Liczenie na palcach w ontogenezie i jego znaczenie  dla rozwoju kompetencji matematycznych

Monika Szczygieł,

Krzysztof Cipora,

Mateusz Hohol

Abstrakt

Finger counting and its role in the development of math competence

Finger counting plays an important role in mathematical cognition, especially in the acquisition of the concept of number and elementary math competence. Fingers are spontaneously used to count because of their constant availability and easiness of manipulation. Stable counting order within hand facilitates the acquisition of ordinal as well as cardinal numbers. Additionally, using fingers to count alleviates working memory load and allows constant control of counting accuracy. Apart from the usefulness for counting practice, cognitive representations of fingers are strongly interconnected with representations of numbers. Finger gnosis (the quality of the brain representations of fingers) is a good predictor of current as well as future math achievement. There is also evidence that the training of finger differentiation leads to improvements in math achievement.
 

Słowa kluczowe: rozwój poznawczy, poznanie matematyczne, liczenie na palcach, gnozja palców
References

Andres M., Di Luca S., Pesenti M. (2008), Finger counting: The missing tool? Behavioral and Brain Sciences, 31, 6, 642–643.

Ann J. (1993), A linguistic investigation of the relationship between physiology and handshape. Doctoral dissertation, University of Arizona.

Alibali M. W., DiRusso A.A. (1999), The function of gesture in learning to count: More than keeping track. Cognitive Development, 14, 1, 37–56.

Beller S., Bender A. (2011), Explicating numerical information: When and how fingers support (or hinder) number comprehension and handling. Frontiers in Psychology, 2, 7–9.

Bender A., Beller S. (2011). Fingers as a tool for counting-naturally fixed or culturally flexible? Frontiers in Psychology, 2, 10–12.

Brissiaud R. (2003), Comment les enfants apprennent à calculer. Paris: Retz.

Butterworth B. (1999), The Mathematical Brain. London: Macmillan.

Butterworth B. (2005), The development of arithmetical abilities. Journal of Child Psychology and Psychiatry, 46, 1, 3–18.

Butterworth B., Reeve R., Reynolds F. (2011), Using mental representations of space when words are unavailable: Studies of enumeration and arithmetic in indigenous Australia. Journal of Cross-Cultural Psychology, 42, 4, 630–638.

Cipora K., Szczygieł M. (2013), Wyścig Liczb – The Number Race – polska wersja językowa narzędzia wczesnej interwencji w przypadku ryzyka dyskalkulii rozwojowej oraz wspomagania rozwoju kompetencji arytmetycznych. Psychologia – Etologia – Genetyka 27, 71–85.

Cipora K., Szczygieł M., Hohol M. (2014), Palce, które liczą: znaczenie liczenia na palcach dla poznania matematycznego u człowieka dorosłego. Psychologia – Etologia – Genetyka, 30, 59–73.

Crollen V., Mahe R., Collignon O., Seron X. (2011), The role of vision in the development of finger–number interactions: Finger-counting and finger-montring in blind children. Journal of Experimental Child Psychology, 109, 4, 525–539.

Domahs F., Krinzinger H., Willmes K. (2008), Mind the gap between both hands: Evidence for internal finger-based number representations in children’s mental calculation. Cortex, 44, 4, 359–367.

Domahs F., Moeller K., Huber S., Willmes K., Nuerk H.C. (2010), Embodied numerosity: Implicit hand-based representations influence symbolic number processing across cultures. Cognition, 116, 2, 251–266.

Emerson J., Babtie P. (2010), The dyscalculia assessment. London: Continuum.

Fayol M., Barrouillet P., Marinthe C. (1998), Predicting arithmetical achievement from neuro-psychological performance: A longitudinal study. Cognition, 68, 2, B63–B70.

Fayol M., Seron X. (2005), About numerical representations: Insights from neuropsychological, experimental, and developmental studies [w:] J.I. Campbell (red.), Handbook of Mathematical Cognition, 3–22. New York: Psychology Press.

Fischer J.P. (2010), Numerical performance increased by finger training: A fallacy due to regression toward the mean? Cortex, 46, 2, 272–273.

Fischer M.H. (2012), A hierarchical view of grounded, embodied and situated numerical cognition. Cognitive Processing, 13, 161–164.

Fischer M. H., Brugger P. (2011), When digits help digits: Spatial–numerical associations point to finger counting as prime example of embodied cognition. Frontiers in Psychology, 2, 41–47.

Fuson K.C., Kwon Y. (1992), Korean children’s understanding of multidigit addition and subtraction. Child Development, 63, 2, 491–506.

Fuson K.C., Secada W.G. (1986), Teaching children to add by counting-on with one-handed finger patterns. Cognition and Instruction, 3, 3, 229–260.

Geary D.G. (1994), Children’s mathematical development, research and practical applications. Washington, DC: American Psychological Association.

Geary D.C., Bow-Thomas C.C., Liu F., Siegler R.S. (1996), Development of arithmetical competencies in Chinese and American children: Influence of age, language, and schooling. Child Development, 67, 5, 2022–2044.

Gelman R., Gallistel C. (1986), The child’s understanding of number. Cambridge, MA: Harvard University Press.

Gracia-Bafalluy M., Noël M.P. (2008), Does finger training increase young children’s numerical performance? Cortex, 44, 4, 368–375.

Groen G.J., Parkman J.M. (1972), A chronometric analysis of simple addition. Psychological Review, 79, 329–343.

Gruszczyk-Kolczyńska E. (2000), Dzieci ze specyficznymi trudnościami w uczeniu się matematyki. Warszawa: WSiP.

Gruszczyk-Kolczyńska E. (2012), Dodawanie i odejmowanie w możliwie szerokim zakresie: od poziomu konkretów, przez zbiory zstępcze aż do rachowania w pamięci. Stosowanie tych umiejętności w rozwiązywaniu zadań [w:] E. Gruszczyk-Kolczyńska (red.), O dzieciach matematycznie uzdolnionych. Książka dla rodziców i nauczycieli, 167–186. Warszawa: Wydawnictwo Nowa Era.

Gruszczyk-Kolczyńska E., Zielińska E. (1999), Dziecięca matematyka: program dla przedzkoli, klas zerowych i placówek integracyjnych, Warszawa: WSiP.

Gruszczyk-Kolczyńska E., Zielińska E. (2009), Kształtowanie umiejętności dodawania i odejmowania od poziomu manipulacji przedmiotami, przez liczenie na zbiorach zastępczych do rachowania w pamięci [w:] E. Gruszczyk-Kolczyńska (red.), Wspomaganie rozwoju umysłowego oraz edukacja matematyczna dzieci w ostatnim roku wychowania przedszkolnego i w pierwszym roku szkolnej edukacji, 135–165. Warszawa: Wydawnictwo Edukacja Polska 2009

Ifrah G. (2000), The universal history of computing: From the abacus to quantum computing. New York: John Wiley & Sons, Inc.

Jordan N.C., Kaplan D., Ramineni C., Locuniak M.N. (2008), Development of number combination skill in the early school years: When do fingers help? Developmental Science, 11, 5, 662–668.

Kaufmann L. (2002), More evidence for the role of the central executive in retrieving arithmetic facts: A case study of severe developmental dyscalculia. Journal of Clinical and Experimental Neuropsychology, 24, 3, 302–310.

Kaufmann L., Vogel S.E., Wood G., Kremser Ch., Schocke M., Zimmerhackl L.B., Koten J.W. (2008), A developmental fMRI study of non-symbolic numerical and spatial processing. Cortex, 44, 376–385.

Klein E., Moeller K., Willmes K., Nuerk H. C., Domahs F. (2011), The influence of implicit hand-based representations on mental arithmetic. Frontiers in Psychology, 2, 1–7.

LeFevre J., DeStefano D., Coleman B., Shanahan T. (2005), Mathematical cognition and working memory [w:] J.I. Campbell (ed.), Handbook of Mathematical Cognition, 361–377. New York: Psychology Press.

Marinthe C., Fayol M., Barrouillet P. (2000). Gnosies digitales et développement des performances arithméthiques [w:] A. Van Hout, C. Meljac (red.), Troubles du calcule et dyscalculies chez l’enfant, s. 239–254. Paris: Masson.

Moeller K., Martignon L., Wessolowski S., Engel J., Nuerk H.C. (2011), Effects of finger counting on numerical development – the opposing views of neurocognition and mathematics education. Frontiers in Psychology, 2, 75–79.

Noël M.P. (2005), Finger gnosia: A predictor of numerical abilities in children? Child Neuropsychology, 11, 5, 413–430.

Noël M.P., Rousselle L., Mussolin C. (2005), Magnitude representation in children. Its development and dysfunction [w:] J.I. Campbell (red.), Handbook of Mathematical Cognition, 179–195. New York: Psychology Press.

Nicoladis E., Pika S., Marentette P. (2010), Are number gestures easier than number words for preschoolers? Cognitive Development, 25, 3, 247–261.

Penner-Wilger M., Anderson M.L. (2008, lipiec), An alternative view of the relation between finger gnosis and math ability: Redeployment of finger representations for the representation of number. Proceedings of the 30th annual meeting of the Cognitive Science Society, Austin, TX, 1647–1652.

Pesenti M., Thioux M., Seron X., De Volder A. (2000), Neuroanatomical substrates of Arabic number processing, numerical comparison, and simple addition: A PET study. Journal of Cognitive Neuroscience, 12, 461–479.

Piaget J. (1966), Studia z psychologii dziecka. Warszawa: PWN.

Piaget J. (1977), Psychologia i epistemologia. Warszawa: PWN.

Pinel P., Piazza M., Le Bihan D., Dehaene S. (2004), Distributed and overlapping cerebral representations of number, size, and luminance during comparative judgments. Neuron 41, 6, 983–993.

Poeck K. (1965), Phantoms following amputation in early childhood and in congenital absence of limbs. Cortex, 1, 269–275.

Reeve R., Humberstone J. (2011), Five-to 7-year-olds’ finger gnosia and calculation abilities. Frontiers in Psychology, 2.

Rusconi E., Pinel P., Dehaene S., Kleinschmidt A. (2010), The enigma of Gerstmann’s syndrome revisited: A telling tale of the vicissitudes of neuropsychology. Brain, 133, 2, 320–332.

Rusconi E., Walsh V., Butterworth B. (2005), Dexterity with numbers: rTMS over left angular gyrus disrupts finger gnosis and number processing. Neuropsychologia, 43, 11, 1609–1624.

Semadeni Z. (2012/2013), Matematyka w edukacji początkowej jako fundament całej matematyki szkolnej. Nauczanie Początkowe, 1, 7–43.

Semadeni Z. (nieopublikowany manuskrypt), Matematyka w edukacji początkowej – podejście konstruktywistyczne.

Thompson I. (1999), Mental calculation strategies for addition and subtraction. Mathematics in School, 28, 1–4.

Suresh P.A., Sebastian S. (2000), Developmental Gerstmann’s syndrome: A distinct clinical entity of learning disabilities. Pediatric Neurology, 22, 4, 267–278.

Wiese H. (2003), Numbers, language and human mind. Cambridge: Cambridge University Press.

Willems G., Feeters-Erenay M.C., Depuydt-Bcrte R. (1980), L’intérêt de la discrimination digitale dans les troubles d’apprentissage. La psychomotricite, 4, 135–140.

Czasopismo ukazuje się w sposób ciągły on-line.
Pierwotną wersją czasopisma jest wersja elektroniczna
publikowana kwartalnie w internecie.