DOI: 10.3724/SP.J.1041.2018.00504

Acta Psychologica Sinica (心理学报) 2018/50:5 PP.504-516

The effect of central executive load on strategy utilization of computational estimation in children with mathematics learning difficulties

An important aspect of human cognition is that performance depends on the strategies that people use in a wide range of cognitive domains. In the field of arithmetic cognition, the performance of strategy utilization is influenced by many factors among which central executive functions (central executive functions, EFs) are involved and play critical roles. In previous studies, researchers tended to focus on the impact of central executive load on the use of arithmetic strategy in children or adults with typically development (TD) of mathematical ability, whereas children with mathematics difficulties (MD) had been out of consideration. Consequently, the present study used the choice/no-choice paradigm to investigate the influence of central executive load on the strategy utilization of children with MD during arithmetic processing.
Seventy-four sixth graders consisting of 36 MD and 38 TD were selected in accordance with previous studies strictly. All participants were asked to finish a two-digit addition computational estimation task with rounding-up or rounding-down strategy and a secondary task at the same time. The task consisted of two parts, strategy execution and strategy choice. Meanwhile, we manipulated varying central executive load as a secondary task by requiring participants to memorize five (high central executive load) or three (low central executive load) digits presented randomly in sequence at the beginning of each trial and ranked them with descending order or no digit (no central executive load).
Results showed that:(1) In terms of the strategy executive, the accuracy rate of MD was significantly lower than TD under the three central executive load conditions. The reaction time of MD was significantly longer than TD under both "no" and low central executive load conditions but not for high central executive loaded condition. With the increasing of central executive load, the MD had distinct manifestation compared with TD on strategy executive; (2) In the case of strategy selection, the accuracy rate of MD was significantly lower than TD and the reaction time of MD was significantly longer than that of TD under three central executive loaded conditions. Compared with TD, the strategy selection of MD was more heavily influenced by the levels of central executive load. Likewise, the performance of MD was influenced by growing central executive load on strategy selection other than TD; (3) For the adaptivity of strategy choice, the higher of the central executive load level was, the worse the adaptivity of strategy choice of participants became, and the adaptivity of strategy choice of MD was significantly worse than TD under all of three central executive load conditions. These findings have important theoretical and practical significance for the profound understanding of the potential mechanism of MD with worse strategy utilization.
In conclusion, the strategy utilization of MD is worse than TD during arithmetic processing. Though strategy utilization of both the MD and TD is getting worse as a function of the levels of central executive load, MD are more heavily influenced by central executive load. The adaptivity of strategy choice of two groups is affected by the strength of central executive load and the adaptivity of strategy choice of MD is always worse than TD. Moreover, the present study contributes to explore how the central executive load influences the process of strategy utilization clearly. Combining with event-related potential (ERP) as well as functional magnetic resonance imaging technology (fMRI), future research should further explore the changes of individuals' ERP components or brain regions activated under different levels of central executive load.

Key words:strategy utilization,central executive load,inhibitory control,mathematics difficulties,computational estimation

ReleaseDate:2018-07-02 16:16:01

Ai, J. R., Zhang, H. D., Si, J. W., Lu, C., & Zhang, T. Z. (2016). The effects of presenting mode, reaction order of dual task on adults' arithmetic strategy choice and execution. Acta Psychologica Sinica, 48(10), 1248-1257.[艾继如, 张红段, 司继伟, 卢淳, 张堂正. (2016). 任务呈现方式、双任务反应顺序影响算术估算策略选择与执行. 心理学报, 48(10), 1248-1257.]

Ardiale, E., & Lemaire, P. (2013). Within-item strategy switching in arithmetic:A comparative study in children. Frontiers in Psychology, 4, 924.

Bergman-Nutley, S., & Klingberg, T. (2014). Effect of working memory training on working memory, arithmetic and following instructions. Psychological Research, 78(6), 869-877.

Cheng, J. P., Luo, Y. J., & Cui, F. (2017). Empathy for pain influenced by cognitive load:Evidence from an ERP study. Acta Psychologica Sinica, 49(5), 622-630.[程家萍, 罗跃嘉, 崔芳. (2017). 认知负荷对疼痛共情的影响:来自ERP研究的证据. 心理学报, 49(5), 622-630.]

Desoete, A., & De Weerdt, F. (2013). Can executive functions help to understand children with mathematical learning disorders and to improve instruction?. Learning Disabilities, 11(2), 27-39.

Ding, X., Lv, N., Yang, Y. L., & Si, J. W. (2017). Age-related differences of different components of working memory:The predictive effect on strategy utilization in arithmetic. Acta Psychologica Sinica, 49(6), 759-770.[丁晓, 吕娜, 杨雅琳, 司继伟. (2017). 工作记忆成分的年龄相关差异对算术策略运用的预测效应. 心理学报, 49(6), 759-770.]

Eysenck, M. W., & Derakshan, N. (2011). New perspectives in attentional control theory. Personality & Individual Differences, 50(7), 955-960.

Eysenck, M. W., Derakshan, N., Santos, R., & Calvo, M. G. (2007). Anxiety and cognitive performance:Attentional control theory. Emotion, 7(2), 336-353.

Fletcher, J. M., Stuebing, K. K., Morris, R. D., & Lyon, G. R. (2013). Classification and definition of learning disabilities. In H. L. Swanson, K. R. Harris, & S. Graham (Eds.), Handbook of learning disabilities (pp. 33-50). New York:Guilford.

Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37(1), 4-15.

Han, S. H., & Kim, M. S. (2004). Visual search does not remain efficient when executive working memory is working. Psychological Science, 15(9), 623-628.

Hinault, T., Dufau, S., & Lemaire, P. (2014). Sequential modulations of poorer-strategy effects during strategy execution:An event-related potential study in arithmetic. Brain & Cognition, 91, 123-130.

Hinault, T., Lemaire, P., & Phillips, N. (2016). Aging and sequential modulations of poorer strategy effects:An EEG study in arithmetic problem solving. Brain Research, 1630, 144-158.

Hinault, T., Lemaire, P., & Touron, D. (2017). Aging effects in sequential modulations of poorer-strategy effects during execution of memory strategies. Memory, 25(2), 176-186.

Hua, X. T. (2013). The effect of shifting/updating executive function on mathematics learning disabilities children's strategy use in computational estimation (Unpublished master's thesis). Shandong Normal University, Ji'nan.[华晓腾. (2013). 转换/刷新执行功能对数学困难儿童算术估计策略运用的影响 (硕士学位论文). 山东师范大学, 济南.]

Hua, X. T., Si, J. W., & Lu, C. (2012). Mathematical estimation capacities of children with mathematics learning disabilities. Advances in Psychological Science, 20(10), 1633-1641.[华晓腾, 司继伟, 卢淳. (2012). 数学困难儿童的数学估计能力. 心理科学进展, 20(10), 1633-1641.]

Huang, B. J., Feng, H. M., Si, J. W., Zhang, J., & Wang, X. Y. (2016). Dual-task coordination and task presentation mode influence arithmetic strategy execution in adults:Evidence from computational estimation. Acta Psychologica Sinica, 48(6), 671-683.[黄碧娟, 封洪敏, 司继伟, 张杰, 王翔艳. (2016). 双任务协调、任务呈现方式影响成人算术策略执行:估算证据. 心理学报, 48(6), 671-683.]

Huang, D. Q., & Chen, Y. H. (2016). Study on the development of math cognitive abilities for mathematic difficulties in grade 2~6 primary students. Journal of Mathematics Education, 25(2), 70-74.[黄大庆, 陈英和. (2016). 小学二至六年级数学困难儿童数学认知能力的发展. 数学教育学报, 25(2), 70-74.]

Imbo, I., Duverne, S., & Lemaire, P. (2007). Working memory, strategy execution, and strategy selection in mental arithmetic. Quarterly Journal of Experimental Psychology, 60(9), 1246-1264.

Imbo, I., & LeFevre, J. A. (2009). Cultural differences in complex addition:Efficient Chinese versus adaptive Belgians and Canadians. Journal of Experimental Psychology:Learning, Memory, & Cognition, 35(6), 1465-1476.

Imbo, I., & LeFevre, J. A. (2011). Cultural differences in strategic behavior:A study in computational estimation. Journal of Experimental Psychology:Learning, Memory, & Cognition, 37(5), 1294-1301.

Imbo, I., Vandierendonck, A., & Rosseel, Y. (2007). The influence of problem features and individual differences on strategic performance in simple arithmetic. Memory & Cognition, 35(3), 454-463.

Lemaire, P., Arnaud, L., & Lecacheur, M. (2004). Adults' age-related differences in adaptivity of strategy choices:Evidence from computational estimation. Psychology and Aging, 19(3), 467-481.

Lemaire, P., & Calliès, S. (2009). Children's strategies in complex arithmetic. Journal of Experimental Child Psychology, 103(1), 49-65.

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., Lecacheur, M., & Farioli, F. (2000). Children's strategy use in computational estimation. Canadian Journal of Experimental Psychology, 54(2), 141-148.

Li, H. X., Si, J. W., Chen, Z. J., & Zhang, T. Z. (2015). Approximate number system in human. Advances in Psychological Science, 23(4), 562-570.[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.]

Liu, C. (2004). Working memory and processing speed in children with arithmetical difficulties. Journal of Nanjing Normal University (Social Science Edition), (3), 81-88.[刘昌. (2004). 数学学习困难儿童的认知加工机制研究. 南京师范大学学报(社会科学版), (3), 81-88.]

Liu, C. Z. (2013). Working memory training research of mathematical learning difficulty students (Unpublished master's thesis). Inner Mongolia Normal University.[刘翠珍. (2013). 数学学习困难学生的工作记忆训练研究(硕士学位论文). 内蒙古师范大学.]

Lv, N., Yang, J., Hua, X. T., Si, J. W., & Wang, X. Y. (2015). Memory updating affects MD children's arithmetic strategy use:Evidences from the chronological age/intelligence-matched design. Studies of Psychology and Behavior, 13(6), 784-793.[吕娜, 杨静, 华晓腾, 司继伟, 王翔艳. (2015). 记忆刷新影响数困儿童的算术策略运用:来自年龄/智力匹配设计的证据. 心理与行为研究, 13(6), 784-793.]

Manuel, A. L., Bernasconi, F., & Spierer, L. (2013). Plastic modifications within inhibitory control networks induced by practicing a stop-signal task:An electrical neuroimaging study. Cortex, 49(4), 1141-1147.

Mata, R., Josef, A. K., & Lemaire, P. (2015). Chapter 6-Adaptive decision making and aging. In T. M. Hess, J. Strough, & C. Lckenhoff (Eds.), Aging and decision making:Empirical and applied perspectives (pp. 105-122). New York:Academic Press.

Passolunghi, M. C. (2011). Cognitive and emotional factors in children with mathematical learning disabilities. International Journal of Disability, Development and Education, 58(1), 61-73.

Passolunghi, M. C., & Siegel, L. S. (2004). Working memory and access to numerical information in children with disability in mathematics. Journal of Experimental Child Psychology, 88(4), 348-367.

Si, J., Li, H., Sun, Y., Xu, Y., & Sun, Y. (2016). Age-related differences of individuals' arithmetic strategy utilization with different level of math anxiety. Frontiers in Psychology, 7, 1612.

Si, J. W., Liu, Y. Q., Jia, G. J., & Huang, B. J. (2016). The central executive load and the individual's strategy use adaptability with cognitive style:Behavioral and eye-tracking evidence. Journal of Soochow University (Educational Science Edition), 4(1), 85-95.[司继伟, 刘亚琼, 贾国敬, 黄碧娟. (2016). 认知风格、中央执行负荷影响算术估算的策略选择适应性:行为与眼动证据. 苏州大学学报(教育科学版), 4(1), 85-95.]

Si, J. W., Xu, Y. L., Feng, H. M., Xu, X. H., & Zhou, C. (2014). Differences of arithmetic strategy use in adults with different math anxieties:An ERP study. Acta Psychologica Sinica, 46(12), 1835-1849.[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.]

Si, J. W., Yang, J., Jia, G. J., & Zhou, C. (2012). The effect of central executive load on adult's strategy using in computational estimation. Acta Psychologica Sinica, 44(11), 1490-1500.[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.]

Torbeyns, J., Verschaffel, L., & Ghesquière, P. (2004a). Strategy development in children with mathematical disabilities. Journal of Learning Disabilities, 37(2), 119-131.

Torbeyns, J., Verschaffel, L., & Ghesquière, P. (2004b). Strategic aspects of simple addition and subtraction:The influence of mathematical ability. Learning & Instruction, 14(2), 177-195.

Uittenhove, K., & Lemaire, P. (2012). Sequential difficulty effects during strategy execution:A study in arithmetic. Experimental Psychology, 59(5), 295-301.

Wahid, S. N. S., Yusof, Y., & Razak, M. R. (2014). Math anxiety among students in higher education level. Procedia-Social and Behavioral Sciences, 123, 232-237.

Wang, M. Y., & Chen, Y. H. (2006). The influence of central executive of working memory on children's arithmetical cognitive strategies. Psychological Development and Education, 22(4), 24-28.[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.]

Xu, C., Wells, E., Lefevre, J. A., & Imbo, I. (2014). Strategic flexibility in computational estimation for Chinese-and Canadian-educated adults. Journal of Experimental Psychology:Learning, Memory, & Cognition, 40(5), 1481-1497.

Zhang, S. D., & Dong, Q. (2012). On the relationship between number processing or dyscalculia and working memory. Chinese Journal of Special Education, (2), 40-47.[张树东, 董奇. (2012). 数字加工和计算障碍与工作记忆的关系研究. 中国特殊教育, (2), 40-47.]