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Éva Jármi
Éva Jármi
Pszichológiai Intézet, Iskolapszichológia Tanszék, ELTE-PPK, Budapest
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Absztrakt
A matematikai megismerés, a számfeldolgozás folyamatának feltérképezése az elmúlt évtizedekben gyors ütemben elindult, mégis számos kérdés továbbra is nyitott. A fejlődési szempont és különösen a matematikai képességek tipikus fejlődésének vizsgálata sajnos viszonylag háttérbe szorult, pedig ez mind gyakorlati, mind elméleti szempontból releváns téma a kognitív pszichológia számára. Napjaink egyre inkább elfogadott nézete szerint a tipikus fejlődésmenet megismerése nélkülözhetetlen az atipikus fejlődés, így a fejlődési diszkalkulia megértéséhez, továbbá a felnőtt számfeldolgozás olyan modelljeinek megalkotásához, amelyek fejlődési szempontból is plauzibilisek.
Összefoglaló tanulmányunkban ezért a tipikus fejlődésre fókuszálunk, amelyben kitüntetett jelentőségű a veleszületett számérzék, illetve a biológiailag elsődleges matematikai képességek kibontásának, kiterjesztésének időszaka, az óvodáskor. A számnevek elsajátításával lehetővé válik a mennyiségek pontos reprezentációja, a számlálás, és alapvető számtani műveletek elvégzése nagyobb számkörben. A számfogalom kialakulásával, a számok terén szerzett tapasztalatok bővülésével a formális matematikatanulás első éveiben további mérföldköveit találjuk a számolási képességek fejlődésének. A számok reprezentációját végző mentális számegyenes egyre pontosabb, a számtani műveletek elvégzése során a kisiskolások egyre inkább számtani emlékezetükre támaszkodnak és egyre hatékonyabban alkalmazzák a rendelkezésükre álló számolási stratégiákat.
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-
1. Ashcraft, M. H. (1995): Cognitive psychology and simple arithmetic: A review and summary of new directions. Mathematical Cognition, 1, 3–34.
-
2. Baroody, A. J. (1999): The roles of estimation and the commutativity principle in the development of third-graders’ mental multiplication. Journal of Experimental Child Psychology, 75, 157–193.
-
3. Briars, D. J., Siegler, R. S. (1984): A featural analysis of preschoolers’ counting knowledge. Developmental Psychology, 20, 607–618.
-
4. Brown, J. S., Burton, R. B. (1978): Diagnostic models for procedural bugs in basic mathematical skills. 5. Cognitive Science, 2 (2), 155–192.
-
5. Bryant, P., Christie, C., Rendu, A. (1999): Children's understanding of the relation between addition and subtraction: Inversion, identity, and decomposition. Journal of Experimental Child Psychology, 74, 194–212.
-
6. Butterworth, B. (1999): The Mathematical Brain. London, Macmillan.
-
7. Butterworth, B. (2005): The development of arithmetical abilities. Journal of Child Psychology and Psychiatry, 46 (1), 3–18.
-
8. Butterworth, B., Girelli, L., Zorzi, M., Jonckheere, A. R. (2001): Organisation of addition facts in memory. Quarterly Journal of Experimental Psychology, 54A, 1005–1029.
-
9. Butterworth, B., Marchesini, N., Girelli, L. (2003): Organisation of multiplication facts in memory: Developmental trends. In: A. J. Baroody, A. Dowker (eds), The Development of Arithmetical Concepts and Skills: Constructing adaptive expertise. Mahwah, NJ, LEA, 189–202.
-
10. Camos, V. (2003): Counting strategies from 5 years to adulthood: Adaptation to structural features. European Journal of Psychology of Education, 18 (3), 251–265.
-
11. Campbell, J. I. D. (1994): Architectures for numerical cognition. Cognition, 53, 1–44.
-
12. Campbell, J. I. D., Graham, D. J. (1985): Mental multiplication skill: Structure, process and acquisition. Canadian Journal of Psychology, 39, 338–366.
-
13. Campbell, J. I. D., Gunter, R. (2002): Calculation, culture, and the repeated operand effect. Cognition, 86, 71–96.
-
14. Carpenter, T. P., Moser, J. M. (1982): The development of addition and subtraction problem solving skills. In: T. P. Carpenter, J. M. Moser, T. A. Romberg (eds), Addition and Subtraction: A cognitive perspective. Hillsdale, NJ, LEA, 9–24.
-
15. Chinn, C. A. (2006): The microgenetic method: Current work and extensions to classroom research. In: J. L. Green, G. Camilli, P. Elmore (eds), Handbook of Complementary Methods in Education Research. Washington, DC, American Educational Research Association, 439–456.
-
16. Cooney, J. B., Swanson, H. L., Ladd, S. F. (1988): Acquisition of mental multiplication skill: Evidence for the transition between counting and retrieval strategies. Cognition and Instruction, 5, 323–345.
-
17. Csépe Valéria (2005): Kognitív fejlődés-neuropszichológia. Budapest, Gondolat Kiadó.
-
18. De Brauwer, J., Verguts, T., Fias, W. (2006): The representation of multiplication facts: Developmental changes in the problem size, five, and tie effects. Journal of Experimental Child Psychology, 94 (1), 43–56.
-
19. Dehaene, S. (1992): Varieties of numerical abilities. Cognition, 44, 1–42.
-
20. Dehaene, S. (2003): A számérzék: miként alkotja meg az elme a matematikát? Budapest, Osiris Kiadó.
-
21. Dehaene, S., Cohen, L. (1997): Cerebral pathways for calculation: Double dissociation between rote verbal and quantitative knowledge of arithmetic. Cortex, 33, 219–250.
-
22. Dehaene, S., Spelke, E., Pinel, P., Stanescu, R., Tsivkin, S. (1999): Sources of mathematical thinking: Behavioral and brain-imaging evidence. Science, 284, 970–974.
-
23. De Rammelaere, S., Stuyven, E., Vandierendonck, A. (2001): Verifying simple arithmetic sums and products: Are the phonological loop and the central executive involved? Memory and Cognition, 29 (2), 267–273.
-
24. Dowker, A. (2003): Young children's estimates for addition: The zone of partial knowledge and understanding. In: A. J. Baroody, A. Dowker (eds), The Development of Arithmetic Concepts and Skills: Constructing adaptive expertise. Mahwah, NJ, LEA, 243–265.
-
25. Duncan, E. M., McFarland, C. E. (1980): Isolating the effect of symbolic distance and semantic congruity in comparative judgments: An additive-factors analysis. Memory & Cognition, 2, 95–110.
-
26. Ebersbach, M., Luwel, K., Frick, A., Onghena, P., Verschaffel, L. (2008): The relationship between the shape of the mental number line and familiarity with numbers in 5- to 9-year old children: Evidence for a segmented linear model. Journal of Experimental Child Psychology, 99, 1–17.
-
27. Ellis, S. (1997): Strategy choice in sociocultural context. Developmental Review, 17, 490–524.
-
28. Fayol, M., Barrouillet, P., Marinthe, C. (1998): Predicting arithmetical achievement from neuro-psychological performance: A longitudinal study. Cognition, 68, 63–70.
-
29. Fuson, K. C. (1988): Children's Counting and Concept s of Number. New York, Springer-Verlag.
-
30. Fuson, K. C. (1992): Research on whole number addition and subtraction. In: D. Grouws (ed.), Handbook of Research on Mathematics Teaching and Learning. New York, Macmillan, 243–275.
-
31. Fuson, K. C., Burghardt, B. H. (2003): Multi-digit addition and subtraction methods invented in small groups and teacher support of problem solving and reflection. In: A. J. Baroody, A. Dowker (eds), The Development of Arithmetic Concepts and Skills: Constructing adaptive expertise. Hillsdale, NJ, Erlbaum, 267–304.
-
32. Fuson, K. C., Kwon, Y. (1992): Learning addition and subtraction: Effects of number words and other cultural tools. In: J. Bideaud, C. Meljac, J-P. Fischer (eds), Pathways to Number. Hillsdale, NJ, Erlbaum, 283–306.
-
33. Fuson, K. C., Wearne, D., Hiebert, J., Human, P., Murray, H., Olivier, A., Carpenter, T. P., Fennema, E. (1997): Children's conceptual structures for multidigit numbers and methods of multidigit addition and subtraction. Journal for Research in Mathematics Education, 28, 130–162.
-
34. Geary, D. C. (1994): Children's Mathematical Development: Research and practical applications. Washington, DC, American Psychological Association.
-
35. Geary, D. C. (1995): Reflections of evolution and culture in children's cognition: Implications for mathematical development and instruction. American Psychologist, 50, 24–37.
-
36. Geary, D. C. (2000): From infancy to adulthood: The development of numerical abilities. European Child & Adolescent Psychiatry, 9 (2), 11–16.
-
37. Geary, D. C. (2004): Mathematics and learning disabilities. Journal of Learning Disabilities, 37, 4–15.
-
38. Geary, D. C., Brown, S. C. (1991): Cognitive addition: Strategy choice and speed-of-processing differences in gifted, normal, and mathematically disabled children. Developmental Psychology, 27, 398–406.
-
39. Geary, D. C., Hamson, C. O., Hoard, M. K. (2000): Numerical and arithmetical cognition: A longitudinal study of process and concept deficits in children with learning disability. Journal of Experimental Child Psychology, 77, 236–263.
-
40. Geary, D. C., Widaman, K. F. (1992): Numerical cognition: On the convergence of componential and psychometric models. Intelligence, 16, 47–80.
-
41. Gelman, R., Gallistel, C. R. (1978): The Child's Understanding of Number. Cambridge, MA, Harvard University Press.
-
42. Gelman, R., Meck, E. (1983): Preschoolers’ counting: Principles before skill. Cognition, 13, 343–359.
-
43. Gibbon, J., Church, R. M. (1981): Time left: Linear versus logarithmic subjective time. Journal of the Experimental Analysis of Behavior, 7, 87–107.
-
44. Gordon, P. (2004): Numericalcognitionwithoutwords: EvidencefromAmazonia. Science, 306, 496–499.
-
45. Gyarmathy Éva (1998): A tanulási zavarok szindróma a szakirodalomban I. Új Pedagógiai Szemle, 10, 59–68.
-
46. Huntley-Fenner, G. (2001): Children's understanding of number is similar to adults’ and rats’: Numerical estimation by 5–7-year-olds. Cognition, 78, 27–40.
-
47. Imbo, I., Vandierendonck, A. (2007): The development of strategy use in elementary school children: Working memory and individual differences. Journal of Experimental Child Psychology, 96, 284–309.
-
48. Józsa Krisztián (2003): A számolási készség fejlesztése. In: Dubiczné Mile Katalin és Farkas Istvánné (szerk.), Az általános iskola alapozó szakaszának megújítása. Székesfehérvár, Fejér Megyei Pedagógiai Szakmai és Szakszolgáltató Intézet, 27–44.
-
49. Kanayet, F., Opfer, J. E. (2009): Why children's number-line estimates follow Fechner's law. In: N. Taatgen, H. van Rijn (eds), Proceedings of the XXXI Annual Cognitive Science Society. Mahwah, NJ, Erlbaum.
-
50. Kaufman, E. L., Lord, M. W., Reese, T. W., Volkmann, J. (1949): The discrimination of visual number. American Journal of Psychology, 62, 498–525.
-
51. Kaufmann, L., Nuerk, H-C. (2005): Numerical development: Current issues and future perspectives. Psychology Science,42, 142–170.
-
52. Laski, E. V., Siegler, R. S. (2007): Is 27 a big number? Correlational and causal connections among numerical categorization, number line estimation, and numerical magnitude comparison. Child Development, 76, 1723–1743.
-
53. Lee, K. M., Kang, S. Y. (2002): Arithmetic operation and working memory: Differential suppression in dual tasks. Cognition, 83, 63–68.
-
54. Lemaire, P., Fayol, M., Abdi, H. (1991): Associative confusion effect in cognitive arithmetic: Evidence for partially autonomous processes. European Bulletin of Cognitive Psychology, 11, 587–604.
-
55. Lemaire, P., Siegler, R. S. (1995): Four aspects of strategic change: contributions to children's learning of multiplication. Journal of Experimental Psychology: General, 124 (1), 83–97.
-
56. Márkus Attila (2007): Számok, számolás, számolászavarok. Budapest, Pro Die Kiadó.
-
57. McCloskey, M. (1992): Cognitive mechanisms in numerical processing: Evidence from acquired dyscalculia. Cognition, 44, 107–157.
-
58. Mix, K. S. (1999): Preschoolers’ recognition of numerical equivalence: sequential sets. Journal of Experimental Child Psychology, 74, 309–332.
-
59. Moeller, K., Klein, E., Fischer, M. H., Nuerk, H-C., Willmes, K. (2011): Representation of multiplication facts – Evidence for partial verbal coding. Behavioral and Brain Function, 7, 1–9.
-
60. Moyer, R. S., Landauer, T. K. (1967): Time required for judgments of numerical inequalities. Nature, 215, 1519–1520.
-
61. Opfer, J. E., Siegler, R. S. (2007): Representational change and children's numerical estimation. Cognitive Psychology, 55, 169–195.
-
62. Osborne, R. T., Lindsey, J. M. (1967): A longitudinal investigation of change in the factorial composition of intelligence with age in young school children. Journal of Genetic Psychology, 110, 49–58.
-
63. Pesenti, M., Thioux, M., Seron, X., De Volder, A. (2000): Neuroanatomical substrate of Arabic number processing, numerical comparison and simple addition: A PET study. Journal of Cognitive Neuroscience, 12 (3), 61–479.
-
64. Piaget, J. (1952): The Child's Conception of Number. London, Routledge & Kegan Paul.
-
65. Pica, P., Lemer, C., Izard, V., Dehaene, S. (2004): Exact and approximate arithmetic in an Amazonian indigene group. Science, 306, 499–503.
-
66. Potter, M. C., Levy, E. I. (1968): Spatial enumeration without counting. Child Development, 39, 265–272.
-
67. Rubinstein, O., Henik, A., Berger, A., Shahar-Shalev, S. (2002): The development of internal representations of magnitude and their association with arabic numerals. Journal of Experimental Child Psychology, 81, 74–92.
-
68. Sekular, R., Mierkiewicz, D. (1977): Children's judgment of numerical inequality. Child Development, 48, 630–633.
-
69. Shrager, J., Siegler, R. S. (1998): SCADS: A model of children's strategy choices and strategy discoveries. Psychological Science, 9, 405–410.
-
70. Siegler, R. S. (1988a): Strategy choice procedures and the development of multiplication skill. Journal of Experimental Psychology: General, 117, 258–275.
-
71. Siegler, R. S. (1988b): Individual differences in strategy choices: good students, not-so-good students, and perfectionists. Child Development, 59 (4), 833–851.
-
72. Siegler, R. S. (1996): Emerging Minds: The process of change in children's thinking. Oxford University Press.
-
73. Siegler, R. S. (1999): Strategic development. Trends in Cognitive Sciences, 3 (11), 430–435.
-
74. Siegler, R. S., Booth, J. L. (2004): Development of numerical estimation in young children. Child Development, 75, 428–444.
-
75. Siegler, R. S., Jenkins, E. (1989): How Children Discover New Strategies. Hillsdale, NJ, Lawrence Erlbaum Associates.
-
76. Siegler, R. S., Opfer, J. E. (2003): The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14, 237–243.
-
77. Siegler, R. S., Shipley, C. (1995): Variation, selection, and cognitive change. In: T. Simon, G. Halford (eds), Developing Cognitive Competence: New approaches to process modeling. Hillsdale, NJ, Erlbaum, 31–76.
-
78. Soltész Fruzsina (2010): Typical and atypical development of magnitude processing. Ph.D. Thesis, ELTE, Budapest.
-
79. Song, M. J., Ginsburg, H. P. (1987): The development of informal and formal mathematical thinking in Korean and U. S. children. Child Development, 58, 1286–1296.
-
80. Spelke, E. S., Tsivkin, S. (2001): Language and number: A bilingual training study. Cognition, 78, 45–88.
-
81. Stazyk, E. H., Ashcraft, M. H., Hamann, M. S. (1982): A network approach to simple mental multiplication. Journal of Experimental Psychology: Learning, Memory, and Cognition, 8, 320–335.
-
82. Temple, E., Posner, M. I. (1998): Brain mechanisms of quantity are similar in 5-year-olds and adults. Proceedings of the National Academy of Sciences USA, 95, 7836–7841.
-
83. Tóth Dénes , Csépe Valéria (2008): Azolvasás fejlődésekognitív pszichológiaiszempontból. Pszichológia, 28 (1), 35–52.
-
84. Vandenberg, S. G. (1962): The hereditary abilities study: Hereditary components in a psychological test battery. American Journal of Human Genetics, 14, 220–237.
-
85. Vandenberg, S. G. (1966): Contributions of twin research to psychology. Psychological Bulletin, 66, 327–352.
-
86. Wynn, K. (1990): Children's understanding of counting. Cognition, 36, 155–193.
-
87. Xu, F., Spelke, E. S., Goddard, S. (2005): Number sense in human infants. Developmental Science, 8, 88–101.
-
88. Zhou, X., Booth, J. R., Lu, J., Zhao, H., Butterworth, B., Chen, C., Dong, Q. (2011): Age-independent and age-dependent neural substrate for single-digit multiplication and addition arithmetic problems. Developmental Neuropsychology, 36 (3), 338–352.
-
89. Zhou, X., Chen, C., Zang, Y., Dong, Q., Chen, C., Qiao, S. (2007): Dissociated brain organizations for single-digit addition and multiplication. NeuroImage, 35, 871–880.
| Pszichológia | |
|---|---|
| Language | Hungarian |
| Year of Foundation |
1981 |
| Publication Programme |
ceased |
| Founder | Természettudományi Kutatóközpont -- Research Centre for Natural Sciences |
| Founder's Address |
H-1117 Budapest, Hungary Magyar Tudósok Körútja 2. |
| Publisher | Akadémiai Kiadó |
| Publisher's Address |
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245. |
| Responsible Publisher |
Chief Executive Officer, Akadémiai Kiadó |
| ISSN | 0230-0508 (Print) |
| ISSN | 2060-2782 (Online) |
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