A Neurociência e a História das Frações
DOI:
10.47976/RBHM2020v20n3951-62Palavras-chave:
Matemática, História, Neurociência, FraçõesResumo
O presente trabalho visa investigar como o cérebro processa as frações, sejam elas simbólicas ou não. Estudos recentes principiam a esclarecer os mecanismos neurológicos subjacentes a esse processo. Eles demonstram que frações não são apenas construtos mentais, resultados de considerá-las como a razão entre dois números inteiros, mas sim são dadas intuitivamente, ou seja, são representações inatas. Investiga-se como esses resultados podem ser traduzidos à luz da História da Matemática, mostrando-se como a neurofisiologia do processamento das frações influiu na evolução histórica desse conceito matemático. Enfatiza-se a importância pedagógica desses resultados.
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Referências
ALMEIDA, Manoel de Campos. Origens da Matemática. Curitiba: Editora Champagnat, 208 p.,1998.
ALMEIDA, Manoel de Campos. Origens da Matemática – A Pré-História da Matemática. vol. II – O Neolítico e o Alvorecer da História. Prefácio por Ubiratan D’Ambrosio. Curitiba: Progressiva, 306 p., 2011.
ALMEIDA, Manoel de Campos. O Nascimento da Matemática – A neurofisiologia e a préhistória da Matemática. São Paulo: Livraria da Física Editora, 2013.
ALMEIDA, Manoel de Campos. A Matemática Na Idade da Pedra. São Paulo: Editora da Livraria da Física, 640 p., 2017.
ALMEIDA, Manoel de Campos. A Gênese do Número – Os Neandertais Sabiam Contar? Curitiba: Manoel de Campos Almeida, 2019.
ANOBILE, Giovanni; BURR, David C.; IAIA, Marika; MARINELLI, Chiara V.; ANGELELLI, Paola and TURI, Marco. Independent adaptation mechanisms for numerosity and size perception provide evidence against a common sense of magnitude. In: Nature: Scientific Reports, 8:13571, 2018.
ANSARI, Daniel; GARCIA, Nicolas; HAMON, Kathleen and DHITAL, Bibek. Neural correlates of symbolic number processing in children and adults. In: NeuroReport, vol. 16, n. 16, 7 November 2005.
BENSON-AMRAM, Sarah; GILFILLAN, Geoff and McCOMB, Karen. Numerical assessment in the wild: insights from social carnivores. In: Phil. Trans. R. Soc. B 373: 20160508. Access in: <http://dx.doi.org/10.1098/rstb.2016.0508>, 2017.
BONGARD, Sylvia and NIEDER, Andreas. Basic mathematical rules are encoded by primate prefrontal cortex neurons. In: PNAS; vol. 107; nº 5; 2.277–2.282, February 2, 2010.
CANTLON, Jessica F. and BRANNON, Elizabeth M. Shared System for Ordering Small and Large Numbers in Monkeys and Humans. In:Psychological Science, 17(5), pp. 401–406. 2006.
CHOCHON, F.; COHEN L; MOORTELE, P.F. and DEHAENE, S. Differential Contributions of the Left and Right Inferior Parietal Lobules to Number Processing. In: Journal of Cognitive Neuroscience 11:6, pp. 617–630, 1999.
D’AMBROSIO, Ubiratan and ALMEIDA, Manoel de Campos. Ethnomathematics and the Emergence of mathematics. In: The Nature and Development of Mathematics; London: Routledge, 2017.
DAMEROW, Peter. Abstraction and Representation. Berlin: Kluwer, 1998.
DAMEROW, Peter. Prehistory and Cognitive Development. Invited Lecture at the TwentyFifth Annual Symposium of the Jean Piaget Society. Berkeley, June 3, 1995.
DAMEROW, Peter. The Material Culture of Calculation: A Conceptual Framework for na Historical Epistemology of the Concept of Number. Preprint 117, Berlin: Max Planck Institute of History of Science, 1999.
DAMEROW, Peter; SCHMIDT, Siegbert. Aritmetik im historischen Prozess: Wie “naturlich” sind die “naturlich Zahlen”? Preprint 163. Max Planck Institute for the History of Science. 2001.
DEHAENE, Stanislas. The Number Sense. New York: Oxford University Press, 274 p., 1997.
JACOB, Simon N. and NIEDER, Andreas. Notation-Independent Representation of Fractions in the Human Parietal Cortex. In: The Journal of Neuroscience, 29(14)–4652–4657, April 8, 2009.
JACOB, Simon N. and NIEDER, Andreas. The ABC of cardinal and ordinal number representations. Trends in Cognitive Sciences, vol. 12 n. 2. 2007.
KADOSH, Roi Cohen and WALSH, Vincent. Numerical Representation in the Parietal Lobes: Abstract or not Abstract? In: Behavioral and Brain Sciences. London: Cambridge Press, 2009.
KADOSH, Roi Cohen; LAMMERTYN, Jan and IZARD, Veronique. Are Numbers Specials? In: Progress in Neurobiology 84, pp. 132–147, 2008.
KADOSH, Roi Cohen; et alii. Notation-Dependent and – Independent Representations of Numbers in the Parietal Lobes. In: Neuron 53, pp. 307–314, January 18, 2007.
KNORR, Wilbur Richard. The ancient tradition of geometric problems. New York, Dover, 1993.
KNORR, Wilbur Richard. Techniques of Fractions in Ancient Egypt and Greece. In: CHISTIANIDES, Jean. Org. Classics in the History of Greek Mathematics. Dordrecht: Kluwer, 2004.
LESLIE Alan M; GELMAN, Rochel and GALLISTEL, C.R. The generative basis of natural number concepts. In: Trends in Cognitive Sciences. vol. 12, n. 5, 2008.
MOCK, Julia; HÜBER, Stefan; BLOECHLE, Johannes and BAHNMUELLER, Julia. Magnitude processing of symbolic and non-symbolic proportions: an fMRI study. In: Behavioral and Brain Functions. DOI: 10.1186/s12993–018–0141-z, December 2018.
MASI, Michael. Boethian Number Theory. Amsterdam: Rodopi, 1983.
MOSKALEVA, Maria and NIEDER, Andreas. Stable numerosity representations irrespective of magnitude context in macaque prefrontal córtex. In European Journal of Neuroscience, vol. 39, pp. 866–874, 2014.
NIEDER, Andreas and MILLER, Earl K. A parieto-frontal network for visual numerical information in the monkey. In: PNAS, n.19. 7457–7462, May 11, 2004.
NIEDER, Andreas; DIESTER, Ilka and TUDUSCIUC, Oana. Temporal and Spatial Enumeration Processes in the Primate Parietal Cortex. In: SCIENCE; vol. 313; 8 September, 2006.
NIEDER, Andreas. Neural constraints on human number concepts. In: Current opinion in neurobiology, 60:28–36, December 2019.
NIEDER, Andreas and MILLER, Earl K. A parieto-frontal network for visual numerical information in the monkey. In: PNAS, n. 19, 7457–7462, May 11, 2004.
NIEDER, Andreas; DIESTER, Ilka; TUDUSCIUC, Oana. Temporal and Spatial Enumeration Processes in the Primate Parietal Cortex. In: SCIENCE; vol. 313, 8 September, 2006.
NIEDER, Andreas. Neural constraints on human number concepts. In: Current opinion in neurobiology, 60:28–36, December 2019.
ALMEIDA, Manoel de Campos. Origens da Matemática – A Pré-História da Matemática. vol. II – O Neolítico e o Alvorecer da História. Prefácio por Ubiratan D’Ambrosio. Curitiba: Progressiva, 306 p., 2011.
ALMEIDA, Manoel de Campos. O Nascimento da Matemática – A neurofisiologia e a préhistória da Matemática. São Paulo: Livraria da Física Editora, 2013.
ALMEIDA, Manoel de Campos. A Matemática Na Idade da Pedra. São Paulo: Editora da Livraria da Física, 640 p., 2017.
ALMEIDA, Manoel de Campos. A Gênese do Número – Os Neandertais Sabiam Contar? Curitiba: Manoel de Campos Almeida, 2019.
ANOBILE, Giovanni; BURR, David C.; IAIA, Marika; MARINELLI, Chiara V.; ANGELELLI, Paola and TURI, Marco. Independent adaptation mechanisms for numerosity and size perception provide evidence against a common sense of magnitude. In: Nature: Scientific Reports, 8:13571, 2018.
ANSARI, Daniel; GARCIA, Nicolas; HAMON, Kathleen and DHITAL, Bibek. Neural correlates of symbolic number processing in children and adults. In: NeuroReport, vol. 16, n. 16, 7 November 2005.
BENSON-AMRAM, Sarah; GILFILLAN, Geoff and McCOMB, Karen. Numerical assessment in the wild: insights from social carnivores. In: Phil. Trans. R. Soc. B 373: 20160508. Access in: <http://dx.doi.org/10.1098/rstb.2016.0508>, 2017.
BONGARD, Sylvia and NIEDER, Andreas. Basic mathematical rules are encoded by primate prefrontal cortex neurons. In: PNAS; vol. 107; nº 5; 2.277–2.282, February 2, 2010.
CANTLON, Jessica F. and BRANNON, Elizabeth M. Shared System for Ordering Small and Large Numbers in Monkeys and Humans. In:Psychological Science, 17(5), pp. 401–406. 2006.
CHOCHON, F.; COHEN L; MOORTELE, P.F. and DEHAENE, S. Differential Contributions of the Left and Right Inferior Parietal Lobules to Number Processing. In: Journal of Cognitive Neuroscience 11:6, pp. 617–630, 1999.
D’AMBROSIO, Ubiratan and ALMEIDA, Manoel de Campos. Ethnomathematics and the Emergence of mathematics. In: The Nature and Development of Mathematics; London: Routledge, 2017.
DAMEROW, Peter. Abstraction and Representation. Berlin: Kluwer, 1998.
DAMEROW, Peter. Prehistory and Cognitive Development. Invited Lecture at the TwentyFifth Annual Symposium of the Jean Piaget Society. Berkeley, June 3, 1995.
DAMEROW, Peter. The Material Culture of Calculation: A Conceptual Framework for na Historical Epistemology of the Concept of Number. Preprint 117, Berlin: Max Planck Institute of History of Science, 1999.
DAMEROW, Peter; SCHMIDT, Siegbert. Aritmetik im historischen Prozess: Wie “naturlich” sind die “naturlich Zahlen”? Preprint 163. Max Planck Institute for the History of Science. 2001.
DEHAENE, Stanislas. The Number Sense. New York: Oxford University Press, 274 p., 1997.
JACOB, Simon N. and NIEDER, Andreas. Notation-Independent Representation of Fractions in the Human Parietal Cortex. In: The Journal of Neuroscience, 29(14)–4652–4657, April 8, 2009.
JACOB, Simon N. and NIEDER, Andreas. The ABC of cardinal and ordinal number representations. Trends in Cognitive Sciences, vol. 12 n. 2. 2007.
KADOSH, Roi Cohen and WALSH, Vincent. Numerical Representation in the Parietal Lobes: Abstract or not Abstract? In: Behavioral and Brain Sciences. London: Cambridge Press, 2009.
KADOSH, Roi Cohen; LAMMERTYN, Jan and IZARD, Veronique. Are Numbers Specials? In: Progress in Neurobiology 84, pp. 132–147, 2008.
KADOSH, Roi Cohen; et alii. Notation-Dependent and – Independent Representations of Numbers in the Parietal Lobes. In: Neuron 53, pp. 307–314, January 18, 2007.
KNORR, Wilbur Richard. The ancient tradition of geometric problems. New York, Dover, 1993.
KNORR, Wilbur Richard. Techniques of Fractions in Ancient Egypt and Greece. In: CHISTIANIDES, Jean. Org. Classics in the History of Greek Mathematics. Dordrecht: Kluwer, 2004.
LESLIE Alan M; GELMAN, Rochel and GALLISTEL, C.R. The generative basis of natural number concepts. In: Trends in Cognitive Sciences. vol. 12, n. 5, 2008.
MOCK, Julia; HÜBER, Stefan; BLOECHLE, Johannes and BAHNMUELLER, Julia. Magnitude processing of symbolic and non-symbolic proportions: an fMRI study. In: Behavioral and Brain Functions. DOI: 10.1186/s12993–018–0141-z, December 2018.
MASI, Michael. Boethian Number Theory. Amsterdam: Rodopi, 1983.
MOSKALEVA, Maria and NIEDER, Andreas. Stable numerosity representations irrespective of magnitude context in macaque prefrontal córtex. In European Journal of Neuroscience, vol. 39, pp. 866–874, 2014.
NIEDER, Andreas and MILLER, Earl K. A parieto-frontal network for visual numerical information in the monkey. In: PNAS, n.19. 7457–7462, May 11, 2004.
NIEDER, Andreas; DIESTER, Ilka and TUDUSCIUC, Oana. Temporal and Spatial Enumeration Processes in the Primate Parietal Cortex. In: SCIENCE; vol. 313; 8 September, 2006.
NIEDER, Andreas. Neural constraints on human number concepts. In: Current opinion in neurobiology, 60:28–36, December 2019.
NIEDER, Andreas and MILLER, Earl K. A parieto-frontal network for visual numerical information in the monkey. In: PNAS, n. 19, 7457–7462, May 11, 2004.
NIEDER, Andreas; DIESTER, Ilka; TUDUSCIUC, Oana. Temporal and Spatial Enumeration Processes in the Primate Parietal Cortex. In: SCIENCE; vol. 313, 8 September, 2006.
NIEDER, Andreas. Neural constraints on human number concepts. In: Current opinion in neurobiology, 60:28–36, December 2019.
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07-10-2020
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ALMEIDA, Manoel de Campos. A Neurociência e a História das Frações. Revista Brasileira de História da Matemática, São Paulo, v. 20, n. 39, p. 51–62, 2020. DOI: 10.47976/RBHM2020v20n3951-62. Disponível em: https://rbhm.org.br/index.php/RBHM/article/view/4. Acesso em: 21 dez. 2024.
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