Developmental Trajectories of Mathematics Metacognition Among Junior High School Students: A Two-and-a-half-year Longitudinal Study

doi:10.12139/j.1672-0628.2023.01.009

Abstract

Abstract:

By using the questionnaire method, 101 junior high school students were tested five times on the development of mathematics metacognition in two and a half years. The latent category growth model was used to explore the developmental trajectories of junior high school students’ mathematics metacognition, and to examine the influence of gender on mathematics metacognition. The results showed that: 1) Junior high school students’ mathematics metacognition and its components showed a downward trend in the second year of junior high school. 2) The development of mathematics metacognition of junior high school students showed three types, namely the high-slow decline group (32.67%), the medium-significant decline group (54.46%), and the low-slow decline group (12.87%). 3) Compared with girls, boys had more mathematics metacognition knowledge and a higher initial level of mathematics metacognition, and were more likely to belong to the high-slow decline group than the low-slow decline group.

Key words: mathematics metacognition, junior high school students, developmental trajectory, longitudinal study

摘要：

采用问卷法对101名初中生在两年半间数学元认知的发展状况进行5次测试。利用潜类别增长模型等探讨初中生数学元认知的发展轨迹，并考察性别对数学元认知的影响。结果发现：(1) 初中生数学元认知及各成分在初二表现出下降趋势。(2) 初中生数学元认知的发展表现出三种类型，即高−缓慢下降组(32.67%)、中−显著下降组(54.46%)以及低−缓慢下降组(12.87%)。(3) 与女生相比，男生有着更多的数学元认知知识和更高的数学元认知初始水平，且与低−缓慢下降组相比，男生比女生更有可能属于高−缓慢下降组。

关键词: 数学元认知, 初中生, 发展轨迹, 追踪研究

CLC Number:

B844

Yuntian XIE, Fanfei MENG. Developmental Trajectories of Mathematics Metacognition Among Junior High School Students: A Two-and-a-half-year Longitudinal Study[J]. Studies of Psychology and Behavior, 2023, 21(1): 58-64.

谢云天, 孟凡斐. 初中生数学元认知的发展轨迹：两年半追踪研究[J]. 心理与行为研究, 2023, 21(1): 58-64.

Figures/Tables 7

References

	陈英和, 韩瑽瑽儿童青少年元认知的发展特点及作用的心理机制. 心理科学, 2012, 35 (3): 537- 543.
	程向阳数学元认知差异的相关研究及启示. 中国特殊教育, 2008, (10): 93- 96. DOI
	范文贵, 李伟华西方数学学习性别差异研究述评. 比较教育研究, 2008, 30 (9): 77- 82.
	郭雯婧, 边玉芳初二学生感知到的社会支持与学习成绩的关系——学业自我概念的中介作用. 心理科学, 2013, 36 (3): 627- 631. DOI
	欧慧谋, 唐剑岚国内数学元认知的研究与思考. 课程·教材·教法 , 2012, 32 (5): 58- 61.
	申继亮, 陈英和. (2014). 中国教育心理测评手册. 北京: 高等教育出版社.
	史滋福, 谢云天数学焦虑对初中生概率推理的影响——一个有调节的中介模型. 数学教育学报, 2020, 29 (4): 13- 19.
	唐剑岚, 周莹, 汤服成数学问题解决中的元认知问卷量表的设计. 数学教育学报, 2005, 14 (4): 44- 48. DOI
	吴先超青少年元认知控制跨时间准确性及一致性发展研究. 教育研究与实验, 2019, (4): 75- 80.
	薛笑然, 黄碧娟, 李红霞, 赵晓萌, 司继伟小学儿童数学态度与数学成就的纵向联系: 学业拖延和数学元认知的作用. 心理发展与教育, 2022, 38 (4): 520- 529.
	朱智贤. (2018). 儿童心理学(第6版). 北京: 人民教育出版社.
	Annevirta, T., & Vauras, M. Metacognitive knowledge in primary grades: A longitudinal study. European Journal of Psychology of Education, 2001, 16 (2): 257- 282. DOI
	Anthonysamy, L. The use of metacognitive strategies for undisrupted online learning: Preparing university students in the age of pandemic. Education and Information Technologies, 2021, 26 (6): 6881- 6899. DOI
	Baker, D. P., & Jones, D. P. Creating gender equality: Cross-national gender stratification and mathematical performance. Sociology of Education, 1993, 66, 91- 103. DOI
	Bevan, R. Boys, girls and mathematics: Beginning to learn from the gender debate. Mathematics in School, 2001, 30 (4): 2- 6.
	Borkowski, J. G. Metacognition: Theory or chapter heading. Learning and Individual Differences, 1996, 8 (4): 391- 402. DOI
	Callan, G. L., Marchant, G. J., Finch, W. H., & German, R. L. Metacognition, strategies, achievement, and demographics: Relationships across countries. Educational Sciences: Theory & Practice, 2016, 16 (5): 1485- 1502.
	Collins, D. W., & Kimura, D. A large sex difference on a two-dimensional mental rotation task. Behavioral Neuroscience, 1997, 111 (4): 845- 849. DOI
	Cromley, J. G., & Kunze, A. J. Metacognition in education: Translational research. Translational Issues in Psychological Science, 2020, 6 (1): 15- 20. DOI
	De Boer, H., Donker, A. S., Kostons, D. D. N. M., & van Der Werf, G. P. C. Long-term effects of metacognitive strategy instruction on student academic performance: A meta-analysis. Educational Research Review, 2018, 24, 98- 115. DOI
	Desoete, A., & De Craene, B. Metacognition and mathematics education: An overview. ZDM—Mathematics Education, 2019, 51 (4): 565- 575. DOI
	Else-Quest, N. M., Hyde, J. S., & Linn, M. C. Cross-national patterns of gender differences in mathematics: A meta-analysis. Psychological Bulletin, 2010, 136 (1): 103- 127. DOI
	Flavell, J. H. (1976). Metacognitive aspects of problem solving. In L. B. Resnick (Ed.), The nature of intelligence (pp. 231–236). Hillsdale, NJ: Lawrence Erlbaum.
	Flavell, J. H. Metacognition and cognitive monitoring: A new area of cognitive-developmental inquiry. American Psychologist, 1979, 34 (10): 906- 911. DOI
	Gómez-Ortiz, O., Roldán, R., Ortega-Ruiz, R., & García-López, L. J. Social anxiety and psychosocial adjustment in adolescents: Relation with peer victimization, self-esteem and emotion regulation. Child Indicators Research, 2018, 11 (6): 1719- 1736. DOI
	Heyes, C., Bang, D., Shea, N., Frith, C. D., & Fleming, S. M. Knowing ourselves together: The cultural origins of metacognition. Trends in Cognitive Sciences, 2020, 24 (5): 349- 362. DOI
	Hoffman, B., & Spatariu, A. The influence of self-efficacy and metacognitive prompting on math problem-solving efficiency. Contemporary Educational Psychology, 2008, 33 (4): 875- 893. DOI
	Hyde, J. S. Gender similarities and differences. Annual Review of Psychology, 2014, 65, 373- 398. DOI
	Ku, K. Y. L., & Ho, I. T. Metacognitive strategies that enhance critical thinking. Metacognition and Learning, 2010, 5 (3): 251- 267. DOI
	Kuhn, D. Metacognitive development. Current Directions in Psychological Science, 2000, 9 (5): 178- 181. DOI
	Lenroot, R. K., & Giedd, J. N. Sex differences in the adolescent brain. Brain and Cognition, 2010, 72 (1): 46- 55. DOI
	Mok, Y. F., Fan, R. M. T., & Pang, N. S. K. Developmental patterns of school students’ motivational- and cognitive-metacognitive competencies. Educational Studies, 2007, 33 (1): 81- 98. DOI
	Morales, J., Lau, H., & Fleming, S. M. Domain-general and domain-specific patterns of activity supporting metacognition in human prefrontal cortex. Journal of Neuroscience, 2018, 38 (14): 3534- 3546. DOI
	Nelson, T. O. Metamemory: A theoretical framework and new findings. Psychology of Learning and Motivation, 1990, 26, 125- 173.
	Özdemir, A., Utkualp, N., & Palloş, A. Physical and psychosocial effects of the changes in adolescence period. International Journal of Caring Sciences, 2016, 9 (2): 717- 723.
	Perry, J., Lundie, D., & Golder, G. Metacognition in schools: What does the literature suggest about the effectiveness of teaching metacognition in schools. Educational Review, 2019, 71 (4): 483- 500. DOI
	Pintrich, P. R. The role of metacognitive knowledge in learning, teaching, and assessing. Theory into Practice, 2002, 41 (4): 219- 225. DOI
	Reilly, D., Neumann, D. L., & Andrews, G. Investigating gender differences in mathematics and science: Results from the 2011 trends in mathematics and science survey. Research in Science Education, 2019, 49 (1): 25- 50. DOI
	Roebers, C. M., & Spiess, M. The development of metacognitive monitoring and control in second graders: A short-term longitudinal study. Journal of Cognition and Development, 2017, 18 (1): 110- 128. DOI
	Sapta, A., Hamid, A., & Syahputra, E. Assistance of parents in the learning at home. Journal of Physics: Conference Series, 2018, 1114, 012020. DOI
	Siagian, M. V., Saragih, S., & Sinaga, B. Development of learning materials oriented on problem-based learning model to improve students’ mathematical problem solving ability and metacognition ability. International Electronic Journal of Mathematics Education, 2019, 14 (2): 331- 340.
	van Der Stel, M., & Veenman, M. V. J. Metacognitive skills and intellectual ability of young adolescents: A longitudinal study from a developmental perspective. European Journal of Psychology of Education, 2014, 29 (1): 117- 137. DOI
	Wang, M. T., Binning, K. R., Del Toro, J., Qin, X., & Zepeda, C. D. Skill, thrill, and will: The role of metacognition, interest, and self-control in predicting student engagement in mathematics learning over time. Child Development, 2021, 92 (4): 1369- 1387. DOI

	T₁	T₂	T₃	T₄	T₅
男生	67(60.36%)	65(59.63%)	65(60.19%)	63(60.00%)	59(58.42%)
女生	44(39.64%)	44(40.37%)	43(39.81%)	42(40.00%)	42(41.58%)
总体	111	109	108	105	101

	T₁	T₂	T₃	T₄	T₅
男生	67(60.36%)	65(59.63%)	65(60.19%)	63(60.00%)	59(58.42%)
女生	44(39.64%)	44(40.37%)	43(39.81%)	42(40.00%)	42(41.58%)
总体	111	109	108	105	101

	M±SD	1	2	3	4	5
1.MM1	3.00±0.54
2.MM2	3.00±0.53	0.48***
3.MM3	2.85±0.51	0.58***	0.62**
4.MM4	2.73±0.61	0.60***	0.62***	0.61***
5.MM5	2.93±0.60	0.49***	0.45***	0.54***	0.55***
6.性别	0.58±0.50	0.15	0.17	0.17	0.11	0.20*

	M±SD	1	2	3	4	5
1.MM1	3.00±0.54
2.MM2	3.00±0.53	0.48***
3.MM3	2.85±0.51	0.58***	0.62**
4.MM4	2.73±0.61	0.60***	0.62***	0.61***
5.MM5	2.93±0.60	0.49***	0.45***	0.54***	0.55***
6.性别	0.58±0.50	0.15	0.17	0.17	0.11	0.20*

模型	AIC	BIC	aBIC	Entropy	LMR-LRT(p)	BLRT(p)	类别概率
1	859.62	877.92	855.82				1
2	741.51	767.66	736.08	0.75	0.72	<0.001	0.6436/0.3564
3	664.86	698.86	657.80	0.87	<0.01	<0.001	0.3267/0.5446/0.1287
4	665.68	707.52	656.99	0.86	0.22	0.27	0.5347/0.3168/0.1188/0.0297
5	670.17	719.86	659.85	0.78	0.72	1.00	0.0297/0.4753/0.0990/0.3168/0.0792