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Hofmann W, Kinder A, Pekár J. How learning influences non-symbolic numerical processing: effects of feedback in the dot comparison task. Front Psychol 2024; 14:1287429. [PMID: 38352965 PMCID: PMC10861774 DOI: 10.3389/fpsyg.2023.1287429] [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: 09/01/2023] [Accepted: 12/18/2023] [Indexed: 02/16/2024] Open
Abstract
It has long been debated how humans estimate the numerosity of sets of elements and what role continuous visual properties play in this process. The dot comparison task, in which the more numerous of two dot arrays must be selected, is a dominant method to investigate this phenomenon. It has been shown that the visual properties of the two dot patterns strongly influence the comparison. This influence can be systematically investigated by manipulating visual properties congruently and incongruently with numerosity. However, it remains unclear how learning and prior experience affect the influence of the visual properties. To address this question, we introduced feedback into the classical dot comparison task: during the learning phase, participants in the experimental group received feedback after each trial indicating whether their answer was correct whereas participants in the control group did not. After the learning phase, neither group received feedback. The convex hull of the dot patterns and the average dot diameter were manipulated congruently and incongruently with numerosity. Our results show that feedback had no effect on overall performance. However, when manipulated separately, dot diameter no longer affected performance in the experimental group after the learning phase, but it did in the control group. Moreover, this effect remained visible even when diameter and convex hull were manipulated simultaneously. This pattern of results is consistent with the notion of sensory integration which proposes that weights are assigned to different visual cues and that numerical judgments depend on an additive combination of these weights. We also found a correlation between performance on an arithmetic task and performance on trials in which dot size was manipulated incongruently with numerosity. However, there were no correlations between an inhibition task and performance in the dot comparison task. Taken together, the current results suggest that learning with feedback may affect some visual properties but not others. Future studies should further investigate a wider range of visual properties to examine which of them can be influenced by learning and under what conditions learning occurs.
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Affiliation(s)
- Wiebke Hofmann
- Institute of Psychology of Learning, Department of Education and Psychology, Free University of Berlin, Berlin, Germany
- Department of Psychiatry and Neurosciences, Charité – Universitätsmedizin Berlin, Corporate Member of Freie Universität Berlin and Humboldt Universität Zu Berlin, Charité Campus Mitte (CCM), Berlin, Germany
| | - Annette Kinder
- Institute of Psychology of Learning, Department of Education and Psychology, Free University of Berlin, Berlin, Germany
| | - Judit Pekár
- Institute of Psychology of Learning, Department of Education and Psychology, Free University of Berlin, Berlin, Germany
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2
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Bonny JW, Lourenco SF. Electrophysiological Comparison of Cumulative Area and Non-Symbolic Number Judgments. Brain Sci 2023; 13:975. [PMID: 37371453 DOI: 10.3390/brainsci13060975] [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: 05/18/2023] [Revised: 06/13/2023] [Accepted: 06/17/2023] [Indexed: 06/29/2023] Open
Abstract
Despite the importance of representing different magnitudes (i.e., number and cumulative area) for action planning and formal mathematics, there is much debate about the nature of these representations, particularly the extent to which magnitudes interact in the mind and brain. Early interaction views suggest that there are shared perceptual processes that form overlapping magnitude representations. However, late interaction views hold that representations of different magnitudes remain distinct, interacting only when preparing a motor response. The present study sheds light on this debate by examining the temporal onset of ratio and congruity effects as participants made ordinal judgments about number and cumulative area. Event-related potentials (ERPs) were recorded to identify whether the onset of such effects aligned with early versus late views. Ratio effects for both magnitudes were observed starting in the P100. Moreover, a congruity effect emerged within the P100. That interactions were observed early in processing, at the same time that initial ratio effects occurred, suggests that number and cumulative area processes interacted when magnitude representations were being formed, prior to preparing a decision response. Our findings are consistent with an early interaction view of magnitude processing, in which number and cumulative area may rely on shared perceptual mechanisms.
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Affiliation(s)
- Justin W Bonny
- Department of Psychology, Morgan State University, 1700 East Cold Spring Lane, Baltimore, MD 21251, USA
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3
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Ogawa A, Kameda T, Nakatani H. Neural Basis of Social Influence of Observing Other's Perception in Dot-Number Estimation. Neuroscience 2023; 515:1-11. [PMID: 36764600 DOI: 10.1016/j.neuroscience.2023.01.035] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2022] [Revised: 01/26/2023] [Accepted: 01/30/2023] [Indexed: 02/11/2023]
Abstract
Our perceptions and decisions are often implicitly influenced by observing another's actions. However, it is unclear how observing other people's perceptual decisions without interacting with them can engage the processing of self-other discrepancies and change the observer's decisions. In this study, we employed functional magnetic resonance imaging and a computational model to investigate the neural basis of how unilaterally observing the other's perceptual decisions modulated one's own decisions. The experimental task was to discriminate whether the number of presented dots was higher or lower than a reference number. The participants performed the task solely while unilaterally observing the performance of another "participant," who produced overestimations and underestimations in the same task in separate sessions. Results of the behavioral analysis showed that the participants' decisions were modulated to resemble those of the other. Image analysis based on computational model revealed that the activation in the medial prefrontal cortex was associated with the discrepancy between the inferred participant's and the presented other's decisions. In addition, the number-sensitive region in the superior parietal region showed altered activation patterns after observing the other's overestimations and underestimations. The activity of the superior parietal region was not involved in assessing the observation of other's perceptual decisions, but it was engaged in plain numerosity perception. These results suggest that computational modeling can capture the neuro-behavioral processing of self-other discrepancies in perception followed by the activity modulation in the number-sensitive region in the task of dot-number estimation.
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Affiliation(s)
- Akitoshi Ogawa
- Faculty of Medicine, Juntendo University, 2-1-1 Hongo, Bunkyo-ku, Tokyo 113-8421, Japan; Brain Science Institute, Tamagawa University, 6-1-1 Tamagawagakuen, Machida, Tokyo 194-8610, Japan.
| | - Tatsuya Kameda
- Department of Social Psychology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 112-0033, Japan; Brain Science Institute, Tamagawa University, 6-1-1 Tamagawagakuen, Machida, Tokyo 194-8610, Japan
| | - Hironori Nakatani
- School of Information and Telecommunication Engineering, Tokai University, 2-3-23, Takanawa, Minato-ku, Tokyo 153-8902, Japan
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Malykh S, Tarasov S, Baeva I, Nikulchev E, Kolyasnikov P, Ilin D, Marnevskaia I, Malykh A, Ismatullina V, Kuzmina Y. Large-scale study of the precision of the approximate number system: Differences between formats, heterogeneity and congruency effects. Heliyon 2023; 9:e14912. [PMID: 37064479 PMCID: PMC10102223 DOI: 10.1016/j.heliyon.2023.e14912] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2022] [Revised: 03/16/2023] [Accepted: 03/21/2023] [Indexed: 03/30/2023] Open
Abstract
The study used a large sample of elementary schoolchildren in Russia (N = 3,448, 51.6% were girls, with a mean age of 8.70 years, ranging 6-11 years) to investigate the congruency, format and heterogeneity effects in a nonsymbolic comparison test and between-individual differences in these effects with generalized linear mixed effects models (GLMMs). The participants were asked to compare two arrays of figures of different colours in spatially separated or spatially intermixed formats. In addition, the figures could be similar or different for the two arrays. The results revealed that congruency (difference between congruent and incongruent items), format (difference between mixed and separated formats) and heterogeneity (difference between homogeneous and heterogeneous conditions) interacted. The heterogeneity effect was higher in the separated format, while the format effect was higher for the homogeneous condition. The separated format produced a greater congruency effect than the mixed format. In addition, the congruency effect was lower in the heterogeneous condition than in the homogeneous condition. Analysis of between-individual differences revealed that there was significant between-individual variance in the format and congruency effects. Analysis of between-grade differences revealed that accuracy improved from grade 1 to grade 4 only for congruent trials in separated formats. Consequently, the congruency effect increased in separated/homogeneous and separated/heterogeneous conditions. In general, the study demonstrated that the test format and heterogeneity affected accuracy and that this effect varied for congruent and incongruent items.
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Affiliation(s)
- S. Malykh
- Department of Psychology, Lomonosov Moscow State University, Moscow, Russia
- Russian Academy of Education, Moscow, Russia
- Corresponding author. Department of Psychology, Lomonosov Moscow State University, Moscow, Russia.
| | - S. Tarasov
- The Herzen State Pedagogical University of Russia, St. Petersburg, Russia
| | - I. Baeva
- The Herzen State Pedagogical University of Russia, St. Petersburg, Russia
| | - E. Nikulchev
- MIREA—Russian Technological University, Moscow, Russia
| | | | - D. Ilin
- MIREA—Russian Technological University, Moscow, Russia
| | - I. Marnevskaia
- Psychological Institute of Russian Academy of Education, Moscow, Russia
| | - A. Malykh
- Psychological Institute of Russian Academy of Education, Moscow, Russia
| | - V. Ismatullina
- Psychological Institute of Russian Academy of Education, Moscow, Russia
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Medrano J, Prather RW. Rethinking Executive Functions in Mathematical Cognition. JOURNAL OF COGNITION AND DEVELOPMENT 2023. [DOI: 10.1080/15248372.2023.2172414] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/10/2023]
Affiliation(s)
- Josh Medrano
- Department of Human Development and Quantitative Methodology, University of Maryland, College Park, Maryland, USA
| | - Richard W. Prather
- Department of Human Development and Quantitative Methodology, University of Maryland, College Park, Maryland, USA
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6
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L-Miao L, Reynvoet B, Sayim B. Anisotropic representations of visual space modulate visual numerosity estimation. Vision Res 2022; 201:108130. [PMID: 36215795 DOI: 10.1016/j.visres.2022.108130] [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: 05/30/2022] [Revised: 09/11/2022] [Accepted: 09/25/2022] [Indexed: 11/06/2022]
Abstract
Humans can estimate the number of visually displayed items without counting. This capacity of numerosity perception has often been attributed to a dedicated system to estimate numerosity, or alternatively to the exploitation of various stimulus features, such as density, convex hull, the size of items, and occupancy area. The distribution of the presented items is usually not varied with eccentricity in the visual field. However, our visual fields are highly asymmetric. To date, it is unclear how inhomogeneities of the visual field impact numerosity perception. Besides eccentricity, a pronounced asymmetry is the radial-tangential anisotropy. For example, in crowding, radially placed flankers interfere more strongly with target perception than tangentially placed flankers. Similarly, in redundancy masking, the number of perceived items in repeating patterns is reduced when the items are arranged radially but not when they are arranged tangentially. Here, we investigated whether numerosity perception is subject to the radial-tangential anisotropy of spatial vision to shed light on the underlying topology of numerosity perception. In Experiment 1, observers were presented with varying numbers of discs, predominantly arranged radially or tangentially, and asked to report their perceived number. In Experiment 2, observers were presented with the same displays as in Experiment 1, and were asked to encircle items that were perceived as a group. We found that numerosity estimation depended on the arrangement of discs, suggesting a radial-tangential anisotropy of numerosity perception. Grouping among discs did not seem to explain our results. We suggest that the topology of spatial vision modulates numerosity estimation and that asymmetries of visual space should be taken into account when investigating numerosity estimation.
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Affiliation(s)
- Li L-Miao
- Univ. Lille, CNRS, UMR9193 - SCALab - Sciences Cognitives et Sciences Affectives, F-59000 Lille, France; Faculty of Psychology and Educational Sciences, KU Leuven @Kulak, Kortrijk, Belgium.
| | - Bert Reynvoet
- Faculty of Psychology and Educational Sciences, KU Leuven @Kulak, Kortrijk, Belgium; Brain and Cognition, Faculty of Psychology and Educational Sciences, KU Leuven, Leuven, Belgium
| | - Bilge Sayim
- Univ. Lille, CNRS, UMR9193 - SCALab - Sciences Cognitives et Sciences Affectives, F-59000 Lille, France; Institute of Psychology, University of Bern, Bern, Switzerland
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Medrano J, Crnosija N, Prather RW, Payne-Sturges D. Bridging the environment and neurodevelopment for children's health: Associations between real-time air pollutant exposures and cognitive outcomes. Front Psychol 2022; 13:933327. [PMID: 36329746 PMCID: PMC9623017 DOI: 10.3389/fpsyg.2022.933327] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2022] [Accepted: 09/28/2022] [Indexed: 11/29/2023] Open
Abstract
Research suggests that children's exposure to pollutants may impact their neurocognitive development. While researchers have found associations between air pollutants and cognitive development, these associations remain underspecified. Further, these exposures occur in the context of the built environment and may be exacerbated by local social vulnerability; in this context, individuals may experience a suite of socioenvironmental stressors that lead to increased cumulative risk exposure. In this pilot study, we tested whether real-time-measured personal exposure to PM2.5 relates to children's executive function and mathematical skills, outcomes that may predict later mathematical performance, general academic performance and even employment outcomes. We recruited 30 families to participate in two rounds in Winter 2020 and Summer 2021. We collected children's demographic data, as well as data about their living environment. In each round, children carried a small device that collected real-time ambient air pollution data for 3 days; parents logged their children's activities each day. On the last day, children completed cognitive assessments indexing their working memory (n-back), inhibitory control (Go/No-Go), nonsymbolic math skills (dot comparison), and arithmetic skills (equation verification). Overall, 29 participants had pollutant readings from both rounds, and 21 had a full dataset. Nonparametric statistical analysis revealed no significant differences in ambient air pollution and cognitive performance over time, Spearman's rho correlation assessment found that PM2.5 was not significantly correlated with cognitive outcomes in R1 and R2. However, the correlations suggested that an increase in PM2.5 was associated with worse working memory, inhibitory control, nonsymbolic skills, and arithmetic skills, at least in R1. We used each participant's zip code-aggregated Social Vulnerability Index, which range from 0 to 1, with higher numbers indicating more social vulnerability. Wilcoxon Rank-Sum tests indicated that participants living in higher SVI zip codes (≥0.70; n = 15) were not significantly different from those living in lower SVI zip codes (<0.70; n = 14), in terms of their PM2.5 exposures and cognitive performance in each round. We also found that socioeconomic characteristics mattered, such that children whose parent (s) had at least a Master's degree or earned more than $100,000 a year had lower PM2.5 exposures than children in the other end.
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Affiliation(s)
- Josh Medrano
- Department of Human Development and Quantitative Methodology, University of Maryland, College Park, MD, United States
| | - Natalie Crnosija
- Maryland Institute for Applied Environmental Health, School of Public Health, University of Maryland, College Park, MD, United States
| | - Richard W Prather
- Department of Human Development and Quantitative Methodology, University of Maryland, College Park, MD, United States
| | - Devon Payne-Sturges
- Maryland Institute for Applied Environmental Health, School of Public Health, University of Maryland, College Park, MD, United States
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8
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The malleable impact of non-numeric features in visual number perception. Acta Psychol (Amst) 2022; 230:103737. [PMID: 36095870 DOI: 10.1016/j.actpsy.2022.103737] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2022] [Revised: 07/20/2022] [Accepted: 09/03/2022] [Indexed: 11/21/2022] Open
Abstract
Non-numeric stimulus features frequently influence observers' number judgments: when judging the number of items in a display, we will often (mis)perceive the set with a larger cumulative surface area as more numerous. These "congruency effects" are often used as evidence for how vision extracts numeric information and have been invoked in arguments surrounding whether non-numeric cues (e.g., cumulative area, density, etc.) are combined for number perception. We test whether congruency effects for one such cue - cumulative area - provide evidence that it is necessarily used and integrated in number perception, or if its influence on number is malleable. In Experiment 1, we replicate and extend prior work showing that the presence of feedback eliminates congruency effects between number and cumulative area, suggesting that the role of cumulative area in number perception is malleable rather than obligatory. In Experiment 2, we test whether this malleable influence is because of use of prior experiences about how number naturalistically correlates with cumulative area, or the result of response competition, with number and cumulative area actively competing for the same behavioral decision. We preserve cumulative area as a visual cue but eliminate response competition with number by replacing one side of the dot array with its corresponding Hindu-Arabic numeral. Independent of the presence or absence of feedback, we do not observe congruency effects in Experiment 2. These experiments suggest that cumulative area is not necessarily integrated in number perception nor a reflection of a rational use of naturalistic correlations, but rather congruency effects between cumulative area and number emerge as a consequence of response competition. Our findings help to elucidate the mechanism through which non-numeric cues and number interact, and provide an explanation for why congruency effects are only sometimes observed across studies.
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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
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Kuzmina Y, Antipkina I. The Association between Approximate Number Sense (ANS) and Math Achievement Depends on the Format of the ANS Test. JOURNAL OF COGNITION AND DEVELOPMENT 2022. [DOI: 10.1080/15248372.2022.2063293] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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11
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Automatic integration of numerical formats examined with frequency-tagged EEG. Sci Rep 2021; 11:21405. [PMID: 34725370 PMCID: PMC8560945 DOI: 10.1038/s41598-021-00738-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2021] [Accepted: 10/13/2021] [Indexed: 01/23/2023] Open
Abstract
How humans integrate and abstract numerical information across different formats is one of the most debated questions in human cognition. We addressed the neuronal signatures of the numerical integration using an EEG technique tagged at the frequency of visual stimulation. In an oddball design, participants were stimulated with standard sequences of numbers (< 5) depicted in single (digits, dots, number words) or mixed notation (dots-digits, number words-dots, digits-number words), presented at 10 Hz. Periodically, a deviant stimulus (> 5) was inserted at 1.25 Hz. We observed significant oddball amplitudes for all single notations, showing for the first time using this EEG technique, that the magnitude information is spontaneously and unintentionally abstracted, irrespectively of the numerical format. Significant amplitudes were also observed for digits-number words and number words-dots, but not for digits-dots, suggesting an automatic integration across some numerical formats. These results imply that direct and indirect neuro-cognitive links exist across the different numerical formats.
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Abstract
On a now orthodox view, humans and many other animals possess a "number sense," or approximate number system (ANS), that represents number. Recently, this orthodox view has been subject to numerous critiques that question whether the ANS genuinely represents number. We distinguish three lines of critique-the arguments from congruency, confounds, and imprecision-and show that none succeed. We then provide positive reasons to think that the ANS genuinely represents numbers, and not just non-numerical confounds or exotic substitutes for number, such as "numerosities" or "quanticals," as critics propose. In so doing, we raise a neglected question: numbers of what kind? Proponents of the orthodox view have been remarkably coy on this issue. But this is unsatisfactory since the predictions of the orthodox view, including the situations in which the ANS is expected to succeed or fail, turn on the kind(s) of number being represented. In response, we propose that the ANS represents not only natural numbers (e.g. 7), but also non-natural rational numbers (e.g. 3.5). It does not represent irrational numbers (e.g. √2), however, and thereby fails to represent the real numbers more generally. This distances our proposal from existing conjectures, refines our understanding of the ANS, and paves the way for future research.
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Adriano A, Girelli L, Rinaldi L. The ratio effect in visual numerosity comparisons is preserved despite spatial frequency equalisation. Vision Res 2021; 183:41-52. [PMID: 33676137 DOI: 10.1016/j.visres.2021.01.011] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2020] [Revised: 01/27/2021] [Accepted: 01/29/2021] [Indexed: 11/30/2022]
Abstract
How non-symbolic numerosity is visually extracted remains a matter of intense debate. Most evidence suggests that numerosity is directly extracted on individual objects following Weber's law, at least for a moderate numerical range. Alternative accounts propose that, whatever the range, numerosity is indirectly derived from summary texture-statistics of the raw image such as spatial frequency (SF). Here, to disentangle these accounts, we tested whether the well-known behavioural signature of numerosity encoding (ratio effect) is preserved despite the equalisation of the SF content. In Experiment 1, participants had to select the numerically larger of two briefly presented moderate-range numerical sets (i.e., 8-18 dots) carefully matched for SF; the ratio between numerosities was manipulated by levels of increasing difficulty (e.g., 0.66, 0.75, 0.8). In Experiment 2, participants performed the same task, but they were presented with both the original and SF equalised stimuli. In both experiments, the results clearly showed a ratio-dependence of the performance: numerosity discrimination became harder and slower as the ratio between numerosities increased. Moreover, this effect was found to be independent of the stimulus type, although the overall performance was better with the original rather than the SF equalised stimuli (Experiment 2). Taken together, these findings indicate that the power spectrum per se cannot explain the main behavioural signature of Weber-like encoding of numerosities (the ratio effect), at least over the tested numerical range, partially challenging alternative indirect accounts of numerosity processing.
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Affiliation(s)
- Andrea Adriano
- Department of Psychology, University of Milano-Bicocca, Italy.
| | - Luisa Girelli
- Department of Psychology, University of Milano-Bicocca, Italy; NeuroMI, Milan Center for Neuroscience, Milano, Italy
| | - Luca Rinaldi
- Department of Brain and Behavioral Sciences, University of Pavia, Pavia, Italy
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Adriano A, Girelli L, Rinaldi L. Non-symbolic numerosity encoding escapes spatial frequency equalization. PSYCHOLOGICAL RESEARCH 2021; 85:3061-3074. [DOI: 10.1007/s00426-020-01458-2] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2020] [Accepted: 12/04/2020] [Indexed: 11/28/2022]
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15
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Ratcliff R, McKoon G. Examining aging and numerosity using an integrated diffusion model. J Exp Psychol Learn Mem Cogn 2020; 46:2128-2152. [PMID: 32730057 PMCID: PMC8054446 DOI: 10.1037/xlm0000937] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Two experiments are presented that use tasks common in research in numerical cognition with young adults and older adults as subjects. In these tasks, one or two arrays of dots are displayed, and subjects decide whether there are more or fewer dots of one kind than another. Results show that older adults, relative to young adults, tend to rely more on the perceptual feature, area, in making numerosity judgments when area is correlated with numerosity. Also, convex hull unexpectedly shows different effects depending on the task (being either correlated with numerosity or anticorrelated). Accuracy and response time (RT) data are interpreted with the integration of the diffusion decision model with models for the representation of numerosity. One model assumes that the representation of the difference depends on the difference between the numerosities and that standard deviations (SDs) increase linearly with numerosity, and the other model assumes a log representation with constant SDs. The representational models have coefficients that are applied to differences between two numerosities to produce drift rates and SDs in drift rates in the decision process. The two tasks produce qualitatively different patterns of RTs: One model fits results from one task, but the results are mixed for the other task. The effects of age on model parameters show a modest decrease in evidence driving the decision process, an increase in the duration of processes outside the decision process (nondecision time), and an increase in the amount of evidence needed to make a decision (boundary separation). (PsycInfo Database Record (c) 2020 APA, all rights reserved).
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Gheorghiu E, Dering BR. Shape facilitates number: brain potentials and microstates reveal the interplay between shape and numerosity in human vision. Sci Rep 2020; 10:12413. [PMID: 32709892 PMCID: PMC7381628 DOI: 10.1038/s41598-020-68788-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2020] [Accepted: 06/19/2020] [Indexed: 12/04/2022] Open
Abstract
Recognition of simple shapes and numerosity estimation for small quantities are often studied independently of each other, but we know that these processes are both rapid and accurate, suggesting that they may be mediated by common neural mechanisms. Here we address this issue by examining how spatial configuration, shape complexity, and luminance polarity of elements affect numerosity estimation. We directly compared the Event Related Potential (ERP) time-course for numerosity estimation under shape and random configurations and found a larger N2 component for shape over lateral-occipital electrodes (250–400 ms), which also increased with higher numbers. We identified a Left Mid Frontal (LMF; 400–650 ms) component over left-lateralised medial frontal sites that specifically separated low and high numbers of elements, irrespective of their spatial configuration. Different luminance-polarities increased N2 amplitude only, suggesting that shape but not numerosity is selective to polarity. Functional microstates confined numerosity to a strict topographic distribution occurring within the LMF time-window, while a microstate responding only to shape-configuration was evidenced earlier, in the N2 time-window. We conclude that shape-coding precedes numerosity estimation, which can be improved when the number of elements and shape vertices are matched. Thus, numerosity estimation around the subitizing range is facilitated by a shape-template matching process.
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Affiliation(s)
- Elena Gheorghiu
- Department of Psychology, University of Stirling, Stirling, FK9 4LA, Scotland, UK.
| | - Benjamin R Dering
- Department of Psychology, University of Stirling, Stirling, FK9 4LA, Scotland, UK
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Attout L, Noël MP, Rousselle L. Magnitude processing in populations with spina-bifida: The role of visuospatial and working memory processes. RESEARCH IN DEVELOPMENTAL DISABILITIES 2020; 102:103655. [PMID: 32413584 DOI: 10.1016/j.ridd.2020.103655] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2019] [Revised: 03/30/2020] [Accepted: 04/05/2020] [Indexed: 06/11/2023]
Abstract
People with Spina Bifida usually experience difficulties with mathematics. In a series of other developmental disorders, a magnitude processing deficit was considered to be the main source of subsequent difficulties in mathematics. The processing of magnitude could be numerical (which is the larger number) or non-numerical such as spatial (e.g., which is the longer?) or temporal (which one last longer?) for instance. However, no study yet has examined directly magnitude processes in a population with Spina Bifida. On the other hand, recent studies in people with genetic syndromes have suggested that visuospatial and working memory processes play an important role in magnitude processing, including number magnitude. Therefore, in this study we explored for the first time magnitude representation using several tasks with different visuospatial and working memory processing requirements, cognitive skills frequently impaired in Spina Bifida. Results showed children with SB presented a global magnitude processing deficit for non-numerical and numerical comparison tasks, but not in symbolic number magnitude tasks compared to controls. Importantly, visuospatial skills and working memory abilities could partially explain the differences between groups in comparison and estimation tasks. This study proposes that magnitude processing difficulties in children with SB could be due to higher cognitive factors such as visuospatial and working memory processes.
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Affiliation(s)
- Lucie Attout
- Research Unit "Enfances", University of Liège, Belgium; Psychological Sciences Research Institute, UCLouvain, Louvain-la-Neuve, Belgium.
| | - Marie-Pascale Noël
- Psychological Sciences Research Institute, UCLouvain, Louvain-la-Neuve, Belgium
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18
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Rubinsten O, Korem N, Levin N, Furman T. Frequency-based Dissociation of Symbolic and Nonsymbolic Numerical Processing during Numerical Comparison. J Cogn Neurosci 2020; 32:762-782. [DOI: 10.1162/jocn_a_01550] [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
Abstract
Recent evidence suggests that during numerical calculation, symbolic and nonsymbolic processing are functionally distinct operations. Nevertheless, both roughly recruit the same brain areas (spatially overlapping networks in the parietal cortex) and happen at the same time (roughly 250 msec poststimulus onset). We tested the hypothesis that symbolic and nonsymbolic processing are segregated by means of functionally relevant networks in different frequency ranges: high gamma (above 50 Hz) for symbolic processing and lower beta (12–17 Hz) for nonsymbolic processing. EEG signals were quantified as participants compared either symbolic numbers or nonsymbolic quantities. Larger EEG gamma-band power was observed for more difficult symbolic comparisons (ratio of 0.8 between the two numbers) than for easier comparisons (ratio of 0.2) over frontocentral regions. Similarly, beta-band power was larger for more difficult nonsymbolic comparisons than for easier ones over parietal areas. These results confirm the existence of a functional dissociation in EEG oscillatory dynamics during numerical processing that is compatible with the notion of distinct linguistic processing of symbolic numbers and approximation of nonsymbolic numerical information.
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19
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Hartmann M, Singer S, Savic B, Müri RM, Mast FW. Anodal High-definition Transcranial Direct Current Stimulation over the Posterior Parietal Cortex Modulates Approximate Mental Arithmetic. J Cogn Neurosci 2019; 32:862-876. [PMID: 31851594 DOI: 10.1162/jocn_a_01514] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Abstract
The representation and processing of numerosity is a crucial cognitive capacity. Converging evidence points to the posterior parietal cortex (PPC) as primary "number" region. However, the exact role of the left and right PPC for different types of numerical and arithmetic tasks remains controversial. In this study, we used high-definition transcranial direct current stimulation (HD-tDCS) to further investigate the causal involvement of the PPC during approximative, nonsymbolic mental arithmetic. Eighteen healthy participants received three sessions of anodal HD-tDCS at 1-week intervals in counterbalanced order: left PPC, right PPC, and sham stimulation. Results showed an improved performance during online parietal HD-tDCS (vs. sham) for subtraction problems. Specifically, the general tendency to underestimate the results of subtraction problems (i.e., the "operational momentum effect") was reduced during online parietal HD-tDCS. There was no difference between left and right stimulation. This study thus provides new evidence for a causal involvement of the left and right PPC for approximate nonsymbolic arithmetic and advances the promising use of noninvasive brain stimulation in increasing cognitive functions.
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20
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21
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Baer C, Odic D. Certainty in numerical judgments develops independently of the approximate number system. COGNITIVE DEVELOPMENT 2019. [DOI: 10.1016/j.cogdev.2019.100817] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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22
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Wilkey ED, Ansari D. Challenging the neurobiological link between number sense and symbolic numerical abilities. Ann N Y Acad Sci 2019; 1464:76-98. [PMID: 31549430 DOI: 10.1111/nyas.14225] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2019] [Revised: 07/25/2019] [Accepted: 08/06/2019] [Indexed: 01/29/2023]
Abstract
A significant body of research links individual differences in symbolic numerical abilities, such as arithmetic, to number sense, the neurobiological system used to approximate and manipulate quantities without language or symbols. However, recent findings from cognitive neuroscience challenge this influential theory. Our current review presents an overview of evidence for the number sense account of symbolic numerical abilities and then reviews recent studies that challenge this account, organized around the following four assertions. (1) There is no number sense as traditionally conceived. (2) Neural substrates of number sense are more widely distributed than common consensus asserts, complicating the neurobiological evidence linking number sense to numerical abilities. (3) The most common measures of number sense are confounded by other cognitive demands, which drive key correlations. (4) Number sense and symbolic number systems (Arabic digits, number words, and so on) rely on distinct neural mechanisms and follow independent developmental trajectories. The review follows each assertion with comments on future directions that may bring resolution to these issues.
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Affiliation(s)
- Eric D Wilkey
- Brain and Mind Institute, Western University, London, Ontario, Canada
| | - Daniel Ansari
- Brain and Mind Institute, Western University, London, Ontario, Canada
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23
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Tsouli A, Dumoulin SO, te Pas SF, van der Smagt MJ. Adaptation reveals unbalanced interaction between numerosity and time. Cortex 2019; 114:5-16. [DOI: 10.1016/j.cortex.2018.02.013] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2017] [Revised: 02/15/2018] [Accepted: 02/16/2018] [Indexed: 11/17/2022]
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24
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Wilkey ED, Pollack C, Price GR. Dyscalculia and Typical Math Achievement Are Associated With Individual Differences in Number-Specific Executive Function. Child Dev 2018; 91:596-619. [PMID: 30597527 DOI: 10.1111/cdev.13194] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Abstract
Deficits in numerical magnitude perception characterize the mathematics learning disability developmental dyscalculia (DD), but recent studies suggest the relation stems from inhibitory control demands from incongruent visual cues in the nonsymbolic number comparison task. This study investigated the relation among magnitude perception during differing congruency conditions, executive function, and mathematics achievement measured longitudinally in children (n = 448) from ages 4 to 13. This relation was investigated across achievement groups and as it related to mathematics across the full range of achievement. Only performance on incongruent trials related to achievement. Findings indicate that executive function in a numerical context, beyond magnitude perception or executive function in a non-numerical context, relates to DD and mathematics across a wide range of achievement.
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25
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Kim N, Jang S, Cho S. Testing the Efficacy of Training Basic Numerical Cognition and Transfer Effects to Improvement in Children's Math Ability. Front Psychol 2018; 9:1775. [PMID: 30333768 PMCID: PMC6175973 DOI: 10.3389/fpsyg.2018.01775] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2018] [Accepted: 09/03/2018] [Indexed: 01/29/2023] Open
Abstract
The goals of the present study were to test whether (and which) basic numerical abilities can be improved with training and whether training effects transfer to improvement in children's math achievement. The literature is mixed with evidence that does or does not substantiate the efficacy of training basic numerical ability. In the present study, we developed a child-friendly software named "123 Bakery" which includes four training modules; non-symbolic numerosity comparison, non-symbolic numerosity estimation, approximate arithmetic, and symbol-to-numerosity mapping. Fifty-six first graders were randomly assigned to either the training or control group. The training group participated in 6 weeks of training (5 times a week, 30 minutes per day). All participants underwent pre- and post-training assessment of their basic numerical processing ability (including numerosity discrimination acuity, symbolic/non-symbolic magnitude estimation, approximate arithmetic, and symbol-to-numerosity mapping), overall math achievement and intelligence, 6 weeks apart. The acuity for numerosity discrimination (approximate number sense acuity; hereafter ANS acuity) significantly improved after training, but this training effect did not transfer to improvement in symbolic, exact calculation, or any other math ability. We conclude that basic numerical cognition training leads to improvement in ANS acuity, but whether this effect transfers to symbolic math ability remains to be further tested.
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Affiliation(s)
- Narae Kim
- Department of Psychology, Chung-Ang University, Seoul, South Korea
| | - Selim Jang
- Department of Psychology, Chung-Ang University, Seoul, South Korea
- Department of Psychology, University of Illinois at Urbana-Champaign, Champaign, IL, United States
| | - Soohyun Cho
- Department of Psychology, Chung-Ang University, Seoul, South Korea
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26
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van Hoogmoed AH, Kroesbergen EH. On the Difference Between Numerosity Processing and Number Processing. Front Psychol 2018; 9:1650. [PMID: 30258376 PMCID: PMC6143766 DOI: 10.3389/fpsyg.2018.01650] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2018] [Accepted: 08/17/2018] [Indexed: 11/16/2022] Open
Abstract
The ANS theory on the processing of non-symbolic numerosities and the ANS mapping account on the processing of symbolic numbers have been the most popular theories on numerosity and number processing, respectively, in the last 20 years. Recently, both the ANS theory and the ANS mapping account have been questioned. In the current study, we examined two main assumptions of both the ANS theory and the ANS mapping account. ERPs were measured in 21 participants during four same-different match-to-sample tasks, involving non-symbolic stimuli, symbolic stimuli, or a combination of symbolic and non-symbolic stimuli (i.e., mapping tasks). We strictly controlled the visual features in the non-symbolic stimuli. Based on the ANS theory, one would expect an early distance effect for numerosity in the non-symbolic task. However, the results show no distance effect for numerosity. When analyzing the stimuli based on visual properties, an early distance effect for area subtended by the convex hull was found. This finding is in line with recent claims that the processing of non-symbolic stimuli may be dependent on the processing of visual properties instead of on numerosity (only). With regards to the processing of symbolic numbers, the ANS mapping account states that symbolic numbers are first mapped onto their non-symbolic representations before further processing, since the non-symbolic representation is at the basis of processing the symbolic number. If the non-symbolic format is the basic format of processing, one would expect that the processing of non-symbolic numerosities would not differ between purely non-symbolic tasks and mapping tasks, resulting in similar ERP waveforms for both tasks. Our results show that the processing of non-symbolic numerosities does differ between the tasks, indicating that processing of non-symbolic number is dependent on task format. This provides evidence against the ANS mapping account. Alternative theories for both the processing of non-symbolic numerosities and symbolic numbers are discussed.
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Affiliation(s)
- Anne H van Hoogmoed
- Department of Pedagogical and Educational Sciences, Utrecht University, Utrecht, Netherlands.,Department of Special Needs Education and Youth Care, University of Groningen, Groningen, Netherlands
| | - Evelyn H Kroesbergen
- Department of Pedagogical and Educational Sciences, Utrecht University, Utrecht, Netherlands.,Behavioural Science Institute, Radboud University, Nijmegen, Netherlands
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27
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Benavides-Varela S, Basso Moro S, Brigadoi S, Meconi F, Doro M, Simion F, Sessa P, Cutini S, Dell'Acqua R. N2pc reflects two modes for coding the number of visual targets. Psychophysiology 2018; 55:e13219. [PMID: 30095174 DOI: 10.1111/psyp.13219] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2018] [Revised: 04/05/2018] [Accepted: 05/31/2018] [Indexed: 01/23/2023]
Abstract
Humans share with a variety of animal species the spontaneous ability to detect the numerical correspondence between limited quantities of visual objects and discrete auditory events. Here, we explored how such mental representation is generated in the visual modality by monitoring a parieto-occipital ERP component, N2pc, whose amplitude covaries with the number of visual targets in explicit enumeration. Participants listened to an auditory sequence of one to three tones followed by a visual search display containing one to three targets. In Experiment 1, participants were asked to respond based on the numerical correspondence between tones and visual targets. In Experiment 2, participants were asked to ignore the tones and detect a target presence in the search display. The results of Experiment 1 showed an N2pc amplitude increase determined by the number of visual targets followed by a centroparietal ERP component modulated by the numerical correspondence between tones and visual targets. The results of Experiment 2 did not show an N2pc amplitude increase as a function of the number of visual targets. However, the numerical correspondence between tones and visual targets influenced N2pc amplitude. By comparing a subset of amplitude/latency parameters between Experiment 1 and 2, the present results suggest N2pc reflects two modes for representing the number of visual targets. One mode, susceptible to subjective control, relies on visual target segregation for exact target individuation, whereas a different mode, likely enabling spontaneous cross-modal matching, relies on the extraction of rough information about number of targets from visual input.
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Affiliation(s)
- S Benavides-Varela
- Department of Developmental Psychology, University of Padova, Padova, Italy.,Department of General Psychology, University of Padova, Padova, Italy
| | - S Basso Moro
- Department of Neuroscience, University of Padova, Padova, Italy.,Cognitive Psychology Unit, Institute of Psychology, Leiden University, Leiden, The Netherlands
| | - S Brigadoi
- Department of Developmental Psychology, University of Padova, Padova, Italy
| | - F Meconi
- Department of Developmental Psychology, University of Padova, Padova, Italy
| | - M Doro
- Department of Developmental Psychology, University of Padova, Padova, Italy
| | - F Simion
- Department of Developmental Psychology, University of Padova, Padova, Italy.,Padova Neuroscience Center, University of Padova, Padova, Italy
| | - P Sessa
- Department of Developmental Psychology, University of Padova, Padova, Italy.,Padova Neuroscience Center, University of Padova, Padova, Italy
| | - S Cutini
- Department of Developmental Psychology, University of Padova, Padova, Italy.,Padova Neuroscience Center, University of Padova, Padova, Italy
| | - R Dell'Acqua
- Department of Developmental Psychology, University of Padova, Padova, Italy.,Padova Neuroscience Center, University of Padova, Padova, Italy
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28
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Norris JE, Clayton S, Gilmore C, Inglis M, Castronovo J. The measurement of approximate number system acuity across the lifespan is compromised by congruency effects. Q J Exp Psychol (Hove) 2018; 72:1037-1046. [DOI: 10.1177/1747021818779020] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Recent studies have highlighted the influence of visual cues such as dot size and cumulative surface area on the measurement of the approximate number system (ANS). Previous studies assessing ANS acuity in ageing have all applied stimuli generated by the Panamath protocol, which does not control nor measure the influence of convex hull. Crucially, convex hull has recently been identified as an influential visual cue present in dot arrays, with its impact on older adults’ ANS acuity yet to be investigated. The current study therefore investigated the manipulation of convex hull by the Panamath protocol, and its effect on the measurement of ANS acuity in younger and older participants. First, analyses of the stimuli generated by Panamath revealed a confound between numerosity ratio and convex hull ratio. Second, although older adults were somewhat less accurate than younger adults on convex hull incongruent trials, ANS acuity was broadly similar between the groups. These findings have implications for the valid measurement of ANS acuity across all ages, and suggest that the Panamath protocol produces stimuli that do not adequately control for the influence of convex hull on numerosity discrimination.
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Affiliation(s)
| | - Sarah Clayton
- Department of Health Sciences, University of Leicester, Leicester, UK
| | - Camilla Gilmore
- Mathematics Education Centre, Loughborough University, Loughborough, UK
| | - Matthew Inglis
- Mathematics Education Centre, Loughborough University, Loughborough, UK
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29
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Zimmermann E. Small numbers are sensed directly, high numbers constructed from size and density. Cognition 2018; 173:1-7. [DOI: 10.1016/j.cognition.2017.12.003] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2017] [Revised: 12/01/2017] [Accepted: 12/04/2017] [Indexed: 12/01/2022]
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30
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Park J. A neural basis for the visual sense of number and its development: A steady-state visual evoked potential study in children and adults. Dev Cogn Neurosci 2018; 30:333-343. [PMID: 28342780 PMCID: PMC6969086 DOI: 10.1016/j.dcn.2017.02.011] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2016] [Revised: 12/22/2016] [Accepted: 02/28/2017] [Indexed: 01/29/2023] Open
Abstract
While recent studies in adults have demonstrated the existence of a neural mechanism for a visual sense of number, little is known about its development and whether such a mechanism exists at young ages. In the current study, I introduce a novel steady-state visual evoked potential (SSVEP) technique to objectively quantify early visual cortical sensitivity to numerical and non-numerical magnitudes of a dot array. I then examine this neural sensitivity to numerical magnitude in children between three and ten years of age and in college students. Children overall exhibit strong SSVEP sensitivity to numerical magnitude in the right occipital sites with negligible SSVEP sensitivity to non-numerical magnitudes, the pattern similar to what is observed in adults. However, a closer examination of age differences reveals that this selective neural sensitivity to numerical magnitude, which is close to absent in three-year-olds, increases steadily as a function of age, while there is virtually no neural sensitivity to other non-numerical magnitudes across these ages. These results demonstrate the emergence of a neural mechanism underlying direct perception of numerosity across early and middle childhood and provide a potential neural mechanistic explanation for the development of humans' primitive, non-verbal ability to comprehend number.
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Affiliation(s)
- Joonkoo Park
- Department of Psychological and Brain Sciences, Commonwealth Honors College, University of Massachusetts, 135 Hicks Way, Amherst, MA 01003, United States.
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31
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Leibovich-Raveh T, Stein I, Henik A, Salti M. Number and Continuous Magnitude Processing Depends on Task Goals and Numerosity Ratio. J Cogn 2018; 1:19. [PMID: 31517193 PMCID: PMC6634598 DOI: 10.5334/joc.22] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2017] [Accepted: 02/27/2018] [Indexed: 12/03/2022] Open
Abstract
A large body of evidence shows that when comparing non-symbolic numerosities, performance is influenced by irrelevant continuous magnitudes, such as total surface area, density, etc. In the current work, we ask whether the weights given to numerosity and continuous magnitudes are modulated by top-down and bottom-up factors. With that aim in mind, we asked adult participants to compare two groups of dots. To manipulate task demands, participants reported after every trial either (1) how accurate their response was (emphasizing accuracy) or (2) how fast their response was (emphasizing speed). To manipulate bottom-up factors, the stimuli were presented for 50 ms, 100 ms or 200 ms. Our results revealed (a) that the weights given to numerosity and continuous magnitude ratios were affected by the interaction of top-down and bottom-up manipulations and (b) that under some conditions, using numerosity ratio can reduce efficiency. Accordingly, we suggest that processing magnitudes is not rigid and static but a flexible and adaptive process that allows us to deal with the ever-changing demands of the environment. We also argue that there is not just one answer to the question 'what do we process when we process magnitudes?', and future studies should take this flexibility under consideration.
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Affiliation(s)
- Tali Leibovich-Raveh
- Department of Mathematics Education, Faculty of Education, The University of Haifa, Haifa, IL
| | - Itamar Stein
- Department of Psychology, Ben-Gurion University of the Negev, Beer-Sheva, IL
- The Zlotowski Center for Neuroscience, Ben-Gurion University of the Negev, Beer-Sheva, IL
| | - Avishai Henik
- Department of Psychology, Ben-Gurion University of the Negev, Beer-Sheva, IL
- The Zlotowski Center for Neuroscience, Ben-Gurion University of the Negev, Beer-Sheva, IL
| | - Moti Salti
- The Zlotowski Center for Neuroscience, Ben-Gurion University of the Negev, Beer-Sheva, IL
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32
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Krajcsi A, Lengyel G, Kojouharova P. Symbolic Number Comparison Is Not Processed by the Analog Number System: Different Symbolic and Non-symbolic Numerical Distance and Size Effects. Front Psychol 2018; 9:124. [PMID: 29491845 PMCID: PMC5817629 DOI: 10.3389/fpsyg.2018.00124] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2017] [Accepted: 01/25/2018] [Indexed: 11/16/2022] Open
Abstract
HIGHLIGHTSWe test whether symbolic number comparison is handled by an analog noisy system. Analog system model has systematic biases in describing symbolic number comparison. This suggests that symbolic and non-symbolic numbers are processed by different systems.
Dominant numerical cognition models suppose that both symbolic and non-symbolic numbers are processed by the Analog Number System (ANS) working according to Weber's law. It was proposed that in a number comparison task the numerical distance and size effects reflect a ratio-based performance which is the sign of the ANS activation. However, increasing number of findings and alternative models propose that symbolic and non-symbolic numbers might be processed by different representations. Importantly, alternative explanations may offer similar predictions to the ANS prediction, therefore, former evidence usually utilizing only the goodness of fit of the ANS prediction is not sufficient to support the ANS account. To test the ANS model more rigorously, a more extensive test is offered here. Several properties of the ANS predictions for the error rates, reaction times, and diffusion model drift rates were systematically analyzed in both non-symbolic dot comparison and symbolic Indo-Arabic comparison tasks. It was consistently found that while the ANS model's prediction is relatively good for the non-symbolic dot comparison, its prediction is poorer and systematically biased for the symbolic Indo-Arabic comparison. We conclude that only non-symbolic comparison is supported by the ANS, and symbolic number comparisons are processed by other representation.
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Affiliation(s)
- Attila Krajcsi
- Cognitive Psychology Department, Institute of Psychology, Eötvös Loránd University, Budapest, Hungary
| | - Gábor Lengyel
- Department of Cognitive Science, Central European University, Budapest, Hungary
| | - Petia Kojouharova
- Doctoral School of Psychology, Eötvös Loránd University, Budapest, Hungary.,Research Centre for Natural Sciences, Institute of Cognitive Neuroscience and Psychology, Hungarian Academy of Sciences, Budapest, Hungary
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Abstract
Models of the representation of numerosity information used in discrimination tasks are integrated with a diffusion decision model. The representation models assume distributions of numerosity either with means and SD that increase linearly with numerosity or with means that increase logarithmically with constant SD. The models produce coefficients that are applied to differences between two numerosities to produce drift rates and these drive the decision process. The linear and log models make differential predictions about how response time (RT) distributions and accuracy change with numerosity and which model is successful depends on the task. When the task is to decide which of two side-by-side arrays of dots has more dots, the log model fits decreasing accuracy and increasing RT as numerosity increases. When the task is to decide, for dots of two colors mixed in a single array, which color has more dots, the linear model fits decreasing accuracy and decreasing RT as numerosity increases. For both tasks, variables such as the areas covered by the dots affect performance, but if the task is changed to one in which the subject has to decide whether the number of dots in a single array is more or less than a standard, the variables have little effect on performance. Model parameters correlate across tasks suggesting commonalities in the abilities to perform them. Overall, results show that the representation used depends on the task and no single representation can account for the data from all the paradigms. (PsycINFO Database Record
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34
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Guillaume M, Mejias S, Rossion B, Dzhelyova M, Schiltz C. A rapid, objective and implicit measure of visual quantity discrimination. Neuropsychologia 2018; 111:180-189. [DOI: 10.1016/j.neuropsychologia.2018.01.044] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2017] [Revised: 01/30/2018] [Accepted: 01/31/2018] [Indexed: 01/29/2023]
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35
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One tamed at a time: A new approach for controlling continuous magnitudes in numerical comparison tasks. Behav Res Methods 2018; 49:1120-1127. [PMID: 27439534 DOI: 10.3758/s13428-016-0772-7] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Non-symbolic stimuli (i.e., dot arrays) are commonly used to study numerical cognition. However, in addition to numerosity, non-symbolic stimuli entail continuous magnitudes (e.g., total surface area, convex-hull, etc.) that correlate with numerosity. Several methods for controlling for continuous magnitudes have been suggested, all with the same underlying rationale: disassociating numerosity from continuous magnitudes. However, the different continuous magnitudes do not fully correlate; therefore, it is impossible to disassociate them completely from numerosity. Moreover, relying on a specific continuous magnitude in order to create this disassociation may end up in increasing or decreasing numerosity saliency, pushing subjects to rely on it more or less, respectively. Here, we put forward a taxonomy depicting the relations between the different continuous magnitudes. We use this taxonomy to introduce a new method with a complimentary Matlab toolbox that allows disassociating numerosity from continuous magnitudes and equating the ratio of the continuous magnitudes to the ratio of the numerosity in order to balance the saliency of numerosity and continuous magnitudes. A dot array comparison experiment in the subitizing range showed the utility of this method. Equating different continuous magnitudes yielded different results. Importantly, equating the convex hull ratio to the numerical ratio resulted in similar interference of numerical and continuous magnitudes.
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36
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Eidlin-Levy H, Rubinsten O. Developmental Dyscalculia and Automatic Magnitudes Processing: Investigating Interference Effects between Area and Perimeter. Front Psychol 2017; 8:2206. [PMID: 29312066 PMCID: PMC5742624 DOI: 10.3389/fpsyg.2017.02206] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2017] [Accepted: 12/04/2017] [Indexed: 11/13/2022] Open
Abstract
The relationship between numbers and other magnitudes has been extensively investigated in the scientific literature. Here, the objectives were to examine whether two continuous magnitudes, area and perimeter, are automatically processed and whether adults with developmental dyscalculia (DD) are deficient in their ability to automatically process one or both of these magnitudes. Fifty-seven students (30 with DD and 27 with typical development) performed a novel Stroop-like task requiring estimation of one aspect (area or perimeter) while ignoring the other. In order to track possible changes in automaticity due to practice, we measured performance after initial and continuous exposure to stimuli. Similar to previous findings, current results show a significant group × congruency interaction, evident beyond exposure level or magnitude type. That is, the DD group systematically showed larger Stroop effects. However, analysis of each exposure period showed that during initial exposure to stimuli the DD group showed larger Stroop effects in the perimeter and not in the area task. In contrast, during continuous exposure to stimuli no triple interaction was evident. It is concluded that both magnitudes are automatically processed. Nevertheless, individuals with DD are deficient in inhibiting irrelevant magnitude information in general and, specifically, struggle to inhibit salient area information after initial exposure to a perimeter comparison task. Accordingly, the findings support the assumption that DD involves a deficiency in multiple cognitive components, which include domain-specific and domain-general cognitive functions.
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Affiliation(s)
- Hili Eidlin-Levy
- Edmond J. Safra Brain Research Center for the Study of Learning Disabilities, Department of Learning Disabilities, University of Haifa, Haifa, Israel
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37
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The contributions of numerical acuity and non-numerical stimulus features to the development of the number sense and symbolic math achievement. Cognition 2017; 168:222-233. [DOI: 10.1016/j.cognition.2017.07.004] [Citation(s) in RCA: 42] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2016] [Revised: 07/06/2017] [Accepted: 07/07/2017] [Indexed: 01/29/2023]
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38
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Sokolowski HM, Fias W, Bosah Ononye C, Ansari D. Are numbers grounded in a general magnitude processing system? A functional neuroimaging meta-analysis. Neuropsychologia 2017; 105:50-69. [DOI: 10.1016/j.neuropsychologia.2017.01.019] [Citation(s) in RCA: 76] [Impact Index Per Article: 10.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2016] [Revised: 01/17/2017] [Accepted: 01/18/2017] [Indexed: 11/24/2022]
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The effect of visual parameters on neural activation during nonsymbolic number comparison and its relation to math competency. Neuroimage 2017; 159:430-442. [PMID: 28801254 DOI: 10.1016/j.neuroimage.2017.08.023] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2017] [Revised: 08/04/2017] [Accepted: 08/06/2017] [Indexed: 01/29/2023] Open
Abstract
Nonsymbolic numerical comparison task performance (whereby a participant judges which of two groups of objects is numerically larger) is thought to index the efficiency of neural systems supporting numerical magnitude perception, and performance on such tasks has been related to individual differences in math competency. However, a growing body of research suggests task performance is heavily influenced by visual parameters of the stimuli (e.g. surface area and dot size of object sets) such that the correlation with math is driven by performance on trials in which number is incongruent with visual cues. Almost nothing is currently known about whether the neural correlates of nonsymbolic magnitude comparison are also affected by visual congruency. To investigate this issue, we used functional magnetic resonance imaging (fMRI) to analyze neural activity during a nonsymbolic comparison task as a function of visual congruency in a sample of typically developing high school students (n = 36). Further, we investigated the relation to math competency as measured by the preliminary scholastic aptitude test (PSAT) in 10th grade. Our results indicate that neural activity was modulated by the ratio of the dot sets being compared in brain regions previously shown to exhibit an effect of ratio (i.e. left anterior cingulate, left precentral gyrus, left intraparietal sulcus, and right superior parietal lobe) when calculated from the average of congruent and incongruent trials, as it is in most studies, and that the effect of ratio within those regions did not differ as a function of congruency condition. However, there were significant differences in other regions in overall task-related activation, as opposed to the neural ratio effect, when congruent and incongruent conditions were contrasted at the whole-brain level. Math competency negatively correlated with ratio-dependent neural response in the left insula across congruency conditions and showed distinct correlations when split across conditions. There was a positive correlation between math competency in the right supramarginal gyrus during congruent trials and a negative correlation in the left angular gyrus during incongruent trials. Together, these findings support the idea that performance on the nonsymbolic comparison task relates to math competency and ratio-dependent neural activity does not differ by congruency condition. With regards to math competency, congruent and incongruent trials showed distinct relations between math competency and individual differences in ratio-dependent neural activity.
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Rinaldi L, Girelli L. Commentary: From 'sense of number' to 'sense of magnitude' - The role of continuous magnitudes in numerical cognition. Front Psychol 2017; 8:652. [PMID: 28515701 PMCID: PMC5413547 DOI: 10.3389/fpsyg.2017.00652] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2017] [Accepted: 04/12/2017] [Indexed: 11/21/2022] Open
Affiliation(s)
- Luca Rinaldi
- Department of Psychology, University of Milano-BicoccaMilan, Italy
- NeuroMI, Milan Center for NeuroscienceMilan, Italy
| | - Luisa Girelli
- Department of Psychology, University of Milano-BicoccaMilan, Italy
- NeuroMI, Milan Center for NeuroscienceMilan, Italy
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McCrink K, Shafto P, Barth H. The relationship between non-symbolic multiplication and division in childhood. Q J Exp Psychol (Hove) 2017; 70:686-702. [PMID: 26880261 PMCID: PMC5228418 DOI: 10.1080/17470218.2016.1151060] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Abstract
Children without formal education in addition and subtraction are able to perform multi-step operations over an approximate number of objects. Further, their performance improves when solving approximate (but not exact) addition and subtraction problems that allow for inversion as a shortcut (e.g., a + b - b = a). The current study examines children's ability to perform multi-step operations, and the potential for an inversion benefit, for the operations of approximate, non-symbolic multiplication and division. Children were trained to compute a multiplication and division scaling factor (*2 or /2, *4 or /4), and were then tested on problems that combined two of these factors in a way that either allowed for an inversion shortcut (e.g., 8*4/4) or did not (e.g., 8*4/2). Children's performance was significantly better than chance for all scaling factors during training, and they successfully computed the outcomes of the multi-step testing problems. They did not exhibit a performance benefit for problems with the a*b/b structure, suggesting that they did not draw upon inversion reasoning as a logical shortcut to help them solve the multi-step test problems.
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Affiliation(s)
- Koleen McCrink
- a Psychology Department , Barnard College, Columbia University , New York , NY , USA
| | - Patrick Shafto
- b Department of Mathematics and Computer Science , Rutgers University , Newark , NJ , USA
| | - Hilary Barth
- c Psychology Department , Wesleyan University , Middletown , CT , USA
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McCaskey U, von Aster M, O’Gorman Tuura R, Kucian K. Adolescents with Developmental Dyscalculia Do Not Have a Generalized Magnitude Deficit - Processing of Discrete and Continuous Magnitudes. Front Hum Neurosci 2017; 11:102. [PMID: 28373834 PMCID: PMC5357648 DOI: 10.3389/fnhum.2017.00102] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2016] [Accepted: 02/20/2017] [Indexed: 01/12/2023] Open
Abstract
The link between number and space has been discussed in the literature for some time, resulting in the theory that number, space and time might be part of a generalized magnitude system. To date, several behavioral and neuroimaging findings support the notion of a generalized magnitude system, although contradictory results showing a partial overlap or separate magnitude systems are also found. The possible existence of a generalized magnitude processing area leads to the question how individuals with developmental dyscalculia (DD), known for deficits in numerical-arithmetical abilities, process magnitudes. By means of neuropsychological tests and functional magnetic resonance imaging (fMRI) we aimed to examine the relationship between number and space in typical and atypical development. Participants were 16 adolescents with DD (14.1 years) and 14 typically developing (TD) peers (13.8 years). In the fMRI paradigm participants had to perform discrete (arrays of dots) and continuous magnitude (angles) comparisons as well as a mental rotation task. In the neuropsychological tests, adolescents with dyscalculia performed significantly worse in numerical and complex visuo-spatial tasks. However, they showed similar results to TD peers when making discrete and continuous magnitude decisions during the neuropsychological tests and the fMRI paradigm. A conjunction analysis of the fMRI data revealed commonly activated higher order visual (inferior and middle occipital gyrus) and parietal (inferior and superior parietal lobe) magnitude areas for the discrete and continuous magnitude tasks. Moreover, no differences were found when contrasting both magnitude processing conditions, favoring the possibility of a generalized magnitude system. Group comparisons further revealed that dyscalculic subjects showed increased activation in domain general regions, whilst TD peers activate domain specific areas to a greater extent. In conclusion, our results point to the existence of a generalized magnitude system in the occipito-parietal stream in typical development. The detailed investigation of spatial and numerical magnitude abilities in DD reveals that the deficits in number processing and arithmetic cannot be explained with a general magnitude deficiency. Our results further indicate that multiple neuro-cognitive components might contribute to the explanation of DD.
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Affiliation(s)
- Ursina McCaskey
- Center for MR-Research, University Children’s Hospital ZurichZurich, Switzerland
- Children’s Research Center, University Children’s Hospital ZurichZurich, Switzerland
| | - Michael von Aster
- Center for MR-Research, University Children’s Hospital ZurichZurich, Switzerland
- Children’s Research Center, University Children’s Hospital ZurichZurich, Switzerland
- Clinic for Child and Adolescent Psychiatry, German Red Cross HospitalsBerlin, Germany
- Neuroscience Center Zurich, University of Zurich and Swiss Federal Institute of Technology ZurichZurich, Switzerland
| | - Ruth O’Gorman Tuura
- Center for MR-Research, University Children’s Hospital ZurichZurich, Switzerland
- Children’s Research Center, University Children’s Hospital ZurichZurich, Switzerland
- Zurich Center for Integrative Human Physiology, University of ZurichZurich, Switzerland
| | - Karin Kucian
- Center for MR-Research, University Children’s Hospital ZurichZurich, Switzerland
- Children’s Research Center, University Children’s Hospital ZurichZurich, Switzerland
- Neuroscience Center Zurich, University of Zurich and Swiss Federal Institute of Technology ZurichZurich, Switzerland
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43
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Hesse PN, Schmitt C, Klingenhoefer S, Bremmer F. Preattentive Processing of Numerical Visual Information. Front Hum Neurosci 2017; 11:70. [PMID: 28261078 PMCID: PMC5313506 DOI: 10.3389/fnhum.2017.00070] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2016] [Accepted: 02/06/2017] [Indexed: 11/30/2022] Open
Abstract
Humans can perceive and estimate approximate numerical information, even when accurate counting is impossible e.g., due to short presentation time. If the number of objects to be estimated is small, typically around 1–4 items, observers are able to give very fast and precise judgments with high confidence—an effect that is called subitizing. Due to its speed and effortless nature subitizing has usually been assumed to be preattentive, putting it into the same category as other low level visual features like color or orientation. More recently, however, a number of studies have suggested that subitizing might be dependent on attentional resources. In our current study we investigated the potentially preattentive nature of visual numerical perception in the subitizing range by means of EEG. We presented peripheral, task irrelevant sequences of stimuli consisting of a certain number of circular patches while participants were engaged in a demanding, non-numerical detection task at the fixation point drawing attention away from the number stimuli. Within a sequence of stimuli of a given number of patches (called “standards”) we interspersed some stimuli of different numerosity (“oddballs”). We compared the evoked responses to visually identical stimuli that had been presented in two different conditions, serving as standard in one condition and as oddball in the other. We found significant visual mismatch negativity (vMMN) responses over parieto-occipital electrodes. In addition to the event-related potential (ERP) analysis, we performed a time-frequency analysis (TFA) to investigate whether the vMMN was accompanied by additional oscillatory processes. We found a concurrent increase in evoked theta power of similar strength over both hemispheres. Our results provide clear evidence for a preattentive processing of numerical visual information in the subitizing range.
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Affiliation(s)
- Philipp N Hesse
- Department of Neurophysics, Philipps-Universität Marburg Marburg, Germany
| | - Constanze Schmitt
- Department of Neurophysics, Philipps-Universität Marburg Marburg, Germany
| | - Steffen Klingenhoefer
- Department of Neurophysics, Philipps-Universität MarburgMarburg, Germany; Center for Molecular and Behavioral Neuroscience (CMBN), Rutgers UniversityNewark, NJ, USA
| | - Frank Bremmer
- Department of Neurophysics, Philipps-Universität Marburg Marburg, Germany
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Naughtin CK, Mattingley JB, Dux PE. Early information processing contributions to object individuation revealed by perception of illusory figures. J Neurophysiol 2016; 116:2513-2522. [PMID: 27605529 PMCID: PMC5133310 DOI: 10.1152/jn.00082.2016] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2016] [Accepted: 09/04/2016] [Indexed: 11/22/2022] Open
Abstract
To isolate multiple coherent objects from their surrounds, each object must be represented as a stable perceptual entity across both time and space. Recent theoretical and empirical work has proposed that this process of object individuation is a mid-level operation that emerges around 200-300 ms after stimulus onset. However, this hypothesis is based on paradigms that have potentially obscured earlier effects. Furthermore, no study to date has directly assessed whether object individuation occurs for task-irrelevant objects. In the present study we used electroencephalography (EEG) to measure the time course of individuation, for stimuli both within and outside the focus of attention, to assess the information processing stage at which object individuation arises for both types of objects. We developed a novel paradigm involving items defined by illusory contours, which allowed us to vary the number of to-be-individuated objects while holding the physical elements of the display constant (a design characteristic not present in earlier work). As early as 100 ms after stimulus onset, event-related potentials tracked the number of objects in the attended hemifield, but not those in the unattended hemifield. By contrast, both attended and unattended objects could be individuated at a later stage. Our findings challenge recent conceptualizations of the time course of object individuation and suggest that this process arises earlier for attended than unattended items, implying that voluntary spatial attention influences the time course of this operation.
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Affiliation(s)
- Claire K Naughtin
- School of Psychology, The University of Queensland, St Lucia, Queensland, Australia; and
| | - Jason B Mattingley
- School of Psychology, The University of Queensland, St Lucia, Queensland, Australia; and
- Queensland Brain Institute, The University of Queensland, St Lucia, Queensland, Australia
| | - Paul E Dux
- School of Psychology, The University of Queensland, St Lucia, Queensland, Australia; and
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Sensory-integration system rather than approximate number system underlies numerosity processing: A critical review. Acta Psychol (Amst) 2016; 171:17-35. [PMID: 27640140 DOI: 10.1016/j.actpsy.2016.09.003] [Citation(s) in RCA: 127] [Impact Index Per Article: 15.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2016] [Accepted: 09/09/2016] [Indexed: 01/29/2023] Open
Abstract
It is widely accepted that human and nonhuman species possess a specialized system to process large approximate numerosities. The theory of an evolutionarily ancient approximate number system (ANS) has received converging support from developmental studies, comparative experiments, neuroimaging, and computational modelling, and it is one of the most dominant and influential theories in numerical cognition. The existence of an ANS system is significant, as it is believed to be the building block of numerical development in general. The acuity of the ANS is related to future arithmetic achievements, and intervention strategies therefore aim to improve the ANS. Here we critically review current evidence supporting the existence of an ANS. We show that important shortcomings and confounds exist in the empirical studies on human and non-human animals as well as the logic used to build computational models that support the ANS theory. We conclude that rather than taking the ANS theory for granted, a more comprehensive explanation might be provided by a sensory-integration system that compares or estimates large approximate numerosities by integrating the different sensory cues comprising number stimuli.
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Abstract
While some researchers propose the existence of a special numerosity sense, others challenge this view and argue that numerosity is derived from low-level features as density information. Here, we used size adaptation to manipulate the apparent area size of an object set without changing its physical density. After size adaptation, two probe patches were shown, each of which contained a specific numerosity of dots. Subjects were required to report, which probe patch contained more dots. Numerosity perception was compared between conditions where probe patches were adapted to appear smaller or larger. Size adaptation affected numerosity perception in a logarithmic fashion, increasing with the numerosity in the probe patch. No changes in density perception were found after size adaptation. Data suggest that size and density information play only a minor role in the estimation of low numerosities. In stark contrast, high numerosities strongly depend on size and density information. The data reinforce recent claims of separate mechanism for the perception of low and high numerosities.
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47
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From “sense of number” to “sense of magnitude”: The role of continuous magnitudes in numerical cognition. Behav Brain Sci 2016; 40:e164. [PMID: 27530053 DOI: 10.1017/s0140525x16000960] [Citation(s) in RCA: 215] [Impact Index Per Article: 26.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
AbstractIn this review, we are pitting two theories against each other: the more accepted theory, the number sense theory, suggesting that a sense of number is innate and non-symbolic numerosity is being processed independently of continuous magnitudes (e.g., size, area, and density); and the newly emerging theory suggesting that (1) both numerosities and continuous magnitudes are processed holistically when comparing numerosities and (2) a sense of number might not be innate. In the first part of this review, we discuss the number sense theory. Against this background, we demonstrate how the natural correlation between numerosities and continuous magnitudes makes it nearly impossible to study non-symbolic numerosity processing in isolation from continuous magnitudes, and therefore, the results of behavioral and imaging studies with infants, adults, and animals can be explained, at least in part, by relying on continuous magnitudes. In the second part, we explain the sense of magnitude theory and review studies that directly demonstrate that continuous magnitudes are more automatic and basic than numerosities. Finally, we present outstanding questions. Our conclusion is that there is not enough convincing evidence to support the number sense theory anymore. Therefore, we encourage researchers not to assume that number sense is simply innate, but to put this hypothesis to the test and consider whether such an assumption is even testable in the light of the correlation of numerosity and continuous magnitudes.
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48
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Haslbeck JMB, Wood G, Witte M. Temporal dynamics of number-space interaction in line bisection: Comment on Cleland and Bull (2015). Q J Exp Psychol (Hove) 2015; 69:1239-42. [PMID: 26448100 DOI: 10.1080/17470218.2015.1095773] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
| | - Guilherme Wood
- a Department of Psychology , University of Graz , Graz , Austria.,b BioTechMed Graz , Graz , Austria
| | - Matthias Witte
- a Department of Psychology , University of Graz , Graz , Austria
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49
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Norris JE, McGeown WJ, Guerrini C, Castronovo J. Aging and the number sense: preserved basic non-symbolic numerical processing and enhanced basic symbolic processing. Front Psychol 2015; 6:999. [PMID: 26236269 PMCID: PMC4502343 DOI: 10.3389/fpsyg.2015.00999] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2015] [Accepted: 07/02/2015] [Indexed: 01/29/2023] Open
Abstract
Aging often leads to general cognitive decline in domains such as memory and attention. The effect of aging on numerical cognition, particularly on foundational numerical skills known as the number sense, is not well-known. Early research focused on the effect of aging on arithmetic. Recent studies have begun to investigate the impact of healthy aging on basic numerical skills, but focused on non-symbolic quantity discrimination alone. Moreover, contradictory findings have emerged. The current study aimed to further investigate the impact of aging on basic non-symbolic and symbolic numerical skills. A group of 25 younger (18-25) and 25 older adults (60-77) participated in non-symbolic and symbolic numerical comparison tasks. Mathematical and spelling abilities were also measured. Results showed that aging had no effect on foundational non-symbolic numerical skills, as both groups performed similarly [RTs, accuracy and Weber fractions (w)]. All participants showed decreased non-symbolic acuity (accuracy and w) in trials requiring inhibition. However, aging appears to be associated with a greater decline in discrimination speed in such trials. Furthermore, aging seems to have a positive impact on mathematical ability and basic symbolic numerical processing, as older participants attained significantly higher mathematical achievement scores, and performed significantly better on the symbolic comparison task than younger participants. The findings suggest that aging and its lifetime exposure to numbers may lead to better mathematical achievement and stronger basic symbolic numerical skills. Our results further support the observation that basic non-symbolic numerical skills are resilient to aging, but that aging may exacerbate poorer performance on trials requiring inhibitory processes. These findings lend further support to the notion that preserved basic numerical skills in aging may reflect the preservation of an innate, primitive, and embedded number sense.
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Affiliation(s)
- Jade E Norris
- Department of Psychology, University of Hull Hull, UK
| | - William J McGeown
- School of Psychological Sciences and Health, University of Strathclyde Glasgow, UK
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50
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DeWind NK, Adams GK, Platt ML, Brannon EM. Modeling the approximate number system to quantify the contribution of visual stimulus features. Cognition 2015; 142:247-65. [PMID: 26056747 DOI: 10.1016/j.cognition.2015.05.016] [Citation(s) in RCA: 127] [Impact Index Per Article: 14.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2014] [Revised: 04/13/2015] [Accepted: 05/15/2015] [Indexed: 01/29/2023]
Abstract
The approximate number system (ANS) subserves estimation of the number of items in a set. Typically, ANS function is assessed by requiring participants to compare the number of dots in two arrays. Accuracy is determined by the numerical ratio of the sets being compared, and each participant's Weber fraction (w) provides a quantitative index of ANS acuity. When making numerical comparisons, however, performance is also influenced by non-numerical features of the stimuli, such as the size and spacing of dots. Current models of numerosity comparison do not account for these effects and consequently lead to different estimates of w depending on the methods used to control for non-numerical features. Here we proffer a new model that teases apart the effects of ANS acuity from the effects of non-numerical stimulus features. The result is an estimate of w that is a more theoretically valid representation of numerical acuity and novel terms that denote the degree to which a participant's perception of number is affected by non-numerical features. We tested this model in a sample of 20 adults and found that, by correctly attributing errors due to non-numerical stimulus features, the w obtained was more reliable across different stimulus conditions. We found that although non-numerical features biased numerosity discriminations in all participants, number was the primary feature driving discriminations in most of them. Our findings support the idea that, while numerosity is a distinct visual quantity, the internal representation of number is tightly bound to the representation of other magnitudes. This tool for identifying the different effects of the numerical and non-numerical features of a stimulus has important implications not only for the behavioral investigation of the ANS, but also for the collection and analyses of neural data sets associated with ANS function.
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Affiliation(s)
- Nicholas K DeWind
- Center for Cognitive Neuroscience, Duke University, Durham, NC, USA; Department of Neurobiology, Duke University, Durham, NC, USA.
| | - Geoffrey K Adams
- Center for Cognitive Neuroscience, Duke University, Durham, NC, USA; Department of Neurobiology, Duke University, Durham, NC, USA
| | - Michael L Platt
- Center for Cognitive Neuroscience, Duke University, Durham, NC, USA; Department of Neurobiology, Duke University, Durham, NC, USA
| | - Elizabeth M Brannon
- Center for Cognitive Neuroscience, Duke University, Durham, NC, USA; Department of Psychology and Neuroscience, Duke University, Durham, NC, USA
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