数学能力的改善：针对工作记忆训练的元分析

doi:10.3724/SP.J.1042.2018.01576

摘要/Abstract

摘要：

工作记忆训练指针对工作记忆各成分进行的训练, 以实现个体记忆与其他认知能力的提升。该领域一直都是研究者关注的热点, 越来越多的研究正在试图利用工作记忆训练改善个体的数学能力。然而回顾过往的研究, 发现研究所关注的数学能力类型、针对的被试人群、使用的方法、结论等存在较大差异, 目前尚没有系统性综述专门探讨工作记忆训练对数学能力的影响。因此, 本文首先回顾和数学能力有关的工作记忆训练方式, 然后结合元分析, 从数感、运算能力和数学推理能力三个方面, 分别回顾归纳工作记忆训练对数学能力的提升作用。具体而言, 尽管研究数量相对有限, 工作记忆训练可能有效改善数感, 其效应量为中等(Cohen’s d = 0.51); 而可能无法有效改善运算和数学推理能力, 它们的效应量小(运算：Cohen’s d = 0.04; 数学推理：Cohen’s d = -0.06)。此外, 训练目标类型与训练效果有着密切的联系。

关键词: 工作记忆训练, 数学能力, 数感, 运算, 数学推理

Abstract:

Working memory training can effectively improve individual’s cognitive performance. In last decades, accumulating studies examined the transfer effects of working memory training on the mathematical abilities. However, findings from these studies render inconsistent depending on the measure of mathematical abilities, types of working memory training, and participants. In this meta-analysis, we thus reviewed two types of trainings strategies-uni-dimensional and multi-dimensional trainings - and their effects on the enhancement of mathematical skills, including number sense, arithmetic and mathematics reasoning. Results showed that working memory training significantly improved number sense with a medium effect size (Cohen’s d = 0.51), rather than arithmetic (Cohen’s d = 0.04) and mathematics reasoning (Cohen’s d = -0.06). Furthermore, the types of working memory training significantly moderated the transfer effects of working memory training on mathematical performance.

Key words: working memory training, mathematical ability, number sense, arithmetic, mathematical reasoning

中图分类号:

B849:G44

郭丽月, 严超, 邓赐平. (2018). 数学能力的改善：针对工作记忆训练的元分析. 心理科学进展 , 26(9), 1576-1589.

Liyue GUO, Chao YAN, Ciping DENG. (2018). Enhancing mathematical abilities: A meta-analysis on the effect of working memory training. Advances in Psychological Science, 26(9), 1576-1589.

参考文献

1	陈英和, 耿柳娜 . ( 2004). 工作记忆与算术认知的研究现状与前瞻. 北京师范大学学报(社会科学版), ( 1), 40-44.
2	陈英和, 王明怡 . ( 2006). 工作记忆广度对儿童算术认知策略的影响. 心理发展与教育, ( 2), 29-35.
3	黎翠红, 何旭, 郭春彦 . ( 2014). 工作记忆训练的研究述评. 心理与行为研究, 12( 3), 407-412.
4	刘春雷, 周仁来 . ( 2012). 工作记忆训练对认知功能和大脑神经系统的影响. 心理科学进展, 20( 7), 1003-1011.
5	王明怡, 陈英和 . ( 2006). 工作记忆中央执行对儿童算术认知策略的影响. 心理发展与教育, 22( 4), 24-28.
6	张明, 陈骐 . ( 2006). 工作记忆子成分在听觉障碍儿童心算过程中的作用. 心理科学, 29( 1), 76-79.
7	张清芳, 朱滢 . ( 2000). 工作记忆和推理. 心理学动态, 8( 1), 12-17.
8	赵鑫, 王一雪, 刘丹玮, 周仁来 . ( 2011). 工作记忆刷新训练对儿童流体智力的影响. 科学通报, 56( 17), 1345-1348.
9	*Alloway, T. ( 2012). Can interactive working memory training improve learning. Journal of Interactive Learning Research, 23( 3), 197-207.
10	Alloway, T. P., & Alloway, R. G. ( 2008). Jungle memory training program. Edinburgh, United Kingdom: Memosyne.
11	Alloway T. P., Gathercole S. E., Kirkwood H., & Elliott J. ( 2008). Evaluating the validity of the Automated Working Memory Assessment. Educational Psychology, 28( 7), 725-734.
12	*Alloway T. P., Bibile V., & Lau G. ( 2013). Computerized working memory training: Can it lead to gains in cognitive skills in students? Computers in Human Behavior, 29( 3), 632-638.
13	*Ang S. Y., Lee K., Cheam F., Poon K., & Koh J. ( 2015). Updating and working memory training: Immediate improvement, long-term maintenance, and generalisability to non-trained tasks. Journal of Applied Research in Memory and Cognition, 4( 2), 121-128.
14	Au J., Sheehan E., Tsai N., Duncan G. J., Buschkuehl M., & Jaeggi S. M. ( 2015). Improving fluid intelligence with training on working memory: A meta-analysis. Psychonomic Bulletin & Review, 22( 2), 366-377.
15	Bachot J., Gevers W., Fias W., & Roeyers H. ( 2005). Number sense in children with visuospatial disabilities: Orientation of the mental number line. Psychology Science, 47, 172-183.
16	*Bergman-Nutley, S., & Klingberg, T. ( 2014). Effect of working memory training on working memory, arithmetic and following instructions. Psychological Research, 78( 6), 869-877.
17	Borella E., Carretti B., Cornoldi C., & De Beni R. ( 2007). Working memory, control of interference and everyday experience of thought interference: When age makes the difference. Aging Clinical and Experimental Research, 19( 3), 200-206.
18	Borella E., Carretti B., & De Beni R. ( 2008). Working memory and inhibition across the adult life-span. Acta Psychologica, 128( 1), 33-44.
19	Borella E., Carretti B., Riboldi F., & De Beni R. ( 2010). Working memory training in older adults: Evidence of transfer and maintenance effects. Psychology and Aging, 25( 4), 767-778.
20	Borenstein M., Hedges L., Higgins J., & Rothstein H. ( 2005). Compreshensive meta-analysis (Version 2) [Software]. Engelwood, NJ: Biostat.
21	Brainerd, C. J. ( 1983). Young children's mental arithmetic errors: A working-memory analysis. Child Development, 54( 4), 812-830.
22	Carretti B., Cornoldi C., De Beni R., & Palladino P. ( 2004). What happens to information to be suppressed in working-memory tasks? Short and long term effects. The Quarterly Journal of Experimental Psychology Section A, 57( 6), 1059-1084.
23	Caviola S., Mammarella I. C., Cornoldi C., & Lucangeli D. ( 2012). The involvement of working memory in children's exact and approximate mental addition. Journal of Experimental Child Psychology, 112( 2), 141-160.
24	*Cornoldi C., Carretti B., Drusi S., & Tencati C. ( 2015). Improving problem solving in primary school students: The effect of a training programme focusing on metacognition and working memory. British Journal of Educational Psychology, 85( 3), 424-439.
25	Cragg, L., & Gilmore, C. ( 2014). Skills underlying mathematics: The role of executive function in the development of mathematics proficiency. Trends in Neuroscience and Education, 3( 2), 63-68.
26	*Dahlin, K. I. E. ( 2013). Working memory training and the effect on mathematical achievement in children with attention deficits and special needs. Journal of Education and Learning, 2( 1), 118-133.
27	Dehaene, S. ( 2001). Précis of the number sense. Mind and Language, 16( 1), 16-36.
28	Demir Ö. E., Prado J., & Booth J. R. ( 2014). The differential role of verbal and spatial working memory in the neural basis of arithmetic. Developmental Neuropsychology, 39( 6), 440-458.
29	*Dunning D. L., Holmes J., & Gathercole S. E. ( 2013). Does working memory training lead to generalized improvements in children with low working memory? A randomized controlled trial. Developmental Science, 16( 6), 915-925.
30	*Fälth L., Jaensson L., & Johansson K. ( 2015). Working memory training - A Cogmed intervation. International Journal of Learning, Teaching and Educational Research, 14( 2), 28-35.
31	Friso-van den Bos I., Kroesbergen E. H., & van Luit, J. E. H. ( 2014). Number sense in kindergarten children: Factor structure and working memory predictors. Learning and Individual Differences, 33, 23-29.
32	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.
33	Geary, D. C. ( 2006). Development of mathematical understanding. In W. Damon, R. M. Lerner, D. Kuhn, & R. S. Sielger (Eds.), Handbook of child psychology: Vol 2. Cognition, perception, and language ( 6th ed., pp. 777- 810). New York: Wiley.
34	Giofrè D., Mammarella I. C., & Cornoldi C. ( 2013). The structure of working memory and how it relates to intelligence in children. Intelligence, 41( 5), 396-406.
35	Gray J. R., Chabris C. F., & Braver T. S. ( 2003). Neural mechanisms of general fluid intelligence. Nature Neuroscience, 6( 3), 316-322.
36	Harrison T. L., Shipstead Z., Hicks K. L., Hambrick D. Z., Redick T. S., & Engle R. W. ( 2013). Working memory training may increase working memory capacity but not fluid intelligence. Psychological Science, 24( 12), 2409-2419.
37	Henry, L. A. ( 2001). How does the severity of a learning disability affect working memory performance? Memory, 9( 4-6), 233-247.
38	Herrera A., Macizo P., & Semenza C. ( 2008). The role of working memory in the association between number magnitude and space. Acta Psychologica, 128( 2), 225-237.
39	Hitch, G. J., & McAuley, E. ( 1991). Working memory in children with specific arithmetical learning difficulties. British Journal of Psychology, 82( 3), 375-386.
40	*Holmes J., Gathercole S. E., & Dunning D. L. ( 2009). Adaptive training leads to sustained enhancement of poor working memory in children. Developmental Science, 12( 4), F9-F15.
41	Hubber P. J., Gilmore C., & Cragg L. ( 2014). The roles of the central executive and visuospatial storage in mental arithmetic: A comparison across strategies. Quarterly Journal of Experimental Psychology, 67( 5), 936-954.
42	Jaeggi S. M., Buschkuehl M., Jonides J., & Perrig W. J. ( 2008). Improving fluid intelligence with training on working memory. Proceedings of the National Academy of Sciences of the United States of America, 105( 19), 6829-6833.
43	Jaeggi S. M., Buschkuehl M., Jonides J., & Shah P. ( 2011). Short- and long-term benefits of cognitive training. Proceedings of the National Academy of Sciences of the United States of America, 108( 25), 10081-10086.
44	Jahanshahi M., Saleem T., Ho, A. K, Fuller, R., & Dirnberger G. ( 2008). A preliminary investigation of the running digit span as a test of working memory. Behavioural Neurology, 20( 1-2), 17-25.
45	Jordan N. C., Kaplan D., Ola′h L. N., & Locuniak M. N. ( 2006). Number sense growth in kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. Child Development, 77( 1), 153-175.
46	Kane, M. J., & Engle, R. W. ( 2002). The role of prefrontal cortex in working-memory capacity, executive attention, and general fluid intelligence: An individual-differences perspective. Psychonomic Bulletin & Review, 9( 4), 637-671.
47	Klingberg T., Fernell E., Olesen P. J., Johnson M., Gustafsson P., Dahlström K., … Westerberg H. ( 2005). Computerized training of working memory in children with ADHD: A randomized, controlled trial. Journal of the American Academy of Child & Adolescent Psychiatry, 44( 2), 177-186
48	Krichner, W. K. ( 1958). Age differences in short-term retention of rapidly changing information. Journal of Experimental Psychology, 55( 4), 352-358.
49	*Kroesbergen, E. H., Van't Noordende, J. E., & Kolkman, M. E. (2012). Number sense in low-performing kindergarten children: Effects of a working memory and an early math training. In: Z. Breznitz, O. Rubinsten, V. Molfese, & D. Molfese (Eds.), Reading, writing, mathematics and the developing brain: Listening to many voices (pp. 295-313). Netherlands: Springer.
50	*Kroesbergen E. H., Van't Noordende J. E., & Kolkman M. E. ( 2014). Training working memory in kindergarten children: Effects on working memory and early numeracy. Child Neuropsychology, 20( 1), 23-37.
51	Kuhn, J.-T., & Holling, H. ( 2014). Number sense or working memory? The effect of two computer-based trainings on mathematical skills in elementary school. Advances in Cognitive Psychology, 10( 2), 59-67.
52	Kyttälä M., Aunio P., Lehto J. E., Van Luit J., & Hautamäki J. ( 2003). Visuospatial working memory and early numeracy. Educational and Child Psychology, 20( 3), 65-76.
53	*Kyttälä M., Kanerva K., & Kroesbergen E. ( 2015). Training counting skills and working memory in preschool. Scandinavian Journal of Psychology, 56( 4), 363-370.
54	*Mansur-Alves, M., & Flores-Mendoza, C. ( 2015). Working memory training does not improve intelligence: Evidence from Brazilian children. Psicologia: Reflexão e Crítica, 28( 3), 474-482.
55	Melby-Lervåg, M., & Hulme, C. ( 2013). Is working memory training effective? A meta-analytic review. Developmental Psychology, 49( 2), 270-291.
56	Melby-Lervåg M., Redick T. S., & Hulme C. ( 2016). Working memory training does not improve performance on measures of intelligence or other measures of "far transfer": Evidence from a meta-analytic review. Perspectives on Psychological Science, 11( 4), 512-534.
57	*Minear M., Brasher F., Guerrero C. B., Brasher M., Moore A., & Sukeena J. ( 2016). A simultaneous examination of two forms of working memory training: Evidence for near transfer only. Memory & Cognition, 44( 7), 1014-1037.
58	Morrison, A. B., & Chein, J. M. ( 2011). Does working memory training work? The promise and challenges of enhancing cognition by training working memory. Psychonomic Bulletin & Review, 18( 1), 46-60.
59	*Nelwan, M., & Kroesbergen, E. H. ( 2016). Limited near and far transfer effects of Jungle Memory working memory training on learning mathematics in children with attentional and mathematical difficulties. Frontiers in Psychology, 7, 1384.
60	Nunes T., Bryant P., Barros R., & Sylva K. ( 2012). The relative importance of two different mathematical abilities to mathematical achievement. British Journal of Educational Psychology, 82, 136-156.
61	*Partanen P., Jansson B., Lisspers J., & Sundin Ö. ( 2015). Metacognitive strategy training adds to the effects of working memory training in children with special educational needs. International Journal of Psychological Studies, 7( 3), 130-140.
62	*Passolunghi, M. C., & Costa, H. M. ( 2016). Working memory and early numeracy training in preschool children. Child Neuropsychology, 22( 1), 81-98.
63	Peijnenborgh J. C., Hurks P. M., Aldenkamp A. P., Vles J. S., & Hendriksen, J. G. M. ( 2016). Efficacy of working memory training in children and adolescents with learning disabilities: A review study and meta-analysis. Neuropsychological Rehabilitation, 26( 5-6), 645-672.
64	Phillips N. L., Mandalis A., Benson S., Parry L., Epps A., Morrow A., & Lah S. ( 2016). Computerized working memory training for children with moderate to severe traumatic brain injury: A double-blind, randomized, placebo-controlled trial. Journal of Neurotrauma, 33( 23), 2097-2104.
65	Pollack I., Johnson L. B., & Knaff P. R. ( 1959). Running memory span. Jounal of Experimental Psychology, 57( 3), 137-146.
66	Raghubar K. P., Barnes M. A., & Hecht S. A. ( 2010). Working memory and mathematics: A review of developmental, individual difference, and cognitive approaches. Learning and Individual Differences, 20( 2), 110-122.
67	*Redick T. S., Shipstead Z., Harrison T. L., Hicks K. L., Fried D. E., Hambrick D. Z., .. Engle R. W. ( 2013). No evidence of intelligence improvement after working memory training: A randomized, placebo-controlled study. Journal of Experimental Psychology: General, 142( 2), 359-379.
68	*Roberts G., Quach J., Spencer-Smith M., Anderson P. J., Gathercole S., Gold L., .. Wake M. ( 2016). Academic outcomes 2 years after working memory training for children with low working memory: A randomized clinical trial. JAMA Pediatrics, 170( 5), e154568.
69	*Rode C., Robson R., Purviance A., Geary D. C., & Mayr U. ( 2014). Is working memory training effective? A study in a school setting. PLoS One, 9( 8), e104796.
70	Rotzer S., Loenneker T., Kucian K., Martin E., Klaver P., & von Aster M. ( 2009). Dysfunctional neural network of spatial working memory contributes to developmental dyscalculia. Neuropsychologia, 47( 13), 2859-2865.
71	*Söderqvist, S., & Nutley, S. B. ( 2015). Working memory training is associated with long term attainments in math and reading. Frontiers in Psychology, 6, 1711.
72	Schwaighofer M., Fischer F., & Bühner M. ( 2015). Does working memory training transfer? A meta-analysis including training conditions as moderators. Educational Psychologist, 50( 2), 138-166.
73	Stevenson C. E., Heiser W. J., & Resing, W. C. M.( 2013). Working memory as a moderator of training and transfer of analogical reasoning in children. Contemporary Educational Psychology, 38( 3), 159-169.
74	Titz, C., & Karbach, J. ( 2014). Working memory and executive functions: Effects of training on academic achievement. Psychological Research, 78, 852-868.
75	*van der Molen, M. J., van Luit, J. E., van der Molen, M. W., Klugkist I., & Jongmans M. J. ( 2010). Effectiveness of a computerised working memory training in adolescents with mild to borderline intellectual disabilities. Journal of Intellectual Disability Research, 54( 5), 433-447.
76	von Bastian C. C., Langer N., Jäncke L., & Oberauer K. ( 2013). Effects of working memory training in young and old adults. Memory & Cognition, 41( 4), 611-624.
77	*Witt, M. ( 2011). School based working memory training: Preliminary finding of improvement in children's mathematical performance. Advances in Cognitive Psychology, 7, 7-15.
78	Wu S. S., Meyer M. L., Maeda U., Salimpoor V., Tomiyama S., Geary D. C., & Menon V. ( 2008). Standardized assessment of strategy use and working memory in early mental arithmetic performance. Developmental Neuropsychology, 33( 3), 365-393.

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[14]	连四清;林崇德. 工作记忆在数学运算过程中的作用[J]. 心理科学进展, 2007, 15(1): 36-41.
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