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2/2017 -
Přehledová studie Overview Paper

(CZ) Úvod do aproximálního numerického systému
(EN) Introduction to the Approximal Number System

Strana / Page: 161-176
Autor / Author: Plassová, M., Stuchlíková, I., Vavrečka, M.
Klíčová slova / Key words: aproximální numerický systém, matematické nadání, neuropsychologie, intraparietální sulkus, kognice
approximate number system, mathematical talent, neuropsychology, intraparietal sulcus, cognition

Anotace:

V následující přehledové studii se snažíme shrnout základní poznatky o aproximálním numerickém systému (ANS) u člověka. V úvodu se věnujeme vymezení ANS, popisujeme jeho základní principy, mechanismy a neuroanatomickou lokalizaci systému. V další části studie identifikujeme průnik kognitivních funkcí ANS se základními kognitivními funkcemi, jež jsou nutné pro úspěšné zvládnutí školní i předškolní matematiky. Zaměřujeme se primárně na vzájemný vztah mezi ANS a matematickými schopnostmi a prostor věnujeme i kontroverzi, která v současné chvíli panuje v otázkách metodologického uchopení tohoto vztahu. V textu dále uvádíme poznatky z aktuálních studií, jež se pokoušejí o trénink ANS s cílem pozitivně působit na obecné matematické schopnosti. Poslední část patří možnostem využití ANS v pedagogické praxi, včetně zdůraznění klíčových mechanismů pro efektivní zařazení do praktické výuky.



Annotation:

In the following review study we try to summarise basic findings about the Approximate Number System (ANS) in human beings. We start with the definition of ANS, and describe its basic principles, mechanisms and the neuro-anatomical location of the system. We then go on to identitfy the intersection between ANS cognitive functions and the basic cognitive functions necessary for the successful mastery of school and pre-school mathematics. We focus primarily on the interaction between ANS and mathematical abilities and devote space to the current controversy in questions of the methodological approach to this interaction. In the text we also present findings from recent studies directed to developing training in ANS with the aim of positively affecting general mathematical abilities. The last section of the study looks at the possibilities for the exploitation of ANS in educational practice, including emphasis on the key mechanisms for its effective integration into practical teaching.



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Literatura / References:

Binterová, H., & Hošpesová, A. (2003). Objevování v matematickém vyučování podporované Excelem. Univ. S. Boh. Dept. Math. Rep., 10, 267–273.

Binterová, H., Milota, J., & Vaníček, J. (2005). Global School – virtuální prostředí pro výuku matematiky na ZŠ formou e-learningu. Univ. S. Boh. Dept. Math. Rep., 13.

Brannon, E. M. (2006). The representation of numerical magnitude. Current Opinion in Neurobiology, 16(2), 222–229.
https://doi.org/10.1016/j.conb.2006.03.002

Brannon E. M., & Terrace H. S. (1998). Ordering of the numerosities 1 to 9 by monkeys. Science, 282, 746–749.
https://doi.org/10.1126/science.282.5389.746

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(5), e125.
https://doi.org/10.1371/journal.pbio.0040125

Castelli, F., Glaser, D. E., & Butterworth, B. (2006). Discrete and analogue quantity processing in the parietal lobe: a functional MRI study. Proceeding of the National Academy of Sciences of the USA, 103, 4693–98.
https://doi.org/10.1073/pnas.0600444103

Castronovo, J., & Gobel, S. M. (2012). Impact of high mathematics education on the number sense. PLoS ONE, 7(4), e33832.
https://doi.org/10.1371/journal.pone.0033832

Cohen Kadosh R., Cohen Kadosh K., & Henik A. (2008). When brightness counts: the neuronal correlate of numerical luminance interference. Cerebral Cortex, 18, 337–343.
https://doi.org/10.1093/cercor/bhm058

Čihák, R. (1997). Anatomie 3. Praha: Grada.

Davis, H., & Perusse, R. (1988). Numerical competence in animals: definitional issues, current evidence, and a new research agenda. Behavioral and Brain Sciences, 11, 561–615.
https://doi.org/10.1017/S0140525X00053437

Dehaene, S. (1999). The number sense: How the mind creates mathematics. New York: Oxford University Press.

Dehaene, S. (2011). The number sense: How the mind creates mathematics. 2. vyd. New York: Oxford University Press.

Dehaene, S., & Changeux, J. P. (1996). Cerebral networks for number processing: Evidence from a case of posterior callosal lesion. NeuroCase, 2:155-174.
https://doi.org/10.1093/neucas/2.3.155-a
https://doi.org/10.1080/13554799608402394

Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20, 487–506.
https://doi.org/10.1080/02643290244000239

Dehaene, S., Izard, V., & Piazza, M. (2005). Control over non-numerical parameters in numerosity experiments. Dostupné z www.unicog.org/publications/piazza_tuningcurves_neuron2004.pdf

DeWind, N. K., & Brannon, E. M. (2012). Malleability of the approximate number system: Effects of feedback and training. Frontiers in Human Neuroscience, 6.
https://doi.org/10.3389/fnhum.2012.00068

Eger, E., Sterzer, P., Russ, M. O., Giraud, A. L., & Kleinschmidt, A. (2003). A supramodal number representation in human intraparietal cortex. Neuron 37, 719–25.
https://doi.org/10.1016/S0896-6273(03)00036-9

Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307–314.
https://doi.org/10.1016/j.tics.2004.05.002

Fuhs, M. W., & McNeil, N. M. (2013). ANS acuity and mathematics ability in preschoolers from low-income homes: Contributions of inhibitory control. Developmental Science, 16(1), 136–148.
https://doi.org/10.1111/desc.12013

Gallistel, C. R., & Gelman, R. (2000). Non-verbal numerical cognition: From reals to integers. Trends in Cognitive Sciences, 4(2), 59–65.
https://doi.org/10.1016/S1364-6613(99)01424-2

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

Gerstmann, J. (1940). Syndrome of finger agnosia, disorientation for right and left, agraphia, acalculia. Archives of Neurology and Psychology, 44, 398–408.
https://doi.org/10.1001/archneurpsyc.1940.02280080158009

Gilmore, C. K., McCarthy, S. E., & Spelke, E. S. (2007). Symbolic arithmetic knowledge without instruction. Nature, 447, 589–591.
https://doi.org/10.1038/nature05850

Gilmore, C. K., McCarthy, S. E., & Spelke, E. S. (2010). Non-symbolic arithmetic abilities and mathematics achievement in the first year of formal schooling. Cognition, 115, 394–406.
https://doi.org/10.1016/j.cognition.2010.02.002

Gobel, S. M., Watson, S. E., Lervag, A., & Hulme, C. (2014). Children's arithmetic development: It is number knowledge, not the approximate number sense, that counts. Psychological Science, 25(3), 789–798.
https://doi.org/10.1177/0956797613516471

Gordon, P. (2004). Numerical cognition without words: Evidence from Amazonia. Science 306, 496–499.
https://doi.org/10.1126/science.1094492

Haist, F., Wazny, J. H., Toomarian, E., & Adamo, M. (2015). Development of brain systems for nonsymbolic numerosity and the relationship to formal math academic achievement. Human Brain Mapping. 36, 804–826.
https://doi.org/10.1002/hbm.22666

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.
https://doi.org/10.1037/a0012682

Halberda, J., Mazzocco, M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature 455, 665– 668.
https://doi.org/10.1038/nature07246

Halberda, J., Ly, R., Wilmer, J. B., Naiman, D. Q., & Germine, L. (2012). Number sense across the lifespan as revealed by a massive Internetbased sample. Proceeding of the National Academy of Sciences of the USA, 109, 11116–11120.
https://doi.org/10.1073/pnas.1200196109

Hauser, M. D., Carey, S., & Hauser, L. B. (2000). Spontaneous number representation in semifree-ranging rhesus monkeys. Proceeding of the Royal Society of London B, 267, 829–33
https://doi.org/10.1098/rspb.2000.1078

Henschen, S. E. (1919). Uber Sprach-, Musik- und Rechenmechanismen und ihre Lokalisation im Großhirn. Zeitshrift für die gesamte neurologie und psychiatry, 52, 273–298.
https://doi.org/10.1007/BF02872428

Henschen, S. E. (1920). Klinische und anatomische Beiträge zur Pathologie des Gehirns. Stockholm: Nordiska Bokhandeln.

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.
https://doi.org/10.1016/j.jecp.2008.04.001

Chochon, F., Cohen, L., van de Moortele, P. F., & Dehaene, S. (1999). Differential contributions of the left and right inferior parietal lobules to number processing. Journal of Cognitive Neuroscience, 11, 617–630.
https://doi.org/10.1162/089892999563689

Hyde, C. D. (2011). Two Systems of Non-Symbolic Numerical Cognition. Frontiers in Human Neuroscience, 5, 150.
https://doi.org/10.3389/fnhum.2011.00150

Inglis, M., Attridge, N., Batchelor, S., & Gilmore, C. (2011). Non-verbal number acuity correlates with symbolic mathematics achievement: But only in children. Psychonomic Bulletin and Review, 18(6), 1222–1229.
https://doi.org/10.3758/s13423-011-0154-1

Isaacs, E. B., Edmonds, C. J., Lucas, A., & Gadian, D. G. (2001). Calculation difficulties in children of very low birthweight: A neural correlate. Brain, 124(Pt 9): 1701–1707.
https://doi.org/10.1093/brain/124.9.1701

Izard, V., Dehaene-Lambertz, G., & Dehaene, S. (2008). Distinct cerebral pathways for object identity and number in human infants. PLoS Biology, 6, e11.
https://doi.org/10.1371/journal.pbio.0060011

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(25), 10382–10385.
https://doi.org/10.1073/pnas.0812142106

Kaufman, E. L., Lord, M. W., Reese, T. W, & Volkmann, J. (1949). The discrimination of visual number. American Journal of Psychology, 62(4), 498−525.
https://doi.org/10.2307/1418556

Kaufmann, L., Vogel, S. E., Starke, M., Kremser, C., Schocke, M., & Wood, G. (2009). Developmental dyscalculia: compensatory mechanisms in left intraparietal regions in response to nonsymbolic magnitudes. Behavioral and Brain Functions, 5, 35.
https://doi.org/10.1186/1744-9081-5-35

Knops, A., Thirion, B., Hubbard, E. M., Michel, V., & Dehaene, S. (2009). Recruitment of an area involved in eye movements during mental arithmetic. Science, 324, 1583–1585.
https://doi.org/10.1126/science.1171599

Libertus, M., Feigenson, L., & Halberda, J. (2013). Numerical approximation abilities correlate with and predict informal but not formal mathematics abilities. Journal of Experimental Child Psychology, 116(4), 829–838.
https://doi.org/10.1016/j.jecp.2013.08.003

Libertus, M. E., Odic, D., & Halberda, J. (2012). Intuitive sense of number correlates with math scores on college-entrance examination. Acta Psychologica, 141(3), 373–379.
https://doi.org/10.1016/j.actpsy.2012.09.009

Lewandowsky, M. & Stadelmann, E. (1908). Über einen bemerkenswerten Fall von Hirnblutung und über Rechenstörungen bei Herderkrankung des Gehirns. Journal für Psychologie und Neurologie, 11, 249-265.

Luria, A. R. (1973). The working brain. New York: Basic Books.

Mazzocco, M. M. M., Feigenson, L., & Halberda, J. (2011a). Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia). Child Development, 82(4), 1224–1237.
https://doi.org/10.1111/j.1467-8624.2011.01608.x

Mazzocco, M. M. M., Feigenson, L., & Halberda, J. (2011b). Preschoolers' precision of the approximate number system predicts later school mathematics performance. PLoS ONE, 6(9), 1–8.
https://doi.org/10.1371/journal.pone.0023749

McCrink, K., & Wynn, K. (2007). Ratio abstraction by 6-month-old infants. Psychological Science, 18, 740–745.
https://doi.org/10.1111/j.1467-9280.2007.01969.x

Merritt, D. J, DeWind, N. K., & Brannon, E. M. (2012). Comparative cognition of number representation. In T. R. Zentall & E. A. Wasserman (Eds.), The oxford handbook of comparative cognition (s. 451–476). 2. vyd. New York: Oxford University Press.
https://doi.org/10.1093/oxfordhb/9780195392661.013.0024

Mussolin, C., Mejias, S., & Noël, M. P. (2010). Symbolic and nonsymbolic number comparison in children with and without dyscalculia. Cognition, 115(1), 10–25.
https://doi.org/10.1016/j.cognition.2009.10.006

Negen, J., & Sarnecka, B. W. (2015). Is there really a link between exact-number knowledge and approximate number system acuity in young children? British Journal of Developmental Psychology, 33, 92–105.
https://doi.org/10.1111/bjdp.12071

Nieder, A. (2013). Coding of abstract quantity by 'number neurons' of the primate brain. Journal of Comparative Physiology A, 199, 1–16.
https://doi.org/10.1007/s00359-012-0763-9

Nieder, A. & Dehaene, S. (2009). Representation of number in the brain. Annual Review of Neuroscience, 32, 185–208.
https://doi.org/10.1146/annurev.neuro.051508.135550

Owen, A. M., Hampshire, A., Grahn, J. A., Stenton, R., Dajani, S., Burns, A. S., Howard, R. J. & Ballard, G. C. (2010). Putting brain training to the test. Nature, 465(7299), 775–778.
https://doi.org/10.1038/nature09042

Park, J., & Brannon, E. M. (2013). Training the approximate number system improves math proficiency. Psychological Science, 24, 2013–2019.
https://doi.org/10.1177/0956797613482944

Park, J., Brannon, E. M. (2014). Improving arithmetic performance with number sense training: an investigation of underlying mechanism. Cognition, 133, 188–200.
https://doi.org/10.1016/j.cognition.2014.06.011

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(12), 278–293.
https://doi.org/10.1016/j.jecp.2016.07.011

Piaget, J. (1954). The construction of reality in the child. New York: Ballentine.
https://doi.org/10.1037/11168-000

Piazza, M., Izard, V., Pinel, P., Le Bihan, D., & Dehaene, S. (2004). Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron, 44(3), 547–555.
https://doi.org/10.1016/j.neuron.2004.10.014

Piazza, M., Facoetti, A., Trussardi, A. N., Berteletti, I., Conte, S., Lucangeli, D., et al. (2010). Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition, 116(1), 33–41.
https://doi.org/10.1016/j.cognition.2010.03.012

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(1), 177–188.
https://doi.org/10.1016/j.brainres.2006.05.104

Pinel, P., Dehaene, S., Riviere, D., & LeBihan, D. (2001). Modulation of parietal activation by semantic distance in a number comparison task. Neuroimage, 14, 1013–1026.
https://doi.org/10.1006/nimg.2001.0913

Plassová, M., Tesař, M., Vavrečka, M., & Valuchová, K. (2016). Approximate number system in children. In M. McGreevy & R. Rita (Eds.), Proceedings of the 6th Biannual CER Comparative European Research Conference (182–187). London: Science.

Plháková, A. (2009). Učebnice obecné psychologie. Praha: Academia.

Price, G. R., Palmer, D., Battista, C., & Ansari, D. (2012). Nonsymbolic numerical magnitude comparison: Reliability and validity of different task variants and outcome measures, and their relationship to arithmetic achievement in adults. Acta Psychologica, 140(1), 50–57.
https://doi.org/10.1016/j.actpsy.2012.02.008

Redick, T. S., Shipstead, Z., Harrison, T. L., Hicks, K. L., Fried, D., Hambrick, D. Z., Kane, M. J. & Engle, R. W. (2013). No evidence of intelligence improvement after working memory training: a randomized, placebo-controlled study. Journal of Experimental Psychology, 142, 359–379.
https://doi.org/10.1037/a0029082

Roitman, J. D., Brannon, E. M., & Platt, M. L. (2012). Representation of numerosity in posterior parietal cortex. Frontiers in Integrative Neuroscience, 6, 25.
https://doi.org/10.3389/fnint.2012.00025

Rotzer, S., Kucian, K., Martin, E., von Aster, M., Klaver, P., & Loenneker, T. (2008). Optimized voxel-based morphometry in children with developmental dyscalculia. Neuroimage, 39, 417–422.
https://doi.org/10.1016/j.neuroimage.2007.08.045

Rotzer, S., Loenneker, T., Kucian, K., Martin, E., Klaver, P., & von Aster, M. (2009). Dysfunctional neural network of spatial working memory contributes to developmental dyscalculia. Neuropsychologia, 47, 2859–2865.
https://doi.org/10.1016/j.neuropsychologia.2009.06.009

Rykhlevskaia, E., Uddin, L. Q., Kondos, L., & Menon, V. (2009). Neuroanatomical correlates of developmental dyscalculia: combined evidence from morphometry and tractography. Frontiers in Human Neuroscience, 3(51), 1−13.
https://doi.org/10.3389/neuro.09.051.2009

Samková, L. (2013). Využití programu GeoGebra při nácviku odhadů. Sborník 6. konference Užití počítačů ve výuce matematiky, s. 323−336.

Sasanguie, D., Defever, E., Maertens, B., & Reynvoet, B. (2013). The approximate number system is not predictive for symbolic number processing in kindergartners. Quarterly Journal of Experimental Psychology, 1–26.

Sasanguie, D., Gobel, S. M., Moll, K., Smets, K., & Reynvoet, B. (2013). Approximate number sense, symbolic number processing, or number-space mappings: What underlies mathematics achievement? Journal of Experimental Child Psychology, 114(3), 418–431.
https://doi.org/10.1016/j.jecp.2012.10.012

Schacter, D. L., Gilbert, D. T., & Wegner, D. M. (2010). Psychology (2. vyd.). New York: Worth.

Sousa, D. (2010). Mind, brain, and education: Neuroscience implications for the classroom. Bloomington, IN: Solution Tree.

Spaepen, E., Coppola, M., Spelke, E. S., Carey, S. E., & Goldin-Meadow, S. (2011). Number without a language model. Proceeding of the National Academy of Sciences of the USA, 108, 3163–3168.
https://doi.org/10.1073/pnas.1015975108

Starkey, P., & Cooper, R. G. (1980). Perception of numbers by human infants. Science, 210, 1033–1035.
https://doi.org/10.1126/science.7434014

Tibber, M. S., Manasseh, G. S., Clarke, R. C., Gagin, G., Swanbeck, S. N., Butterworth, B., et al. (2013). Sensitivity to numerosity is not a unique visuospatial psychophysical predictor of mathematical ability. Vision Research, 89, 1–9.
https://doi.org/10.1016/j.visres.2013.06.006

Xu, F., & Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition, 74, B1–B11.
https://doi.org/10.1016/S0010-0277(99)00066-9

Wang, 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.
https://doi.org/10.1016/j.jecp.2016.03.002

Wilson, M. L., Hauser, M. D., & Wrangham, R. W. (2001). Does participation in intergroup conflict depend on numerical assessment, range location, or rank for wild chimpanzees? Animal Behaviour, 61, 1203–1216.
https://doi.org/10.1006/anbe.2000.1706

Wynn, K. (1992). Addition and subtraction by human infants. Nature, 358, 749–750.
https://doi.org/10.1038/358749a0


Binterová, H., & Hošpesová, A. (2003). Objevování v matematickém vyučování podporované Excelem. Univ. S. Boh. Dept. Math. Rep., 10, 267–273.

Binterová, H., Milota, J., & Vaníček, J. (2005). Global School – virtuální prostředí pro výuku matematiky na ZŠ formou e-learningu. Univ. S. Boh. Dept. Math. Rep., 13.

Brannon, E. M. (2006). The representation of numerical magnitude. Current Opinion in Neurobiology, 16(2), 222–229.
https://doi.org/10.1016/j.conb.2006.03.002

Brannon E. M., & Terrace H. S. (1998). Ordering of the numerosities 1 to 9 by monkeys. Science, 282, 746–749.
https://doi.org/10.1126/science.282.5389.746

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(5), e125.
https://doi.org/10.1371/journal.pbio.0040125

Castelli, F., Glaser, D. E., & Butterworth, B. (2006). Discrete and analogue quantity processing in the parietal lobe: a functional MRI study. Proceeding of the National Academy of Sciences of the USA, 103, 4693–98.
https://doi.org/10.1073/pnas.0600444103

Castronovo, J., & Gobel, S. M. (2012). Impact of high mathematics education on the number sense. PLoS ONE, 7(4), e33832.
https://doi.org/10.1371/journal.pone.0033832

Cohen Kadosh R., Cohen Kadosh K., & Henik A. (2008). When brightness counts: the neuronal correlate of numerical luminance interference. Cerebral Cortex, 18, 337–343.
https://doi.org/10.1093/cercor/bhm058

Čihák, R. (1997). Anatomie 3. Praha: Grada.

Davis, H., & Perusse, R. (1988). Numerical competence in animals: definitional issues, current evidence, and a new research agenda. Behavioral and Brain Sciences, 11, 561–615.
https://doi.org/10.1017/S0140525X00053437

Dehaene, S. (1999). The number sense: How the mind creates mathematics. New York: Oxford University Press.

Dehaene, S. (2011). The number sense: How the mind creates mathematics. 2. vyd. New York: Oxford University Press.

Dehaene, S., & Changeux, J. P. (1996). Cerebral networks for number processing: Evidence from a case of posterior callosal lesion. NeuroCase, 2:155-174.
https://doi.org/10.1093/neucas/2.3.155-a
https://doi.org/10.1080/13554799608402394

Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20, 487–506.
https://doi.org/10.1080/02643290244000239

Dehaene, S., Izard, V., & Piazza, M. (2005). Control over non-numerical parameters in numerosity experiments. Dostupné z www.unicog.org/publications/piazza_tuningcurves_neuron2004.pdf

DeWind, N. K., & Brannon, E. M. (2012). Malleability of the approximate number system: Effects of feedback and training. Frontiers in Human Neuroscience, 6.
https://doi.org/10.3389/fnhum.2012.00068

Eger, E., Sterzer, P., Russ, M. O., Giraud, A. L., & Kleinschmidt, A. (2003). A supramodal number representation in human intraparietal cortex. Neuron 37, 719–25.
https://doi.org/10.1016/S0896-6273(03)00036-9

Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307–314.
https://doi.org/10.1016/j.tics.2004.05.002

Fuhs, M. W., & McNeil, N. M. (2013). ANS acuity and mathematics ability in preschoolers from low-income homes: Contributions of inhibitory control. Developmental Science, 16(1), 136–148.
https://doi.org/10.1111/desc.12013

Gallistel, C. R., & Gelman, R. (2000). Non-verbal numerical cognition: From reals to integers. Trends in Cognitive Sciences, 4(2), 59–65.
https://doi.org/10.1016/S1364-6613(99)01424-2

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

Gerstmann, J. (1940). Syndrome of finger agnosia, disorientation for right and left, agraphia, acalculia. Archives of Neurology and Psychology, 44, 398–408.
https://doi.org/10.1001/archneurpsyc.1940.02280080158009

Gilmore, C. K., McCarthy, S. E., & Spelke, E. S. (2007). Symbolic arithmetic knowledge without instruction. Nature, 447, 589–591.
https://doi.org/10.1038/nature05850

Gilmore, C. K., McCarthy, S. E., & Spelke, E. S. (2010). Non-symbolic arithmetic abilities and mathematics achievement in the first year of formal schooling. Cognition, 115, 394–406.
https://doi.org/10.1016/j.cognition.2010.02.002

Gobel, S. M., Watson, S. E., Lervag, A., & Hulme, C. (2014). Children's arithmetic development: It is number knowledge, not the approximate number sense, that counts. Psychological Science, 25(3), 789–798.
https://doi.org/10.1177/0956797613516471

Gordon, P. (2004). Numerical cognition without words: Evidence from Amazonia. Science 306, 496–499.
https://doi.org/10.1126/science.1094492

Haist, F., Wazny, J. H., Toomarian, E., & Adamo, M. (2015). Development of brain systems for nonsymbolic numerosity and the relationship to formal math academic achievement. Human Brain Mapping. 36, 804–826.
https://doi.org/10.1002/hbm.22666

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.
https://doi.org/10.1037/a0012682

Halberda, J., Mazzocco, M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature 455, 665– 668.
https://doi.org/10.1038/nature07246

Halberda, J., Ly, R., Wilmer, J. B., Naiman, D. Q., & Germine, L. (2012). Number sense across the lifespan as revealed by a massive Internetbased sample. Proceeding of the National Academy of Sciences of the USA, 109, 11116–11120.
https://doi.org/10.1073/pnas.1200196109

Hauser, M. D., Carey, S., & Hauser, L. B. (2000). Spontaneous number representation in semifree-ranging rhesus monkeys. Proceeding of the Royal Society of London B, 267, 829–33
https://doi.org/10.1098/rspb.2000.1078

Henschen, S. E. (1919). Uber Sprach-, Musik- und Rechenmechanismen und ihre Lokalisation im Großhirn. Zeitshrift für die gesamte neurologie und psychiatry, 52, 273–298.
https://doi.org/10.1007/BF02872428

Henschen, S. E. (1920). Klinische und anatomische Beiträge zur Pathologie des Gehirns. Stockholm: Nordiska Bokhandeln.

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.
https://doi.org/10.1016/j.jecp.2008.04.001

Chochon, F., Cohen, L., van de Moortele, P. F., & Dehaene, S. (1999). Differential contributions of the left and right inferior parietal lobules to number processing. Journal of Cognitive Neuroscience, 11, 617–630.
https://doi.org/10.1162/089892999563689

Hyde, C. D. (2011). Two Systems of Non-Symbolic Numerical Cognition. Frontiers in Human Neuroscience, 5, 150.
https://doi.org/10.3389/fnhum.2011.00150

Inglis, M., Attridge, N., Batchelor, S., & Gilmore, C. (2011). Non-verbal number acuity correlates with symbolic mathematics achievement: But only in children. Psychonomic Bulletin and Review, 18(6), 1222–1229.
https://doi.org/10.3758/s13423-011-0154-1

Isaacs, E. B., Edmonds, C. J., Lucas, A., & Gadian, D. G. (2001). Calculation difficulties in children of very low birthweight: A neural correlate. Brain, 124(Pt 9): 1701–1707.
https://doi.org/10.1093/brain/124.9.1701

Izard, V., Dehaene-Lambertz, G., & Dehaene, S. (2008). Distinct cerebral pathways for object identity and number in human infants. PLoS Biology, 6, e11.
https://doi.org/10.1371/journal.pbio.0060011

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(25), 10382–10385.
https://doi.org/10.1073/pnas.0812142106

Kaufman, E. L., Lord, M. W., Reese, T. W, & Volkmann, J. (1949). The discrimination of visual number. American Journal of Psychology, 62(4), 498−525.
https://doi.org/10.2307/1418556

Kaufmann, L., Vogel, S. E., Starke, M., Kremser, C., Schocke, M., & Wood, G. (2009). Developmental dyscalculia: compensatory mechanisms in left intraparietal regions in response to nonsymbolic magnitudes. Behavioral and Brain Functions, 5, 35.
https://doi.org/10.1186/1744-9081-5-35

Knops, A., Thirion, B., Hubbard, E. M., Michel, V., & Dehaene, S. (2009). Recruitment of an area involved in eye movements during mental arithmetic. Science, 324, 1583–1585.
https://doi.org/10.1126/science.1171599

Libertus, M., Feigenson, L., & Halberda, J. (2013). Numerical approximation abilities correlate with and predict informal but not formal mathematics abilities. Journal of Experimental Child Psychology, 116(4), 829–838.
https://doi.org/10.1016/j.jecp.2013.08.003

Libertus, M. E., Odic, D., & Halberda, J. (2012). Intuitive sense of number correlates with math scores on college-entrance examination. Acta Psychologica, 141(3), 373–379.
https://doi.org/10.1016/j.actpsy.2012.09.009

Lewandowsky, M. & Stadelmann, E. (1908). Über einen bemerkenswerten Fall von Hirnblutung und über Rechenstörungen bei Herderkrankung des Gehirns. Journal für Psychologie und Neurologie, 11, 249-265.

Luria, A. R. (1973). The working brain. New York: Basic Books.

Mazzocco, M. M. M., Feigenson, L., & Halberda, J. (2011a). Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia). Child Development, 82(4), 1224–1237.
https://doi.org/10.1111/j.1467-8624.2011.01608.x

Mazzocco, M. M. M., Feigenson, L., & Halberda, J. (2011b). Preschoolers' precision of the approximate number system predicts later school mathematics performance. PLoS ONE, 6(9), 1–8.
https://doi.org/10.1371/journal.pone.0023749

McCrink, K., & Wynn, K. (2007). Ratio abstraction by 6-month-old infants. Psychological Science, 18, 740–745.
https://doi.org/10.1111/j.1467-9280.2007.01969.x

Merritt, D. J, DeWind, N. K., & Brannon, E. M. (2012). Comparative cognition of number representation. In T. R. Zentall & E. A. Wasserman (Eds.), The oxford handbook of comparative cognition (s. 451–476). 2. vyd. New York: Oxford University Press.
https://doi.org/10.1093/oxfordhb/9780195392661.013.0024

Mussolin, C., Mejias, S., & Noël, M. P. (2010). Symbolic and nonsymbolic number comparison in children with and without dyscalculia. Cognition, 115(1), 10–25.
https://doi.org/10.1016/j.cognition.2009.10.006

Negen, J., & Sarnecka, B. W. (2015). Is there really a link between exact-number knowledge and approximate number system acuity in young children? British Journal of Developmental Psychology, 33, 92–105.
https://doi.org/10.1111/bjdp.12071

Nieder, A. (2013). Coding of abstract quantity by 'number neurons' of the primate brain. Journal of Comparative Physiology A, 199, 1–16.
https://doi.org/10.1007/s00359-012-0763-9

Nieder, A. & Dehaene, S. (2009). Representation of number in the brain. Annual Review of Neuroscience, 32, 185–208.
https://doi.org/10.1146/annurev.neuro.051508.135550

Owen, A. M., Hampshire, A., Grahn, J. A., Stenton, R., Dajani, S., Burns, A. S., Howard, R. J. & Ballard, G. C. (2010). Putting brain training to the test. Nature, 465(7299), 775–778.
https://doi.org/10.1038/nature09042

Park, J., & Brannon, E. M. (2013). Training the approximate number system improves math proficiency. Psychological Science, 24, 2013–2019.
https://doi.org/10.1177/0956797613482944

Park, J., Brannon, E. M. (2014). Improving arithmetic performance with number sense training: an investigation of underlying mechanism. Cognition, 133, 188–200.
https://doi.org/10.1016/j.cognition.2014.06.011

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(12), 278–293.
https://doi.org/10.1016/j.jecp.2016.07.011

Piaget, J. (1954). The construction of reality in the child. New York: Ballentine.
https://doi.org/10.1037/11168-000

Piazza, M., Izard, V., Pinel, P., Le Bihan, D., & Dehaene, S. (2004). Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron, 44(3), 547–555.
https://doi.org/10.1016/j.neuron.2004.10.014

Piazza, M., Facoetti, A., Trussardi, A. N., Berteletti, I., Conte, S., Lucangeli, D., et al. (2010). Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition, 116(1), 33–41.
https://doi.org/10.1016/j.cognition.2010.03.012

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(1), 177–188.
https://doi.org/10.1016/j.brainres.2006.05.104

Pinel, P., Dehaene, S., Riviere, D., & LeBihan, D. (2001). Modulation of parietal activation by semantic distance in a number comparison task. Neuroimage, 14, 1013–1026.
https://doi.org/10.1006/nimg.2001.0913

Plassová, M., Tesař, M., Vavrečka, M., & Valuchová, K. (2016). Approximate number system in children. In M. McGreevy & R. Rita (Eds.), Proceedings of the 6th Biannual CER Comparative European Research Conference (182–187). London: Science.

Plháková, A. (2009). Učebnice obecné psychologie. Praha: Academia.

Price, G. R., Palmer, D., Battista, C., & Ansari, D. (2012). Nonsymbolic numerical magnitude comparison: Reliability and validity of different task variants and outcome measures, and their relationship to arithmetic achievement in adults. Acta Psychologica, 140(1), 50–57.
https://doi.org/10.1016/j.actpsy.2012.02.008

Redick, T. S., Shipstead, Z., Harrison, T. L., Hicks, K. L., Fried, D., Hambrick, D. Z., Kane, M. J. & Engle, R. W. (2013). No evidence of intelligence improvement after working memory training: a randomized, placebo-controlled study. Journal of Experimental Psychology, 142, 359–379.
https://doi.org/10.1037/a0029082

Roitman, J. D., Brannon, E. M., & Platt, M. L. (2012). Representation of numerosity in posterior parietal cortex. Frontiers in Integrative Neuroscience, 6, 25.
https://doi.org/10.3389/fnint.2012.00025

Rotzer, S., Kucian, K., Martin, E., von Aster, M., Klaver, P., & Loenneker, T. (2008). Optimized voxel-based morphometry in children with developmental dyscalculia. Neuroimage, 39, 417–422.
https://doi.org/10.1016/j.neuroimage.2007.08.045

Rotzer, S., Loenneker, T., Kucian, K., Martin, E., Klaver, P., & von Aster, M. (2009). Dysfunctional neural network of spatial working memory contributes to developmental dyscalculia. Neuropsychologia, 47, 2859–2865.
https://doi.org/10.1016/j.neuropsychologia.2009.06.009

Rykhlevskaia, E., Uddin, L. Q., Kondos, L., & Menon, V. (2009). Neuroanatomical correlates of developmental dyscalculia: combined evidence from morphometry and tractography. Frontiers in Human Neuroscience, 3(51), 1−13.
https://doi.org/10.3389/neuro.09.051.2009

Samková, L. (2013). Využití programu GeoGebra při nácviku odhadů. Sborník 6. konference Užití počítačů ve výuce matematiky, s. 323−336.

Sasanguie, D., Defever, E., Maertens, B., & Reynvoet, B. (2013). The approximate number system is not predictive for symbolic number processing in kindergartners. Quarterly Journal of Experimental Psychology, 1–26.

Sasanguie, D., Gobel, S. M., Moll, K., Smets, K., & Reynvoet, B. (2013). Approximate number sense, symbolic number processing, or number-space mappings: What underlies mathematics achievement? Journal of Experimental Child Psychology, 114(3), 418–431.
https://doi.org/10.1016/j.jecp.2012.10.012

Schacter, D. L., Gilbert, D. T., & Wegner, D. M. (2010). Psychology (2. vyd.). New York: Worth.

Sousa, D. (2010). Mind, brain, and education: Neuroscience implications for the classroom. Bloomington, IN: Solution Tree.

Spaepen, E., Coppola, M., Spelke, E. S., Carey, S. E., & Goldin-Meadow, S. (2011). Number without a language model. Proceeding of the National Academy of Sciences of the USA, 108, 3163–3168.
https://doi.org/10.1073/pnas.1015975108

Starkey, P., & Cooper, R. G. (1980). Perception of numbers by human infants. Science, 210, 1033–1035.
https://doi.org/10.1126/science.7434014

Tibber, M. S., Manasseh, G. S., Clarke, R. C., Gagin, G., Swanbeck, S. N., Butterworth, B., et al. (2013). Sensitivity to numerosity is not a unique visuospatial psychophysical predictor of mathematical ability. Vision Research, 89, 1–9.
https://doi.org/10.1016/j.visres.2013.06.006

Xu, F., & Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition, 74, B1–B11.
https://doi.org/10.1016/S0010-0277(99)00066-9

Wang, 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.
https://doi.org/10.1016/j.jecp.2016.03.002

Wilson, M. L., Hauser, M. D., & Wrangham, R. W. (2001). Does participation in intergroup conflict depend on numerical assessment, range location, or rank for wild chimpanzees? Animal Behaviour, 61, 1203–1216.
https://doi.org/10.1006/anbe.2000.1706

Wynn, K. (1992). Addition and subtraction by human infants. Nature, 358, 749–750.
https://doi.org/10.1038/358749a0



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