Citation: | LIU Di, YANG Chun. A Review of Researches on Magnitude Representation[J]. Journal of East China Normal University (Educational Sciences), 2017, 35(5): 138-145. doi: 10.16382/j.cnki.1000-5560.2017.05.012 |
[1] |
陈英和.(2015).儿童数量表征与数概念的发展特点及机制.心理发展与教育, 31(1), 21-28. http://cpfd.cnki.com.cn/Article/CPFDTOTAL-ZGXG201410001765.htm
|
[2] |
陈英和, 赖颖慧.(2013).儿童非符号数量表征的特点及作用探析.北京师范大学学报(社会科学版), 1, 33-41. http://www.cnki.com.cn/Article/CJFDTOTAL-BJSF201301008.htm
|
[3] |
赖颖慧, 陈英和, 陈聪. (2012).视知觉线索对幼儿小数离散数量表征的影响.心理发展与教育, 4, 337-344. http://www.cnki.com.cn/Article/CJFDTOTAL-XLFZ201204001.htm
|
[4] |
刘国芳, 辛自强.(2012).数字线估计研究:"模型"背后的策略.心理研究, 5(2), 27-33. http://www.cnki.com.cn/Article/CJFDTOTAL-OXLY201202005.htm
|
[5] |
卢淳, 郭红力, 司继伟, 孙燕. (2014).不同数字线下儿童与成人分数估计的表征模式.心理发展与教育, 30(5), 449-456. http://www.cnki.com.cn/Article/CJFDTOTAL-XLFZ201405001.htm
|
[6] |
徐华. (2011). 幼儿线性数量表征的形成及其机制(博士学位论文). 北京师范大学, 北京.
|
[7] |
徐华, 陈英和.(2012).儿童数字线估计研究的述评与前瞻.心理研究, 5(5), 46-50. http://www.cnki.com.cn/Article/CJFDTOTAL-OXLY201205009.htm
|
[8] |
张丽, 卢彩芳, 杨新荣.(2014).3-6年级儿童整数数量表征与分数数量表征的关系.心理发展与教育, 1, 1-8. http://www.cnki.com.cn/Article/CJFDTOTAL-XLFZ201401001.htm
|
[9] |
周广东, 莫雷, 温红博.(2009).儿童数字估计的表征模式与发展.心理发展与教育, 4, 21-29. http://www.cnki.com.cn/Article/CJFDTOTAL-XLFZ200904004.htm
|
[10] |
Bailey, D.H., Siegler, R.S., & Geary, D.C.(2014). Early predictors of middle school fraction knowledge. Developmental Science, 17, 775-785. doi: 10.1111/desc.2014.17.issue-5
|
[11] |
Booth, J.L., & Siegler, R.S.(2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 42, 189-201. doi: 10.1037/0012-1649.41.6.189
|
[12] |
Brysbaert, M.(2004). Number recognition in different formats. In J. I. D Campbell, (Ed.), Handbook of Mathematical Cognition (pp. 23-42). Psychology Press:New York. http://psycnet.apa.org/psycinfo/2005-04876-002
|
[13] |
Bulthé, J., De Smedt, B., & Op de Beeck, H.(2014). Format-dependent representations of symbolic and non-symbolic numbers in the human cortex as revealed by multi-voxel pattern analyses. Neuro Image, 87, 311-322. http://www.ncbi.nlm.nih.gov/pubmed/24201011
|
[14] |
Butterworth, B(2010). Foundational numerical capacities and the origins of dyscalculia. Trends in Cognitive Sciences, 14, 534-541. doi: 10.1016/j.tics.2010.09.007
|
[15] |
Cantlon, J. F., Safford, K. E., & Brannon, E. M. (2010).Spontaneous analog number representations in 3-year-old children. Developmental Science, 13, 289-297. doi: 10.1111/desc.2010.13.issue-2
|
[16] |
Cohen, K. R., Lammertyn, J., & Izard, V.(2008). Are numbers special? An overview of chronometric, neuro imaging, developmental and comparative studies of magnitude representation. Progress in Neurobiology, 84, 132-147. doi: 10.1016/j.pneurobio.2007.11.001
|
[17] |
Dehaene, S. (2008). Symbols and quantities in parietal cortex:Elements of a mathematical theory of number representation and manipulation. In P. Haggard, Y. Rossetti, & Y.M.Kawato (Eds.), Sensorimotor foundations of higher cognition, attention, and performance (Attention and Performance Series), 22 (pp. 527-574). New York:Oxford University Press. http://www.oalib.com/references/12434854
|
[18] |
Dehaene, S., Izard, V., Spelke, E., Pica, P. (2008). Log or linear? Distinct intuitions of the number scale in Western and Amazonian indigene cultures. Science, 320, 1217-20. doi: 10.1126/science.1156540
|
[19] |
Dewind, N.K., & Brannon, E.M.(2012). Malleability of the approximate number system:Effects of feedback and training. Frontiers in Human Neuroscience, 6, 68. http://pubmedcentralcanada.ca/pmcc/articles/PMC3329901/
|
[20] |
Duncan, G.J., Dowsett, C.J., Claessens, A., Magnuson, K., Huston, A.C., & Klebanov, P. et al.(2007).School readiness and later achievement. Developmental Psychology, 43, 1428-1446. doi: 10.1037/0012-1649.43.6.1428
|
[21] |
Fazio, L.K., Bailey, D.H., Thompson, C.A., & Siegler, R.S.(2014). Relations of different types of numerical magnitude representations to each other and to mathematics achievement. Journal of Experimental Child Psychology, 123, 53-72. doi: 10.1016/j.jecp.2014.01.013
|
[22] |
Feigenson, L., Dehaene, S., & Spelke, E.(2004). Core systems of number. Trends in Cognitive Sciences, 8, 307-314. doi: 10.1016/j.tics.2004.05.002
|
[23] |
Fischer, M.H., & Brugger, P.(2011). When digits help digits:Spatial-numerical associations point to finger counting as prime examples of embodied cognition. Frontiers in Psychology, 2, 260. http://pubmedcentralcanada.ca/pmcc/articles/PMC3198540/
|
[24] |
Friso-van den Bos, I., van der Ven, S.H.G., Kroesbergen, E.H., & Van Luit, J.E.H.(2013). Working memory and mathematics in primary school children:A meta-analysis. Educational Research Review, 10, 29-44. doi: 10.1016/j.edurev.2013.05.003
|
[25] |
Fuchs, L.S., Schumacher, R.F., Long, J., Namkung, J., Hamlett, C.L. et al.(2013). Improving at-risk learners' understanding of fractions. Journal of Educational Psychology, 105, 683-700. doi: 10.1037/a0032446
|
[26] |
Fuhs, M.W., & McNeil, N.M.(2013). ANS acuity and mathematics ability in preschoolers from low-income homes:Contributions of inhibitory control. Developmental Science, 16, 136-148. doi: 10.1111/desc.2012.16.issue-1
|
[27] |
Geary, D.C., Hoard, M.K., Byrd-Craven, J., Nugent, L., & Numtee, C.(2007). Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child Development, 78, 1343-1359. doi: 10.1111/cdev.2007.78.issue-4
|
[28] |
Gilmore, C.K., McCarthy, S.E., & Spelke, E.S.(2010). Nonsymbolic arithmetic abilities and mathematics achievement in the first year of formal schooling. Cognition, 115, 394-406. doi: 10.1016/j.cognition.2010.02.002
|
[29] |
Halberda, J., Ly, R., Wilmer, J.B., Naiman, D.Q., & Germine, L. (2012). Number sense across the Life span as revealed by a massive Internet-based sample. Proceedings of the National Academy of Sciences of the United States of America, 109, 11116-11120. doi: 10.1073/pnas.1200196109
|
[30] |
Halberda, J., Mazzocco, M.M.M., & Feigenson, L.(2008).Individual differences in non-verbal number acuity correlate with math achievement. Nature, 455, 665-668. doi: 10.1038/nature07246
|
[31] |
Hyde, D.C., Khanum, S., & Spelke, E.S.(2014). Brief nonsymbolic, approximate number practice enhances subsequentexact symbolic arithmetic in children. Cognition, 131, 92-107. doi: 10.1016/j.cognition.2013.12.007
|
[32] |
Jacob, S.N., & Nieder, A.(2009). Notation-independent representation of fractions in the human parietal cortex. Journal of Neuroscience, 29, 4652-4657. doi: 10.1523/JNEUROSCI.0651-09.2009
|
[33] |
Jacob, S.N., Vallentin, D., & Nieder, A.(2012). Relating magnitudes:The brain's code for proportions. Trends in Cognitive Sciences, 16, 157-166. doi: 10.1016/j.tics.2012.02.002
|
[34] |
Jordan, K.E., & Brannon, E.M.(2006). The multisensory representation of number in infancy. Proceedings of the National Academy of Sciences of the United States of America, 103, 3486-3489. doi: 10.1073/pnas.0508107103
|
[35] |
Jordan, N.C., Hansen, N., Fuchs, L.S., Siegler, R.S., Gersten, R. et al.(2013). Developmental predictors of fraction concepts and procedures. Journal of Experimental Child Psychology, 116, 45-58. doi: 10.1016/j.jecp.2013.02.001
|
[36] |
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, 78, 1723-1743. doi: 10.1111/cdev.2007.78.issue-6
|
[37] |
Laski, E.V., & Siegler, R.S.(2014). Learning from number board games:You learn what you encode. Developmental Psychology, 50, 853-864. doi: 10.1037/a0034321
|
[38] |
Le Corre, M., & Carey, S.(2007). One, two, three, four, nothing more:An investigation of the conceptual sources of the verbal counting principles. Cognition, 105, 395-438. doi: 10.1016/j.cognition.2006.10.005
|
[39] |
Lipton, J., & Spelke, E.S.(2003). Origins of number sense:Large number discrimination in human infants. Psychological Science, 14, 396-401. doi: 10.1111/1467-9280.01453
|
[40] |
Lourenco, S.F., & Longo, M.R.(2010). General magnitude representation in human infants. Psychological Science, 21, 873-881. doi: 10.1177/0956797610370158
|
[41] |
Lourenco, S.F., & Longo, M.R. (2011). Origins and development of generalized magnitude representation. In S. Dehaene & E. Brannon (Eds.), Space, time, and number in the brain:Searching for the foundations of mathematical thought (pp.225-244). London:Elsevier. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.473.4222
|
[42] |
Lyons, I.M., Price, G.R., Vaessen, A., Blomert, L., & Ansari, D. (2014). Numerical predictors of arithmetic success ingrades 1-6. Developmental Science, 17, 714-726. doi: 10.1111/desc.2014.17.issue-5
|
[43] |
Newcombe, N.S., Levine, S.C., & Mix, K.(2015). Thinking about quantity:The intertwined development of spatial and numerical cognition. Wiley Interdisciplinary Reviews:Cognitive Science, 6, 491-505. doi: 10.1002/wcs.1369
|
[44] |
Nieder, A. (2011). The neural code for numbers. In S. Dehaene & E. Brannon (Eds.), Space, time, and number in the brain:Searching for the foundations of mathematical thought (pp.103-118). London:Elsevier.
|
[45] |
Nys, J., Ventura, P., Fernandes, T., Querido, L., Leybaert, J., & Content, A. (2013). Does math education modify the approximate number system? A comparison of schooled and unschooled adults. Trends in Neuroscience and Education, 2(1), 13-22. doi: 10.1016/j.tine.2013.01.001
|
[46] |
Park, J., & Brannon, E.M.(2013). Training the approximate number system improves math proficiency. Psychological Science, 24, 2013-2019. doi: 10.1177/0956797613482944
|
[47] |
Piazza, M., Pinel, P., Le Bihan, D., & Dehaene, S.(2007). A magnitude code common to numerosities and number symbols in human intraparietal cortex. Neuron, 53, 293-305. doi: 10.1016/j.neuron.2006.11.022
|
[48] |
Ramani, G.B., & Siegler, R.S.(2008). Promoting broad and stable improvements in low-income children's numerical knowledge through playing number board games. Child Development, 79, 375-394. doi: 10.1111/j.1467-8624.2007.01131.x
|
[49] |
Ritchie, S.J., & Bates, T.C.(2013). Enduring links from childhood mathematics and reading achievement to adult socioeconomic status. Psychological Science, 24, 1301-1308. doi: 10.1177/0956797612466268
|
[50] |
Sadler, P.M., & Tai, R.H.(2007). The two high-school pillars supporting college science. Science, 317, 457-458. doi: 10.1126/science.1144214
|
[51] |
Siegler, R.S.(2016).Magnitude knowledge:the common core of numerical development. Developmental science, 19(3), 341-361. doi: 10.1111/desc.12395
|
[52] |
Siegler, R. S., Booth, J.L.(2004). Development of numerical estimation in young children. Child Development, 75(2), 428-444. doi: 10.1111/cdev.2004.75.issue-2
|
[53] |
Siegler, R.S., Duncan, G.J., Davis-Kean, P.E., Duckworth, K., Claessens, A. et al. (2012). Early predictors of high school mathematics achievement. Psychological Science, 23, 691-697. doi: 10.1177/0956797612440101
|
[54] |
Siegler, R.S., & Mu, Y. (2008). Chinese children excel on novel mathematics problems even before elementary school. Psychological Science, 19, 759-763. doi: 10.1111/j.1467-9280.2008.02153.x
|
[55] |
Siegler, R.S., & Pyke, A.A.(2013). Developmental and individual differences in understanding fractions. Developmental Psychology, 49, 1994-2004. doi: 10.1037/a0031200
|
[56] |
Siegler, R.S., & Ramani, G.B.(2009). Playing linear number board games-but not circular ones improves low-income preschoolers' numerical understanding. Journal of Educational Psychology, 101, 545-560. doi: 10.1037/a0014239
|
[57] |
Siegler, R. S., Thompson, C. A., & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62 (4), 273-296. doi: 10.1016/j.cogpsych.2011.03.001
|
[58] |
Thompson, C.A., & Opfer, J.E.(2008). Costs and benefits of representational change:Effects of context on age and sex differences in symbolic magnitude estimation. Journal of Experimental Child Psychology, 101(1), 20-51. doi: 10.1016/j.jecp.2008.02.003
|
[59] |
Thompson, C.A., & Opfer, J.E.(2010). How 15 hundred is like15 cherries:Effect of progressive alignment on representational changes in numerical cognition. Child Development, 81, 1768-1786. doi: 10.1111/cdev.2010.81.issue-6
|
[60] |
Torbeyns, J., Schneider, M., Xin, Z. Q., & Siegler, R. S.(2015). Bridging the gap:Fraction understanding is central to mathematics achievement in students from three different continents. Learning and Instruction, 37, 5-13. doi: 10.1016/j.learninstruc.2014.03.002
|
[61] |
Vukovic, R.K., Fuchs, L.S., Geary, D.C., Jordan, N.C., Gersten, R. et al.(2014). Sources of individual differences in children's understanding of fractions. Child Development, 85, 1461-1476. doi: 10.1111/cdev.2014.85.issue-4
|
[62] |
Watts, T.W., Duncan, G.J., Siegler, R.S., & Davis-Kean, P.E.(2014). What's past is prologue:Relations between early mathematics knowledge and high school achievement. Educational Researcher, 43, 352-360. doi: 10.3102/0013189X14553660
|
[63] |
Xu, F., & Arriaga, R.I.(2007). Number discrimination in 10-month-old infants. British Journal of Developmental Psychology, 25, 103-108. doi: 10.1348/026151005X90704
|