算术策略运用能力的年龄差异：元认知监测与算术知识的作用

摘要/Abstract

摘要： 采用选择/无选法，以估算与精确心算为研究任务，考察了元认知监测与算术知识影响个体算术计算策略选择与执行的年龄相关差异。129名不同年龄儿童与成人被试参加实验。结果发现：（1）算术知识对儿童及成人的估算复杂策略有促进作用，并对提升他们心算策略运用的速度和减少错误有作用；（2）元认知监测显著影响儿童的估算策略选择，能够促进使用最佳策略；（3）算术知识在估算及心算策略执行的年龄差异方面起完全中介作用，元认知监测则在估算策略选择的年龄发展中起部分中介作用；（4）算术知识对元认知监测在估算及心算策略执行上的作用起完全中介作用，而对估算的策略选择则不存在中介作用，这表明元认知监测在估算策略选择上具有举足轻重的地位。

关键词: 元认知监测, 算术知识, 策略选择, 策略执行, 估算, 心算

Abstract: Choice/No-choice method was used to explore the contributions of arithmetic knowledge and metacognitive monitoring in arithmetic strategy use in computational estimation and mental arithmetic during individual development. Total 129 participants took part in the study. The results revealed that: 1) arithmetic knowledge had an influence on complex strategy selection in computational estimation for adults and children. It also had an important role in mental arithmetic strategy execution; 2) metacognitive monitoring had a great role in computational estimation strategy selection for children. Selection of best strategy was always higher; 3) a fully mediational effect of arithmetic knowledge on age differences in strategy execution in both computational estimation and mental arithmetic had been found; a partial mediational effect of metacognitive monitoring on age differences in strategy selection in computational estimation was showed; 4) a fully mediational effect of arithmetic knowledge on metacognitive monitoring in strategy execution in both computational estimation and mental arithmetic was showed. But there was no effect on metacognitive monitoring in strategy selection which showed that metacognitive monitoring played unique role in strategy selection in computational estimation.

Key words: metacognitive monitoring, arithmetic knowledge, strategy selection, strategy execution, computational estimation, mental arithmetic

中图分类号:

B844

刘伟方, 华晓腾, 封洪敏, 胡冬梅, 司继伟. 算术策略运用能力的年龄差异：元认知监测与算术知识的作用[J]. 心理发展与教育, 2014, 30(3): 234-243.

LIU Wei-fang, HUA Xiao-teng, FENG Hong-min, HU Dong-mei, SI Ji-wei. The Age-Related Differences of Arithmetic Strategy Use in Calculation：The Role of Metacognitive Monitoring and Arithmetic Knowledge[J]. Psychological Development and Education, 2014, 30(3): 234-243.

参考文献

Barulli, D. J., Rakitin, B. C., Lemaire, P., & Stern, Y. (2013). The influence of cognitive reserve on strategy selection in normal aging. Journal of the International Neuropsychological Society, 19(7), 1-4.
Bull, R. (2008).Short-term memory, working memory, and executive functioning in preschoolers: Longitudinal predictors of mathematical achievement at age 7 years. Developmental Neuropsychology, 33(3), 205-228.
Campbell, J. I. D. (2005). Handbook of mathematical cognition. New York: Psychology Press.
Desoete, A., Roeyers, H., & De Clercq. A. (2003). Can offline metacognition enhance mathematical problem Solving. Journal of Educational Psychology, 95(1), 188-200.
Dunlosky, J., & Hertzog, C. (2000). Updating knowledge about strategy effectiveness: A componential analysis of learning about strategy effectiveness from task experience. Psychology and aging, 15(3), 462-474.
Fernandez-Duque, D., Baird, J.A., & Posner, M.I. (2000). Executive attention and metacognitive regulation. Consciousness and Cognition, 9(2), 288-307.
Flavell, J. H. (1979). Metacognition and cognitive monitoring: A new area of psychology inquiry. In: T.O. Nelson (Ed.), Metacognition: Core readings (pp. 3-8). Boston: Allyn and Bacon.
Geary, D. C., Hoard, M. K., Byrd-Craven, J., & DeSoto, M. C. (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.
Hatano, G. (2003). Foreword. In A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills (pp. 11-13). Mahwah, NJ: Erlbaum.
Heirdsfield, A. M. (2002). Flexible mental computation: What about accuracy? In Cockburn, A. and Nardi, E. (Eds.), Proceedings 26th Annual Conference of the International Group for the Psychology of Mathematics Education. 3, 89-96, Norwich, UK.
Keeler, M. L., & Swanson, H. L. (2001). Does strategy knowledge influence working memory in children with mathematical disabilities? Journal of Learning Disabilities, 34(5), 418-434.
Klein, E., Nuerk, H., Wood, G., Knops, A., & Willmes, K. (2009). The exact vs. approximate distinction in numerical cognition may not be exact, but only approximate: How different processes work together in multi-digit addition. Brain and Cognition, 69(2), 369-381.
Koriat, A. (2012). The relationships between monitoring, regulation and performance. Learning and Instruction, 22(4), 296-298.
Lemaire, P., & Calliès, S. (2009). children's strategies in complex arithmetic. Journal of Experimental Child Psychology, 103(1), 49-65.
Lemaire, P., & Lecacheur, M. (2002). children's strategies in computational estimation. Journal of Experimental Child Psychology, 82(4), 281-304.
Lemaire, P., & Lecacheur, M. (2010). Strategy switch costs in arithmetic problem solving. Memory & Cognition, 38(3), 322-332.
Lemaire, P., & Lecacheur, M. (2011). Age-related changes in children's executive functions and strategy selection: A study in computational estimation. Cognitive Development, 26(3), 282-294.
Lemaire, P., & Leclère, M. (2013, in press). Strategy Repetition in Young and Older Adults: A Study in Arithmetic. Developmental Psychology. DOI: 10.1037/a0033527.
Lemaire, P., & Siegler, R. S. (1995). Four aspects of strategic change: Contributions to children's learning of multiplication. Journal of Experimental Psychology: General, 124(1), 83-97.
Lemaire, P., Arnaud, L., & Lecacheur, M. (2004). Adults' age-related differences in adaptativity of strategy choices: Evidence from computational estimation. Psychology and Aging, 10(3), 467-481.
Luwel, K., Foustana, A., Onghena, P., & Verschaffel, L. (2013). The role of verbal and performance intelligence in children's strategy selection and execution. Learning and Individual Differences, 24, 134-138.
Luwel, K., Schillemans, V., Onghen, P., & Verschaffel, L. (2009). Does switching between strategies within the same task involve a cost? British Journal of Psychology, 100(4), 753-771.
Pennequin, V., Sorel, O., Nanty, I., & Fontaine, R. (2010). Metacognition and low achievement in mathematics: The effect of training in the use of metacognitive skills to solvemathematical word problems. Thinking & Reasoning, 16(3), 198-220.
Rittle-Johnson, B., & Star, J. R. (2007). Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations. Journal of Educational Psychology, 99(3), 561-574.
Siegler, R. S., & Booth, J. (2005). Development of numerical estimation: A Review. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp.197-212). New York: Psychology Press.
Star, J. R., Rittle-Johnson, B., Lynch, K., & Perova, N. (2009). The role of prior knowledge in the development of strategy flexibility: the case of computational estimation[J]. ZDM Mathematics Education, 41, 569-579.
Throndsen, I. (2011). Self-regulated learning of basic arithmetic skills: A longitudinal study. British Journal of Educational Psychology 81(4), 558-578.
Uittenhove, K., Poletti, C., Dufau, S., & Lemaire, P. (2013). The time course of strategy sequential difficulty effects：An ERP study in arithmetic. Experimental Brain Research,227(1), 1-8.
Verschaffel, L., Luwel, K., Torbeyns, J., & Van Dooren, W. (2009). Conceptualizing, investigating, and enhancing adaptive expertise in elementary mathematics education. European Journal of Psychology of Education, 24(3), 335-359.
Verschaffel, L., Luwel, K., Torbeyns, J., & Van Dooren, W. (2011). Analyzing and developing strategy flexibility in mathematics education. In. J. Elen, E. Stahl, R. Bromme, G. Clarebout. (Eds.), Links between beliefs and cognitive flexibility: Lessons learned (pp.175-197). Springer, London.
Vígh-Kiss, E. R. (2013). Adaptive strategy use in mathematics education. In J. T. Karlovitz (Eds.), Questions and perspectives in education (pp. 342-352). Komárno: International Research Institute.
李美华, 沈德立, 白学军. (2007). 不同年级学生认知灵活性研究. 中国特殊教育, (8), 80-86.
刘伟方, 司继伟, 王玉璇. (2011). 认知策略选择的元认知因素. 心理科学进展, 19(9), 1328-1338.
司继伟. (2002). 小学儿童估算能力研究. 博士学位论文, 西南大学.
司继伟, 杨佳, 贾国敬, 周超. (2012). 中央执行负荷对成人估算策略运用的影响. 心理学报, 44(11), 1490-1500.
孙燕, 司继伟, 徐艳丽. (2012). 数学焦虑影响大学生/儿童估算策略运用的对比研究. 心理发展与教育, 28(3), 263-270.
吴灵丹, 刘电芝. (2006). 儿童计算的元认知监测及其对策略选择的影响. 心理科学, 29(2), 354-357.

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