Perspektywy wykorzystania wyników badań nad przestrzennym komponentem reprezentacji liczb w edukacji
Słowa kluczowe:
efekt SNARC, reprezentacja przestrzenna, diagnoza, treningi, edukacjaAbstrakt
Przestrzenny komponent reprezentacji liczb był obiektem dużego zainteresowania badaczy w ciągu ostatnich 20 lat. W badaniach z zakresu psychologii i neuronauki wykazano, że reprezentacje liczb są w sposób naturalny mapowane w przestrzeni. W niniejszej pracy dokonano przeglądu możliwości zastosowania wyników tych badań w dziedzinie edukacji. Teoretycznie wskazać można 3 obszary takich zastosowań: diagnoza specyficznych trudności w uczeniu, ocena kompetencji matematycznych uczniów oraz trenowanie zdolności matematycznych. Biorąc pod uwagę niewielką moc diagnostyczną aktualnie stosowanych metod badawczych oraz niejednoznaczne wyniki, można stwierdzić, że możliwości z zakresu diagnozy i oceny kompetencji są na chwilę obecną ograniczone. Z drugiej strony obiecujące są wyniki wstępnych badań nad trenowaniem zdolności numerycznych w atrakcyjnej dla dzieci formie.Bibliografia
Bachot, J., Gevers, W., Fias, W. & Roeyers, H. (2005). Number sense in children with visuospatial disabilities: orientation of the mental number line. Psychology Science, 47(1), 172-183.
Bächtold, D., Baumuller, M. & Brugger, P. (1998). Stimulus-response compatibility in representational space. Neuropsychologia, 36, 731-735.
Berch, D. B., Foley, E. J., Hill, R. J. & Ryan, P. M. (1999). Extracting parity and magnitude from Arabic numerals: Developmental changes in number processing and mental representation. Journal of Experimental Child Psychology, 74, 286-308.
Brysbaert, M. (1995). Arabic number reading: On the nature of the numerical scale and the origin of phonological recoding. Journal of Experimental Psychology: General, 124, 434-452.
Cipora, K., Czernecka, K., Żelechowska, D. & Szewczyk, J. (2011). Sources of individual differences in the magnitude of the SNARC effect. International Society for the Study of Individual Differences, London, Wielka Brytania. Poster.
Cipora, K. & Nęcka, E. (w druku). Kontinua a przestrzeń - przegląd badań nad przestrzennym komponentem poznawczej reprezentacji wielkości i nasilenia. Psychologia-Etologia-Genetyka.
Cipora, K. & Szczygieł, M. (w recenzji). „Wyścig Liczb - The Number Race” - polska adaptacja narzędzia wczesnej interwencji w dyskalkulii rozwojowej oraz wspomagania rozwoju kompetencji matematycznych.
Cohen Kadosh, R., Lammertyn, J. & Izard, V. (2008). Are numbers special? An overview of chronometric, neuroimaging, developmental and comparative studies of magnitude representation. Progress in Neurobiology, 84(2), 132-147.
Dehaene, S. (2001). Precis of the number sense. Mind & Lang, 16, 16-36.
Dehaene, S. (2011). The number sense. How the mind creates mathematics? Nowy Jork: Oxford University Press.
Dehaene, S., Dupoux, E. & Mehler, J. (1990). Is numerical comparison digital: Analogical and symbolic effects in two-digit number comparison. Journal of Experimental Psychology: Human Perception and Performance, 16, 626-641.
Dehaene, S., Bossini, S. & Giraux, P. (1993). The Mental Representation of Parity and Number Magnitude. Journal of Experimental Psychology: General, 122, 371-396.
Dehaene, S., Piazza, M., Pinel, P. & Cohen, L. (2005). Three Parietal Circuits for Number Processing. In J. I. D. Campbell (Ed.), Handbook of Mathematical Cognition (pp. 433-453). New York: Psychology Press.
Fayol, M. & Seron, X. (2005). About numerical representations: insights from neuropsychological, experimental and developmental studies. In J. B. Campbell (Ed.), Handbook of Mathematical Cognition (pp. 3-22). New York: Psychology Press.
Fischer, M. H., Castel, A. D., Dodd, M. D. & Pratt, J. (2003). Perceiving numbers causes spatial shifts of attention. Nature Neuroscience, 6, 555-556.
Fischer, M. H., Ellis, R., Cangelosi, A. & Mychakov, A. (2011). The oculomotor resonance effect during auditory number comprehension. Poster zaprezentowany podczas XXIXth European Workshop on Cognitive Neuropsychology. Bressanone, Włochy.
Fischer, M. H., Mills, R. A. & Shaki, S. (2010). How to cook a SNARC: number placement in text rapidly changes spatial-numerical associations. Brain and cognition, 72(3), 333-336.
Fischer, M. & Rottmann, J. (2005). Do negative numbers have a place on the mental number line? Psychology Science, 47(1), 22-32.
Fischer, U., Moeller, K., Bientzle, M., Cress, U. & Nuerk, H. C. (2011). Sensori-motor spatial training of number magnitude representation. Psychonomic Bulletin & Review, 18(1), 177-183.
Galen, M. S. van, & Reitsma, P. (2008). Developing access to number magnitude: a study of the SNARC effect in 7- to 9-year-olds. Journal of experimental child psychology, 101(2), 99-113.
Galton, F. (1880). Visualised numerals. Nature, 21, 252-256.
Gevers, W., Verguts, T., Reynvoet, B., Caessens, B. & Fias, W. (2006). Numbers and space: A computational model of the SNARC effect. Journal of Experimental Psychology. Human Perception and Performance, 32, 32-44.
Hubbard, E. M., Piazza, M., Pinel, P. & Dehaene, S. (2005). Interactions between number and space in parietal cortex. Nature Reviews Neuroscience, 6, 435-448.
Kielar-Turska, M. (2000). Rozwój człowieka w pełnym cyklu życia. In J. Strelau (Ed.), Psychologia, Podręcznik Akademicki (pp. 285-332). Gdańsk: GWP.
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, 5934.
Knops, A., Viarouge, A. & Dehaene, S. (2009). Dynamic representations underlying symbolic and nonsymbolic calculation: Evidence from. Attention, Perception & Psychophysics, 71(4), 803-821.
Kucian, K., Grond, U., Rotzer, S., Henzi, B., Schönmann, C., Plangger, F., Gälli, M., Martin, E., von & Aster, M. (2011). Mental number line training in children with developmental dyscalculia. NeuroImage, 57(3), 782-795.
Lammertyn, J., Fias, W. & Lauwereyns, J. (2002). Semantic Influences On Feature-Based Attention Due To Overlap Of Neural Circuits. Cortex, 38, 878-882.
Mackiewicz, R. (2012). Liczby w decyzjach ekonomicznych: instynkt numeryczny i wrażliwość cenowa. In A. Falkowski & T. Zaleśkiewicz (Eds.), Psychologia poznawcza w praktyce. Ekonomia, Biznes, Polityka (pp. 137-185). Warszawa: PWN.
Moyer, R. S. & Landauer, T. K. (1967). Time required for judgments of numerical inequality. Nature, 215, 1519-1520.
Patro, K. & Haman, M. (2012). The spatial-numerical congruity effect in preschoolers. Journal of Experimental Child Psychology, 111(3), 534-542.
Ramani, G. B. & Siegler, R. S. (2008). Promoting Broad and Stable Improvements in Low-Income Children’s Numerical Knowledge Through Playing Number Board Games. Child Development, 79(2), 375-394.
Ramani, G. B. & Siegler, R. S. (2011). Reducing the gap in numerical knowledge between lowand middle-income preschoolers. Journal of Applied Developmental Psychology, 32(3), 146-159.
Räsänen, P., Salminen, J., Wilson, A. J., Aunio, P. & Dehaene, S. (2009). Computer-assisted intervention for children with low numeracy skills. Cognitive Development, 24(4), 450-472.
Restle, F. (1970). Speed of adding and comparing numbers. Journal of Experimental Psychology, 95, 437-444.
Santens, S. & Gevers, W. (2008). The SNARC effect does not imply a mental number line. Cognition, 108(1), 263-270.
Schneider, M., Grabner, R. H. & Paetsch, J. (2009). Mental number line, number line estimation, and mathematical achievement: Their interrelations in grades 5 and 6. Journal of Educational Psychology, 101(2), 359-372.
Siegler, R. S. (2009). Improving the numerical understanding of children from low-income families. Child Development Perspectives, 3, 118-124.
Siegler, R. S. & Booth, J. L. (2005). Development of numerical estimation: A review. In J. B. Campbell (Ed.), Handbook of Mathematical Cognition (pp. 197-212). New York: Psychology Press.
Siegler, R. S. & Ramani, G. B. (2009). Playing linear number board games - but not circular ones - improves low-income preschoolers’ numerical understanding. Journal of Educational Psychology, 101, 545-560.
Siegler, R. S. & Ramani, G. B. (2011). Improving Low-Income Children’s Number Sense. In S. Dehaene & E. Brannon (Eds.), Space, Time and Number in the Brain: Searching for the Foundations of Mathematical Thought (pp. 343-354). London, UK: Elsevier.
van Dijck, J.-P. & Fias, W. (2011). A working memory account for spatial-numerical associations. Cognition, 119(1), 114-119.
Whyte, J. C. & Bull, R. (2008). Number games, magnitude representation, and basic number skills in preschoolers. Developmental psychology, 44(2), 588-596.
Wilson, A. J., Dehaene, S., Pinel, P., Revkin, S. K., Cohen, L. & Cohen, D. (2006a). Principles underlying the design of “the number race”, an adaptive computer game for remediation of dyscalculia. Behavioural and Brain Functioning, 2, 19.
Wilson, A. J., Revkin, S. K., Cohen, D., Cohen, L. & Dehaene, S. (2006b). An open trial assessment of “The Number Race”, an adaptive computer game for remediation of dyscalculia. Behavioral and brain functions, 2, 20.
Wilson, A. J., Dehaene, S. & Fayol, M. (2009). Effects of an Adaptive Game Intervention on Accessing Number Sense in Kindergarten Children. Mind, Brain and Education, 3(4), 224-234.
Wood, G., Willmes, K., Nuerk, H. C. & Fischer, M. H. (2008). On the cognitive link between space and number: A meta-analysis of the SNARC effect. Psychology Science Quarterly, 50(4), 489-525.
Zebian, S. (2005). Linkages between number concepts, spatial thinking, and directionality of writing: The SNARC effect and the reverse SNARC effect in English and Arabic monoliterates, biliterates, and illiterate Arabic speakers. Journal of Cognition and Culture, 5(1-2), 165-190.
Bächtold, D., Baumuller, M. & Brugger, P. (1998). Stimulus-response compatibility in representational space. Neuropsychologia, 36, 731-735.
Berch, D. B., Foley, E. J., Hill, R. J. & Ryan, P. M. (1999). Extracting parity and magnitude from Arabic numerals: Developmental changes in number processing and mental representation. Journal of Experimental Child Psychology, 74, 286-308.
Brysbaert, M. (1995). Arabic number reading: On the nature of the numerical scale and the origin of phonological recoding. Journal of Experimental Psychology: General, 124, 434-452.
Cipora, K., Czernecka, K., Żelechowska, D. & Szewczyk, J. (2011). Sources of individual differences in the magnitude of the SNARC effect. International Society for the Study of Individual Differences, London, Wielka Brytania. Poster.
Cipora, K. & Nęcka, E. (w druku). Kontinua a przestrzeń - przegląd badań nad przestrzennym komponentem poznawczej reprezentacji wielkości i nasilenia. Psychologia-Etologia-Genetyka.
Cipora, K. & Szczygieł, M. (w recenzji). „Wyścig Liczb - The Number Race” - polska adaptacja narzędzia wczesnej interwencji w dyskalkulii rozwojowej oraz wspomagania rozwoju kompetencji matematycznych.
Cohen Kadosh, R., Lammertyn, J. & Izard, V. (2008). Are numbers special? An overview of chronometric, neuroimaging, developmental and comparative studies of magnitude representation. Progress in Neurobiology, 84(2), 132-147.
Dehaene, S. (2001). Precis of the number sense. Mind & Lang, 16, 16-36.
Dehaene, S. (2011). The number sense. How the mind creates mathematics? Nowy Jork: Oxford University Press.
Dehaene, S., Dupoux, E. & Mehler, J. (1990). Is numerical comparison digital: Analogical and symbolic effects in two-digit number comparison. Journal of Experimental Psychology: Human Perception and Performance, 16, 626-641.
Dehaene, S., Bossini, S. & Giraux, P. (1993). The Mental Representation of Parity and Number Magnitude. Journal of Experimental Psychology: General, 122, 371-396.
Dehaene, S., Piazza, M., Pinel, P. & Cohen, L. (2005). Three Parietal Circuits for Number Processing. In J. I. D. Campbell (Ed.), Handbook of Mathematical Cognition (pp. 433-453). New York: Psychology Press.
Fayol, M. & Seron, X. (2005). About numerical representations: insights from neuropsychological, experimental and developmental studies. In J. B. Campbell (Ed.), Handbook of Mathematical Cognition (pp. 3-22). New York: Psychology Press.
Fischer, M. H., Castel, A. D., Dodd, M. D. & Pratt, J. (2003). Perceiving numbers causes spatial shifts of attention. Nature Neuroscience, 6, 555-556.
Fischer, M. H., Ellis, R., Cangelosi, A. & Mychakov, A. (2011). The oculomotor resonance effect during auditory number comprehension. Poster zaprezentowany podczas XXIXth European Workshop on Cognitive Neuropsychology. Bressanone, Włochy.
Fischer, M. H., Mills, R. A. & Shaki, S. (2010). How to cook a SNARC: number placement in text rapidly changes spatial-numerical associations. Brain and cognition, 72(3), 333-336.
Fischer, M. & Rottmann, J. (2005). Do negative numbers have a place on the mental number line? Psychology Science, 47(1), 22-32.
Fischer, U., Moeller, K., Bientzle, M., Cress, U. & Nuerk, H. C. (2011). Sensori-motor spatial training of number magnitude representation. Psychonomic Bulletin & Review, 18(1), 177-183.
Galen, M. S. van, & Reitsma, P. (2008). Developing access to number magnitude: a study of the SNARC effect in 7- to 9-year-olds. Journal of experimental child psychology, 101(2), 99-113.
Galton, F. (1880). Visualised numerals. Nature, 21, 252-256.
Gevers, W., Verguts, T., Reynvoet, B., Caessens, B. & Fias, W. (2006). Numbers and space: A computational model of the SNARC effect. Journal of Experimental Psychology. Human Perception and Performance, 32, 32-44.
Hubbard, E. M., Piazza, M., Pinel, P. & Dehaene, S. (2005). Interactions between number and space in parietal cortex. Nature Reviews Neuroscience, 6, 435-448.
Kielar-Turska, M. (2000). Rozwój człowieka w pełnym cyklu życia. In J. Strelau (Ed.), Psychologia, Podręcznik Akademicki (pp. 285-332). Gdańsk: GWP.
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, 5934.
Knops, A., Viarouge, A. & Dehaene, S. (2009). Dynamic representations underlying symbolic and nonsymbolic calculation: Evidence from. Attention, Perception & Psychophysics, 71(4), 803-821.
Kucian, K., Grond, U., Rotzer, S., Henzi, B., Schönmann, C., Plangger, F., Gälli, M., Martin, E., von & Aster, M. (2011). Mental number line training in children with developmental dyscalculia. NeuroImage, 57(3), 782-795.
Lammertyn, J., Fias, W. & Lauwereyns, J. (2002). Semantic Influences On Feature-Based Attention Due To Overlap Of Neural Circuits. Cortex, 38, 878-882.
Mackiewicz, R. (2012). Liczby w decyzjach ekonomicznych: instynkt numeryczny i wrażliwość cenowa. In A. Falkowski & T. Zaleśkiewicz (Eds.), Psychologia poznawcza w praktyce. Ekonomia, Biznes, Polityka (pp. 137-185). Warszawa: PWN.
Moyer, R. S. & Landauer, T. K. (1967). Time required for judgments of numerical inequality. Nature, 215, 1519-1520.
Patro, K. & Haman, M. (2012). The spatial-numerical congruity effect in preschoolers. Journal of Experimental Child Psychology, 111(3), 534-542.
Ramani, G. B. & Siegler, R. S. (2008). Promoting Broad and Stable Improvements in Low-Income Children’s Numerical Knowledge Through Playing Number Board Games. Child Development, 79(2), 375-394.
Ramani, G. B. & Siegler, R. S. (2011). Reducing the gap in numerical knowledge between lowand middle-income preschoolers. Journal of Applied Developmental Psychology, 32(3), 146-159.
Räsänen, P., Salminen, J., Wilson, A. J., Aunio, P. & Dehaene, S. (2009). Computer-assisted intervention for children with low numeracy skills. Cognitive Development, 24(4), 450-472.
Restle, F. (1970). Speed of adding and comparing numbers. Journal of Experimental Psychology, 95, 437-444.
Santens, S. & Gevers, W. (2008). The SNARC effect does not imply a mental number line. Cognition, 108(1), 263-270.
Schneider, M., Grabner, R. H. & Paetsch, J. (2009). Mental number line, number line estimation, and mathematical achievement: Their interrelations in grades 5 and 6. Journal of Educational Psychology, 101(2), 359-372.
Siegler, R. S. (2009). Improving the numerical understanding of children from low-income families. Child Development Perspectives, 3, 118-124.
Siegler, R. S. & Booth, J. L. (2005). Development of numerical estimation: A review. In J. B. Campbell (Ed.), Handbook of Mathematical Cognition (pp. 197-212). New York: Psychology Press.
Siegler, R. S. & Ramani, G. B. (2009). Playing linear number board games - but not circular ones - improves low-income preschoolers’ numerical understanding. Journal of Educational Psychology, 101, 545-560.
Siegler, R. S. & Ramani, G. B. (2011). Improving Low-Income Children’s Number Sense. In S. Dehaene & E. Brannon (Eds.), Space, Time and Number in the Brain: Searching for the Foundations of Mathematical Thought (pp. 343-354). London, UK: Elsevier.
van Dijck, J.-P. & Fias, W. (2011). A working memory account for spatial-numerical associations. Cognition, 119(1), 114-119.
Whyte, J. C. & Bull, R. (2008). Number games, magnitude representation, and basic number skills in preschoolers. Developmental psychology, 44(2), 588-596.
Wilson, A. J., Dehaene, S., Pinel, P., Revkin, S. K., Cohen, L. & Cohen, D. (2006a). Principles underlying the design of “the number race”, an adaptive computer game for remediation of dyscalculia. Behavioural and Brain Functioning, 2, 19.
Wilson, A. J., Revkin, S. K., Cohen, D., Cohen, L. & Dehaene, S. (2006b). An open trial assessment of “The Number Race”, an adaptive computer game for remediation of dyscalculia. Behavioral and brain functions, 2, 20.
Wilson, A. J., Dehaene, S. & Fayol, M. (2009). Effects of an Adaptive Game Intervention on Accessing Number Sense in Kindergarten Children. Mind, Brain and Education, 3(4), 224-234.
Wood, G., Willmes, K., Nuerk, H. C. & Fischer, M. H. (2008). On the cognitive link between space and number: A meta-analysis of the SNARC effect. Psychology Science Quarterly, 50(4), 489-525.
Zebian, S. (2005). Linkages between number concepts, spatial thinking, and directionality of writing: The SNARC effect and the reverse SNARC effect in English and Arabic monoliterates, biliterates, and illiterate Arabic speakers. Journal of Cognition and Culture, 5(1-2), 165-190.
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2012-12-01
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Cipora, K. (2012). Perspektywy wykorzystania wyników badań nad przestrzennym komponentem reprezentacji liczb w edukacji. Annales Universitatis Paedagogicae Cracoviensis Studia Psychologica, 5(1), 54–66. Pobrano z https://studia-psychologica.uken.krakow.pl/article/view/5579
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