최소 단어 이상 선택하여야 합니다.
최대 10 단어까지만 선택 가능합니다.
다음과 같은 기능을 한번의 로그인으로 사용 할 수 있습니다.
NTIS 바로가기Journal of the Korean Society of Mathematical Education. Series A. The Mathematical Education, v.52 no.1, 2013년, pp.19 - 41
What is the foundation of mathematical thinking? Is it logic based symbolic language system? or does it rely more on mental imagery and visuo-spatial abilities? What kind of neural changes happen if someone's mathematical abilities improve through practice? To answer these questions, basic cognitive...
핵심어 | 질문 | 논문에서 추출한 답변 |
---|---|---|
추상화 과정이란? | 그런데 많은 경우에 구체적 개념(강아지)은 추상적 개념(함수)보다 쉽게 인식되고 잘 기억된다. 추상화 과정은 구체적인 개념이나 관찰 가능한 현상으로부터 특정한 목적에 적합한 정보만을 추출해서 높은 단계의 개념을 형성하는 것이다. 그런데 추상적인 개념을 이해하는 것은 왜 더 어려울까? 자명해 보이는 이 질문을 인간의 머릿속에서 일어나는 사고과정으로 바꾸면 해석이 단순하지 않다. | |
가장 영향력있는 작업 기억 모형중 하나인 Baddeley & Hitch(1974)의 모형은 무엇인가? | 영향력 있는 작업 기억의 모형 중 하나가 Baddeley & Hitch(1974)의 모형이다. 그들에 의하면 작업 기억이 하나의 저장고로 이루어진 것이 아니라, 상호작용하는 분리된 요소들로 이루어진 기억 시스템이다. 작업 기억의 구조는 각각 언어적 정보와 시공간적 정보를 담당하는 두 개의 영역 특정적(domain specific)인 하부 저장 시스템과, 이들로부터 정보를 수렴 받아, 조절하고, 명령을 내리는 영역 일반적(domain general)인 중심 실행기능으로 이루어진 구조라는 개념이다. | |
작업 기억이란? | 작업 기억이란 추론, 이해 등과 같은 과제를 해결하기 위하여 짧은 시간 동안 정보를 저장하면서 동시에 조작하고 처리하는 것으로 인지과학에서 60년대에 사용하던 단기 기억의 개념이 진화된 것이다. 단기 기억은 수동적으로 정보를 유지하는 것인데 반하여 작업 기억은 정보를 적극적으로 처리하고 조작한다는 것을 강조한다. |
황우형 (2003). 수학교육에서 바라본 학습심리학의 발달과 전망, 수학교육 42(2), 121-135.(Whang, W. H. (2003). Prospective view of developmental process and the future prospect of psychology of learning mathematics, The Mathematical Education 42(2), 121-135.)
Alloway, T.P., Gathercole, S.E., Kirkwood, H., & Elliott, J. (2009). The cognitive and behavioral characteristics of children with low working memory, Child Development 80(2), 606-621.
Alloway, T.P., Alloway, R.G. (2010). Investigating the predictive roles of working memory and IQ in academic attainment, Journal of Experimental Child Psychology 106(1), 20-29.
Anderson, J. (2005). Human symbol manipulation within an integrated cognitive architecture, Cognitive Science 29(3), 313-341.
Baddley, A.D. & Hitch, G. (1974). Working memory. In G.H. Bower (Ed.), The psychology of learning and motivation: Advances in research and theory 8 (47-89). New York: Academic Press.
Barsalou, L.W., Simmons, W., Barbey, A.K., & Wilson, C.D. (1999). Grounding conceptual knowledge in modalityspecific systems, Trends in Cognitive Sciences 7(2), 84-91.
Barsalou, L.W., & Wiemer-Hastings, K. (2005). Situating abstract concepts. In D. Pecher & R.A. Zwaan (Eds.), Grounding cognition: The role of perception and action in memory, language, and thinking (129-163). Cambridge: Cambridge University Press.
Chan, J., McDermott, K., & Roediger, I.H. (2006). Retrieval-Induced Facilitation: Initially Nontested Material Can Benefit From Prior testing of Related Material, Journal of Experimental Psychology General 135(4), 553-571.
Changeux, J.P. & Conne, A. (2002). 정신, 물질 그리고 수학 (강주현 역), 서울: 경문사. (원저 1989 출판)
Davis, G., Hill, D., & Smith, N. (2000). A memorybased model for aspects of mathematics teaching. In T. Nakahara & M. Koyama(Eds.), Proceedings of 24th Conference of the International Group for the Psychology of Mathematics Education 2, 25-232. Hiroshima: Hiroshima University.
Dehaene, S. (1997). The number sense, New York: Oxford University Press.
Dehaene, S. & Cohen, L. (1997). Cerebral pathways for calculation: double dissociation between rote verbal and quantitative knowledge of arithmetic. Cortex 33(2), 219-250.
Dehaene, S., Piazza, M., Pinel, P. & Cohen, L. (2003). Three parietal circuits for number processing, Cognitive Neuropsychology 20(3/4/5/6), 487-560.
Delazer, M., Domahs, F., Bartha, L., Brenneis, C., Lochy, A., Trieb, T., & Benke, T. (2003). Learning complex arithmetic-An fMRI Study. Cogn Brain Res 18(1), 76-88.
Dragansky, B., Gaser, C., Kempermann, G., Kuhn, H., Winkler, J., Buchel, C., & May, A. (2006). Temporal and Spatial Dynamics of Brain Structure Changes during Extensive Learning, The Journal of Neuroscience 26(23), 6314- 6317.
Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall, (Ed.). Advanced Mathematical Thinking (95-126). Dordrecht: Kluwer.
Geary, D.C., Hoard, M.K. (2005). Learning disabilities in arithmetic and mathematics: theoretical and empirical perspectives. In Campbell, J.I.D. (Ed.), Handbook of mathematical cognition (253-267). New York: Psychology Press.
Geary, D.C. (2011). Consequences, characterristics, characteristics, and causes of poor mathematics achevement and mathematical learning disabilities, Journal of Developmental and Behavioral Pediatrics 32(3), 250-263.
Goel, V. & Dolan, R.J. (2001) Functional neuroanatomy of three-term relational reasoning, Neuropsychologia 39(9), 901-909.
Grabner, R.H., Ischebeck A., Koppelstatter F., Reishofer, G., Koschutnig, K. Delazer, M., Ebner, F., & Neuper, C. (2009). Fact Learning in Complex Arithmetic and Figural-Spatial Tasks: The Role of the Angular Gyrus and its Relation to Mathematical Competence, Human Brain Mapping 30(9), 2936-2952.
Goswami, U. (2004). Neuroscience and Education, British Journal of Educational Psychology 74(1), 1-14.
Hadamard, J. (1990). 수학 분야에서 발명의 심리학 (정계섭 역). 서울: 범양사. (원저 1957년 출판)
Heathcote, D. (1994). The role of visuo-spatial working memory in the mental addition of multi-digit addends, Current Psychology of Cognition 13(2), 207-245.
Holmes, J., & Adams., J. W. (2006). Working memory and children's mathematical skills: Implications for mathematical development and mathematical curricula. Educational Psychology 26, 339-366.
Jarrold, C. & Bayliss, D.M. (2007). Variation in working memory due to typical and typical development. In A.R.A. Conway, C. Jarrold, M.J. Kane, A. Miyake & J.N. Towse (Eds.). Variation in working memory (137-161). New York: Oxford University Press.
Jung, R.E., & Haier, R.J. (2007). The parieto-frontal integration theory (P-FIT) of intelligence: converging neuroimaging evidence. Behav. Brain Sci. 30(2), 135-154.
Knauff, M., Mulack, T., Kassubek, J., Salih, H.R. & Greenlee, M.W. (2002). Spatial imagery in deductive reasoning: A functional MRI study, Brain Research: Cognitive Brain Research 13(2), 203-312.
Kong, J., Wang, C., Kong, K., vangel, M., Chua, E., & Gollup, R. (2005). The neural substrates of arithmetic operations and procedure complexity, Cognitive Brain Research 22(3), 397-405.
Kosslyn, S.M. (2007). Human intelligence can be increased, and can be increased dramatically, Edge World Question Center. Reprinted in J. Brockman (Ed.), What are you optimistic about: Today's leading thinkers on why things are good and getting better (285-287). New York: Harper.
Krueger, F., Spampinato, M.V., Pardini, M., Pajevic, S., Wood, J.N., Weiss, G.H., Landgraf, S., & Grafman. (2008). Integral calculus problem solving: an fMRI study, Neuroreport 19(11), 1095-1099.
Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren, Chicago: University of Chicago Press.
Lee, K., Lim, Z.Y., Yeong, S., Ng, S.F., Venkatraman, V., & Chee, M. (2007). Strategic differences in algebraic problem solving: Neuroanatomical correlates, Brain Research 1155(June), 163-171.
Maguire, E., Woollett, K., & Spiers, H. (2006). London Taxi drivers and bus drivers: a structural MRI and neuropsychological analysis, Hippocampus 16(12), 1091-1101.
McGee, M. (1979). Human spatial abi1ities: Psychometric studies and environmental, genetic, hormonal, and neurological Influences, Psychological Bulletin 86(5), 889-918.
Mc Neil, N.M. & Jarvin, L. (2007). When theories don't add up: Disentangling the manipulatives debate, Theory into Practice 46(4), 309-316.
Michelli, A., Crinion, J., Noppeney, U., O'Doherty, J., Ashburner, J., Frackowiak, R., & Price, C. (2004). Structural plasticity in the bilingual brain, Nature 431(October).
Mohler, J.L. (1997). An instructional method for the AutoCAD modelling environment, Engineering Design Graphics Journal 61(1), 5-13.
Newman, S.D.& Just, M.A. (2005). The neural bases of intelligence: a per-spective based on functional neuroimaging. In J. Sternberg & J. Pretz (Eds.), Cognition and Intelligence: Identifying the Mechanisms of the Mind (88-103). New York: Cambridge University Press.
Paivio, A. (1991). Dual coding theory: Retrospect and current status. Canadian Journal of Psychology/ Revue canadienne de psychologie 45(3), 255-287.
Pauli, P., Lutzenberger, W., Rau, H., Birbaumer, N., Rickard, T.C., Yaroush, R.A., & Bourne, L.E. Jr. (1994). Brain potentials during mental arithmetic: Effects of extensive practice and problem difficulty. Brain Research, Cognitive Brain Research 2, 21-29.
Prabhakaran, V., Rypma, B., Gabrieli, J. (2001). Neural substrates of mathematical reasoning: an fMRI study of neocortical activation during performance of a necessary mathematics operations test, Neuropsychology 15(1), 115-127.
Qin, Y., Carter, C.S., Silk, E., Stenger, V.A., Fissell, K., Goode, A. & Anderson, J.R. (2004). The change of the brain activation patterns as children learn algebra equation solving, Proceedings of National Academy of Sciences 101(15), 5686-5691.
Rasmussen, C., & Bisanz, J. (2005). Representation and working memory in early arithmetic, Journal of Experimental Child Psychology 91, 137-157.
Rittle-Johnson, B. & Aliblai, M.W. (1999). Conceptual and procedural knowledge in learning mathematics: Does one lead to another? Journal of educational Psychology 91(1), 175-189.
Rivera, S.M., Reiss, A.L., Eckert, M.A., & Menon, V. (2005). Developmental changes in mental arithmetic: Evidence for increased specialization in the left inferior parietal cortex, Cerebral Cortex 15(11), 1779-1790.
Rubinsten O. & Henik A. (2009). Developmental dyscalculia: heterogeneity might not mean different mechanisms, Trends in Cognitive. Science 13(2), 92-99.
Schroeder, B. (2011). Investigating a metacognitive strategy for solving indefinite integration problems in Calculus, thesis, University of Connecticut.
Schwanenflugel, P.J. (1991). Why are abstract concepts hard to understand? In P.J. Schwanenflugel (Ed.), The psychology of word meanings (235-250). Hillsdale: Erlbaum.
Simon, T.J. (1999). The foundations of numerical thinking in a brain without numbers, Trends in Cognitive Sciences 3(10), 363-365.
Sohn, M.H., Goode, A., Koedinger, K.R., Stenger, V.A., Fissell, K., & Carter, C.S.. (2004). Behavioral equivalence, but not neural equivalence-neural evidence of alternative strategies in mathematical thinking, Nature Neuroscience 7(11), 1193-1194.
Squire, L.R. (1994). Declarative and non-declarative memory: Multiple brain systems supporing learning and memory. In D.L. Schacter & E. Tulving (Eds.), Memory Systems (203-231). Cambridge: MIT Press.
Tall, D.O. (1998). Symbols and the Bifurcation between Procedural and Conceptual Thinking, Plenary presentation at the International Conference on the Teaching of Mathematics, Samos.
Tang, Y., Zhang, W., Chen, K., Feng, S., Ti, Y., Shen, T. Reiman, E., & Liu, Y. (2006). Arithemetic Processing in the brain shaped by cultures, PNAS 103(28), 10775-10780.
Terao, A., Koedinger, K.R., Sohn, M.H., Qin, Y., Anderson, J.R., Carter, C.S., (2004). An fMRI study of the interplay of symbolic and visuo-spatial systems in mathematical reasoning, Proceedings of the Twenty-sixth Annual Conference of the Cognitive Science Society. Mahwah: Erlbaum.
Thomas, M., Wilson, A., Corballis, M., Lim, V., & Yoon, C. (2010). Evidence from cognitive neuroscience for the role of graphical and algebraic representations in understanding function, ZDM Mathematics Education 42(6), 607-619.
Thompson-Schill, S.L., D'Esposito, M., Aguirre, G.K., & Farah, M.J. (1997). Role of left prefrontal cortex in retrieval of semantic knowledge: A re-evaluation, Proceedings of the National Academy of Science 94(26), 14792-14797.
Tulving, E. (1983). Elements of Episodic Memory, Oxford: Oxford University Press.
van Nes, F. & De Lange, J. (2007). Mathematics Education and Neuroscience: Relating spatial structures for the development of spatial sense and number sense, The Montana Council of Teachers of Mathematics 4(2), 210-229.
Varma, S., McCallin, B, & Schwartz, D. (2008). Scientific and pragmatic challenges for bridging education and neuroscience, Educational Researcher 37(3), 140-152.
Wynn, K. (1992). Addition and subtraction by human infant, Nature 358(6389), 749-750
Wright, R. Thompson, W., Gains, G., Newcombe, N. & Kosslyn, S. (2008). Training generalized skills, Psychonomic Bulletin & Review 15(4), 763-771.
Zago, L., Pesenti, M., Mellet, E., Crivello, F., Mazoyer, B., & Tzourio-Mazoyer, N. (2001). Neural correlates of simple and complex mental calculation, Neuroimage 13(2), 314-327.
Zhu, Z. (2007). Gender differences in mathematical problem solving patterens: A review of literature, International Educational Joural Education 8(2), 187-203.
*원문 PDF 파일 및 링크정보가 존재하지 않을 경우 KISTI DDS 시스템에서 제공하는 원문복사서비스를 사용할 수 있습니다.
Free Access. 출판사/학술단체 등이 허락한 무료 공개 사이트를 통해 자유로운 이용이 가능한 논문
※ AI-Helper는 부적절한 답변을 할 수 있습니다.