DOI: 10.3724/SP.J.1042.2017.00810

Advances in Psychological Science (心理科学进展) 2017/25:5 PP.810-824

Evolutionary evidences of primitive mathematics ability in human beings

Mathematics ability is one of key advanced cognitive functions in human beings. Previous research provided numerous evidences in the evolutionary studies about mathematics ability, which is adaptively significance of the survival and reproduction of organisms. In recent years, the findings of comparative psychology have revealed that behavioral performance and brain physiological mechanism of primitive mathematics abilities of nonhuman animals are parallel to those of adults and infants in human. Furthermore, studies of molecular genetics also show that mathematics ability is hereditary. These findings provide further understandings on the nature and inherent developing mechanism of this capacity in human beings.

Key words:primitive mathematics ability,non-human animals,infant,neuralphysiological mechanism,evolutionary genetics

ReleaseDate:2017-05-31 14:49:40

胡林成. (2009). 数量模块的理论与实验研究(博士学位论文). 华东师范大学, 上海.

李红霞, 司继伟, 陈泽建, 张堂正. (2015). 人类的近似数量系统. 心理科学进展, 23, 562–570.

晏倩, 熊哲宏. (2006). 国外人类先天“数字模块”的研究现状及展望. 心理发展与教育, 22, 115–118.

杨红, 王芳, 周加仙, 赵晖. (2014). 数学学习的认知与脑机制研究成果对数学教育的启示. 教育发展研究, 37–43.

张勇. (2014). 超越进化心理学的理论困境(博士学位论文). 华东师范大学, 上海.

张真, 苏彦捷. (2007). 人类数能力的演化基础——数能力比较研究的启示. 心理科学进展, 15, 57–63.

Abramson, J. Z., Hernández-Lloreda, V., Call, J., & Colmenares, F. (2011). Relative quantity judgments in South American sea lions (Otaria flavescens). Animal Cognition, 14, 695–706.

Abramson, J. Z., Hernández-Lloreda, V., Call, J., & Colmenares, F. (2013). Relative quantity judgments in the beluga whale (Delphinapterus leucas) and the bottlenose dolphin (Tursiops truncatus). Behavioural Processes, 96, 11–19.

Addessi, E., Crescimbene, L., & Visalberghi, E. (2008). Food and token quantity discrimination in capuchin monkeys (Cebus apella). Animal Cognition, 11, 275–282.

Agrillo, C., & Beran, M. J. (2013). Number without language: Comparative psychology and the evolution of numerical cognition. Frontiers in Psychology, 4, 295.

Agrillo, C., Dadda, M., Serena, G., & Bisazza, A. (2009). Use of number by fish. PLoS One, 4, e4786.

Agrillo, C., Petrazzini, M. E. M., Piffer, L., Dadda, M., & Bisazza, A. (2012). A new training procedure for studying discrimination learning in fish. Behavioural Brain Research, 230, 343–348.

Agrillo, C., Piffer, L., Bisazza, A., & Butterworth, B. (2012). Evidence for two numerical systems that are similar in humans and guppies. PLoS One, 7, e31923.

Armstrong, N., Garland, A., & Burns, K. C. (2012). Memory for multiple cache locations and prey quantities in a food-hoarding songbird. Frontiers in Psychology, 3, 584.

Baker, J. M., Morath, J., Rodzon, K. S., & Jordan, K. E. (2012). A shared system of representation governing quantity discrimination in canids. Frontiers in Psychology, 3, 387.

Baker, J. M., Shivik, J., & Jordan, K. E. (2011). Tracking of food quantity by coyotes (Canis latrans). Behavioural Processes, 88, 72–75.

Bánszegi, O., Urrutia, A., Szenczi, P., & Hudson, R. (2016). More or less: Spontaneous quantity discrimination in the domestic cat. Animal Cognition, 19, 879–888.

Beran, M. J. (2012). Quantity judgments of auditory and visual stimuli by chimpanzees (Pan troglodytes). Journal of Experimental Psychology: Animal Behavior Processes, 38, 23–29.

Beran, M. J., Evans, T. A., Leighty, K. A., Harris, E. H., & Rice, D. (2008). Summation and quantity judgments of sequentially presented sets by capuchin monkeys (Cebus apella). American Journal of Primatology, 70, 191–194.

Beran, M. J., Perdue, B. M., Parrish, A. E., & Evans, T. A. (2012). Do social conditions affect capuchin monkeys' (Cebus apella) choices in a quantity judgment task? Frontiers in Psychology, 3, 492.

Berkay, D., Çavdaroğlu, B., & Balcı, F. (2016). Probabilistic numerical discrimination in mice. Animal Cognition, 19, 351–365.

Bisazza, A., Agrillo, C., & Lucon-Xiccato, T. (2014). Extensive training extends numerical abilities of guppies. Animal Cognition, 17, 1413–1419.

Burr, D., & Ross, J. (2008). A visual sense of number. Current Biology, 18, 425–428.

Cacchione, T., Hrubesch, C., & Call, J. (2014). Phylogenetic roots of quantity processing: Apes do not rely on object indexing to process quantities. Cognitive Development, 31, 79–95.

Cantlon, J. F. (2012). Math, monkeys, and the developing brain. Proceedings of the National Academy of Sciences of the United States of America, 109, 10725–10732.

Cantlon, J. F., & Brannon, E. M. (2005). Semantic congruity affects numerical judgments similarly in monkeys and humans. Proceedings of the National Academy of Sciences of the United States of America, 102, 16507–16511.

Cantlon, J. F., & Brannon, E. M. (2007a). How much does number matter to a monkey (Macaca mulatta)? Journal of Experimental Psychology: Animal Behavior Processes, 33, 32–41.

Cantlon, J. F., & Brannon, E. M. (2007b). Basic math in monkeys and college students. PLoS Biology, 5, e328.

Cantlon, J. F., Brannon, E. M., Carter, E. J., & Pelphrey, K. A. (2006). Functional imaging of numerical processing in adults and 4-y-old children. PLoS Biology, 4, e125.

Cantlon, J. F., Platt, M. L., & Brannon, E. M. (2009). Beyond the number domain. Trends in Cognitive Sciences, 13, 83–91.

Carazo, P., Fernández-Perea, R., & Font, E. (2012). Quantity estimation based on numerical cues in the Mealworm Beetle (Tenebrio molitor). Frontiers in Psychology, 3, 502.

Carazo, P., Font, E., Forteza-Behrendt, E., & Desfilis, E. (2009). Quantity discrimination in Tenebrio molitor: Evidence of numerosity discrimination in an invertebrate? Animal Cognition, 12, 463–470.

Carey, S., & Xu, F. (2001). Infants' knowledge of objects: beyond object files and object tracking. Cognition, 80, 179–213.

Clearfield, M. W. (2004). Infants' enumeration of dynamic displays. Cognitive Development, 19, 309–324.

Colby, C. L., Duhamel, J. R., & Goldberg, M. E. (1993). Ventral intraparietal area of the macaque: Anatomic location and visual response properties. Journal of Neurophysiology, 69, 902–914.

Coubart, A., Streri, A., de Hevia, M. D., & Izard, V. (2015). Crossmodal discrimination of 2 vs. 4 objects across touch and vision in 5-month-old infants. PLoS One, 10, e0120868.

Cronin, A. L. (2014). Ratio-dependent quantity discrimination in quorum sensing ants. Animal Cognition, 17, 1261–1268.

Dadda, M., Piffer, L., Agrillo, C., & Bisazza, A. (2009). Spontaneous number representation in mosquitofish. Cognition, 112, 343–348.

Dehaene, S. (2009). Origins of mathematical intuitions: The case of arithmetic. Annals of the New York Academy of Sciences, 1156, 232–259.

Feigenson, L. (2005). A double-dissociation in infants' representations of object arrays. Cognition, 95, B37–B48.

Feigenson, L. (2011). Predicting sights from sounds: 6-month-olds' intermodal numerical abilities. Journal of Experimental Child Psychology, 110, 347–361.

Feigenson, L., Carey, S., & Hauser, M. (2002). The representations underlying infants' choice of more: Object files versus analog magnitudes. Psychological Science, 13, 150–156.

Féron, J., Gentaz, E., & Streri, A. (2006). Evidence of amodal representation of small numbers across visuo- tactile modalities in 5-month-old infants. Cognitive Development, 21, 81–92.

Garland, A., Beran, M. J., McIntyre, J., & Low, J. (2014). Relative quantity judgments between discrete spatial arrays by chimpanzees (Pan troglodytes) and New Zealand robins (Petroica longipes). Journal of Comparative Psychology, 128, 307–317.

Garland, A., & Low, J. (2014a). Addition and subtraction in wild New Zealand robins. Behavioural Processes, 109, 103–110.

Garland, A., & Low, J. (2014b). Wild North Island Robins (Petroica longipes) respond to prey animacy. Animal Behavior and Cognition, 1, 352–367.

Garland, A., Low, J., & Burns, K. C. (2012). Large quantity discrimination by North Island robins (Petroica longipes). Animal Cognition, 15, 1129–1140.

Gimbert, F., Gentaz, E., Camos, V., & Mazens, K. (2016). Children's approximate number system in haptic modality. Perception, 45, 44–55.

Gómez-Laplaza, L. M., & Gerlai, R. (2011). Spontaneous discrimination of small quantities: Shoaling preferences in angelfish (Pterophyllum scalare). Animal Cognition, 14, 565–574.

González-Giraldo, Y., Rojas, J., Novoa, P., Mueller, S. T., Piper, B. J., Adan, A., & Forero, D. A. (2014). Functional polymorphisms in BDNF and COMT genes are associated with objective differences in arithmetical functioning in a sample of young adults. Neuropsychobiology, 70, 152–157.

Gordon, P. (2004). Numerical cognition without words: Evidence from Amazonia. Science, 306, 496–499.

Gross, H. J., Pahl, M., Si, A., Zhu, H., Tautz, J., & Zhang, S. W. (2009). Number-based visual generalisation in the honeybee. PLoS One, 4, e4263.

Halberda, J., & Feigenson, L. (2008). Developmental change in the acuity of the “number sense”: The approximate number system in 3-, 4-, 5-, and 6-year-olds and adults. Developmental Psychology, 44, 1457–1465.

Hare, B., Rosati, A., Kaminski, J., Bräuer, J., Call, J., & Tomasello, M. (2010). The domestication hypothesis for dogs' skills with human communication: A response to Udell et al. (2008) and Wynne et al. (2008). Animal Behaviour, 79, e1–e6.

Hauser, M. D., & Carey, S. (2003). Spontaneous representations of small numbers of objects by rhesus macaques: Examinations of content and format. Cognitive Psychology, 47, 367–401.

Hope, T., Stoianov, I., & Zorzi, M. (2010). Through neural stimulation to behavior manipulation: A novel method for analyzing dynamical cognitive models. Cognitive Science, 34, 406–433.

Hyde, D. C., & Mou, Y. (2016). Neural and behavioral signatures of core numerical abilities and early symbolic number development. In D. B. Berch, D. C. Geary, & K. Mann Koepke (Eds.), Development of mathematical cognition: Neural substrates and genetic influences (pp. 51–77). San Diego, CA: Academic Press.

Irie, N., & Hasegawa, T. (2012). Summation by Asian elephants (Elephas maximus). Behavioral Sciences, 2, 50–56.

Izard, V., Sann, C., Spelke, E. S., & Streri, A. (2009). Newborn infants perceive abstract numbers. Proceedings of the National Academy of Sciences of the United States of America, 106, 10382–10385.

Jones, S. M. (2012). Comparative studies of numerical cognition in nonhuman primates: From numerical comparison to arithmetic (Unpublished doctorial dissertation). Durham, North Carolina: Duke University.

Jones, S. M., & Brannon, E. M. (2012). Prosimian primates show ratio dependence in spontaneous quantity discriminations. Frontiers in Psychology, 3, 550.

Jones, S. M., Cantlon, J. F., Merritt, D. J., & Brannon, E. M. (2010). Context affects the numerical semantic congruity effect in rhesus monkeys (Macaca mulatta). Behavioural Processes, 83, 191–196.

Jordan, K. E., MacLean, E. L., & Brannon, E. M. (2006). Monkeys match sequentially presented sets with simultaneously presented arrays based on numerosity. Poster presented at the annual meeting of the Vision Sciences Society, Sarasota, FL.

Jordan, K. E., MacLean, E. L., & Brannon, E. M. (2008). Monkeys match and tally quantities across senses. Cognition, 108, 617–625.

Júlio-costa, A., Antunes, A. M., Lopes-silva, J. B., Moreira, B. C., Vianna, G. S., Wood, G., … Haase, V. G. (2013). Count on dopamine: Influences of COMT polymorphisms on numerical cognition. Frontiers in Psychology, 4, 531.

Kahneman, D., Treisman, A., & Gibbs, B. J. (1992). The reviewing of object files: Object-specific integration of information. Cognitive Psychology, 24, 175–219.

Kamijo, M., & Taniuchi, T. (2015). Acquisition and limited transfer of numerical discrimination of object stimuli in rats. The Psychological Record, 65, 289–300.

Kamkar, N. (2015). From primates to ants: Reviewing the evidence of numerical cognition in non-human species. Western Undergraduate Psychology Journal, 3, 1–11. Retrieved from htp://

Kobayashi, T., Hiraki, K., Mugitani, R., & Hasegawa, T. (2004). Baby arithmetic: One object plus one tone. Cognition, 91, B23–B34.

Krusche, P., Uller, C., & Dicke, U. (2010). Quantity discrimination in salamanders. Journal of Experimental Biology, 213, 1822–1828.

Libertus, M. E, & Brannon, E. M. (2010). Stable individual differences in number discrimination in infancy. Developmental Science, 13, 900–906.

Lindqvist, C., Lind, J., & Jensen, P. (2009). Effects of domestication on food deprivation-induced behaviour in Red Junglefowl, Gallus gallus, and White Leghorn layers. Animal Behaviour, 77, 893–899.

Lipton, J. S., & Spelke, E. S. (2004). Discrimination of large and small numerosities by human infants. Infancy, 5, 271–290.

McCrink, K., Spelke, E. S., Dehaene, S., & Pica, P. (2013). Non-symbolic halving in an Amazonian indigene group. Developmental Science, 16, 451–462.

Mehlis, M., Thünken, T., Bakker, T. C. M., & Frommen, J. G. (2015). Quantification acuity in spontaneous shoaling decisions of three-spined sticklebacks. Animal Cognition, 18, 1125–1131.

Merritt, D. J., MacLean, E. L., Crawford, J. C., & Brannon, E. M. (2011). Numerical rule-learning in ring-tailed lemurs (Lemur catta). Frontiers in Psychology, 2, 23.

Miletto Petrazzini, M. E. (2014). Trained quantity abilities in horses (Equus caballus): A preliminary investigation. Behavioral Sciences, 4, 213–225.

Mori, Y., & Koaze, A. (2013). Cognition of different length by Physarum polycephalum: Weber's law in an amoeboid organism. Mycoscience, 54, 426–428.

Nelson, X. J., & Jackson, R. R. (2012). The role of numerical competence in a specialized predatory strategy of an araneophagic spider. Animal Cognition, 15, 699–710.

Nieder, A. (2013). Coding of abstract quantity by ‘number neurons’ of the primate brain. Journal of Comparative Physiology A, 199, 1–16.

Nieder, A., Diester, I., & Tudusciuc, O. (2006). Temporal and spatial enumeration processes in the primate parietal cortex. Science, 313, 1431–1435.

Nieder, A., Freedman, D. J., & Miller, E. K. (2002). Representation of the quantity of visual items in the primate prefrontal cortex. Science, 297, 1708–1711.

Nieder, A., & Merten, K. (2007). A labeled-line code for small and large numerosities in the monkey prefrontal cortex. Journal of Neuroscience, 27, 5986–5993.

Nieder, A., & Miller, E. K. (2003). Coding of cognitive magnitude: compressed scaling of numerical information in the primate prefrontal cortex. Neuron, 37, 149–157.

Nieder, A., & Miller, E. K. (2004). A parieto-frontal network for visual numerical information in the monkey. Proceedings of the National Academy of Sciences of the United States of America, 101, 7457–7462.

Panteleeva, S., Reznikova, Z., & Vygonyailova, O. (2013). Quantity judgments in the context of risk/reward decision making in striped field mice: First “count,” then hunt. Frontiers in Psychology, 4, 53.

Pepperberg, I. M. (2012). Further evidence for addition and numerical competence by a Grey parrot (Psittacus erithacus). Animal Cognition, 15, 711–717.

Perdue, B. M., Talbot, C. F., Stone, A. M., & Beran, M. J. (2012). Putting the elephant back in the herd: elephant relative quantity judgments match those of other species. Animal Cognition, 15, 955–961.

Petrazzini, M. E. M., Agrillo, C., Izard, V., & Bisazza, A. (2015). Relative versus absolute numerical representation in fish: Can guppies represent "fourness"? Animal Cognition, 18, 1007–1017.

Piazza, M. (2010). Neurocognitive start-up tools for symbolic number representations. Trends in Cognitive Sciences, 14, 542–551.

Piazza, M., Izard, V., Pinel, P., Le Bihan, D., & Dehaene, S. (2004). Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron, 44, 547–555.

Piazza, M., Mechelli, A., Price, C. J., & Butterworth, B. (2006). Exact and approximate judgements of visual and auditory numerosity: An fMRI study. Brain Research, 1106, 177–188.

Piazza, M., Pica, P., Izard, V., Spelke, E. S., & Dehaene, S. (2013). Education enhances the acuity of the nonverbal approximate number system. Psychological Science, 24, 1037–1043.

Pica, P., Lemer, C., Izard, V., & Dehaene, S. (2004). Exact and approximate arithmetic in an Amazonian indigene group. Science, 306, 499–503.

Piffer, L., Petrazzini, M. E. M., & Agrillo, C. (2013). Large number discrimination in newborn fish. PLoS One, 8, e62466.

Reznikova, Z., & Ryabko, B. (2011). Numerical competence in animals, with an insight from ants. Behaviour, 148, 405–434.

Rugani, R., Cavazzana, A., Vallortigara, G., & Regolin, L. (2013). One, two, three, four, or is there something more? Numerical discrimination in day-old domestic chicks. Animal Cognition, 16, 557–564.

Rugani, R., Vallortigara, G., & Regolin, L. (2013). Numerical abstraction in young domestic chicks (Gallus gallus). PLoS One, 8, e65262.

Rugani, R., Vallortigara, G., & Regolin, L. (2015). The use of proportion by young domestic chicks (Gallus gallus). Animal Cognition, 18, 605–616.

Sawamura, H., Shima, K., & Tanji, J. (2002). Numerical representation for action in the parietal cortex of the monkey. Nature, 415, 918–922.

Sawamura, H., Shima, K., & Tanji, J. (2010). Deficits in action selection based on numerical information after inactivation of the posterior parietal cortex in monkeys. Journal of Neurophysiology, 104, 902–910.

Scarf, D., Hayne, H., & Colombo, M. (2011). Pigeons on par with primates in numerical competence. Science, 334, 1664.

Schleger, F., Landerl, K., Muenssinger, J., Draganova, R., Reinl, M., Kiefer-Schmidt, I., … Preissl, H. (2014). Magnetoencephalographic signatures of numerosity discrimination in fetuses and neonates. Developmental Neuropsychology, 39, 316–329.

Stancher, G., Rugani, R., Regolin, L., & Vallortigara, G. (2015). Numerical discrimination by frogs (Bombina orientalis). Animal Cognition, 18, 219–229.

Starr, A., Libertus, M. E., & Brannon, E. M. (2013). Number sense in infancy predicts mathematical abilities in childhood. Proceedings of the National Academy of Sciences of the United States of America, 110, 18116–18120.

Stoianov, I., & Zorzi, M. (2012). Emergence of a 'visual number sense' in hierarchical generative models. Nature Neuroscience, 15, 194–196.

Taniuchi, T., Sugihara, J., Wakashima, M., & Kamijo, M. (2016). Abstract numerical discrimination learning in rats. Learning & Behavior, 44, 122–136.

Tokita, M., Ashitani, Y., & Ishiguchi, A. (2013). Is approximate numerical judgment truly modality- independent? Visual, auditory, and cross-modal comparisons. Attention, Perception, & Psychophysics, 75, 1852–1861.

Tosto, M. G., Petrill, S. A., Halberda, J., Trzaskowski, M., Tikhomirova, T. N., Bogdanova, O. Y., … Kovas, Y. (2014). Why do we differ in number sense? Evidence from a genetically sensitive investigation. Intelligence, 43, 35–46.

van Loosbroek, E., & Smitsman, A. W. (1990). Visual perception of numerosity in infancy. Developmental Psychology, 26, 916–922.

vanMarle, K. (2013). Infants use different mechanisms to make small and large number ordinal judgments. Journal of Experimental Child Psychology, 114, 102–110.

vanMarle, K., & Wynn, K. (2011). Tracking and quantifying objects and non-cohesive substances. Developmental Science, 14, 502–515.

Vonk, J. (2014). Quantity matching by an orangutan (Pongo abelii). Animal Cognition, 17, 297–306.

Vonk, J., & Beran, M. J. (2012). Bears ‘count’ too: Quantity estimation and comparison in black bears, Ursus americanus. Animal Behaviour, 84, 231–238.

Vonk, J., Torgerson-White, L., McGuire, M., Thueme, M., Thomas, J., & Beran, M. J. (2014). Quantity estimation and comparison in western lowland gorillas (Gorilla gorilla gorilla). Animal Cognition, 17, 755–765.

Wood, J. N., & Spelke, E. S. (2005). Infants' enumeration of actions: Numerical discrimination and its signature limits. Developmental Science, 8, 173–181.

Wynn, K., Bloom, P., & Chiang, W. C. (2002). Enumeration of collective entities by 5-month-old infants. Cognition, 83, B55–B62.

Xu, F. (2003). Numerosity discrimination in infants: Evidence for two systems of representations. Cognition, 89, B15–B25.

Xu, F., & Arriaga, R. I. (2007). Number discrimination in 10-month-old infants. British Journal of Developmental Psychology, 25, 103–108.

Xu, F., Spelke, E. S., & Goddard, S. (2005). Number sense in human infants. Developmental Science, 8, 88–101.

Zebian, S., & Ansari, D. (2012). Differences between literates and illiterates on symbolic but not nonsymbolic numerical magnitude processing. Psychonomic Bulletin & Review, 19, 93–100.