- 권한신청
- P-ISSN1226-9654
- E-ISSN2733-466X
- KCI
초기 수학 능력 발달과 인지 책략 변화 관련 종단적 뇌 활동 변화 분석
Longitudinal Changes in Brain Activity Related to Maturation of Children’s Arithmetic Skills and Cognitive Strategy Use
초록
초등학교 저학년 시기에 습득하는 기초 수학 능력은 청소년기와 성인기 수학 능력의 근간이 된다. 기억에 기반한 효율적인 인지 책략(cognitive strategy)의 사용은 초기 학령기의 수학 문제 풀이 능력의 향상에 가장 크게 기여하는 요소이다. 본 연구는 초등학교 2학년부터 3학년까지 일 년 동안 수학 능력 발달과 관련한 뇌 활동의 변화를 기능적 자기 공명 영상(fMRI)을 이용하여 종단적으로 분석하였다. 연구 결과, 2학년과 비교하여 3학년 시기에 아동들의 문제 풀이의 정확도와 속도가 모두 향상되었다. 이학년 시기에 수행이나 책략 사용 면에서 발달 수준이 더 저조했던 아동들이 일 년 후 수행이나 책략 사용 면에서 더 큰 향상을 보였다. 뇌 활동 분석을 통해 아동의 수학 문제 해결 능력의 발달과 관련하여 해마 및 그 주변 영역을 포함하는 내측 측두엽(medial temporal lobe), 외측 전전두엽(lateral prefrontal cortex)과 이를 포함한 전두-두정 주의 신경망(fronto-parietal attention network), 복측 시각 피질(ventral visual stream) 영역의 중요성을 확인하였다. 이는 수학적 지식이 안정적인 기억 표상으로 저장되고 인출되는 과정에 연합 학습(associative learning)과 의미적 기억(semantic memory) 과정에 중추적 역할을 하는 내측 측두엽과 하향식 주의/인지 통제 체계(top-down attention/cognitive control system)의 역할이 중요함을 시사한다. 또한 복측 시각 피질의 활동은 숫자와 기호들을 신속하게 재인(recognize)하여 효율적으로 처리할 수 있도록 하여 문제 풀이 속도의 향상에 기여하는 것으로 해석할 수 있다.
- keywords
- memory, math, fMRI, children, longitudinal study, 기억, 수학, 기능성 자기 공명 영상, 아동, 종단 연구, memory, math, fMRI, children, longitudinal study
Abstract
Acquisition of basic mathematical skills during early elementary school years serves as a critical foundation for mathematical development in adolescence and adulthood. The present study examined longitudinal changes in children’s behavior and brain activity during mathematical problem solving. Over a 1 year interval, children became more accurate and faster at math problem solving. Children who performed worse at 2nd grade showed greater performance improvements at 3rd grade. Children who were lower in retrieval use for problem solving showed greater increase in retrieval use after a year. We found significant over-additive increases in activation from 2nd to 3rd grade for Addition vs. Control problem solving in the anterior temporal cortex important for semantic memory. Individuals with greater increase in retrieval use had greater activation increase in the lateral prefrontal cortex and the fronto-parietal attention network. Performance improvements were positively correlated with activation increases mainly in the medial temporal lobe and the ventral visual stream. These findings indicate that the development of mathematical problem solving is dependent on the contribution of the fronto-parietal top-down attention and medial temporal lobe memory systems. In addition, higher order visual cortex in the ventral visual stream known to be important for visual symbol recognition seems to contribute to accurate and efficient math problem solving.
- keywords
- memory, math, fMRI, children, longitudinal study, 기억, 수학, 기능성 자기 공명 영상, 아동, 종단 연구, memory, math, fMRI, children, longitudinal study
참고문헌
Allison, T., McCarthy, G., Nobre, A., Puce, A., & Belger, A. (1994). Human extrastriate visual cortex and the perception of faces, words, numbers and colors. Cerebral Cortex, 5 (5), 544-554.
Ashcraft, M., Fierman, B., et al. (1984). The production and verification tasks in mental addition - An empirical comparison. Developmental Review, 4 (2), 157-170.
Ashcraft, M. H. (1982). The Development of Mental Arithmetic - a Chronometric Approach. Developmental Review, 2 (3), 213-236.
Ashcraft, M. H., & Battaglia, J. (1978). Cognitive arithmetic: Evidence for retrieval and decision processes in mental addition. Journal of Experimental Psychology: Human Learning & Memory, 4 (5), 527-538.
Badre, D., & Wagner, A. D. (2002). Semantic retrieval, mnemonic control, and prefrontal cortex. Behav. Cogn. Neurosci. Rev, 1 (3), 206- 218.
Badre, D., Poldrack, R., et al. (2005). Dissociable controlled retrieval and generalized selection mechanisms in ventrolateral prefrontal cortex. Neuron, 47 (6), 907-918.
Badre, D., & Wagner, A. D. (2007). Left ventrolateral prefrontal cortex and the cognitive control of memory, Neuropsychologia, 45 (13), 2883-2901.
Barrouillet, P., & Lepine, R. (2005). Working memory and children's use of retrieval to solve addition problems. Journal of Experimental Child Psychology, 91 (3), 183-204.
Butterworth, B., Varma, S., & Laurillard, D. (2011). Dyscalculia: From Brain to Education. Science, 332 (6033), 1049-1053.
Chan, S., Tang, S., Tang, K., Lee, W., Lo, S., & Kwong, K. (2009). Hierarchical coding of characters in the ventral and dorsal visual streams of Chinese language processing. NeuroImage, 48 (2), 423-435.
Cho, S., Ryali, S., Geary, D. C., & Menon, V. (2011). How does a child solve 7 + 8?: Decoding brain activity patterns associated with counting and retrieval strategies. Developmental Science, 14, 989-1001.
Cho, S., Metcalfe, A. W. S., Young, C. B., Ryali, S., Geary, D. C., and Menon, V. (2012). Hippocampal-Prefrontal Engagement and Dynamic Causal Interactions in the Maturation of Childrenʼs Fact Retrieval. Journal of Cognitive Neuroscience, 24 (9), 1849-66.
Ciaramelli, E., Grady, C., Levine, B., Ween, J., & Moscovitch, M. (2010). Top-Down and Bottom-Up Attention to Memory Are Dissociated in Posterior Parietal Cortex: Neuroimaging and Neuropsychological Evidence. The Journal of Neuroscience, 30 (14), 4943-4956.
Corbetta, M., & Shulman, G. L. (2002). Control of goal-directed and stimulus-driven attention in the brain. Nat. Rev. Neurosci, 3 (3), 215-229.
Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cogn Neuropsychol, 20 (3-6), 487- 506.
Dehaene, S., Molko, N., Cohen, L., & Wilson. A. J. (2004). Arithmetic and the brain. Current Opinion in Neurobiology, 14 (2), 218-224.
Desikan, R. S., Ségonne, F., Fischl, B., Quinn, B. T., Dickerson, B. C., Blacker, D., Buckner, R. L., Dale, A. M., Maguire, R. P., Hyman, B. T., Albert, M. S., & Killiany, R. J. (2006). An automated labeling system for subdividing the human cerebral cortex on MRI scans into gyral based regions of interest. Neuroimage, 31 (3), 968-980.
D'Esposito, M., Postle, B. R., Jonides, J., & Smith, E. E. (1999). The neural substrate and temporal dynamics of interference effects in working memory as revealed by event-related functional MRI. Proceedings of the National Academy of Sciences USA, 96 (13), 7514-7519.
Dormal, V., Andres, M., & Pesenti, M. (2011). Contribution of the right intraparietal sulcus to numerosity and length processing: An fMRI-guided TMS study, Cortex, 48 (5), 623- 529.
Eger, E., Sterzer, P., Russ, M. O., Giraud, A. L., & Kleinschmidt, A. (2003). A supramodal number representation in human intraparietal cortex. Neuron, 37 (4), 719-726.
Eickhoff S. B., Stephan, K. E., Mohlberg, H., Grefkes, C., Fink, G. R., Amunts, K., & Zilles, K. (2005). A new SPM toolbox for combining probabilistic cytoarchitectonic maps and functional imaging data. Neuroimage, 25 (4), 1325-1335.
Forman, S. D., Cohen, J. D., Fitzgerald, M., Eddy, W. F., Mintun, M. A., & Noll, D. C. (1995). Improved assessment of significant activation in functional magnetic resonance imaging (fMRI): Use of a cluster-size threshold. Magnetic Resonance in Medicine, 33 (5), 636-647.
Friston, K. J., Zarahn, E., Josephs, O., Henson, R. N. A., & Dale, A. M. (1999). Stochastic designs in event-related fMRI. Neuroimage, 10 (5), 607-619.
Geary, D. C. (1993). Mathematical disabilities: Cognitive, neuropsychological and genetic components. Psychological Bulletin, 114(2), 345-362.
Geary, D. C. (1994). Childrenʼs 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.
Geary, D. C., & Brown, S. (1991). Cognitive addition-Strategy choice and speed-of- processing differences in gifted, normal and mathematically disabled-children. Developmental Psychology, 27 (3), 398-406.
Geary, D. C., Hoard, M. K., Byrd-Craven, J., & DeSoto, C. M. (2004). Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability. Journal of Experimental Child Psychology, 88 (2), 121- 151.
Glover, G. H., & Lai, S. (1998). Self-navigated spiral fMRI: Interleaved versus single-shot. Magnetic Resonance in Medicine, 39 (3), 361- 368.
Grabner, R. H., Ansari, D., Koschutnig, K., Reishofer, G., Ebner, F., & Neuper, C. (2009). To retrieve or to calculate? Left angular gyrus mediates the retrieval of arithmetic facts during problem solving. Neuropsychologia, 47 (2), 604-608.
Groen, G. J., & Parkman, J. M. (1972). A chronometric analysis of simple addition. Psychological Review, 79 (4), 329-343.
Gross, J., Hudson, C., & Price, D. (2009). The Long Term Costs of Numeracy Difficulties. London (UK): Every Child a Chance Trust and KPMG.
Ischebeck, A., Zamarian, L., Egger, K., Schocke, M., & Delazer, M. (2006). Imaging early practice effects in arithmetic. Neuroimage, 36 (3), 993-1003.
James, K. H., James, Y., Jobard, G., Wong, A. C. N., & Gauthier, I. (2005). Letter processing in the visual system: Different activation patterns for single letters and strings. Cognitive, Affective, & Behavioural Neuroscience, 5 (4), 452-466.
Jordan, N. C., Hanich, L. B., & Kaplan, D. (2003). Arithmetic fact mastery in young children: a longitudinal investigation. J. Exp. Child Psychol, 85 (2), 103-119.
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): 782-95.
Karmiloff-Smith, A. (1981). Getting developmental differences or studying child development? Cognition, 10, 151-158.
Karmiloff-Smith, A. (2010). Neuroimaging of the developing brain: Taking “developing” seriously. Human Brain Mapping, 31 (3), 934- 941.
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., Lochy, A., Drexler, A., & Semenza, C. (2004). Deficient arithmetic fact retrieval- storage or access problem? A case study. Neuropsychologia, 42 (4), 482-496.
Martin, A., & Chao, L. (2001). Semantic memory and the brain: structure and processes. Current Opinion in Neurobiology, 11 (2), 194-201.
McCandliss, B. D., Cohen, L., & Dehaene, S. (2003). The visual word form area: Expertise for reading in the fusiform gyrus. Trends in Cognitive Science, 7 (7), 293-299.
OECD, The High Cost of Low Educational Performance: The Long-Run Economic Impact of Improving Educational Outcomes (OECD, Paris, 2010).
Parsons, S., & Bynner, J. (2005). Does Numeracy Matter More?. National Research and Development Centre for Adult Literacy and Numeracy. London: Institute of Education.
Passolunghi, M. C., & Siegel, L. S. (2004). Working memory and access to numerical information in children with disability in mathematics. Journal of Experimental Child Psychology, 88 (4), 348-367.
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.
Piazza, M. (2010). Neurocognitive start-up tools for symbolic number representations. Trends Cogn Sci, 14 (12), 542-551.
Piazza, M., Facoetti, A., Trussardi, A. N., Berteletti, I., Conte, S., Lucangeli, D., Dehaene, S., & Zorzi, M. (2010). Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition, 116 (1), 33-41.
Pinel, P., Dehaene, S., Riviere, D., & Le Bihan, D. (2001). Modulation of parietal activation by semantic distance in a number comparison task. NeuroImage, 14 (5), 1013-1026.
Price, G. R., Holloway, I., Rasanen, P., Vesterinen, M., & Ansari, D. (2007). Impaired parietal magnitude processing in developmental dyscalculia. Current Biology, 17 (24), R1042- R1043.
Reinke, K., Fernandes, M., Schwindt, G., O’Craven, K., & Grady, C. L. (2008). Functional specificity of the visual word form area: General activation for words and symbols but specific network activation for words. Brain and Language, 104 (2), 180-189.
Rivera, S. M., Reiss, A. L., Eckert, M. A., & Menon, V. (2005). Developmental changes in mental arithmetic: Evidence for increased functional specialization in the left inferior parietal cortex. Cerebral Cortex, 15 (11), 1779- 1790.
Rosenberg-Lee, M., Barth, M., & Menon, M. (2011). What difference does a year of schooling make? Maturation of brain response and connectivity between 2nd and 3rd grades during arithmetic problem solving. NeuroImage, 57 (3), 796-808.
Siegler, R. S. (1987). The perils of averaging data over strategies: An example from childrenʼs addition. Journal of Experimental Psychology: General, 116 (3), 250-264.
Siegler, R. S., Shipley, C., Simon, T. J., & Halford, G. S. (1995). Variation, selection, and cognitive change. Developing cognitive competence: New approaches to process modeling, 31- 76.
Siegler, R. S., & Shrager, J. (1984). Strategy choice in addition and subtraction: How do children know what to do?. Origins of cognitive skills, 229-293.
Squire, L. R., Stark, C. E., & Clark, R. E. (2004). The medial temporal lobe. Annual Review of Neuroscience, 27, 279-306.
Sridharan, D., Levitin, D., & Menon, V. (2008). A critical role for the right fronto-insular cortex in switching between central-executive and default-mode networks. Proc Natl Acad Sci U S A, 105 (34), 12569-12574.
Suzuki, W. A. (2007). Making new memories: The role of hippocampus in new associative learning. Annals of the New York Academy of Sciences, 1097 (1), 1-11.
Tzourio-Mazoyer, N., Landeau, B., Papathanassiou, D., Crivello, F., Etard, O., Delcroix, N., Mazoyer, B., & Joliot, M. (2002). Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. Neuroimage, 15 (1), 273-289.
Vinckier, F., Dehaene, S., Jobert, A., Dubus, J. P., Sigman, M., & Cohen, L. (2007). Hierarchical coding of letter strings in the ventral stream: dissecting the inner organization of the visual word-form system. Neuron, 55 (1), 143-156.
Visser, M., Embleton, K. V., Jefferies, E., Parker, G. J., & Ralph, M. A. (2010). The inferior, anterior temporal lobes and semantic memory clarified: novel evidence from distortion- corrected fMRI. Neuropsychologia, 48 (6), 1689- 1696.
Wager, T. D., & Smith, E. E. (2003). Neuroimaging studies of working memory: a meta-analysis. Cognitive Affective Behavioral Neuroscience, 3 (4), 255-274.
Ward, B. D. (2000). Simultaneous inference for fMRI data. AFNI 3dDeconvolve Documentation, Medical College of Wisconsin, Milwaukee, WI.
Whitney, C., Kirk, M., OʼSullivan, J., Lambon Ralph, M. A., & Jefferies, E. (2012). Executive semantic processing is underpinned by a large-scale neural network: Revealing the contribution of left prefrontal, posterior temporal, and parietal cortex to controlled retrieval and selection using TMS. Journal of Cognitive Neuroscience, 24 (1), 133-147.
Wicker B, Keysers C, Plailly J, Royet JP, Gallese V, Rizzolatti G (2003). Both of us disgusted in My insula: the common neural basis of seeing and feeling disgust. Neuron 40 (3): 655-64.
Wu, S., Meyer, M., Maeda, U., Salimpoor, V., Tomiyama, S., Geary, D. C., et al. (2008). Standardized assessment of strategy use and working memory in early mental arithmetic performance. Developmental Neuropsychology, 33 (3), 365-393.
- 다운로드 수
- 조회수
- 0KCI 피인용수
- 0WOS 피인용수