执行功能在不同年级儿童数学能力中的作用

doi:10.3724/SP.J.1041.2023.00696

摘要/Abstract

摘要：

选取812名三~六年级的儿童, 采用相关分析和结构方程模型等方法考察了各执行功能成分在不同年级儿童三种数学能力中的作用。结果显示, 在低年级阶段, 工作记忆广度是数学运算能力、空间想象能力和逻辑思维能力最重要的预测因素; 在高年级阶段, 工作记忆广度对三种数学能力的预测作用下降, 而工作记忆刷新和认知灵活性对数学能力的预测作用提升。这表明, 各执行功能成分对不同数学能力的预测作用存在差异, 并将随儿童年级的增长而发生变化。

关键词: 执行功能, 数学能力, 小学儿童, 结构方程模型

Abstract:

Mathematical ability is an important component of children's academic achievement and critical to individual development. Executive function, as an essential cognitive ability, is a core cognitive element that supports children’s mathematical processing. However, there have only been a few studies focusing on the effects of each component of executive function on different mathematical abilities (mathematical operation, spatial imagination, and logical thinking). Primary school is the key period during which children acquire basic mathematical ability. However, limited studies have examined the developmental relationships between the various components of executive function and the different mathematical abilities of children at different grade levels. Consequently, the purpose of this study was to examine the role of each component of executive function in the different mathematical abilities of children at different grade levels.

A total of 812 children in grades 3, 4, 5, and 6 completed tests covering mathematical operations, spatial imagination, and logical thinking to measure their basic mathematical ability. The Stroop task and the GO/NOGO task were used to measure interference inhibition and response inhibition. Children’s working memory span was assessed using forward and backward digit span tasks. Children’s working memory updating was investigated using simple and difficult digital updating tasks. Children’s cognitive flexibility was examined using digit shifting tasks. Finally, a correlation analysis and a structural equation model (SEM) were used to investigate the impact of each component of executive function on children’s mathematical abilities at different grade levels.

The results revealed that working memory was the most important factor affecting children’s mathematical skills, over inhibitory control and cognitive flexibility. Specifically, working memory span was the most statistically significant predictor of ability with respect to mathematical operations, while working memory updating was a stronger predictor of spatial imagination and logical thinking ability from grade 3 to grade 6. In a further analysis of the data, we divided the four grades into two stages, with grades 3 and 4 set as the younger group and grades 5 and 6 set as the older group. The results showed working memory span to be the most important predictor of mathematical operation ability, spatial imagination ability, and logical thinking ability in the junior grades. In the older students, the predictive effect of working memory span on basic math ability dropped, and the effects of working memory updating and cognitive flexibility on basic math ability increased.

These results indicate that different components of executive function play various roles in different mathematical abilities in school-age children, and that this pattern of influence appears to change as children progress through the grades. Specifically, the lower-order components of executive function components, specifically working memory span, were found to play an important role in the development of three mathematical abilities in younger students, while the higher-order executive function components, specifically working memory updating and cognitive flexibility, were found to play a more important role in processing mathematical tasks in older students.

Key words: executive function, mathematical abilities, primary school student, structural equation modeling

中图分类号:

B844

祝孝亮, 赵鑫. (2023). 执行功能在不同年级儿童数学能力中的作用. 心理学报, 55(5), 696-710.

ZHU Xiaoliang, ZHAO Xin. (2023). Role of executive function in mathematical ability of children in different grades. Acta Psychologica Sinica, 55(5), 696-710.

图/表 9

参考文献 72

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年级	总计	男	女	年龄(M ± SD, 岁)
三年级	183	82	101	8.90 ± 0.50
四年级	202	92	110	9.84 ± 0.41
五年级	210	104	106	10.90 ± 0.40
六年级	217	112	105	11.94 ± 0.50
总计	812	390	422	10.46 ± 1.22

年级	总计	男	女	年龄(M ± SD, 岁)
三年级	183	82	101	8.90 ± 0.50
四年级	202	92	110	9.84 ± 0.41
五年级	210	104	106	10.90 ± 0.40
六年级	217	112	105	11.94 ± 0.50
总计	812	390	422	10.46 ± 1.22

测验	三年级 (n = 183)		四年级 (n = 202)		五年级 (n = 210)		六年级 (n = 217)		F(3, 808)	η_p²	事后比较
测验	M	SD	M	SD	M	SD	M	SD	F(3, 808)	η_p²	事后比较
运算
加法	18.51	3.61	19.37	3.72	21.34	3.80	22.97	3.98	56.67^***	0.17	六>五>四>三
减法	17.25	3.92	17.53	4.43	19.55	4.57	20.95	4.55	32.47^***	0.11	六>五>四=三
逻辑思维
续写数字	11.20	3.31	11.35	3.35	12.28	2.91	12.47	3.28	7.92^***	0.03	六=五>四=三
目测长度	7.21	4.50	9.67	5.69	12.03	5.22	13.65	6.91	54.09^***	0.15	六>五>四>三
空间想象
方块计数	14.13	3.65	15.52	4.31	17.11	4.62	19.23	4.81	52.72^***	0.16	六>五>四>三
干扰抑制
Stroop干扰效应(ms)	−0.82	73.73	19.37	69.70	10.47	69.44	7.84	63.95	2.79^*	0.01	四>三
反应抑制
NOGO正确率	0.76	0.13	0.79	0.12	0.81	0.10	0.79	0.15	5.55^**	0.02	六=五=四>三
工作记忆刷新
简单刷新正确率	0.57	0.24	0.64	0.18	0.71	0.18	0.74	0.17	26.54^***	0.10	六=五>四>三
困难刷新正确率	0.61	0.24	0.69	0.19	0.74	0.18	0.77	0.17	22.00^***	0.09	六=五>四>三
工作记忆广度
正背广度	5.74	1.35	6.22	1.31	6.79	1.24	6.72	1.71	25.15^***	0.08	六=五>四>三
倒背广度	4.16	0.89	4.74	1.18	5.09	1.36	5.46	1.40	49.52^***	0.13	六>五>四>三
认知灵活性
转换代价(ms)	145.33	195.95	235.31	216.08	235.61	222.96	312.45	247.51	19.36^***	0.07	六>五=四>三

测验	三年级 (n = 183)		四年级 (n = 202)		五年级 (n = 210)		六年级 (n = 217)		F(3, 808)	η_p²	事后比较
测验	M	SD	M	SD	M	SD	M	SD	F(3, 808)	η_p²	事后比较
运算
加法	18.51	3.61	19.37	3.72	21.34	3.80	22.97	3.98	56.67^***	0.17	六>五>四>三
减法	17.25	3.92	17.53	4.43	19.55	4.57	20.95	4.55	32.47^***	0.11	六>五>四=三
逻辑思维
续写数字	11.20	3.31	11.35	3.35	12.28	2.91	12.47	3.28	7.92^***	0.03	六=五>四=三
目测长度	7.21	4.50	9.67	5.69	12.03	5.22	13.65	6.91	54.09^***	0.15	六>五>四>三
空间想象
方块计数	14.13	3.65	15.52	4.31	17.11	4.62	19.23	4.81	52.72^***	0.16	六>五>四>三
干扰抑制
Stroop干扰效应(ms)	−0.82	73.73	19.37	69.70	10.47	69.44	7.84	63.95	2.79^*	0.01	四>三
反应抑制
NOGO正确率	0.76	0.13	0.79	0.12	0.81	0.10	0.79	0.15	5.55^**	0.02	六=五=四>三
工作记忆刷新
简单刷新正确率	0.57	0.24	0.64	0.18	0.71	0.18	0.74	0.17	26.54^***	0.10	六=五>四>三
困难刷新正确率	0.61	0.24	0.69	0.19	0.74	0.18	0.77	0.17	22.00^***	0.09	六=五>四>三
工作记忆广度
正背广度	5.74	1.35	6.22	1.31	6.79	1.24	6.72	1.71	25.15^***	0.08	六=五>四>三
倒背广度	4.16	0.89	4.74	1.18	5.09	1.36	5.46	1.40	49.52^***	0.13	六>五>四>三
认知灵活性
转换代价(ms)	145.33	195.95	235.31	216.08	235.61	222.96	312.45	247.51	19.36^***	0.07	六>五=四>三

变量	1	2	3	4	5	6	7	8	9	10
1. 性别	1
2. 年龄	0.08^*	1
3. 运算成绩	0.08^*	0.32^**	1
4. 逻辑思维成绩	0.05	0.32^**	0.52^**	1
5. 空间想象成绩	0.15^**	0.32^**	0.43^**	0.49^**	1
6. 干扰抑制	−0.06	0.02	0.03	0.09^**	0.04	1
7. 反应抑制	−0.23^**	0.07^*	0.05	0.05	0.05	0.12^**	1
8. 工作记忆刷新	−0.07^*	0.26^**	0.36^**	0.36^**	0.32^**	0.10^**	0.14^**	1
9. 工作记忆广度	0.02	0.35^**	0.39^**	0.36^**	0.34^**	0.09^**	0.11^**	0.46^**	1
10. 认知灵活性	−0.02	0.20^**	0.18^**	0.20^**	0.20^**	0.04	0.06	0.23^**	0.16^**	1