects, far beyond the three objects used during training. We conclude that important aspects of a facility with numbers and quantities may be learned with supervision from a simple pre-training task. Our observations suggest that cross-modal learning is a powerful learning mechanism that may be harnessed in artificial intelligence.
Collapse
|
7
|
Mielicki MK, Mbarki R, Wang JJ. Understanding the social-emotional components of our "number sense": insights from a novel non-symbolic numerical comparison task. Front Psychol 2024; 15:1175591. [PMID: 38505363 PMCID: PMC10948494 DOI: 10.3389/fpsyg.2024.1175591] [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: 02/27/2023] [Accepted: 02/02/2024] [Indexed: 03/21/2024] Open
Abstract
Introduction A large body of work has identified a core sense of number supported by the Approximate Number System (ANS) that is present in infancy and across species. Although it is commonly assumed that the ANS directly processes perceptual input and is relatively independent from affective factors, some evidence points at a correlation between ANS performance and math anxiety. However, the evidence is mixed. We tested whether giving participants active control in completing a numerical task would change the relationship between math anxiety on performance. Methods Adult participants (N = 103) completed a novel four-alternative-forced-choice non-symbolic numerical comparison task. In a repeated-measures design, participants either passively viewed different dot arrays or actively chose to view each array (i.e., active information-seeking) before deciding on the largest quantity. Participants also provided confidence judgments during the passive version of the task. Results We replicated the ratio-dependent signature in participants' accuracy in both the passive and active versions of the task using this novel paradigm, as well as in trial-level confidence judgments and information-seeking behavior. Participants' self-reported math anxiety significantly correlated with their accuracy on the passive version of the task. Critically, the correlation disappeared in the active version of the task. Gender also emerged as a predictor of confidence judgments and a moderator of the effect of task on overall accuracy and the effect of active information seeking on accuracy in the active version of the task. Exploratory analysis of estimated Weber Fraction suggests that these results may be driven by auxiliary factors instead of changes in ANS acuity. Conclusion These findings have implications for understanding the relationship between math anxiety and performance on numerical tasks.
Collapse
Affiliation(s)
- Marta K. Mielicki
- Center for Cognitive Science, Rutgers University–New Brunswick, New Brunswick, NJ, United States
| | - Rahma Mbarki
- Department of Psychology, Rutgers University–New Brunswick, New Brunswick, NJ, United States
| | - Jinjing Jenny Wang
- Center for Cognitive Science, Rutgers University–New Brunswick, New Brunswick, NJ, United States
- Department of Psychology, Rutgers University–New Brunswick, New Brunswick, NJ, United States
| |
Collapse
|
8
|
Dramkin D, Odic D. Children dynamically update and extend the interface between number words and perceptual magnitudes. Dev Sci 2024; 27:e13433. [PMID: 37436040 DOI: 10.1111/desc.13433] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2023] [Revised: 06/19/2023] [Accepted: 06/25/2023] [Indexed: 07/13/2023]
Abstract
As adults, we represent and think about number, space, and time in at least two ways: our intuitive-but imprecise-perceptual representations, and the slowly learned-but precise-number words. With development, these representational formats interface, allowing us to use precise number words to estimate imprecise perceptual experiences. We test two accounts of this developmental milestone. Either slowly learned associations are required for the interface to form, predicting that deviations from typical experiences (e.g., presentation of a novel unit or unpracticed dimension) will disrupt children's ability to map number words to their perceptual experiences or children's understanding of the logical similarity between number words and perceptual representations allows them to flexibly extend this interface to novel experiences (e.g., units and dimensions they have not yet learned how to formally measure). 5-11-year-olds completed verbal estimation and perceptual sensitivity tasks across three dimensions: Number, Length, and Area. For verbal estimation, they were given novel units (i.e., a three-dot unit called one "toma" for Number, a 44 px long line called one "blicket" for Length, a 111 px2 blob called one "modi" for Area) and asked to estimate how many tomas/blickets/modies they saw when shown a larger set of dots, lines, and blobs. Children could flexibly link number words to novel units across dimensions, demonstrating positive estimation slopes, even for Length and Area, which younger children had limited experience with. This suggests that the logic of structure mapping can be dynamically utilized across perceptual dimensions, even without extensive experience.
Collapse
Affiliation(s)
- Denitza Dramkin
- Department of Psychology, University of British Columbia, Vancouver, Canada
| | - Darko Odic
- Department of Psychology, University of British Columbia, Vancouver, Canada
| |
Collapse
|
9
|
Zang Z, Chi X, Luan M, Hu S, Zhou K, Liu J. Inter-individual, hemispheric and sex variability of brain activations during numerosity processing. Brain Struct Funct 2024; 229:459-475. [PMID: 38197958 PMCID: PMC10917853 DOI: 10.1007/s00429-023-02747-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2023] [Accepted: 12/04/2023] [Indexed: 01/11/2024]
Abstract
Numerosity perception is a fundamental and innate cognitive function shared by both humans and many animal species. Previous research has primarily focused on exploring the spatial and functional consistency of neural activations that were associated with the processing of numerosity information. However, the inter-individual variability of brain activations of numerosity perception remains unclear. In the present study, with a large-sample functional magnetic resonance imaging (fMRI) dataset (n = 460), we aimed to localize the functional regions related to numerosity perceptions and explore the inter-individual, hemispheric, and sex differences within these brain regions. Fifteen subject-specific activated regions, including the anterior intraparietal sulcus (aIPS), posterior intraparietal sulcus (pIPS), insula, inferior frontal gyrus (IFG), inferior temporal gyrus (ITG), premotor area (PM), middle occipital gyrus (MOG) and anterior cingulate cortex (ACC), were delineated in each individual and then used to create a functional probabilistic atlas to quantify individual variability in brain activations of numerosity processing. Though the activation percentages of most regions were higher than 60%, the intersections of most regions across individuals were considerably lower, falling below 50%, indicating substantial variations in brain activations related to numerosity processing among individuals. Furthermore, significant hemispheric and sex differences in activation location, extent, and magnitude were also found in these regions. Most activated regions in the right hemisphere had larger activation volumes and activation magnitudes, and were located more lateral and anterior than their counterparts in the left hemisphere. In addition, in most of these regions, males displayed stronger activations than females. Our findings demonstrate large inter-individual, hemispheric, and sex differences in brain activations related to numerosity processing, and our probabilistic atlas can serve as a robust functional and spatial reference for mapping the numerosity-related neural networks.
Collapse
Affiliation(s)
- Zhongyao Zang
- Beijing Key Laboratory of Applied Experimental Psychology, National Demonstration Center for Experimental Psychology Education (Beijing Normal University), Faculty of Psychology, Beijing Normal University, Beijing, 100875, China
| | - Xiaoyue Chi
- Beijing Key Laboratory of Applied Experimental Psychology, National Demonstration Center for Experimental Psychology Education (Beijing Normal University), Faculty of Psychology, Beijing Normal University, Beijing, 100875, China
| | - Mengkai Luan
- Department of Psychology, Shanghai University of Sport, 650 Qing Yuan Huan Road, Shanghai, 200438, People's Republic of China
| | - Siyuan Hu
- Beijing Key Laboratory of Applied Experimental Psychology, National Demonstration Center for Experimental Psychology Education (Beijing Normal University), Faculty of Psychology, Beijing Normal University, Beijing, 100875, China.
| | - Ke Zhou
- Beijing Key Laboratory of Applied Experimental Psychology, National Demonstration Center for Experimental Psychology Education (Beijing Normal University), Faculty of Psychology, Beijing Normal University, Beijing, 100875, China.
| | - Jia Liu
- Tsinghua Laboratory of Brain and Intelligence, Department of Psychology, Tsinghua University, Beijing, 100084, China
| |
Collapse
|
10
|
Sanford EM, Topaz CM, Halberda J. Modeling Magnitude Discrimination: Effects of Internal Precision and Attentional Weighting of Feature Dimensions. Cogn Sci 2024; 48:e13409. [PMID: 38294098 DOI: 10.1111/cogs.13409] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2023] [Revised: 11/20/2023] [Accepted: 01/17/2024] [Indexed: 02/01/2024]
Abstract
Given a rich environment, how do we decide on what information to use? A view of a single entity (e.g., a group of birds) affords many distinct interpretations, including their number, average size, and spatial extent. An enduring challenge for cognition, therefore, is to focus resources on the most relevant evidence for any particular decision. In the present study, subjects completed three tasks-number discrimination, surface area discrimination, and convex hull discrimination-with the same stimulus set, where these three features were orthogonalized. Therefore, only the relevant feature provided consistent evidence for decisions in each task. This allowed us to determine how well humans discriminate each feature dimension and what evidence they relied on to do so. We introduce a novel computational approach that fits both feature precision and feature use. We found that the most relevant feature for each decision is extracted and relied on, with minor contributions from competing features. These results suggest that multiple feature dimensions are separately represented for each attended ensemble of many items and that cognition is efficient at selecting the appropriate evidence for a decision.
Collapse
Affiliation(s)
- Emily M Sanford
- Department of Psychological & Brain Sciences, Johns Hopkins University
| | | | - Justin Halberda
- Department of Psychological & Brain Sciences, Johns Hopkins University
| |
Collapse
|
11
|
Czajko S, Vignaud A, Eger E. Human brain representations of internally generated outcomes of approximate calculation revealed by ultra-high-field brain imaging. Nat Commun 2024; 15:572. [PMID: 38233387 PMCID: PMC10794709 DOI: 10.1038/s41467-024-44810-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2023] [Accepted: 01/03/2024] [Indexed: 01/19/2024] Open
Abstract
Much of human culture's advanced technology owes its existence to the ability to mentally manipulate quantities. Neuroscience has described the brain regions overall recruited by numerical tasks and the neuronal codes representing individual quantities during perceptual tasks. Nevertheless, it remains unknown how quantity representations are combined or transformed during mental computations and how specific quantities are coded in the brain when generated as the result of internal computations rather than evoked by a stimulus. Here, we imaged the brains of adult human subjects at 7 Tesla during an approximate calculation task designed to disentangle in- and outputs of the computation from the operation itself. While physically presented sample numerosities were distinguished in activity patterns along the dorsal visual pathway and within frontal and occipito-temporal regions, a representation of the internally generated result was most prominently detected in higher order regions such as angular gyrus and lateral prefrontal cortex. Behavioral precision in the task was related to cross-decoding performance between sample and result representations in medial IPS regions. This suggests the transformation of sample into result may be carried out within dorsal stream sensory-motor integration regions, and resulting outputs maintained for task purposes in higher-level regions in a format possibly detached from sensory-evoked inputs.
Collapse
Affiliation(s)
- Sébastien Czajko
- Cognitive Neuroimaging Unit, INSERM, CEA, CNRS, Université Paris-Saclay, NeuroSpin center, Gif-sur-Yvette, France
- EDUWELL team, Lyon Neuroscience Research Centre, INSERM U1028, CNRS UMR5292, Lyon 1 University, Lyon, France
| | - Alexandre Vignaud
- UNIRS, CEA, Université Paris-Saclay, NeuroSpin center, Gif-sur-Yvette, France
| | - Evelyn Eger
- Cognitive Neuroimaging Unit, INSERM, CEA, CNRS, Université Paris-Saclay, NeuroSpin center, Gif-sur-Yvette, France.
| |
Collapse
|
12
|
Kaminski J, Stengelin R, Girndt A, Haun D, Liebal K. Understanding others' preferences: A comparison across primate species and human societies. PLoS One 2024; 19:e0295221. [PMID: 38232055 DOI: 10.1371/journal.pone.0295221] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2022] [Accepted: 11/20/2023] [Indexed: 01/19/2024] Open
Abstract
We investigated children's and non-human great apes' ability to anticipate others' choices from their evident food preferences-regardless of whether these preferences deviate or align with one's own. We assessed children from three culturally-diverse societies (Namibia, Germany, and Samoa; N = 71; age range = 5-11) and four non-human great ape species (chimpanzees (Pan troglodytes), bonobos (Pan paniscus), gorillas (Gorilla gorilla), and orangutans (Pongo abelii); N = 25; age range = 7-29) regarding their choices in a dyadic food-retrieval task. Across conditions, participants' preferences were either aligned (same preference condition) or opposed (opposite preference condition) to those of their competitors. Children across societies altered their choices based on their competitor's preferences, indicating a cross-culturally recurrent capacity to anticipate others' choices relying on preferences-based inferences. In contrast to human children, all non-human great apes chose according to their own preferences but independent of those of their competitors. In sum, these results suggest that the tendency to anticipate others' choices based on their food preferences is cross-culturally robust and, among the great apes, most likely specific to humans.
Collapse
Affiliation(s)
- Juliane Kaminski
- Department of Psychology, University of Portsmouth, Portsmouth, United Kingdom
| | - Roman Stengelin
- Department of Comparative Cultural Psychology, Max-Planck Institute for Evolutionary Anthropology, Leipzig, Germany
- Department of Psychology and Social Work, University of Namibia, Windhoek, Namibia
| | - Antje Girndt
- Department of Developmental and Comparative Psychology, Max-Planck Institute for Evolutionary Anthropology, Leipzig, Germany
| | - Daniel Haun
- Department of Comparative Cultural Psychology, Max-Planck Institute for Evolutionary Anthropology, Leipzig, Germany
- Faculty of Education, Leipzig Research Centre for Early Child Development & Department for Early Child Development and Culture, Leipzig University, Leipzig, Germany
| | - Katja Liebal
- Department of Comparative Cultural Psychology, Max-Planck Institute for Evolutionary Anthropology, Leipzig, Germany
- Life Sciences, Institute of Biology, Leipzig University, Leipzig, Germany
| |
Collapse
|
13
|
Holt S, Fan JE, Barner D. Creating ad hoc graphical representations of number. Cognition 2024; 242:105665. [PMID: 37992512 DOI: 10.1016/j.cognition.2023.105665] [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: 07/04/2023] [Revised: 11/09/2023] [Accepted: 11/11/2023] [Indexed: 11/24/2023]
Abstract
The ability to communicate about exact number is critical to many modern human practices spanning science, industry, and politics. Although some early numeral systems used 1-to-1 correspondence (e.g., 'IIII' to represent 4), most systems provide compact representations via more arbitrary conventions (e.g., '7' and 'VII'). When people are unable to rely on conventional numerals, however, what strategies do they initially use to communicate number? Across three experiments, participants used pictures to communicate about visual arrays of objects containing 1-16 items, either by producing freehand drawings or combining sets of visual tokens. We analyzed how the pictures they produced varied as a function of communicative need (Experiment 1), spatial regularities in the arrays (Experiment 2), and visual properties of tokens (Experiment 3). In Experiment 1, we found that participants often expressed number in the form of 1-to-1 representations, but sometimes also exploited the configuration of sets. In Experiment 2, this strategy of using configural cues was exaggerated when sets were especially large, and when the cues were predictably correlated with number. Finally, in Experiment 3, participants readily adopted salient numerical features of objects (e.g., four-leaf clover) and generally combined them in a cumulative-additive manner. Taken together, these findings corroborate historical evidence that humans exploit correlates of number in the external environment - such as shape, configural cues, or 1-to-1 correspondence - as the basis for innovating more abstract number representations.
Collapse
Affiliation(s)
- Sebastian Holt
- Department of Psychology, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA.
| | - Judith E Fan
- Department of Psychology, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA; Department of Psychology, Stanford University, 450 Jane Stanford Way, Stanford, CA 94305, USA
| | - David Barner
- Department of Psychology, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA; Department of Linguistics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA
| |
Collapse
|
14
|
Ohki T, Kunii N, Chao ZC. Efficient, continual, and generalized learning in the brain - neural mechanism of Mental Schema 2.0. Rev Neurosci 2023; 34:839-868. [PMID: 36960579 DOI: 10.1515/revneuro-2022-0137] [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: 11/15/2022] [Accepted: 02/26/2023] [Indexed: 03/25/2023]
Abstract
There has been tremendous progress in artificial neural networks (ANNs) over the past decade; however, the gap between ANNs and the biological brain as a learning device remains large. With the goal of closing this gap, this paper reviews learning mechanisms in the brain by focusing on three important issues in ANN research: efficiency, continuity, and generalization. We first discuss the method by which the brain utilizes a variety of self-organizing mechanisms to maximize learning efficiency, with a focus on the role of spontaneous activity of the brain in shaping synaptic connections to facilitate spatiotemporal learning and numerical processing. Then, we examined the neuronal mechanisms that enable lifelong continual learning, with a focus on memory replay during sleep and its implementation in brain-inspired ANNs. Finally, we explored the method by which the brain generalizes learned knowledge in new situations, particularly from the mathematical generalization perspective of topology. Besides a systematic comparison in learning mechanisms between the brain and ANNs, we propose "Mental Schema 2.0," a new computational property underlying the brain's unique learning ability that can be implemented in ANNs.
Collapse
Affiliation(s)
- Takefumi Ohki
- International Research Center for Neurointelligence (WPI-IRCN), The University of Tokyo Institutes for Advanced Study, The University of Tokyo, Tokyo 113-0033, Japan
| | - Naoto Kunii
- Department of Neurosurgery, The University of Tokyo, Tokyo 113-0033, Japan
| | - Zenas C Chao
- International Research Center for Neurointelligence (WPI-IRCN), The University of Tokyo Institutes for Advanced Study, The University of Tokyo, Tokyo 113-0033, Japan
| |
Collapse
|
15
|
Bahreini N, Artemenko C, Plewnia C, Nuerk HC. tDCS effects in basic symbolic number magnitude processing are not significantly lateralized. Sci Rep 2023; 13:21515. [PMID: 38057342 PMCID: PMC10700326 DOI: 10.1038/s41598-023-48189-z] [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: 08/04/2023] [Accepted: 11/23/2023] [Indexed: 12/08/2023] Open
Abstract
Functional lateralization was previously established for various cognitive domains-but not for number processing. Although numbers are considered to be bilaterally represented in the intraparietal sulcus (IPS), there are some indications of different functional roles of the left vs. right IPS in processing number pairs with small vs. large distance, respectively. This raises the question whether number size plays a distinct role in the lateralization within the IPS. In our preregistered study, we applied anodal transcranial direct current stimulation (tDCS) over the left vs. right IPS to investigate the effect of stimulation as compared to sham on small vs. large distance, in both single-digit and two-digit number comparison. We expected that anodal tDCS over the left IPS facilitates number comparison with small distance, while anodal tDCS over the right IPS facilitates number comparison with large distance. Results indicated no effect of stimulation; however, exploratory analyses revealed that tDCS over the right IPS slowed down single-digit number processing after controlling for the training effect. In conclusion, number magnitude processing might be bilaterally represented in the IPS, however, our exploratory analyses emphasise the need for further investigation on functional lateralization of number processing.
Collapse
Affiliation(s)
- Narjes Bahreini
- Department of Psychology, University of Tuebingen, Tuebingen, Germany.
| | | | - Christian Plewnia
- Department of Psychiatry and Psychotherapy, Neurophysiology and Interventional Neuropsychiatry, University Hospital of Tuebingen, Tuebingen, Germany
- German Centre for Mental Health (DZPG), Jena, Germany
| | - Hans-Christoph Nuerk
- Department of Psychology, University of Tuebingen, Tuebingen, Germany
- German Centre for Mental Health (DZPG), Jena, Germany
| |
Collapse
|
16
|
Szymanik J, Kochari A, Bremnes HS. Questions About Quantifiers: Symbolic and Nonsymbolic Quantity Processing by the Brain. Cogn Sci 2023; 47:e13346. [PMID: 37867321 DOI: 10.1111/cogs.13346] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2020] [Revised: 05/11/2023] [Accepted: 09/06/2023] [Indexed: 10/24/2023]
Abstract
One approach to understanding how the human cognitive system stores and operates with quantifiers such as "some," "many," and "all" is to investigate their interaction with the cognitive mechanisms for estimating and comparing quantities from perceptual input (i.e., nonsymbolic quantities). While a potential link between quantifier processing and nonsymbolic quantity processing has been considered in the past, it has never been discussed extensively. Simultaneously, there is a long line of research within the field of numerical cognition on the relationship between processing exact number symbols (such as "3" or "three") and nonsymbolic quantity. This accumulated knowledge can potentially be harvested for research on quantifiers since quantifiers and number symbols are two different ways of referring to quantity information symbolically. The goal of the present review is to survey the research on the relationship between quantifiers and nonsymbolic quantity processing mechanisms and provide a set of research directions and specific questions for the investigation of quantifier processing.
Collapse
Affiliation(s)
- Jakub Szymanik
- Center for Brain/Mind Sciences and the Department of Information Engineering and Computer Science, University of Trento
| | - Arnold Kochari
- Institute for Logic, Language, and Computation, University of Amsterdam
| | | |
Collapse
|
17
|
Chen CC, Jang S, Piazza M, Hyde DC. Characterizing exact arithmetic abilities before formal schooling. Cognition 2023; 238:105481. [PMID: 37182405 DOI: 10.1016/j.cognition.2023.105481] [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: 10/20/2022] [Revised: 03/07/2023] [Accepted: 05/03/2023] [Indexed: 05/16/2023]
Abstract
Children appear to have some arithmetic abilities before formal instruction in school, but the extent of these abilities as well as the mechanisms underlying them are poorly understood. Over two studies, an initial exploratory study of preschool children in the U.S. (N = 207; Age = 2.89-4.30 years) and a pre-registered replication of preschool children in Italy (N = 130; Age = 3-6.33 years), we documented some basic behavioral signatures of exact arithmetic using a non-symbolic subtraction task. Furthermore, we investigated the underlying mechanisms by analyzing the relationship between individual differences in exact subtraction and assessments of other numerical and non-numerical abilities. Across both studies, children performed above chance on the exact non-symbolic arithmetic task, generally showing better performance on problems involving smaller quantities compared to those involving larger quantities. Furthermore, individual differences in non-verbal approximate numerical abilities and exact cardinal number knowledge were related to different aspects of subtraction performance. Specifically, non-verbal approximate numerical abilities were related to subtraction performance in older but not younger children. Across both studies we found evidence that cardinal number knowledge was related to performance on subtraction problems where the answer was zero (i.e., subtractive negation problems). Moreover, subtractive negation problems were only solved above chance by children who had a basic understanding of cardinality. Together these finding suggest that core non-verbal numerical abilities, as well as emerging knowledge of symbolic numbers provide a basis for some, albeit limited, exact arithmetic abilities before formal schooling.
Collapse
Affiliation(s)
- Chi-Chuan Chen
- Department of Psychology, University of Illinois at Urbana-Champaign, USA
| | - Selim Jang
- Department of Psychology, University of Illinois at Urbana-Champaign, USA
| | - Manuela Piazza
- Center for Mind/Brain Sciences (CiMEC), University of Trento, Italy
| | - Daniel C Hyde
- Department of Psychology, University of Illinois at Urbana-Champaign, USA; Neuroscience Program, University of Illinois at Urbana-Champaign, USA.
| |
Collapse
|
18
|
Short DS, McLean JF. The relationship between numerical mapping abilities, maths achievement and socioeconomic status in 4- and 5-year-old children. BRITISH JOURNAL OF EDUCATIONAL PSYCHOLOGY 2023; 93:641-657. [PMID: 36645028 DOI: 10.1111/bjep.12582] [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: 12/21/2021] [Accepted: 12/24/2022] [Indexed: 01/17/2023]
Abstract
BACKGROUND Early numeracy skills are associated with academic and life-long outcomes. Children from low-income backgrounds typically have poorer maths outcomes, and their learning can already be disadvantaged before they begin formal schooling. Understanding the relationship between the skills that support the acquisition of early maths skills could scaffold maths learning and improve life chances. AIMS The present study aimed to examine how the ability of children from different SES backgrounds to map between symbolic (Arabic numerals) and non-symbolic (dot arrays) at two difficulty ratios related to their math performance. SAMPLE Participants were 398 children in their first year of formal schooling (Mean age = 60 months), and 75% were from low SES backgrounds. METHOD The children completed symbolic to non-symbolic and non-symbolic to symbolic mapping tasks at two difficulty ratios (1:2; 2:3) plus standardized maths tasks. RESULTS The results showed that all the children performed better for symbolic to non-symbolic mapping and when the ratio was 1:2. Mapping task performance was significantly related to maths task achievement, but low-SES children showed significantly lower performance on all tasks. CONCLUSION The results suggest that mapping tasks could be a useful way to identify children at risk of low maths attainment.
Collapse
Affiliation(s)
- Dawn S Short
- Division of Psychology, Abertay University, Dundee, UK
| | | |
Collapse
|
19
|
Wußing M, Grabner RH, Sommer H, Saalbach H. Language-switching and retrieval-based learning: an unfavorable combination. Front Psychol 2023; 14:1198117. [PMID: 37564306 PMCID: PMC10411513 DOI: 10.3389/fpsyg.2023.1198117] [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: 03/31/2023] [Accepted: 06/30/2023] [Indexed: 08/12/2023] Open
Abstract
Language-switching costs arise when learners encode information in one language and subsequently recall that information in a different language. The assumed cognitive mechanism behind these costs is the principle of encoding specificity that implies language-dependent representations of information. The aim of our study was to test this mechanism and to gain insights into the impact of language-switching on subsequent learning. To this end, we used retrieval-based learning as a carrier-paradigm. In a 2×3-design, 117 participants learned mathematical concepts with a practice-test or a restudy opportunity (within-subjects factor). In addition, the sample was divided into three groups regarding language-switching (between-subjects factor): one group without switching, one switched for the final tests, and one switched between initial learning and subsequent learning. Results show the expected main effects: participants performed better for the items learned via retrieval-based learning (testing-effect) and worse in conditions with language-switching (language-switching-costs). Most importantly, we were able to find an interaction between learning condition and language-switching: retrieval-based learning suffers particularly from language-switching. Additionally, our results indicate that language switching before subsequent learning seems to be particularly detrimental. These results provide both validation for encoding specificity as mechanism underlying language-switching costs and new information on the impact of the time of language-switching that can be considered in educational designs such as "Content and Language Integrated Learning."
Collapse
Affiliation(s)
- Moritz Wußing
- Faculty of Education, Leipzig University, Leipzig, Germany
| | | | - Hannah Sommer
- Institute of Psychology, University of Graz, Graz, Austria
| | | |
Collapse
|
20
|
Ciccione L, Sablé-Meyer M, Boissin E, Josserand M, Potier-Watkins C, Caparos S, Dehaene S. Trend judgment as a perceptual building block of graphicacy and mathematics, across age, education, and culture. Sci Rep 2023; 13:10266. [PMID: 37355745 PMCID: PMC10290641 DOI: 10.1038/s41598-023-37172-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2023] [Accepted: 06/17/2023] [Indexed: 06/26/2023] Open
Abstract
Data plots are widely used in science, journalism and politics, since they efficiently allow to depict a large amount of information. Graphicacy, the ability to understand graphs, has thus become a fundamental cultural skill comparable to literacy or numeracy. Here, we introduce a measure of intuitive graphicacy that assesses the perceptual ability to detect a trend in noisy scatterplots ("does this graph go up or down?"). In 3943 educated participants, responses vary as a sigmoid function of the t-value that a statistician would compute to detect a significant trend. We find a minimum level of core intuitive graphicacy even in unschooled participants living in remote Namibian villages (N = 87) and 6-year-old 1st-graders who never read a graph (N = 27). The sigmoid slope that we propose as a proxy of intuitive graphicacy increases with education and tightly correlates with statistical and mathematical knowledge, showing that experience contributes to refining graphical intuitions. Our tool, publicly available online, allows to quickly evaluate and formally quantify a perceptual building block of graphicacy.
Collapse
Affiliation(s)
- Lorenzo Ciccione
- Cognitive Neuroimaging Unit, CEA, INSERM, NeuroSpin Center, Université Paris-Saclay, 91191, Gif-sur-Yvette, France.
- Collège de France, Université Paris Sciences Lettres (PSL), 75005, Paris, France.
| | - Mathias Sablé-Meyer
- Cognitive Neuroimaging Unit, CEA, INSERM, NeuroSpin Center, Université Paris-Saclay, 91191, Gif-sur-Yvette, France
- Collège de France, Université Paris Sciences Lettres (PSL), 75005, Paris, France
| | - Esther Boissin
- LaPsyDÉ, CNRS, Université Paris Cité, 75005, Paris, France
| | - Mathilde Josserand
- Laboratoire Dynamique Du Langage, UMR 5596, Université Lumière Lyon 2, 69363, Lyon, France
| | | | - Serge Caparos
- DysCo Lab, Department of Psychology, Université Paris 8, 93526, Saint-Denis, France
- Human Sciences Section, Institut Universitaire de France, 75005, Paris, France
| | - Stanislas Dehaene
- Cognitive Neuroimaging Unit, CEA, INSERM, NeuroSpin Center, Université Paris-Saclay, 91191, Gif-sur-Yvette, France
- Collège de France, Université Paris Sciences Lettres (PSL), 75005, Paris, France
| |
Collapse
|
21
|
Cheng C, Kibbe MM. Is Nonsymbolic Arithmetic Truly "Arithmetic"? Examining the Computational Capacity of the Approximate Number System in Young Children. Cogn Sci 2023; 47:e13299. [PMID: 37303302 DOI: 10.1111/cogs.13299] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2022] [Revised: 01/09/2023] [Accepted: 05/10/2023] [Indexed: 06/13/2023]
Abstract
Young children with limited knowledge of formal mathematics can intuitively perform basic arithmetic-like operations over nonsymbolic, approximate representations of quantity. However, the algorithmic rules that guide such nonsymbolic operations are not entirely clear. We asked whether nonsymbolic arithmetic operations have a function-like structure, like symbolic arithmetic. Children (n = 74 4- to -8-year-olds in Experiment 1; n = 52 7- to 8-year-olds in Experiment 2) first solved two nonsymbolic arithmetic problems. We then showed children two unequal sets of objects, and asked children which of the two derived solutions should be added to the smaller of the two sets to make them "about the same." We hypothesized that, if nonsymbolic arithmetic follows similar function rules to symbolic arithmetic, then children should be able to use the solutions of nonsymbolic computations as inputs into another nonsymbolic problem. Contrary to this hypothesis, we found that children were unable to reliably do so, suggesting that these solutions may not operate as independent representations that can be used inputs into other nonsymbolic computations. These results suggest that nonsymbolic and symbolic arithmetic computations are algorithmically distinct, which may limit the extent to which children can leverage nonsymbolic arithmetic intuitions to acquire formal mathematics knowledge.
Collapse
Affiliation(s)
- Chen Cheng
- Division of Social Science, Hong Kong University of Science and Technology
| | - Melissa M Kibbe
- Department of Psychological and Brain Sciences, Boston University
| |
Collapse
|
22
|
Hyde DC. Cognitive neuroscience: An abstract sense of number in the infant brain. Curr Biol 2023; 33:R400-R402. [PMID: 37220730 DOI: 10.1016/j.cub.2023.03.079] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
The human infant brain automatically extracts number from the environment. A new study recovers an abstract code for number from the brain electrophysiology of sleeping infants.
Collapse
Affiliation(s)
- Daniel C Hyde
- Department of Psychology, University of Illinois Urbana-Champaign, 603 E Daniel St, Champaign, IL 61820, USA.
| |
Collapse
|
23
|
Guerrero D, Park J. Arithmetic thinking as the basis of children's generative number concepts. DEVELOPMENTAL REVIEW 2023. [DOI: 10.1016/j.dr.2022.101062] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
|
24
|
Park J, Im SH, Varma S. A language compatibility effect in fraction processing. Q J Exp Psychol (Hove) 2023; 76:596-605. [PMID: 35400219 DOI: 10.1177/17470218221095747] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
A language compatibility effect occurs when there is a match between what a language provides and what a mathematical task demands. Here, we investigated whether such an effect exists for fraction processing in English, which names the numerator first, versus Korean, which names the denominator first. We developed two new tasks: a fraction span task where participants view and then recall four fractions and a fraction identification task where they view one fraction and then another and judge whether the two fractions are the same or not. We generally found that English speakers were advantaged when the numerator drove task performance and Korean speakers were advantaged when the denominator was critical. These findings, particularly from the fraction identification task, were inconsistent with the attentional focus hypothesis, which proposes that the serialisation bias of a language guides which fraction component is attended to first. Rather, they were better explained by the verbal encoding hypothesis, which states that a necessary condition for observing language compatibility effects may be that the fraction components must be encoded in verbal working memory and rehearsed there.
Collapse
Affiliation(s)
- Jimin Park
- Department of Educational Psychology, University of Minnesota Twin Cities, Minneapolis, MN, USA
| | - Soo-Hyun Im
- Department of Education, Hanyang University, Seoul, Republic of Korea
| | - Sashank Varma
- Schools of Interactive Computing and Psychology, Georgia Institute of Technology, Atlanta, GA, USA
| |
Collapse
|
25
|
Mou Y, Zhang B, Hyde DC. Directionality in the interrelations between approximate number, verbal number, and mathematics in preschool-aged children. Child Dev 2023; 94:e67-e84. [PMID: 36528845 DOI: 10.1111/cdev.13879] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
A fundamental question in numerical development concerns the directional relation between an early-emerging non-verbal approximate number system (ANS) and culturally acquired verbal number and mathematics knowledge. Using path models on longitudinal data collected in preschool children (Mage = 3.86 years; N = 216; 99 males; 80.8% White; 10.8% Multiracial, 3.8% Latino; 1.9% Black; collected 2013-2017) over 1 year, this study showed that earlier verbal number knowledge was associated with later ANS precision (average β = .32), even after controlling for baseline differences in numerical, general cognitive, and language abilities. In contrast, earlier ANS precision was not associated with later verbal number knowledge (β = -.07) or mathematics abilities (average β = .10). These results suggest that learning about verbal numbers is associated with a sharpening of pre-existing non-verbal numerical abilities.
Collapse
Affiliation(s)
- Yi Mou
- Department of Psychology, Sun Yat-sen University, Guangzhou, People's Republic of China
| | - Bo Zhang
- School of Labor and Employment Relations, University of Illinois Urbana-Champaign, Champaign, Illinois, USA.,Department of Psychology, University of Illinois at Urbana-Champaign, Champaign, Illinois, USA
| | - Daniel C Hyde
- Department of Psychology, University of Illinois at Urbana-Champaign, Champaign, Illinois, USA
| |
Collapse
|
26
|
Matthews N, Folivi F. Omit needless words: Sentence length perception. PLoS One 2023; 18:e0282146. [PMID: 36827285 PMCID: PMC9955962 DOI: 10.1371/journal.pone.0282146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2022] [Accepted: 02/08/2023] [Indexed: 02/25/2023] Open
Abstract
Short sentences improve readability. Short sentences also promote social justice through accessibility and inclusiveness. Despite this, much remains unknown about sentence length perception-an important factor in producing readable writing. Accordingly, we conducted a psychophysical study using procedures from Signal Detection Theory to examine sentence length perception in naive adults. Participants viewed real-world full-page text samples and judged whether a bolded target sentence contained more or fewer than 17 words. The experiment yielded four findings. First, naïve adults perceived sentence length in real-world text samples quickly (median = 300-400 ms) and precisely (median = ~90% correct). Second, flipping real-world text samples upside-down generated no reaction-time cost and nearly no loss in the precision of sentence length perception. This differs from the large inversion effects that characterize other highly practiced, real-world perceptual tasks involving canonically oriented stimuli, most notably face perception and reading. Third, participants significantly underestimated the length of mirror-reversed sentences-but not upside-down, nor standard sentences. This finding parallels participants' familiarity with commonly occurring left-justified right-ragged text, and suggests a novel demonstration of left-lateralized anchoring in scene syntax. Fourth, error patterns demonstrated that participants achieved their high speed, high precision sentence-length judgments by heuristically counting text lines, not by explicitly counting words. This suggests practical advice for writing instructors to offer students. When copy editing, students can quickly and precisely identify their long sentences via a line-counting heuristic, e.g., "a 17-word sentence spans about 1.5 text lines". Students can subsequently improve a long sentence's readability and inclusiveness by omitting needless words.
Collapse
Affiliation(s)
- Nestor Matthews
- Department of Psychology, Denison University, Granville, OH, United States of America
- * E-mail:
| | - Folly Folivi
- Department of Psychology, Denison University, Granville, OH, United States of America
| |
Collapse
|
27
|
Haman M, Lipowska K, Soltanlou M, Cipora K, Domahs F, Nuerk HC. The plural counts: Inconsistent grammatical number hinders numerical development in preschoolers - A cross-linguistic study. Cognition 2023; 235:105383. [PMID: 36753808 DOI: 10.1016/j.cognition.2023.105383] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2022] [Revised: 01/16/2023] [Accepted: 01/19/2023] [Indexed: 02/09/2023]
Abstract
The role of grammar in numerical development, and particularly the role of grammatical number inflection, has already been well-documented in toddlerhood. It is unclear, however, whether the influence of grammatical language structure further extends to more complex later stages of numerical development. Here, we addressed this question by exploiting differences between Polish, which has a complex grammatical number paradigm, leading to a partially inconsistent mapping between numerical quantities and grammatical number, and German, which has a comparatively easy verbal paradigm: 151 Polish-speaking and 123 German-speaking kindergarten children were tested using a symbolic numerical comparison task. Additionally, counting skills (Give-a-Number and count-list), and mapping between non-symbolic (dot sets) and symbolic representations of numbers, as well as working memory (Corsi blocks and Digit span) were assessed. Based on the Give-a-Number and mapping tasks, the children were divided into subset-knowers, CP-knowers-non-mappers, and CP-knowers-mappers. Linguistic background was related to performance in several ways: Polish-speaking children expectedly progressed to the CP-knowers stage later than German children, despite comparable non-numerical capabilities, and even after this stage was achieved, they fared worse in the numerical comparison task. There were also meaningful differences in spatial-numerical mapping between the Polish and German groups. Our findings are in line with the theory that grammatical number paradigms influence. the development of representations and processing of numbers, not only at the stage of acquiring the meaning of the first number-words but at later stages as well, when dealing with symbolic numbers.
Collapse
Affiliation(s)
- Maciej Haman
- Faculty of Psychology, University of Warsaw, Warsaw, Poland.
| | | | - Mojtaba Soltanlou
- Department of Psychology, University of Tübingen, Tübingen, Germany; LEAD Graduate School & Research Network, University of Tübingen, Tübingen, Germany; School of Psychology, University of Surrey, UK
| | - Krzysztof Cipora
- Department of Psychology, University of Tübingen, Tübingen, Germany; LEAD Graduate School & Research Network, University of Tübingen, Tübingen, Germany; Centre for Mathematical Cognition, Loughborough University, Loughborough, UK
| | - Frank Domahs
- Department of Linguistics, University of Erfurt, Erfurt, Germany
| | - Hans-Christoph Nuerk
- Department of Psychology, University of Tübingen, Tübingen, Germany; LEAD Graduate School & Research Network, University of Tübingen, Tübingen, Germany
| |
Collapse
|
28
|
Yao Y, Zhou H, Xu T, Ge X, Du F, Wang C, Chen F. Different impacts of long-term abacus training on symbolic and non-symbolic numerical magnitude processing in children. Biol Psychol 2023; 178:108514. [PMID: 36740009 DOI: 10.1016/j.biopsycho.2023.108514] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2022] [Revised: 01/30/2023] [Accepted: 02/01/2023] [Indexed: 02/05/2023]
Abstract
Abacus-based mental calculation (AMC) has been shown to be effective in promoting math ability in children. Given that AMC relies on a visuospatial strategy to perform rapid and precise arithmetic, previous studies mostly focused on the promotion of AMC training on arithmetic ability and mathematical visual-spatial ability, as well as its transfer of advanced cognitive ability. However, little attention has been given to its impact on basic numerical comparison ability. Here, we aim to examine whether and how long-term AMC training impacts symbolic and non-symbolic numerical comparisons. The distance effect (DE) was utilized as a marker, indicating that the comparison between two numbers becomes faster as their numerical distance enlarges. In the current study, forty-one children matched for age and sex were recruited at primary school entry and randomly assigned to the AMC group and the control group. After three years of training, the event-related potential (ERP) recording technique was used to explore the temporal dynamics of number comparison, of which tasks were given in symbolic (Arabic number) or non-symbolic (dot array) format. In the symbolic task, the children in the AMC group showed a smaller DE than those in the control group. Two ERP components, N1 and P2p, located in parietal areas (PO7, PO8) were selected as neural markers of numerical processing. Both groups showed DE in the P2p component in both tasks, but only the children in the AMC group showed DE in the N1 component in the non-symbolic task. In addition, the DE size calculated from reaction times and ERP amplitudes was correlated with higher cognitive capacities, such as coding ability. Taken together, the present results provide evidence that long-term AMC training may be beneficial for numerical processing in children, which may be associated with neurocognitive indices of parietal brain regions.
Collapse
Affiliation(s)
- Yuan Yao
- Bio-X Laboratory, Department of Physics, Zhejiang University, Hangzhou, China; Department of Psychology, Suzhou University of Science and Technology, Suzhou, China
| | - Hui Zhou
- Department of Psychology and Behavioral Sciences, Zhejiang University, Hangzhou, China
| | - Tianyong Xu
- Bio-X Laboratory, Department of Physics, Zhejiang University, Hangzhou, China
| | - Xuelian Ge
- Bio-X Laboratory, Department of Physics, Zhejiang University, Hangzhou, China
| | - Fenglei Du
- Bio-X Laboratory, Department of Physics, Zhejiang University, Hangzhou, China; Department of Radiation Oncology, Zhejiang Cancer Hospital, Hangzhou, China
| | - Chunjie Wang
- Bio-X Laboratory, Department of Physics, Zhejiang University, Hangzhou, China; Institute of Brain Science and Department of Physiology, School of Basic Medical Sciences, Hangzhou Normal University, Hangzhou, China
| | - Feiyan Chen
- Bio-X Laboratory, Department of Physics, Zhejiang University, Hangzhou, China.
| |
Collapse
|
29
|
Sheng Y, Yu M, Liu P, Wang X, Bai X, Zhou X. The association between experience-based risky choice and mathematical ability. Psych J 2023; 12:137-149. [PMID: 36223898 DOI: 10.1002/pchj.612] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2021] [Accepted: 09/20/2022] [Indexed: 11/06/2022]
Abstract
Mathematical ability has always been considered an important influencing factor in description-based risky choices. Experience-based risky choices, which occur frequently in daily life, are very different from description-based risky choices. The association between experience-based risky choice and mathematical ability remains unknown. This study adopts the feedback paradigm for experience-based risky choice to explore the association between multiple mathematical abilities and experience-based risky choice. The results show that, in experience-based risky choice, mathematical ability did not influence the decision to pursue higher expected value, but it did influence preference for risky. Thus, our study contributes to a more comprehensive view of mathematical ability and risky choice.
Collapse
Affiliation(s)
- Youyu Sheng
- State Key Laboratory of Cognitive Neuroscience and Learning, IDG/McGovern Institute for Brain Research, Beijing Normal University, Beijing, China.,Faculty of Psychology, Tianjin Normal University, Tianjin, China
| | - Mingxin Yu
- State Key Laboratory of Cognitive Neuroscience and Learning, IDG/McGovern Institute for Brain Research, Beijing Normal University, Beijing, China
| | - Pengfei Liu
- State Key Laboratory of Cognitive Neuroscience and Learning, IDG/McGovern Institute for Brain Research, Beijing Normal University, Beijing, China
| | - Xiaozhuang Wang
- Faculty of Psychology, Tianjin Normal University, Tianjin, China
| | - Xuejun Bai
- Faculty of Psychology, Tianjin Normal University, Tianjin, China
| | - Xinlin Zhou
- State Key Laboratory of Cognitive Neuroscience and Learning, IDG/McGovern Institute for Brain Research, Beijing Normal University, Beijing, China
| |
Collapse
|
30
|
Thompson CA, Mielicki MK, Rivera F, Fitzsimmons CJ, Scheibe DA, Sidney PG, Schiller LK, Taber JM, Waters EA. Leveraging Math Cognition to Combat Health Innumeracy. PERSPECTIVES ON PSYCHOLOGICAL SCIENCE 2023; 18:152-177. [PMID: 35943825 DOI: 10.1177/17456916221083277] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
Rational numbers (i.e., fractions, percentages, decimals, and whole-number frequencies) are notoriously difficult mathematical constructs. Yet correctly interpreting rational numbers is imperative for understanding health statistics, such as gauging the likelihood of side effects from a medication. Several pernicious biases affect health decision-making involving rational numbers. In our novel developmental framework, the natural-number bias-a tendency to misapply knowledge about natural numbers to all numbers-is the mechanism underlying other biases that shape health decision-making. Natural-number bias occurs when people automatically process natural-number magnitudes and disregard ratio magnitudes. Math-cognition researchers have identified individual differences and environmental factors underlying natural-number bias and devised ways to teach people how to avoid these biases. Although effective interventions from other areas of research can help adults evaluate numerical health information, they circumvent the core issue: people's penchant to automatically process natural-number magnitudes and disregard ratio magnitudes. We describe the origins of natural-number bias and how researchers may harness the bias to improve rational-number understanding and ameliorate innumeracy in real-world contexts, including health. We recommend modifications to formal math education to help children learn the connections among natural and rational numbers. We also call on researchers to consider individual differences people bring to health decision-making contexts and how measures from math cognition might identify those who would benefit most from support when interpreting health statistics. Investigating innumeracy with an interdisciplinary lens could advance understanding of innumeracy in theoretically meaningful and practical ways.
Collapse
Affiliation(s)
| | | | - Ferdinand Rivera
- Department of Mathematics and Statistics, San Jose State University
| | | | | | | | - Lauren K Schiller
- Department of Human Development, Teachers College, Columbia University
| | | | - Erika A Waters
- Department of Surgery, Washington University School of Medicine in St. Louis
| |
Collapse
|
31
|
The approximate number system cannot be the leading factor in the acquisition of the first symbolic numbers. COGNITIVE DEVELOPMENT 2023. [DOI: 10.1016/j.cogdev.2022.101285] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
|
32
|
Li LHL. Lexical cue and perceptual clue to the interpretation of animal-monster hybrids: Classifier selection as a probing stimulant. NEW IDEAS IN PSYCHOLOGY 2022. [DOI: 10.1016/j.newideapsych.2022.100951] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
|
33
|
Sablé-Meyer M, Ellis K, Tenenbaum J, Dehaene S. A language of thought for the mental representation of geometric shapes. Cogn Psychol 2022; 139:101527. [PMID: 36403385 DOI: 10.1016/j.cogpsych.2022.101527] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2021] [Revised: 10/26/2022] [Accepted: 10/31/2022] [Indexed: 11/18/2022]
Abstract
In various cultures and at all spatial scales, humans produce a rich complexity of geometric shapes such as lines, circles or spirals. Here, we propose that humans possess a language of thought for geometric shapes that can produce line drawings as recursive combinations of a minimal set of geometric primitives. We present a programming language, similar to Logo, that combines discrete numbers and continuous integration to form higher-level structures based on repetition, concatenation and embedding, and we show that the simplest programs in this language generate the fundamental geometric shapes observed in human cultures. On the perceptual side, we propose that shape perception in humans involves searching for the shortest program that correctly draws the image (program induction). A consequence of this framework is that the mental difficulty of remembering a shape should depend on its minimum description length (MDL) in the proposed language. In two experiments, we show that encoding and processing of geometric shapes is well predicted by MDL. Furthermore, our hypotheses predict additive laws for the psychological complexity of repeated, concatenated or embedded shapes, which we confirm experimentally.
Collapse
Affiliation(s)
- Mathias Sablé-Meyer
- Unicog, CEA, INSERM, Université Paris-Saclay, NeuroSpin Center, 91191 Gif/Yvette, France; Collège de France, Université Paris-Sciences-Lettres (PSL), 75005 Paris, France.
| | - Kevin Ellis
- Cornell University, Ithaca, NY, United States
| | - Josh Tenenbaum
- Massachusetts Institute of Technology, Cambridge, MA, United States
| | - Stanislas Dehaene
- Unicog, CEA, INSERM, Université Paris-Saclay, NeuroSpin Center, 91191 Gif/Yvette, France; Collège de France, Université Paris-Sciences-Lettres (PSL), 75005 Paris, France
| |
Collapse
|
34
|
Hao X, Chen Z, Huang T, Song Y, Kong X, Liu J. Dissociation of categorical and coordinate spatial relations on dynamic network organization states. Front Hum Neurosci 2022; 16:972375. [DOI: 10.3389/fnhum.2022.972375] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2022] [Accepted: 11/04/2022] [Indexed: 11/18/2022] Open
Abstract
Humans can flexibly represent both categorical and coordinate spatial relations. Previous research has mainly focused on hemisphere lateralization in representing these two types of spatial relations, but little is known about how distinct network organization states support representations of the two. Here we used dynamic resting-state functional connectivity (FC) to explore this question. To do this, we separated a meta-identified navigation network into a ventral and two other subnetworks. We revealed a Weak State and a Strong State within the ventral subnetwork and a Negative State and a Positive State between the ventral and other subnetworks. Further, we found the Weak State (i.e., weak but positive FC) within the ventral subnetwork was related to the ability of categorical relation recognition, suggesting that the representation of categorical spatial relations was related to weak integration among focal regions in the navigation network. In contrast, the Negative State (i.e., negative FC) between the ventral and other subnetworks was associated with the ability of coordinate relation processing, suggesting that the representation of coordinate spatial relations may require competitive interactions among widely distributed regions. In sum, our study provides the first empirical evidence revealing different focal and distributed organizations of the navigation network in representing different types of spatial information.
Collapse
|
35
|
Stengård E, Juslin P, Hahn U, van den Berg R. On the generality and cognitive basis of base-rate neglect. Cognition 2022; 226:105160. [DOI: 10.1016/j.cognition.2022.105160] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2021] [Revised: 04/27/2022] [Accepted: 05/04/2022] [Indexed: 01/29/2023]
|
36
|
Zhang Y, An N, Chen J, Zhou X, Cui Z. Numerosity sense correlates with fluent mathematical abilities. Acta Psychol (Amst) 2022; 228:103655. [DOI: 10.1016/j.actpsy.2022.103655] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2021] [Revised: 05/11/2022] [Accepted: 06/20/2022] [Indexed: 01/29/2023] Open
|
37
|
Boni I, Jara-Ettinger J, Sackstein S, Piantadosi ST. Verbal counting and the timing of number acquisition in an indigenous Amazonian group. PLoS One 2022; 17:e0270739. [PMID: 35913931 PMCID: PMC9342773 DOI: 10.1371/journal.pone.0270739] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2021] [Accepted: 06/16/2022] [Indexed: 01/29/2023] Open
Abstract
Children in industrialized cultures typically succeed on Give-N, a test of counting ability, by age 4. On the other hand, counting appears to be learned much later in the Tsimane’, an indigenous group in the Bolivian Amazon. This study tests three hypotheses for what may cause this difference in timing: (a) Tsimane’ children may be shy in providing behavioral responses to number tasks, (b) Tsimane’ children may not memorize the verbal list of number words early in acquisition, and/or (c) home environments may not support mathematical learning in the same way as in US samples, leading Tsimane’ children to primarily acquire mathematics through formalized schooling. Our results suggest that most of our subjects are not inhibited by shyness in responding to experimental tasks. We also find that Tsimane’ children (N = 100, ages 4-11) learn the verbal list later than US children, but even upon acquiring this list, still take time to pass Give-N tasks. We find that performance in counting varies across tasks and is related to formal schooling. These results highlight the importance of formal education, including instruction in the count list, in learning the meanings of the number words.
Collapse
Affiliation(s)
- Isabelle Boni
- Department of Psychology, University of California Berkeley, Berkeley, CA, United States of America
- * E-mail:
| | - Julian Jara-Ettinger
- Department of Psychology, Yale University, New Haven, CT, United States of America
| | - Sophie Sackstein
- Department of Brain and Cognitive Sciences, University of Rochester, Rochester, NY, United States of America
| | - Steven T. Piantadosi
- Department of Psychology, University of California Berkeley, Berkeley, CA, United States of America
| |
Collapse
|
38
|
Silver AM, Libertus ME. Environmental influences on mathematics performance in early childhood. NATURE REVIEWS PSYCHOLOGY 2022; 1:407-418. [PMID: 36330081 PMCID: PMC9624502 DOI: 10.1038/s44159-022-00061-z] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 04/15/2022] [Indexed: 06/16/2023]
Abstract
Math skills relate to lifelong career, health, and financial outcomes. Individuals' own cognitive abilities predict math performance and there is growing recognition that environmental influences including differences in culture and variability in math engagement also impact math skills. In this Review, we summarize evidence indicating that differences between languages, exposure to math-focused language, socioeconomic status, attitudes and beliefs about math, and engagement with math activities influence young children's math performance. These influences play out at the community and individual level. However, research on the role of these environmental influences for foundational number skills, including understanding of number words, is limited. Future research is needed to understand individual differences in the development of early emerging math skills such as number word skills, examining to what extent different types of environmental input are necessary and how children's cognitive abilities shape the impact of environmental input.
Collapse
Affiliation(s)
- Alex M. Silver
- Department of Psychology, University of Pittsburgh, Pittsburgh, PA, USA
| | | |
Collapse
|
39
|
Lee SH, Kim D, Opfer JE, Pitt MA, Myung JI. A number-line task with a Bayesian active learning algorithm provides insights into the development of non-symbolic number estimation. Psychon Bull Rev 2022; 29:971-984. [PMID: 34918270 DOI: 10.3758/s13423-021-02041-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 11/11/2021] [Indexed: 01/29/2023]
Abstract
To characterize numerical representations, the number-line task asks participants to estimate the location of a given number on a line flanked with zero and an upper-bound number. An open question is whether estimates for symbolic numbers (e.g., Arabic numerals) and non-symbolic numbers (e.g., number of dots) rely on common processes with a common developmental pathway. To address this question, we explored whether well-established findings in symbolic number-line estimation generalize to non-symbolic number-line estimation. For exhaustive investigations without sacrificing data quality, we applied a novel Bayesian active learning algorithm, dubbed Gaussian process active learning (GPAL), that adaptively optimizes experimental designs. The results showed that the non-symbolic number estimation in participants of diverse ages (5-73 years old, n = 238) exhibited three characteristic features of symbolic number estimation.
Collapse
Affiliation(s)
- Sang Ho Lee
- Department of Psychology, The Ohio State University, 212 Psychology Building, 1835 Neil Avenue, Columbus, OH, 43210, USA.
| | - Dan Kim
- Department of Psychology, The Ohio State University, 212 Psychology Building, 1835 Neil Avenue, Columbus, OH, 43210, USA
| | - John E Opfer
- Department of Psychology, The Ohio State University, 212 Psychology Building, 1835 Neil Avenue, Columbus, OH, 43210, USA
| | - Mark A Pitt
- Department of Psychology, The Ohio State University, 212 Psychology Building, 1835 Neil Avenue, Columbus, OH, 43210, USA
| | - Jay I Myung
- Department of Psychology, The Ohio State University, 212 Psychology Building, 1835 Neil Avenue, Columbus, OH, 43210, USA
| |
Collapse
|
40
|
Cui J, Xiao R, Ma M, Yuan L, Cohen Kodash R, Zhou X. Children skilled in mental abacus show enhanced non-symbolic number sense. CURRENT PSYCHOLOGY 2022. [DOI: 10.1007/s12144-020-00717-0] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
|
41
|
Ching BHH, Kong KHC. Understanding additive composition is important for symbolic numerical magnitude processing. COGNITIVE DEVELOPMENT 2022. [DOI: 10.1016/j.cogdev.2022.101170] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
|
42
|
Zhang D, Zhou L, Yang A, Li S, Chang C, Liu J, Zhou K. A connectome-based neuromarker of nonverbal number acuity and arithmetic skills. Cereb Cortex 2022; 33:881-894. [PMID: 35254408 PMCID: PMC9890459 DOI: 10.1093/cercor/bhac108] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2021] [Revised: 02/15/2022] [Accepted: 02/16/2022] [Indexed: 02/04/2023] Open
Abstract
The approximate number system (ANS) is vital for survival and reproduction in animals and is crucial for constructing abstract mathematical abilities in humans. Most previous neuroimaging studies focused on identifying discrete brain regions responsible for the ANS and characterizing their functions in numerosity perception. However, a neuromarker to characterize an individual's ANS acuity is lacking, especially one based on whole-brain functional connectivity (FC). Here, based on the resting-state functional magnetic resonance imaging (rs-fMRI) data obtained from a large sample, we identified a distributed brain network (i.e. a numerosity network) using a connectome-based predictive modeling (CPM) analysis. The summed FC strength within the numerosity network reliably predicted individual differences in ANS acuity regarding behavior, as measured using a nonsymbolic number-comparison task. Furthermore, in an independent dataset of the Human Connectome Project (HCP), we found that the summed FC strength within the numerosity network also specifically predicted individual differences in arithmetic skills, but not domain-general cognitive abilities. Therefore, our findings revealed that the identified numerosity network could serve as an applicable neuroimaging-based biomarker of nonverbal number acuity and arithmetic skills.
Collapse
Affiliation(s)
- Dai Zhang
- Beijing Key Laboratory of Applied Experimental Psychology, School of Psychology, Beijing Normal University, No. 19, Xinjiekouwai Street, Haidian District, Beijing 100875, China,Guangdong Key Laboratory for Biomedical Measurements and Ultrasound Imaging, School of Biomedical Engineering, Shenzhen University Health Science Center, No. 1066, Xueyuan Street, Nanshan District, Shenzhen 518060, China
| | - Liqin Zhou
- Beijing Key Laboratory of Applied Experimental Psychology, School of Psychology, Beijing Normal University, No. 19, Xinjiekouwai Street, Haidian District, Beijing 100875, China
| | - Anmin Yang
- Beijing Key Laboratory of Applied Experimental Psychology, School of Psychology, Beijing Normal University, No. 19, Xinjiekouwai Street, Haidian District, Beijing 100875, China
| | - Shanshan Li
- Beijing Key Laboratory of Applied Experimental Psychology, School of Psychology, Beijing Normal University, No. 19, Xinjiekouwai Street, Haidian District, Beijing 100875, China
| | - Chunqi Chang
- Guangdong Key Laboratory for Biomedical Measurements and Ultrasound Imaging, School of Biomedical Engineering, Shenzhen University Health Science Center, No. 1066, Xueyuan Street, Nanshan District, Shenzhen 518060, China
| | - Jia Liu
- Department of Psychology & Tsinghua Laboratory of Brain and Intelligence, Tsinghua University, No. 30, Shuangqing Street, Haidian District, Beijing 100084, China
| | - Ke Zhou
- Corresponding author: Beijing Key Laboratory of Applied Experimental Psychology, School of Psychology, Beijing Normal University, No. 19, Xinjiekouwai Street, Haidian District, Beijing 100875, China.
| |
Collapse
|
43
|
Pitt B, Gibson E, Piantadosi ST. Exact Number Concepts Are Limited to the Verbal Count Range. Psychol Sci 2022; 33:371-381. [PMID: 35132893 PMCID: PMC9096449 DOI: 10.1177/09567976211034502] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2021] [Accepted: 06/25/2021] [Indexed: 01/29/2023] Open
Abstract
Previous findings suggest that mentally representing exact numbers larger than four depends on a verbal count routine (e.g., "one, two, three . . ."). However, these findings are controversial because they rely on comparisons across radically different languages and cultures. We tested the role of language in number concepts within a single population-the Tsimane' of Bolivia-in which knowledge of number words varies across individual adults. We used a novel data-analysis model to quantify the point at which participants (N = 30) switched from exact to approximate number representations during a simple numerical matching task. The results show that these behavioral switch points were bounded by participants' verbal count ranges; their representations of exact cardinalities were limited to the number words they knew. Beyond that range, they resorted to numerical approximation. These results resolve competing accounts of previous findings and provide unambiguous evidence that large exact number concepts are enabled by language.
Collapse
Affiliation(s)
- Benjamin Pitt
- Department of Psychology, University of
California, Berkeley
| | - Edward Gibson
- Department of Brain and Cognitive
Sciences, Massachusetts Institute of Technology
| | | |
Collapse
|
44
|
|
45
|
Szkudlarek E, Zhang H, DeWind NK, Brannon EM. Young Children Intuitively Divide Before They Recognize the Division Symbol. Front Hum Neurosci 2022; 16:752190. [PMID: 35280204 PMCID: PMC8913505 DOI: 10.3389/fnhum.2022.752190] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2021] [Accepted: 01/24/2022] [Indexed: 01/29/2023] Open
Abstract
Children bring intuitive arithmetic knowledge to the classroom before formal instruction in mathematics begins. For example, children can use their number sense to add, subtract, compare ratios, and even perform scaling operations that increase or decrease a set of dots by a factor of 2 or 4. However, it is currently unknown whether children can engage in a true division operation before formal mathematical instruction. Here we examined the ability of 6- to 9-year-old children and college students to perform symbolic and non-symbolic approximate division. Subjects were presented with non-symbolic (dot array) or symbolic (Arabic numeral) dividends ranging from 32 to 185, and non-symbolic divisors ranging from 2 to 8. Subjects compared their imagined quotient to a visible target quantity. Both children (Experiment 1 N = 89, Experiment 2 N = 42) and adults (Experiment 3 N = 87) were successful at the approximate division tasks in both dots and numeral formats. This was true even among the subset of children that could not recognize the division symbol or solve simple division equations, suggesting intuitive division ability precedes formal division instruction. For both children and adults, the ability to divide non-symbolically mediated the relation between Approximate Number System (ANS) acuity and symbolic math performance, suggesting that the ability to calculate non-symbolically may be a mechanism of the relation between ANS acuity and symbolic math. Our findings highlight the intuitive arithmetic abilities children possess before formal math instruction.
Collapse
|
46
|
Bryer MAH, Koopman SE, Cantlon JF, Piantadosi ST, MacLean EL, Baker JM, Beran MJ, Jones SM, Jordan KE, Mahamane S, Nieder A, Perdue BM, Range F, Stevens JR, Tomonaga M, Ujfalussy DJ, Vonk J. The evolution of quantitative sensitivity. Philos Trans R Soc Lond B Biol Sci 2022; 377:20200529. [PMID: 34957840 PMCID: PMC8710878 DOI: 10.1098/rstb.2020.0529] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Abstract
The ability to represent approximate quantities appears to be phylogenetically widespread, but the selective pressures and proximate mechanisms favouring this ability remain unknown. We analysed quantity discrimination data from 672 subjects across 33 bird and mammal species, using a novel Bayesian model that combined phylogenetic regression with a model of number psychophysics and random effect components. This allowed us to combine data from 49 studies and calculate the Weber fraction (a measure of quantity representation precision) for each species. We then examined which cognitive, socioecological and biological factors were related to variance in Weber fraction. We found contributions of phylogeny to quantity discrimination performance across taxa. Of the neural, socioecological and general cognitive factors we tested, cortical neuron density and domain-general cognition were the strongest predictors of Weber fraction, controlling for phylogeny. Our study is a new demonstration of evolutionary constraints on cognition, as well as of a relation between species-specific neuron density and a particular cognitive ability. This article is part of the theme issue ‘Systems neuroscience through the lens of evolutionary theory’.
Collapse
Affiliation(s)
- Margaret A H Bryer
- Department of Psychology, Carnegie Mellon University, Pittsburgh, PA 15213, USA.,Department of Psychology, University of California-Berkeley, Berkeley, CA 94720, USA
| | - Sarah E Koopman
- School of Psychology and Neuroscience, University of St. Andrews, St Andrews KY16 9AJ, UK
| | - Jessica F Cantlon
- Department of Psychology, Carnegie Mellon University, Pittsburgh, PA 15213, USA
| | - Steven T Piantadosi
- Department of Psychology, University of California-Berkeley, Berkeley, CA 94720, USA
| | - Evan L MacLean
- School of Anthropology, University of Arizona, Tucson, AZ 85719, USA.,College of Veterinary Medicine, University of Arizona, Tucson, AZ 85719, USA
| | - Joseph M Baker
- Center for Interdisciplinary Brain Sciences Research, Division of Brain Sciences, Department of Psychiatry and Behavioral Sciences, School of Medicine, Stanford University, Stanford, CA 94305, USA
| | - Michael J Beran
- Department of Psychology and Language Research Center, Georgia State University, Atlanta, GA 30302, USA
| | - Sarah M Jones
- Psychology Program, Berea College, Berea, KY 40403, USA
| | - Kerry E Jordan
- Department of Psychology, Utah State University, Logan, UT 84322, USA
| | - Salif Mahamane
- Behavioral and Social Sciences Department, Western Colorado University, Gunnison, CO 81231, USA
| | - Andreas Nieder
- Animal Physiology Unit, Institute of Neurobiology, University of Tübingen, Tübingen 72076, Germany
| | - Bonnie M Perdue
- Department of Psychology, Agnes Scott College, Decatur, GA 30030, USA
| | - Friederike Range
- Domestication Lab, Konrad Lorenz Institute of Ethology, Department of Interdisciplinary Life Sciences, University of Veterinary Medicine Vienna, Savoyenstrasse 1a, Vienna 1160, Austria
| | - Jeffrey R Stevens
- Department of Psychology and Center for Brain, Biology and Behavior, University of Nebraska-Lincoln, Lincoln, NE 68588, USA
| | | | - Dorottya J Ujfalussy
- MTA-ELTE Comparative Ethology Research Group, Eötvös Loránd University of Sciences (ELTE), Budapest 1117, Hungary.,Department of Ethology, Eötvös Loránd University of Sciences (ELTE), Budapest 1117, Hungary
| | - Jennifer Vonk
- Department of Psychology, Oakland University, Rochester, MI 48309, USA
| |
Collapse
|
47
|
OUP accepted manuscript. Cereb Cortex 2022; 32:4733-4745. [DOI: 10.1093/cercor/bhab513] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2021] [Revised: 12/15/2021] [Accepted: 12/16/2021] [Indexed: 01/29/2023] Open
|
48
|
Lopiccolo D, Chang CB. Cultural factors weaken but do not reverse left-to-right spatial biases in numerosity processing: Data from Arabic and English monoliterates and Arabic-English biliterates. PLoS One 2021; 16:e0261146. [PMID: 34914756 PMCID: PMC8675726 DOI: 10.1371/journal.pone.0261146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2020] [Accepted: 11/24/2021] [Indexed: 01/29/2023] Open
Abstract
Directional response biases due to a conceptual link between space and number, such as a left-to-right hand bias for increasing numerical magnitude, are known as the SNARC (Spatial-Numerical Association of Response Codes) effect. We investigated how the SNARC effect for numerosities would be influenced by reading-writing direction, task instructions, and ambient visual environment in four literate populations exemplifying opposite reading-writing cultures-namely, Arabic (right-to-left script) and English (left-to-right script). Monoliterates and biliterates in Jordan and the U.S. completed a speeded numerosity comparison task to assess the directionality and magnitude of a SNARC effect in their numerosity processing. Monoliterates' results replicated previously documented effects of reading-writing direction and task instructions: the SNARC effect found in left-to-right readers was weakened in right-to-left readers, and the left-to-right group exhibited a task-dependency effect (SNARC effect in the smaller condition, reverse SNARC effect in the larger condition). Biliterates' results did not show a clear effect of environment; instead, both biliterate groups resembled English monoliterates in showing a left-to-right, task-dependent SNARC effect, albeit weaker than English monoliterates'. The absence of significant biases in all Arabic-reading groups (biliterates and Arabic monoliterates) points to a potential conflict between distinct spatial-numerical mapping codes. This view is explained in terms of the proposed Multiple Competing Codes Theory (MCCT), which posits three distinct spatial-numerical mapping codes (innate, cardinal, ordinal) during numerical processing-each involved at varying levels depending on individual and task factors.
Collapse
Affiliation(s)
- Dominique Lopiccolo
- Department of Linguistics, Boston University, Boston, Massachusetts, United States of America
| | - Charles B. Chang
- Department of Linguistics, Boston University, Boston, Massachusetts, United States of America
- * E-mail:
| |
Collapse
|
49
|
Real models: The limits of behavioural evidence for understanding the ANS. Behav Brain Sci 2021; 44:e186. [PMID: 34907874 DOI: 10.1017/s0140525x21001151] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
Clarke and Beck use behavioural evidence to argue that (1) approximate ratio computations are sufficient for claiming that the approximate number system (ANS) represents the rationals, and (2) the ANS does not represent the reals. We argue that pure behaviour is a poor litmus test for this problem, and that we should trust the psychophysical models that place ANS representations within the reals.
Collapse
|
50
|
Sokolowski HM, Merkley R, Kingissepp SSB, Vaikuntharajan P, Ansari D. Children's attention to numerical quantities relates to verbal number knowledge: An introduction to the Build-A-Train task. Dev Sci 2021; 25:e13211. [PMID: 34889002 DOI: 10.1111/desc.13211] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2021] [Revised: 10/24/2021] [Accepted: 12/02/2021] [Indexed: 01/29/2023]
Abstract
Which dimension of a set of objects is more salient to young children: number or size? The 'Build-A-Train' task was developed and used to examine whether children spontaneously use a number or physical size approach on an un-cued matching task. In the Build-A-Train task, an experimenter assembles a train using one to five blocks of a particular length and asks the child to build the same train. The child's blocks differ in length from the experimenter's blocks, causing the child to build a train that matches based on either the number of blocks or length of the train, as it is not possible to match on both. One hundred and nineteen children between 2 years 2 months and 6 years 0 months of age (M = 4.05, SD = 0.84) completed the Build-A-Train task, and the Give-a-Number task, a classic task used to assess children's conceptual knowledge of verbal number words. Across train lengths and verbal number knowledge levels, children used a number approach more than a size approach on the Build-A-Train task. However, children were especially likely to use a number approach over a size approach when they knew the verbal number word that corresponded to the quantity of blocks in the train, particularly for quantities smaller than four. Therefore, children's attention to number relates to their knowledge of verbal number words. The Build-A-Train task and findings from the current study set a foundation for future longitudinal research to investigate the causal relationship between children's acquisition of symbolic mathematical concepts and attention to number.
Collapse
Affiliation(s)
- H Moriah Sokolowski
- Rotman Research Institute, Baycrest Hospital, Toronto, Ontario, Canada.,Department of Psychology, Faculty of Education, Brain and Mind Institute, University of Western Ontario, London, Ontario, Canada
| | - Rebecca Merkley
- Department of Cognitive Science, Carleton University, Ottawa, Ontario, Canada
| | - Sarah Samantha Bray Kingissepp
- Department of Psychology, Faculty of Education, Brain and Mind Institute, University of Western Ontario, London, Ontario, Canada
| | - Praja Vaikuntharajan
- Department of Psychology, Faculty of Education, Brain and Mind Institute, University of Western Ontario, London, Ontario, Canada
| | - Daniel Ansari
- Department of Psychology, Faculty of Education, Brain and Mind Institute, University of Western Ontario, London, Ontario, Canada
| |
Collapse
|