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Cui Z, Hu Y, Wang X, Li C, Liu Z, Cui Z, Zhou X. Form perception is a cognitive correlate of the relation between subitizing ability and math performance. Cogn Process 2024; 25:321-331. [PMID: 38421459 DOI: 10.1007/s10339-024-01175-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Accepted: 01/16/2024] [Indexed: 03/02/2024]
Abstract
"Subitizing" defines a phenomenon whereby approximately four items can be quickly and accurately processed. Studies have shown the close association between subitizing and math performance, however, the mechanism for the association remains unclear. The present study was conducted to investigate whether form perception assessed on a serial figure matching task is a potential non-numerical mechanism between subitizing ability and math performance. Three-hundred and seventy-three Chinese primary school students completed four kinds of dot comparison tasks, serial figure matching task, math performance tasks (including three arithmetic computation tasks and math word problem task), and other cognitive tasks as their general cognitive abilities were observed as covariates. A series of hierarchical regression analyses showed that after controlling for age, gender, nonverbal matrix reasoning, and visual tracking, subitizing comparison (subitizing vs. subitizing, subitizing vs. estimation) still contributed to simple addition or simple subtraction but not to complex subtraction ability or math word problem. After taking form perception as an additional control variable, the predictive power of different dot comparison conditions disappeared. A path model also showed that form perception fully mediates the relation between numerosity comparison (within and beyond the subitizing range) and arithmetic performance. These findings support the claim that form perception is a non-numerical cognitive correlate of the relation between subitizing ability and math performance (especially arithmetic computation).
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Affiliation(s)
- Zhijun Cui
- State Key Laboratory of Cognitive Neuroscience and Learning & IDG/McGovern Institute of Brain Research, Beijing Normal University, Beijing, 100875, China
- Children's Health Care Center, Beijing Children's Hospital, Beijing, 100045, China
| | - Yuwei Hu
- State Key Laboratory of Cognitive Neuroscience and Learning & IDG/McGovern Institute of Brain Research, Beijing Normal University, Beijing, 100875, China
- Institute of Psychology, Chinese Academy of Sciences, Beijing, 100101, China
- Department of Psychology, University of Chinese Academy of Sciences, Beijing, 101408, China
| | - Xinnan Wang
- State Key Laboratory of Cognitive Neuroscience and Learning & IDG/McGovern Institute of Brain Research, Beijing Normal University, Beijing, 100875, China
| | - Chen Li
- College of Education, Hebei Normal University, Shijiazhuang, 050024, China
| | - Zhengkui Liu
- Institute of Psychology, Chinese Academy of Sciences, Beijing, 100101, China
- Department of Psychology, University of Chinese Academy of Sciences, Beijing, 101408, China
| | - Zhanling Cui
- College of Education, Hebei Normal University, Shijiazhuang, 050024, China.
| | - Xinlin Zhou
- State Key Laboratory of Cognitive Neuroscience and Learning & IDG/McGovern Institute of Brain Research, Beijing Normal University, Beijing, 100875, China.
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Messina A, Potrich D, Schiona I, Sovrano VA, Vallortigara G. The Sense of Number in Fish, with Particular Reference to Its Neurobiological Bases. Animals (Basel) 2021; 11:ani11113072. [PMID: 34827804 PMCID: PMC8614421 DOI: 10.3390/ani11113072] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2021] [Revised: 10/13/2021] [Accepted: 10/22/2021] [Indexed: 01/29/2023] Open
Abstract
Simple Summary The ability to deal with quantity, both discrete (numerosities) and continuous (spatial or temporal extent) developed from an evolutionarily conserved system for approximating numerical magnitude. Non-symbolic number cognition based on an approximate sense of magnitude has been documented in a variety of vertebrate species, including fish. Fish, in particular zebrafish, are widely used as models for the investigation of the genetics and molecular mechanisms of behavior, and thus may be instrumental to development of a neurobiology of number cognition. We review here the behavioural studies that have permitted to identify numerical abilities in fish, and the current status of the research related to the neurobiological bases of these abilities with special reference to zebrafish. Combining behavioural tasks with molecular genetics, molecular biology and confocal microscopy, a role of the retina and optic tectum in the encoding of continuous magnitude in larval zebrafish has been reported, while the thalamus and the dorso-central subdivision of pallium in the encoding of discrete magnitude (number) has been documented in adult zebrafish. Research in fish, in particular zebrafish, may reveal instrumental for identifying and characterizing the molecular signature of neurons involved in quantity discrimination processes of all vertebrates, including humans. Abstract It is widely acknowledged that vertebrates can discriminate non-symbolic numerosity using an evolutionarily conserved system dubbed Approximate Number System (ANS). Two main approaches have been used to assess behaviourally numerosity in fish: spontaneous choice tests and operant training procedures. In the first, animals spontaneously choose between sets of biologically-relevant stimuli (e.g., conspecifics, food) differing in quantities (smaller or larger). In the second, animals are trained to associate a numerosity with a reward. Although the ability of fish to discriminate numerosity has been widely documented with these methods, the molecular bases of quantities estimation and ANS are largely unknown. Recently, we combined behavioral tasks with molecular biology assays (e.g c-fos and egr1 and other early genes expression) showing that the thalamus and the caudal region of dorso-central part of the telencephalon seem to be activated upon change in numerousness in visual stimuli. In contrast, the retina and the optic tectum mainly responded to changes in continuous magnitude such as stimulus size. We here provide a review and synthesis of these findings.
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Affiliation(s)
- Andrea Messina
- Centre for Mind/Brain Sciences, University of Trento, 38068 Rovereto, Italy; (D.P.); (I.S.); (V.A.S.)
- Correspondence: (A.M.); (G.V.)
| | - Davide Potrich
- Centre for Mind/Brain Sciences, University of Trento, 38068 Rovereto, Italy; (D.P.); (I.S.); (V.A.S.)
| | - Ilaria Schiona
- Centre for Mind/Brain Sciences, University of Trento, 38068 Rovereto, Italy; (D.P.); (I.S.); (V.A.S.)
| | - Valeria Anna Sovrano
- Centre for Mind/Brain Sciences, University of Trento, 38068 Rovereto, Italy; (D.P.); (I.S.); (V.A.S.)
- Department of Psychology and Cognitive Science, University of Trento, 38068 Rovereto, Italy
| | - Giorgio Vallortigara
- Centre for Mind/Brain Sciences, University of Trento, 38068 Rovereto, Italy; (D.P.); (I.S.); (V.A.S.)
- Correspondence: (A.M.); (G.V.)
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Kreuter N, Christofzik N, Niederbremer C, Bollé J, Schluessel V. Counting on Numbers-Numerical Abilities in Grey Bamboo Sharks and Ocellate River Stingrays. Animals (Basel) 2021; 11:2634. [PMID: 34573600 PMCID: PMC8466846 DOI: 10.3390/ani11092634] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2021] [Revised: 08/05/2021] [Accepted: 08/18/2021] [Indexed: 11/29/2022] Open
Abstract
Over the last decade, studies examining the cognitive abilities of fish have increased, using a broad range of approaches. One of the foci has been to test the ability of fish to discriminate quantities of items and to determine whether fish can solve tasks solely on the basis of numerical information. This study is the first to investigate this ability in two elasmobranch species. All animals were trained in two-alternative forced-choice visual experiments and then examined in transfer tests, to determine if previously gained knowledge could be applied to new tasks. Results show that the grey bamboo shark (Chiloscyllium griseum) and the ocellate river stingray (Potamotrygon motoro) can discriminate quantities based on numerical information alone, while continuous variables were controlled for. Furthermore, the data indicates that similar magnitudes and limits for quantity discrimination exist as in other animals. However, the high degree of intraspecific variation that was observed as well as the low rate of animals proving to be successful suggest that the ability to discriminate quantities may not be as important to these species as to some other vertebrate and invertebrate species tested so far.
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Affiliation(s)
| | | | | | | | - Vera Schluessel
- Institute of Zoology, University of Bonn, Poppelsdorfer Schloss, Meckenheimerallee 169, 53115 Bonn, Germany; (N.K.); (N.C.); (C.N.); (J.B.)
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4
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The Evolutionary History of Brains for Numbers. Trends Cogn Sci 2021; 25:608-621. [PMID: 33926813 DOI: 10.1016/j.tics.2021.03.012] [Citation(s) in RCA: 24] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2021] [Revised: 03/23/2021] [Accepted: 03/24/2021] [Indexed: 11/21/2022]
Abstract
Humans and other animals share a number sense', an intuitive understanding of countable quantities. Having evolved independent from one another for hundreds of millions of years, the brains of these diverse species, including monkeys, crows, zebrafishes, bees, and squids, differ radically. However, in all vertebrates investigated, the pallium of the telencephalon has been implicated in number processing. This suggests that properties of the telencephalon make it ideally suited to host number representations that evolved by convergent evolution as a result of common selection pressures. In addition, promising candidate regions in the brains of invertebrates, such as insects, spiders, and cephalopods, can be identified, opening the possibility of even deeper commonalities for number sense.
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Caicoya AL, Colell M, Holland R, Ensenyat C, Amici F. Giraffes go for more: a quantity discrimination study in giraffes (Giraffa camelopardalis). Anim Cogn 2020; 24:483-495. [PMID: 33128196 DOI: 10.1007/s10071-020-01442-8] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2020] [Revised: 10/01/2020] [Accepted: 10/14/2020] [Indexed: 02/07/2023]
Abstract
Many species, including humans, rely on an ability to differentiate between quantities to make decisions about social relationships, territories, and food. This study is the first to investigate whether giraffes (Giraffa camelopardalis) are able to select the larger of two sets of quantities in different conditions, and how size and density affect these decisions. In Task 1, we presented five captive giraffes with two sets containing a different quantity of identical foods items. In Tasks 2 and 3, we also modified the size and density of the food reward distribution. The results showed that giraffes (i) can successfully make quantity judgments following Weber's law, (ii) can reliably rely on size to maximize their food income, and (iii) are more successful when comparing sparser than denser distributions. More studies on different taxa are needed to understand whether specific selective pressures have favored the evolution of these skills in certain taxa.
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Affiliation(s)
- Alvaro L Caicoya
- Department of Clinical Psychology and Psychobiology, Faculty of Psychology, University of Barcelona, Barcelona, Spain. .,Institute of Neurosciences, University of Barcelona, Barcelona, Spain.
| | - Montserrat Colell
- Department of Clinical Psychology and Psychobiology, Faculty of Psychology, University of Barcelona, Barcelona, Spain.,Institute of Neurosciences, University of Barcelona, Barcelona, Spain
| | | | | | - Federica Amici
- Behavioral Ecology Research Group, Institute of Biology, University of Leipzig, Leipzig, Germany.,Research Group "Primate Behavioural Ecology", Department of Human Behavior, Ecology and Culture, Max Planck Institute for Evolutionary Anthropology, Leipzig, Germany
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Cheyette SJ, Piantadosi ST. A unified account of numerosity perception. Nat Hum Behav 2020; 4:1265-1272. [PMID: 32929205 DOI: 10.1038/s41562-020-00946-0] [Citation(s) in RCA: 32] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2019] [Accepted: 08/07/2020] [Indexed: 01/29/2023]
Abstract
People can identify the number of objects in sets of four or fewer items with near-perfect accuracy but exhibit linearly increasing error for larger sets. Some researchers have taken this discontinuity as evidence of two distinct representational systems. Here, we present a mathematical derivation showing that this behaviour is an optimal representation of cardinalities under a limited informational capacity, indicating that this behaviour can emerge from a single system. Our derivation predicts how the amount of information accessible to viewers should influence the perception of quantity for both large and small sets. In a series of four preregistered experiments (N = 100 each), we varied the amount of information accessible to participants in number estimation. We find tight alignment between the model and human performance for both small and large quantities, implicating efficient representation as the common origin behind key phenomena of human and animal numerical cognition.
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Quantity discrimination in angelfish, Pterophyllum scalare: a novel approach with food as the discriminant. Anim Behav 2018. [DOI: 10.1016/j.anbehav.2018.06.001] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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8
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Capuchin monkeys (Cebus apella) treat small and large numbers of items similarly during a relative quantity judgment task. Psychon Bull Rev 2018; 23:1206-13. [PMID: 26689808 DOI: 10.3758/s13423-015-0986-1] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
A key issue in understanding the evolutionary and developmental emergence of numerical cognition is to learn what mechanism(s) support perception and representation of quantitative information. Two such systems have been proposed, one for dealing with approximate representation of sets of items across an extended numerical range and another for highly precise representation of only small numbers of items. Evidence for the first system is abundant across species and in many tests with human adults and children, whereas the second system is primarily evident in research with children and in some tests with non-human animals. A recent paper (Choo & Franconeri, Psychonomic Bulletin & Review, 21, 93-99, 2014) with adult humans also reported "superprecise" representation of small sets of items in comparison to large sets of items, which would provide more support for the presence of a second system in human adults. We first presented capuchin monkeys with a test similar to that of Choo and Franconeri in which small or large sets with the same ratios had to be discriminated. We then presented the same monkeys with an expanded range of comparisons in the small number range (all comparisons of 1-9 items) and the large number range (all comparisons of 10-90 items in 10-item increments). Capuchin monkeys showed no increased precision for small over large sets in making these discriminations in either experiment. These data indicate a difference in the performance of monkeys to that of adult humans, and specifically that monkeys do not show improved discrimination performance for small sets relative to large sets when the relative numerical differences are held constant.
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DeLong CM, Barbato S, O’Leary T, Wilcox KT. Small and large number discrimination in goldfish (Carassius auratus) with extensive training. Behav Processes 2017; 141:172-183. [DOI: 10.1016/j.beproc.2016.11.011] [Citation(s) in RCA: 31] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2016] [Revised: 11/21/2016] [Accepted: 11/23/2016] [Indexed: 11/26/2022]
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Gómez-Laplaza LM, Caicoya ÁL, Gerlai R. Quantity discrimination in angelfish (Pterophyllum scalare) is maintained after a 30-s retention interval in the large but not in the small number range. Anim Cogn 2017. [PMID: 28620776 DOI: 10.1007/s10071-017-1104-8] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
Abstract
The ability to discriminate between sets that differ in the number of elements can be useful in different contexts and may have survival and fitness consequences. As such, numerical/quantity discrimination has been demonstrated in a diversity of animal species. In the laboratory, this ability has been analyzed, for example, using binary choice tests. Furthermore, when the different number of items first presented to the subjects are subsequently obscured, i.e., are not visible at the moment of making a choice, the task requires memory for the size of the sets. In previous work, angelfish (Pterophyllum scalare) have been found to be able to discriminate shoals differing in the number of shoal members both in the small (less than 4) and the large (4 or more) number range, and they were able to perform well even when a short memory retention interval (2-15 s) was imposed. In the current study, we increased the retention interval to 30 s during which the shoals to choose between were obscured, and investigated whether angelfish could show preference for the larger shoal they saw before this interval. Subjects were faced with a discrimination between numerically small shoals (≤4 fish) and also between numerically large (≥4 fish) shoals of conspecifics. We found angelfish not to be able to remember the location of larger versus smaller shoals in the small number range, but to exhibit significant memory for the larger shoal in the large number range as long as the ratio between these shoals was at least 2:1. These results, together with prior findings, suggest the existence of two separate quantity estimation systems, the object file system for small number of items that does not work with the longer retention interval and the analogue magnitude system for larger number of items that does.
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Affiliation(s)
- Luis M Gómez-Laplaza
- Department of Psychology, University of Oviedo, Plaza de Feijoo s/n, 33003, Oviedo, Spain.
| | - Álvaro L Caicoya
- Department of Psychology, University of Oviedo, Plaza de Feijoo s/n, 33003, Oviedo, Spain
| | - Robert Gerlai
- Department of Psychology, University of Toronto Mississauga, 3359 Mississauga Road North, Mississauga, ON, L5L 1C6, Canada
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Agrillo C, Bisazza A. Understanding the origin of number sense: a review of fish studies. Philos Trans R Soc Lond B Biol Sci 2017; 373:20160511. [PMID: 29292358 PMCID: PMC5784038 DOI: 10.1098/rstb.2016.0511] [Citation(s) in RCA: 57] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 08/11/2017] [Indexed: 02/02/2023] Open
Abstract
The ability to use quantitative information is thought to be adaptive in a wide range of ecological contexts. For nearly a century, the numerical abilities of mammals and birds have been extensively studied using a variety of approaches. However, in the last two decades, there has been increasing interest in investigating the numerical abilities of teleosts (i.e. a large group of ray-finned fish), mainly due to the practical advantages of using fish species as models in laboratory research. Here, we review the current state of the art in this field. In the first part, we highlight some potential ecological functions of numerical abilities in fish and summarize the existing literature that demonstrates numerical abilities in different fish species. In many cases, surprising similarities have been reported among the numerical performance of mammals, birds and fish, raising the question as to whether vertebrates' numerical systems have been inherited from a common ancestor. In the second part, we will focus on what we still need to investigate, specifically the research fields in which the use of fish would be particularly beneficial, such as the genetic bases of numerical abilities, the development of these abilities and the evolutionary foundation of vertebrate number sense.This article is part of a discussion meeting issue 'The origins of numerical abilities'.
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Affiliation(s)
- Christian Agrillo
- Department of General Psychology, University of Padova, Via Venezia 8, Padova 35131, Italy
| | - Angelo Bisazza
- Department of General Psychology, University of Padova, Via Venezia 8, Padova 35131, Italy
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Agrillo C, Miletto Petrazzini ME, Bisazza A. Numerical abilities in fish: A methodological review. Behav Processes 2017; 141:161-171. [PMID: 28167200 DOI: 10.1016/j.beproc.2017.02.001] [Citation(s) in RCA: 42] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2016] [Revised: 01/30/2017] [Accepted: 02/01/2017] [Indexed: 12/01/2022]
Abstract
The ability to utilize numerical information can be adaptive in a number of ecological contexts including foraging, mating, parental care, and anti-predator strategies. Numerical abilities of mammals and birds have been studied both in natural conditions and in controlled laboratory conditions using a variety of approaches. During the last decade this ability was also investigated in some fish species. Here we reviewed the main methods used to study this group, highlighting the strengths and weaknesses of each of the methods used. Fish have only been studied under laboratory conditions and among the methods used with other species, only two have been systematically used in fish-spontaneous choice tests and discrimination learning procedures. In the former case, the choice between two options is observed in a biologically relevant situation and the degree of preference for the larger/smaller group is taken as a measure of the capacity to discriminate the two quantities (e.g., two shoals differing in number). In discrimination learning tasks, fish are trained to select the larger or the smaller of two sets of abstract objects, typically two-dimensional geometric figures, using food or social companions as reward. Beyond methodological differences, what emerges from the literature is a substantial similarity of the numerical abilities of fish with those of other vertebrates studied.
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Affiliation(s)
| | | | - Angelo Bisazza
- Department of General Psychology, University of Padova, Italy
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Lucon-Xiccato T, Dadda M. Individual guppies differ in quantity discrimination performance across antipredator and foraging contexts. Behav Ecol Sociobiol 2016. [DOI: 10.1007/s00265-016-2231-y] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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15
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Gómez-Laplaza LM, Gerlai R. Short-Term Memory Effects on Crossing the Boundary: Discrimination between Large and Small Quantities in Angelfish (Pterophyllum scalare). PLoS One 2016; 11:e0162923. [PMID: 27683275 PMCID: PMC5040265 DOI: 10.1371/journal.pone.0162923] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2016] [Accepted: 08/30/2016] [Indexed: 11/18/2022] Open
Abstract
Rudimentary quantification abilities are found in numerous animal species and in human infants all demonstrating the ability to discriminate between quantities differing in numerical size. An open question is whether individuals rely on different underlying systems to discriminate between large (analogue magnitude system (AMS) for number of items exceeding 3) and small quantities (object-file system (OFS) for number of items below 4), or they use only one system (AMS) for the entire number range. The two-system hypothesis has been supported by finding reduced ability to discriminate between quantities that cross the large-small boundary in several species. Recently, the role of cognitive representation, i.e., memory, in quantity discrimination has also been recognized. Here, we investigated whether angelfish can discriminate quantities across the boundary under two memory conditions. In a binary choice test, single angelfish were allowed to see groups (shoals) of conspecifics of different numerical size on the two sides of their test tank. In Experiment 1, their choice was recorded after a 2-sec retention interval during which shoal size information was unavailable. Angelfish were able to discriminate the larger shoal across the boundary when the shoals differed by a 2:1 or higher ratio, but not when the ratio was lower. In Experiment 2, however, with a 15-sec retention interval, angelfish could only detect a four-fold difference in ratio but failed to detect a three- or a two-fold difference across the boundary. These results suggest that angelfish can remember smaller differences for a short (2 sec) but not for a longer (15 sec) period. Together with previous findings, the current results support the idea that angelfish use two distinct systems for representing quantity, but they may recruit the AMS even for the small number range under some circumstances, e.g., when higher memory demand is imposed by a greater retention interval.
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Affiliation(s)
| | - Robert Gerlai
- Department of Psychology, University of Toronto Mississauga, Mississauga, Canada
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16
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Gatto E, Lucon-Xiccato T, Savaşçı BB, Dadda M, Bisazza A. Experimental setting affects the performance of guppies in a numerical discrimination task. Anim Cogn 2016; 20:187-198. [PMID: 27658676 DOI: 10.1007/s10071-016-1037-7] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2016] [Revised: 09/13/2016] [Accepted: 09/15/2016] [Indexed: 02/04/2023]
Abstract
A recent study found that guppies (Poecilia reticulata) can be trained to discriminate 4 versus 5 objects, a numerical discrimination typically achieved only by some mammals and birds. In that study, guppies were required to discriminate between two patches of small objects on the bottom of the tank that they could remove to find a food reward. It is not clear whether this species possesses exceptional numerical accuracy compared with the other ectothermic vertebrates or whether its remarkable performance was due to a specific predisposition to discriminate between differences in the quality of patches while foraging. To disentangle these possibilities, we trained guppies to the same numerical discriminations with a more conventional two-choice discrimination task. Stimuli were sets of dots presented on a computer screen, and the subjects received a food reward upon approaching the set with the larger numerosity. Though the cognitive problem was identical in the two experiments, the change in the experimental setting led to a much poorer performance as most fish failed even the 2 versus 3 discrimination. In four additional experiments, we varied the duration of the decision time, the type of stimuli, the length of training, and whether correction was allowed in order to identify the factors responsible for the difference. None of these parameters succeeded in increasing the performance to the level of the previous study, although the group trained with three-dimensional stimuli learned the easiest numerical task. We suggest that the different results with the two experimental settings might be due to constraints on learning and that guppies might be prepared to accurately estimate patch quality during foraging but not to learn an abstract stimulus-reward association.
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Affiliation(s)
- Elia Gatto
- Department of General Psychology, University of Padova, Padova, Italy.
| | | | - Beste Başak Savaşçı
- Department of Biology, Faculty of Science, Ankara University, Ankara, Turkey
| | - Marco Dadda
- Department of General Psychology, University of Padova, Padova, Italy
| | - Angelo Bisazza
- Department of General Psychology, University of Padova, Padova, Italy
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17
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Cognitive and brain systems underlying early mathematical development. PROGRESS IN BRAIN RESEARCH 2016; 227:75-103. [PMID: 27339009 DOI: 10.1016/bs.pbr.2016.03.008] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
We review current debate regarding the core competencies that support early mathematics learning, focusing on the contributions of the inherent system for representing approximate magnitudes, and domain-general systems that facilitate learning across academic domains. The latter include the executive control system that enables explicit processing of quantitative symbols, such as Arabic numerals, and the logical problem-solving abilities (intelligence) that facilitate learning the relations among numerals. The neural systems that underlie these abilities, as related to mathematical learning, are also discussed, albeit briefly. We place the contributions of inherent quantitative abilities and domain-general mechanisms in an evolutionary context and provide some discussion as to how they interact during the learning of evolutionarily novel mathematics.
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Dadda M, Agrillo C, Bisazza A, Brown C. Laterality enhances numerical skills in the guppy, Poecilia reticulata. Front Behav Neurosci 2015; 9:285. [PMID: 26578915 PMCID: PMC4620144 DOI: 10.3389/fnbeh.2015.00285] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2015] [Accepted: 10/09/2015] [Indexed: 11/17/2022] Open
Abstract
It has been hypothesized that cerebral lateralization can significantly enhance cognition and that this was one of the primary selective forces shaping its wide-spread evolution amongst vertebrate taxa. Here, we tested this hypothesis by examining the link between cerebral lateralization and numerical discrimination. Guppies, Poecilia reticulata, were sorted into left, right and non-lateralized groups using a standard mirror test and their numerical discrimination abilities tested in both natural shoal choice and abstract contexts. Our results show that strongly lateralized guppies have enhanced numerical abilities compared to non-lateralized guppies irrespective of context. These data provide further credence to the notion that cerebral lateralization can enhance cognitive efficiency.
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Affiliation(s)
- Marco Dadda
- Department of General Psychology, University of PadovaPadova, Italy
- Centro di Neuroscienze Cognitive, University of PadovaPadova, Italy
| | - Christian Agrillo
- Department of General Psychology, University of PadovaPadova, Italy
- Centro di Neuroscienze Cognitive, University of PadovaPadova, Italy
| | - Angelo Bisazza
- Department of General Psychology, University of PadovaPadova, Italy
- Centro di Neuroscienze Cognitive, University of PadovaPadova, Italy
| | - Culum Brown
- Department of Biological Sciences, Macquarie UniversitySydney, NSW, Australia
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Quantification acuity in spontaneous shoaling decisions of three-spined sticklebacks. Anim Cogn 2015; 18:1125-31. [PMID: 26099740 DOI: 10.1007/s10071-015-0884-y] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2014] [Revised: 05/28/2015] [Accepted: 06/08/2015] [Indexed: 10/23/2022]
Abstract
The ability to discriminate between different quantities is widespread throughout the animal kingdom, and the underlying mechanisms of quantity discrimination are currently intensely discussed. In contrast, questions elucidating the limits of quantity estimation received rather little attention so far. Here, we examined fine-tuned quantity estimation in the three-spined stickleback (Gasterosteus aculeatus) in a natural context, i.e. during shoaling decisions. Wild-caught focal fish were given the spontaneous choice between two shoals which differed in group size by 1 fish (0 vs. 1, 1 vs. 2, 2 vs. 3, 3 vs. 4, 4 vs. 5, 5 vs. 6 and 6 vs. 7), based on visual assessment. The results show that sticklebacks generally prefer to shoal with the larger group. They discriminated numerical contrasts up to 6 versus 7, equalling a numerical ratio of 0.86. Preference patterns followed Weber's law, i.e. decreased with increasing numerical ratio. This pattern was found across all numerical conditions as well as within the small number range (ranging from 1 vs. 2 to 3 vs. 4). The results suggest that wild-caught three-spined sticklebacks are spontaneously able (i.e. without prior learning) to detect subtle differences in shoal sizes. Further, they confirm findings of previous studies highlighting the contribution of the analogue magnitude system to quantity estimation in fishes.
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Miletto Petrazzini M, Agrillo C. Turning to the larger shoal: are there individual differences in small- and large-quantity discrimination of guppies? ETHOL ECOL EVOL 2015. [DOI: 10.1080/03949370.2015.1029011] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Miletto Petrazzini ME, Agrillo C, Izard V, Bisazza A. Relative versus absolute numerical representation in fish: Can guppies represent “fourness”? Anim Cogn 2015; 18:1007-17. [DOI: 10.1007/s10071-015-0868-y] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2014] [Revised: 03/26/2015] [Accepted: 03/28/2015] [Indexed: 10/23/2022]
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Trained Quantity Abilities in Horses (Equus caballus): A Preliminary Investigation. Behav Sci (Basel) 2014; 4:213-225. [PMID: 25379278 PMCID: PMC4219264 DOI: 10.3390/bs4030213] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2014] [Revised: 07/11/2014] [Accepted: 07/15/2014] [Indexed: 11/29/2022] Open
Abstract
Once believed to be a human prerogative, the capacity to discriminate between quantities now has also been reported in several vertebrates. To date, only two studies investigated numerical abilities in horses (Equus caballus) but reported contrasting data. To assess whether horses can be trained to discriminate between quantities, I have set up a new experimental protocol using operant conditioning. One adult female was trained to discriminate between 1 and 4 (Test 1) in three different conditions: non-controlled continuous variables (numerical and continuous quantities that co-vary with number are simultaneously available), 50% controlled continuous variables (intermediate condition), and 100% controlled continuous variables (only numerical information available). The subject learned the discrimination in all conditions, showing the capacity to process numerical information. When presented with a higher numerical ratio (2 vs. 4, Test 2), the subject still discriminated between the quantities but its performance was statistically significant only in the non-controlled condition, suggesting that the subject used multiple cues in presence of a more difficult discrimination. On the whole, the results here reported encourage the use of this experimental protocol as a valid tool to investigate the capacity to process numerical and continuous quantities in horses in future research.
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Bisazza A, Agrillo C, Lucon-Xiccato T. Extensive training extends numerical abilities of guppies. Anim Cogn 2014; 17:1413-9. [PMID: 24859818 DOI: 10.1007/s10071-014-0759-7] [Citation(s) in RCA: 55] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2014] [Revised: 05/07/2014] [Accepted: 05/13/2014] [Indexed: 11/28/2022]
Abstract
Recent studies on animal mathematical abilities suggest that all vertebrates show comparable abilities when they are given spontaneous preference tests, such as selecting the larger number of food items, but that mammals and birds generally achieve much better performance than fish when tested with training procedures. At least part of these differences might be due to the fact that fish are usually trained with only one or two dozen trials while extensive training, sometimes with thousands of trials, is normally performed in studies of mammals and birds. To test this hypothesis, female guppies were trained on four consecutive numerical discriminations of increasing difficulty (from 2 vs. 3 to 5 vs. 6 items), with up to 120 trials with each discrimination. Five out of eight subjects discriminated all contrasts up to 4 versus 5 objects at levels significantly better than chance, a much higher limit than the 2 versus 3 limit previously reported in studies that provided fish with only short training sequences. Our findings indicate that the difference in numerical cognition between teleosts and warm-blooded vertebrates might be smaller than previously supposed.
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Affiliation(s)
- Angelo Bisazza
- Department of General Psychology, University of Padova, Via Venezia 8, 35131, Padua, Italy
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Agrillo C, Bisazza A. Spontaneous versus trained numerical abilities. A comparison between the two main tools to study numerical competence in non-human animals. J Neurosci Methods 2014; 234:82-91. [PMID: 24793399 DOI: 10.1016/j.jneumeth.2014.04.027] [Citation(s) in RCA: 80] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2013] [Revised: 04/23/2014] [Accepted: 04/24/2014] [Indexed: 01/29/2023]
Abstract
A large body of experimental evidence shows that animals as diverse as mammals, birds, and fish are capable of processing numerical information. Considerable differences have been reported in some cases among species and a wide debate currently surrounds the issue of whether all vertebrates share the same numerical systems or not. Part of the problem is due to the fact that these studies often use different methods, a circumstance that potentially introduces confounding factors in a comparative analysis. In most studies, two main methodological approaches have been used: spontaneous choice tests and training procedures. The former approach consists of presenting to the subjects two groups of biologically-relevant stimuli (e.g., food items or social companions) differing in numerosity with the assumption that if they are able to discriminate between the two quantities, they are expected to spontaneously select the larger/smaller quantity. In the latter approach, subjects undergo extensive training in which some neutral stimuli (e.g., a quantity of dots) are associated with a reward and the capacity to learn a numerical rule is taken as evidence of numerical abilities. We review the literature on this topic, highlighting the relevance, and potential weaknesses in controlling confounding factors obtained with either approach.
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Affiliation(s)
| | - Angelo Bisazza
- Department of General Psychology, University of Padova, Italy
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