数学焦虑影响儿童的数量表征:认知抑制的调节作用

doi:10.16187/j.cnki.issn1001-4918.2020.01.02

摘要/Abstract

摘要： 为了考察数学焦虑对儿童数量表征表现的可能影响及认知抑制的潜在调节作用，选取70名小学三年级儿童（高焦虑组36人，低焦虑组34人）为被试，在对抑制条件进行操控的情况下，要求其完成符号、非符号数量表征任务。结果发现，被试在两种数量表征任务中均出现距离效应，与符号数量比较任务相比，高焦虑组在非符号数量比较任务中的正确率显著低于低焦虑组，且高焦虑组表现出了更强的距离效应。鉴于非符号数量比较任务更能反映出个体近似数量系统（ANS）的敏锐性，上述结果意味着高数学焦虑儿童的数量表征更不精确，其在相对复杂问题上较差的表现或许源于基本数量能力缺陷。本研究还发现认知抑制能够调节数学焦虑对个体非符号数量表征的影响，抑制条件下高低焦虑组儿童在正确率指标上的差异大于非抑制条件，抑制条件的设置提高了个体对工作记忆资源的需求，此时焦虑情绪对认知资源的消耗会造成任务所需资源的不足，进而削弱高焦虑个体的认知效用。

关键词: 数学焦虑, 认知抑制, 符号数量表征, 非符号数量表征, 儿童

Abstract: The current paper examined differences among children with different level of math anxiety in the processing of numerical magnitude under condition of inhibition and non-inhibition. 70 third graders, including 36 high math anxiety children (HMA) and 34 low math anxiety children (LMA), were employed and asked to accomplish symbolic numerical representation tasks and non-symbolic numerical representation tasks. The results showed that numerical distance effect was found in all participants. Compared to symbolic numerical representation tasks, the ACC of HMA children was lower than LMA children in non-symbolic numerical representation tasks, and the distance effect was larger for HMA group than for LMA group. Additionally, HMA had poorer performance in inhibition condition than LMA children. These findings suggested that math anxiety may not only affect difficult mathematical tasks, but simple numerical tasks. And the cognitive inhibition plays a regulatory role in this processing.

Key words: mathematics anxiety, cognitive inhibition, symbolic numerical representation, non-symbolic numerical representation, children

官冬晓, 艾继如, 黄碧娟, 崔爽, 司继伟. 数学焦虑影响儿童的数量表征:认知抑制的调节作用[J]. 心理发展与教育, 2020, 36(1): 10-18.

GUAN Dongxiao, AI Jiru, HUANG Bijuan, CUI Shuang, SI Jiwei. Math Anxiety Affects Children's Numerical Representation: Cognitive Inhibition as a Moderator[J]. Psychological Development and Education, 2020, 36(1): 10-18.

参考文献

Ashcraft, M. H. (2002). Math anxiety:Personal, educational, and cognitive consequences. Current Directions in Psychological Science, 11(5), 181-185.
Ashcraft, M. H., & Faust, M. W. (1994). Mathematics anxiety and mental arithmetic performance:An exploratory investigation. Cognition & Emotion, 8(2), 97-125.
Ashcraft, M. H., & Kirk, E. P. (2001). The relationships among working memory, math anxiety, and performance. Journal of Experimental Psychology:General, 130(2), 224-37.
Ashcraft, M. H., & Moore, A. M. (2009). Mathematics anxiety and the affective drop in performance. Journal of Psychoeducational Assessment, 27(3), 197-205.
Krajcsi, A., Lengyel, G., & Kojouharova, P. (2018). Symbolic number comparison is not processed by the analog number system:Different symbolic and non-symbolic numerical distance and size effects. Frontiers in Psychology, 9, 124. doi:10.3389/fpsyg.2018.00124
Bonny, J. W., & Lourenco, S. F. (2013). The approximate number system and its relation to early math achievement:Evidence from the preschool years. Journal of Experimental Child Psychology, 114(3), 375-388.
Brysbaert, M. (2005). Number recognition in different formats. In Campbell, J. I. D. (Ed.), Handbook of Mathematical Cognition (pp. 23-42). New York:Psychology Press.
Cantlon. J. F., Platt, M. L., & Brannon, E. M. (2009). Beyond the number domain. Trends in Cognitive Sciences, 13(2), 83-91.
Cargnelutti, E., Tomasetto, C., & Passolunghi, M. C. (2016). How is anxiety related to math performance in young students? A longitudinal study of grade 2 to grade 3 children. Cognition & Emotion, 31(4), 755-764.
De Smedt. B., Verschaffel, L., & Ghesquière, P. (2009). The predictive value of numerical magnitude comparison for individual differences in mathematics achievement. Journal of Experimental Child Psychology, 103(4), 469-479.
Dehaene, S. (1997). The number sense. New York:Oxford University Press.
Dehaene, S., Dehaene-Lambertz, G., & Cohen, L. (1998). Abstract representations of numbers in the animal and human brain. Trends in Neuroscience, 21(8), 355-361.
Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20(3), 487-506.
Dietrich, J. F., Huber, S., Moeller, K., & Klein, E. (2015). The influence of math anxiety on symbolic and non-symbolic magnitude processing.Frontiers in Psychology, 6, 1621. Doi:10.3389/fpsyg.2015.01621
Eysenck, M. W., & Calvo, M. G. (1992). Anxiety and performance:the processing efficiency theory. Cognition and Emotion, 6, 409-434.
Eysenck, M. W., Derakshan, N., Santos, R., & Calvo, M. G. (2007). Anxiety and cognitive performance:Attentional control theory. Emotion, 7(2), 336-353.
Fernanda, D. O. F., Wood, G., Pinheirochagas, P., Lonnemann, J., Krinzinger, H., Willmes, K., et al. (2012). Explaining school mathematics performance from symbolic and nonsymbolic magnitude processing:Similarities and differences between typical and low-achieving children. Psychology & Neuroscience, 5(1), 37-4606.
French, J. W., Ekstrom, R. B., & Price, L. A. (1963). Kit of reference tests for cognitive factors. Princeton, N.J:Educational Testing Service.
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(1), 136-148.
Geary, D. C., & Vanmarle, K. (2016). Young children's core symbolic and nonsymbolic quantitative knowledge in the prediction of later mathematics achievement. Developmental Psychology, 52(12), 2130-2144.
Gilmore, C., Attridge, N., Clayton, S., Cragg, L., Johnson, S., Marlow, N., et al. (2013). Individual differences in inhibitory control, not non-verbal number acuity, correlate with mathematics achievement. Plos One, 8(6), e67374. DOI:10.1371/journal.pone.0067374
Gilmore, C., Keeble, S., Richardson, S., & Cragg, L. (2015). The role of cognitive inhibition in different components of arithmetic. ZDM, 47(5), 771-782.
Halberda, J., & Feigenson, L. (2008). Developmental change in the acuity of the "number sense":the approximate number system in 3-, 4-, 5-, and 6-year-olds and adults. Developmental Psychology, 44(5), 1457-1465.
Holloway, I. D., & Ansari, D. (2009). Mapping numerical magnitudes onto symbols:The numerical distance effect and individual differences in children's mathematics achievement. Journal of Experimental Child Psychology, 103(1), 17-29.
Imbo, I. (2007). Strategy selection and strategy efficiency in mental arithmetic (Doctoral Dissertation). Gent University.
Landerl, Karin, Bevan, Anna, Butterworth, & Brian. (2004). Developmental dyscalculia and basic numerical capacities:A study of 8-9-year-old students. Cognition, 93(2), 99-125.
Lindskog, M., Winman, A., & Poom, L. (2017). Individual differences in nonverbal number skills predict math anxiety. Cognition, 159, 156-162.
Lonnemann, J., Linkersdörfer, J., Hasselhorn, M., & Lindberg, S. (2011). Symbolic and non-symbolic distance effects in children and their connection with arithmetic skills. Journal of Neurolinguistics, 24(5), 583-591.
Lyons, I. M., Ansari, D., & Beilock, S. L. (2015). Qualitatively different coding of symbolic and non-symbolic numbers in the human brain. Human Brain Mapping. 36, 475-488.
Maloney, E. A., Ansari, D., & Fugelsang, J. A. (2011). The effect of mathematics anxiety on the processing of numerical magnitude. The Quarterly Journal of Experimental Psychology, 64(1), 10-16.
Maloney, E. A., Risko, E. F., Ansari, D., & Fugelsang, J. (2010). Mathematics anxiety affects counting but not subitizing during visual enumeration. Cognition, 114(2), 293-297.
Miyake, A., Friedman, N. P., Emerson, M. J., Witzki, A. H., Howerter, A., & Wager, T. D. (2000). The unity and diversity of executive function and their contribution to complex "Frontal Lobe" tasks:A latent variable analysis. Cognitive Psychology, 41(1), 49-100.
Mock, J., Huber, S, Klein, E., & Moeller, K. (2016). Insights into numerical cognition:considering eye-fixations in number processing and arithmetic. Psychological Research, 80(3), 334-359.
Moyer, R. S., & Landauer, T. K. (1967). Time required for judgments of numerical inequality. Nature, 215(5190), 1519-1520.
Núñez-Peña, M. I., & Suárez-Pellicioni, M. (2014). Less precise representation of numerical magnitude in high math-anxious individuals:An ERP study of the size and distance effects. Biological Psychology, 103, 176-183.
Pizzie, R. G., & Kraemer, D. J. M. (2017). Avoiding math on a rapid timescale:Emotional responsivity and anxious attention in math anxiety. Brain and Cognition, 118, 100-107.
Ramirez, G., Chang, H., Maloney, E. A., Levine, S. C., & Beilock, S. L. (2016). On the relationship between math anxiety and math achievement in early elementary school:The role of problem solving strategies. Journal of Experimental Child Psychology, 141, 83-100.
Ramirez, G., Gunderson, E, A., Levine, S, C., & Beilock. S, L. (2013). Math anxiety, working memory, and math achievement in early elementary school. Journal of Cognition & Development, 14(2), 187-202.
Sabourin, J. L., & Lester, J. C. (2014). Affect and engagement in game-based learning environments. IEEE Transactions on Affective Computing, 5(1), 45-56.
Siegler, R. S., & Pyke, A. A. (2013). Developmental and individual differences in understanding of fractions. Developmental Psychology, 49(10), 1994-2004.
Szucs, D., Devine, A., Soltesz, F., Nobes, A., & Gabriel, F. (2013). Developmental dyscalculia is related to visuo-spatial memory and inhibition impairment. Cortex, 49(10), 2674-2688.
Thomas, G., & Dowker, A. (2000). Mathematics anxiety and related factors in young children. Paper presented at British Psychological Society Developmental Section Conference, Bristol, UK.
Titia, G., & Bert, R. (2011). Generating non-symbolic number stimuli. Behavior Research Methods, 43(4), 981-986
陈琪. (2016). 数学焦虑影响数学任务表现的作用机制研究(硕士学位论文). 内蒙古师范大学, 呼和浩特.
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.
陈英和, 耿柳娜. (2005). 数学焦虑对儿童加减法认知策略选择和执行的影响. 心理发展与教育, 21(4), 24-27.
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),21(1), 33-41.
黄碧娟. (2017). 算术技能与数学焦虑的关系及其对数字认知的影响:行为和电生理学证据(硕士学位论文). 山东师范大学,济南.
李红霞, 司继伟, 陈泽建, 张堂正. (2015). 人类的近似数量系统. 心理科学进展, 23(4), 562-570.
刘桂荣, 张景焕. (2017). 教育心理学研究的特点和趋势-基于2011-2015年Journal of Educational Psychology刊载文章的分析. 山东师范大学学报, 62(4), 123-132.
牛玉柏, 张丽芬, 肖帅, 曹贤才. (2018). 小学生近似数量系统敏锐度的发展趋势及其与数学能力的关系:抑制控制的中介作用. 心理科学, 41(2), 344-350.
司继伟, 徐艳丽, 封洪敏, 许晓华, 周超. (2014). 不同数学焦虑成人的算术策略运用差异:ERP研究. 心理学报, 46(12), 1835-1849.
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.
腾静. (2015). 儿童非符号数量表征与数学学业成绩的关系(硕士学位论文). 华东师范大学, 上海.
王翠艳, 刘昌. (2007). 数学焦虑对心算加工的影响. 心理科学进展, 15(5), 795-801.
王君, 陈天勇. (2012). 抑制控制与高级认知功能的关系. 心理科学进展, 20(11), 1768-1778.
闫国利, 熊建萍, 臧传丽, 余莉莉, 崔磊, 白学军. (2013). 阅读研究中的主要眼动指标评述. 心理科学进展, 21(4), 589-605.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed

[1]	王堃炎, 黄英航, 邓珏, 王璇, 张向葵. 从善念到善行:4~7岁儿童社会善念与亲社会行为的发展关联[J]. 心理发展与教育, 2026, 42(4): 457-466.
[2]	于晓, 张雅欣, 戚玥, 常尚钺, 何雯惺, 陈英和. 学龄儿童自然联结的发展轨迹及其与创造力倾向的关系:累加效应还是交互效应？[J]. 心理发展与教育, 2026, 42(4): 467-477.
[3]	陈紫薇, 黄潇潇, 俞国良. 父母教养行为与儿童心理健康关系的三水平元分析[J]. 心理发展与教育, 2026, 42(4): 563-576.
[4]	吴旻, 张杰, 叶攀琴, 龚茜, 袁柯曼. 留守儿童非自杀性自伤行为的发展轨迹:同伴侵害模式的影响[J]. 心理发展与教育, 2026, 42(4): 586-595.
[5]	舒展, 彭申立, 赵纤, 黎志华. 累积家庭风险对低收入家庭儿童外化问题影响的即时与延时效应:有调节的中介模型[J]. 心理发展与教育, 2026, 42(4): 596-608.
[6]	韩燕, 郭筱琳, 杨文静, 张恒, 王腾飞. 阅读困难儿童的执行功能结构分化滞后于正常发展儿童[J]. 心理发展与教育, 2026, 42(3): 326-336.
[7]	范兴华, 靳嘉宁, 燕利飞, 李潇潼, 邓汇溪. 留守困境对初中儿童个人成长主动性发展的影响:社会支持的中介作用[J]. 心理发展与教育, 2026, 42(3): 427-436.
[8]	张攀, 杨娟, 王小英. 象似性手势对3~4岁儿童汉语动作动词记忆和泛化的影响[J]. 心理发展与教育, 2026, 42(2): 153-161.
[9]	袁雯, 张旭然, 郭惠, 李燕芳. 儿童欺凌网络的结构特征与变化特点：基于社会网络分析视角[J]. 心理发展与教育, 2026, 42(2): 234-244.
[10]	谢宇, 贺荟中, 王磊, 戴惟熙. 孤独症儿童与典型发展儿童内隐学习物品情景线索的比较研究[J]. 心理发展与教育, 2025, 41(6): 761-769.
[11]	范兴华, 燕利飞, 靳嘉宁, 李潇潼, 邓汇溪, 余思. 父母关爱对4~6年级留守儿童幸福感发展的影响:积极诠释生活的调节作用[J]. 心理发展与教育, 2025, 41(6): 859-868.
[12]	刘畅, 蒋柳青, 郑天鹏, 边玉芳. 父母情绪调节困难与父母情绪社会化行为的关系:基于主客体互倚模型的交叉滞后研究[J]. 心理发展与教育, 2025, 41(5): 652-662.
[13]	王宇轩, 刘梦连, 杨滢晖, 毕鸿燕. 学龄儿童与成人形音整合的比较研究:字形与字音的相互影响[J]. 心理发展与教育, 2025, 41(4): 457-464.
[14]	王彦姣, 黄家桢, 龙嘉, 王沛. 领域一般和领域特殊能力与计算障碍的内在联系及其启示——基于元分析视角[J]. 心理发展与教育, 2025, 41(4): 473-481.
[15]	冯娜, 梁峰, 王芬, 何春丽, 张慧. 基本情绪与道德情绪对不同年龄群体道德判断的影响[J]. 心理发展与教育, 2025, 41(4): 491-499.