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McCrink, K., & Spelke, E. S. (2016). Non-symbolic division in childhood. Journal of Experimental Child Psychology, 142, 66–82.

McCrink, K., Spelke, E. S., Dehaene, S., & Pica, P. (2013). Non-symbolic halving in an Amazonian indigene group. Developmental Science, 16(3), 451–462.

Scarf, D., Hayne, H., & Colombo, M. (2011). Pigeons on par with primates in numerical competence. Science, 334(6063), 1664–1664.

Мозговые субстраты, отвечающие за системы приблизительных количеств и точных чисел

Cohen Kadosh, R., Henik, A., Rubinsten, O., Mohr, H., Dori, H., van de Ven, V., … Linden, D. E. J. (2005). Are numbers special? The comparison systems of the human brain investigated by fMRI. Neuropsychologia, 43, 1238–1248.

Пространственно-числовые ассоциации ответных реакций (SNARC)

Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122(3), 371–396.

Tversky, B., Kugelmass, S., & Winter, A. (1991). Cross-cultural and developmental trends in graphic productions. Cognitive Psychology, 23(4), 515–557.

Бо́льшая чувствительность к меньшим значениям (закон Вебера – Фехнера)

Cantlon, J. F., Platt, M. L., & Brannon, E. M. (2009). Beyond the number domain. Trends in Cognitive Sciences, 13(2), 83–91.

Бо́льшая чувствительность к меньшим значениям в языке

Talmy, L. (1983). How language structures space. In Spatial orientation (pp. 225–282). Boston, MA: Springer.

Анализ числовой информации в культурах, не имеющих названий для чисел больше трех

Frank, M. C., Everett, D. L., Fedorenko, E., & Gibson, E. (2008). Number as a cognitive technology: Evidence from Pirahã language and cognition. Cognition, 108(3), 819–824.

Gordon, P. (2004). Numerical cognition without words: Evidence from Amazonia. Science, 306(5695), 496–499.

Pica, P., Lemer, C., Izard, V., & Dehaene, S. (2004). Exact and approximate arithmetic in an Amazonian indigene group. Science, 306(5695), 499–503.

Повреждение головного мозга может избирательно разрушать систему приблизительных количеств и систему точных чисел

Dehaene, S. (2011). The number sense: How the mind creates mathematics. New York, NY: Oxford University Press.

Lemer, C., Dehaene, S., Spelke, E., & Cohen, L. (2003). Approximate quantities and exact number words: Dissociable systems. Neuropsychologia, 41(14), 1942–1958.

Системы приблизительных количеств и точных чисел взаимодействуют в неповрежденном мозге

Gallistel, C. R., & Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition, 44, 43–74.

Holloway, I. D., & Ansari, D. (2009). Mapping numerical magnitudes onto symbols: The numerical distance effect and individual differences in children’s mathematics achievement. Journal of Experimental Child Psychology, 103(1), 17–29.

Lonnemann, J., Linkersdörfer, J., Hasselhorn, M., & Lindberg, S. (2011). Symbolic and non-symbolic distance effects in children and their connection with arithmetic skills. Journal of Neurolinguistics, 24(5), 583–591.

Mazzocco, M. M., Feigenson, L., & Halberda, J. (2011). Preschoolers’ precision of the approximate number system predicts later school mathematics performance. PLoS One, 6(9), e23749.

Изучение системы приблизительных количеств помогает изучению системы точных чисел

Libertus, M. E., Feigenson, L., & Halberda, J. (2013). Is approximate number precision a stable predictor of math ability? Learning and Individual Differences, 25, 126–133.

Lyons, I. M., & Beilock, S. L. (2011). Numerical ordering ability mediates the relation between number-sense and arithmetic competence. Cognition, 121(2), 256–261.

Park, J., Bermudez, V., Roberts, R. C., & Brannon, E. M. (2016). Non-symbolic approximate arithmetic training improves math performance in preschoolers. Journal of Experimental Child Psychology, 152, 278–293.

Wang, J. J., Odic, D., Halberda, J., & Feigenson, L. (2016). Changing the precision of preschoolers’ approximate number system representations changes their symbolic math performance. Journal of Experimental Child Psychology, 147, 82–99.

История записи чисел

Aczel, A. D. (2016). Finding zero. New York, NY: St. Martin’s Griffin.

Cajori, F. (1928). A history of mathematical notations. Vol. I, Notations in elementary mathematics. North Chelmsford, MA: Courier Corporation.

Cajori, F. (1928). A history of mathematical notations. Vol. II, Notations mainly in higher mathematics. Chicago, IL: Open Court Publishing.

Ifrah, G. (2000). The universal history of numbers: From prehistory to the invention of the computer. Translated by D. Vellos, E. F. Harding, S. Wood, & I. Monk. Toronto, Canada: Wiley.

Mazur, J. (2014). Enlightening symbols: A short history of mathematical notation and its hidden powers. Princeton, NJ: Princeton University Press.

Запись чисел и письменность Запада начались с бухгалтерского учета

Schmandt-Besserat, D. (1992). Before writing, Vol. I: From counting to cuneiform. Austin: University of Texas Press.

Пространство имеет решающее значение для системы математических обозначений

Dehaene, S. (2011). The number sense: How the mind creates mathematics. New York, NY: Oxford University Press.

Gelman, R., & Gallistel, C. R. (1978). The child’s understanding of number. Cambridge, MA: Harvard University Press.

Lakoff, G., & Núñez, R. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York, NY: Basic Books.

Движения глаз указывают на отсутствующие места

Kahneman, D. (1973). Attention and effort. Englewood Cliffs, NJ: Prentice Hall.

Воображаемая дистанция влияет на время чтения

Bar-Anan, Y., Liberman, N., Trope, Y., & Algom, D. (2007). Automatic processing of psychological distance: Evidence from a Stroop task. Journal of Experimental Psychology: General, 136(4), 610.

Воображаемая дистанция влияет на оценку личности

Liberman, N., Trope, Y., & Stephan, E. (2007). Psychological distance. In A. W. Kruglanski & E. T. Higgins (Eds.), Social psychology: Handbook of basic principles (2nd ed., pp. 353–383). New York, NY: Guilford Press.