References
- 김연미 (2011). 신경심리학에 근거한 수학학습장애의 유형분류 및 심층진단검사의 개발을 위한 기초연구, 초등수학교육 14(3), 237-260.(Kim, Y.M. (2011). Neuropsychological approaches to mathematical learning disabilities and research on the development of diagnostic test, Education of Primary School Mathematics 14(3), 237-260.)
- 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. https://doi.org/10.1111/j.1467-8624.2009.01282.x
- 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. https://doi.org/10.1016/j.jecp.2009.11.003
- Anderson, J. (2005). Human symbol manipulation within an integrated cognitive architecture, Cognitive Science 29(3), 313-341. https://doi.org/10.1207/s15516709cog0000_22
- 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. https://doi.org/10.1037/0096-3445.135.4.553
- 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. https://doi.org/10.1016/S0010-9452(08)70002-9
- Dehaene, S., Piazza, M., Pinel, P. & Cohen, L. (2003). Three parietal circuits for number processing, Cognitive Neuropsychology 20(3/4/5/6), 487-560. https://doi.org/10.1080/02643290244000239
- 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. https://doi.org/10.1016/j.cogbrainres.2003.09.005
- 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. https://doi.org/10.1523/JNEUROSCI.4628-05.2006
- 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. https://doi.org/10.1097/DBP.0b013e318209edef
- Goel, V. & Dolan, R.J. (2001) Functional neuroanatomy of three-term relational reasoning, Neuropsychologia 39(9), 901-909. https://doi.org/10.1016/S0028-3932(01)00024-0
- 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. https://doi.org/10.1002/hbm.20720
- Goswami, U. (2004). Neuroscience and Education, British Journal of Educational Psychology 74(1), 1-14. https://doi.org/10.1348/000709904322848798
- 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. https://doi.org/10.1080/01443410500341056
- 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. https://doi.org/10.1017/S0140525X07001185
- 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. https://doi.org/10.1016/S0926-6410(01)00116-1
- 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. https://doi.org/10.1016/j.cogbrainres.2004.09.011
- 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. https://doi.org/10.1097/WNR.0b013e328303fd85
- 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. https://doi.org/10.1016/j.brainres.2007.04.040
- Maguire, E., Woollett, K., & Spiers, H. (2006). London Taxi drivers and bus drivers: a structural MRI and neuropsychological analysis, Hippocampus 16(12), 1091-1101. https://doi.org/10.1002/hipo.20233
- McGee, M. (1979). Human spatial abi1ities: Psychometric studies and environmental, genetic, hormonal, and neurological Influences, Psychological Bulletin 86(5), 889-918. https://doi.org/10.1037/0033-2909.86.5.889
- Mc Neil, N.M. & Jarvin, L. (2007). When theories don't add up: Disentangling the manipulatives debate, Theory into Practice 46(4), 309-316. https://doi.org/10.1080/00405840701593899
- 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. https://doi.org/10.1037/h0084295
- 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. https://doi.org/10.1016/0926-6410(94)90017-5
- 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. https://doi.org/10.1037/0894-4105.15.1.115
- 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. https://doi.org/10.1016/j.jecp.2005.01.004
- 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. https://doi.org/10.1037/0022-0663.91.1.175
- 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. https://doi.org/10.1093/cercor/bhi055
- 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. https://doi.org/10.1016/S1364-6613(99)01383-2
- 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. https://doi.org/10.1038/nn1337
- 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. https://doi.org/10.1073/pnas.0604416103
- 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. https://doi.org/10.1007/s11858-010-0272-7
- 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. https://doi.org/10.3102/0013189X08317687
- Wynn, K. (1992). Addition and subtraction by human infant, Nature 358(6389), 749-750 https://doi.org/10.1038/358749a0
- Wright, R. Thompson, W., Gains, G., Newcombe, N. & Kosslyn, S. (2008). Training generalized skills, Psychonomic Bulletin & Review 15(4), 763-771. https://doi.org/10.3758/PBR.15.4.763
- 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.
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