数学韧性向学前阶段的概念迁移:界定重述、形成因素与教育启示
Keywords:
数学韧性;STEM教育;数学教育;文献综述Abstract
学前阶段(3-6岁)是儿童数学认知与学习态度形成关键期,但数学活动常伴挑战与情绪挫折,易引发焦虑与回避。数学韧性指学习者在压力与失败情境下仍能保持积极态度、坚持投入并灵活寻求支持的心理资源与行为倾向。本文检索Web of Science、Scopus及CNKI、万方等文献,梳理数学韧性概念演进、学前适用性、影响因素与教育启示。综述发现,学前数学韧性宜理解为在支持性环境中“遇挫—恢复—再投入”的过程,受认知基础、情感动机、教学支持及家庭同伴环境共同作用,并与数学成就、学习投入和心理适应呈正相关。文章提出构建高挑战—高支持课堂生态与低压力家庭数学互动建议,并展望测量工具本土化与多方法评估,为学前数学教育实践中缓解儿童数学焦虑、培养积极学习品质提供理论支撑与实操指引。
References
[1] HOWELLS K. The future of education and skills: Education 2030: the future we want[J/OL]. 2018. https://repository.canterbury.ac.uk/item/88qzy/the-future-of-education-and-skills-education-2030-the-future-we-want.
[2] LI Y, WANG K, XIAO Y. Research and trends in STEM education: a systematic review of journal publications[J/OL]. International Journal of STEM Education, 2020, 7(1): 11, s40594-020-00207-6.
[3] SCHWEINGRUBER H, PEARSON G, HONEY M. STEM integration in K-12 education: Status, prospects, and an agenda for research[M/OL]. National Academies Press, 2014.
[4] 马红芹. 美国K-12阶段“科学、技术、工程和数学”(STEM)教育研究[D/OL]. 南京师范大学, 2015. https://d.wanfangdata.com.cn/thesis/Y2909798.
[5] LEE S W Y, TU H Y, CHEN G L. Exploring the multifaceted roles of mathematics learning in predicting students’ computational thinking competency[J/OL]. International Journal of STEM Education, 2023, 10(1): 64.
[6] GOOS M, CARREIRA S, NAMUKASA I K. Mathematics and interdisciplinary STEM education: recent developments and future directions[J/OL]. ZDM – Mathematics Education, 2023, 55(7): 1199-1217.
[7] FINDELL B, SWAFFORD J, KILPATRICK J. Adding it up: Helping children learn mathematics[M/OL]. National Academies Press, 2001.
[8] 李扬. STEM教育视野下的科学课程构建[D/OL]. 浙江师范大学, 2014. https://d.wanfangdata.com.cn/thesis/Y2664806.
[9] TEN BRAAK D, LENES R, PURPURA D J. Why do early mathematics skills predict later mathematics and reading achievement? The role of executive function[J]. Journal of Experimental Child Psychology, 2022, 214: 105306.
[10] ASHCRAFT M H. Math Anxiety: Personal, Educational, and Cognitive Consequences[J/OL]. Current Directions in Psychological Science, 2002, 11(5): 181-185.
[11] CAREY E, HILL F, DEVINE A. The chicken or the egg? The direction of the relationship between mathematics anxiety and mathematics performance[J]. Frontiers in Psychology, 2016, 6: 1987.
[12] 王凤葵, 罗增儒. 数学焦虑的研究概况[J/OL]. 数学教育学报, 2002, 11(1): 39-42.
[13] 刘怡轩, 胡浩博, 郭衎. 我国基础教育学生数学焦虑与数学学业表现关系研究 ——基于68篇中文文献的元分析[J]. 教育学报, 2024, 20(2): 165-178.
[14] 付钰. 数学焦虑与数学学业成绩的关系研究 ——基于中国基础教育阶段73项实证研究的元分析[J]. 数学教育学报, 2025, 34(3): 90-96.
[15] TARKAR A, MATALKA B, CARTWRIGHT M. Student-guided math practice in elementary school: Relation among math anxiety, emotional self-efficacy, and children’s choices when practicing math[J]. Education Sciences, 2022, 12(9): 611.
[16] LEE C, JOHNSTON-WILDER S. Mathematical resilience[M/OL]//The Mathematical Resilience Book. Routledge, 2024: 9-24[2026-01-02]. https://www.taylorfrancis.com/chapters/edit/10.4324/9781003334354-3/mathematical-resilience-clare-lee-sue-johnston-wilder.
[17] MUÑEZ D, BULL R, KHNG K H. Mathematics resilience in preschool and executive functions[J]. Learning and Instruction, 2025, 100: 102197.
[18] RUTTER M. Psychosocial resilience and protective mechanisms.[J/OL]. American Journal of Orthopsychiatry, 1987, 57(3): 316-331.
[19] MASTEN A S. Ordinary magic: Resilience processes in development.[J/OL]. American Psychologist, 2001, 56(3): 227-238.
[20] JOHNSTON-WILDER S, LEE C. Developing mathematical resilience[J/OL]. 2010[2026-01-01]. https://oro.open.ac.uk/24261/2/3C23606C.pdf.
[21] LEE C, JOHNSTON-WILDER S. The construct of mathematical resilience[M/OL]//Understanding emotions in mathematical thinking and learning. Elsevier, 2017: 269-291[2025-12-14]. https://www.sciencedirect.com/science/article/pii/B9780128022184000108.
[22] EISENBERG N, SPINRAD T L, EGGUM N D. Emotion-Related Self-Regulation and Its Relation to Children’s Maladjustment[J/OL]. Annual Review of Clinical Psychology, 2010, 6(1): 495-525.
[23] BINTI ISHAK N H F, YUSOFF N F B M, MADIHIE A. Resilience in Mathematics, Academic Resilience, or Mathematical Resilience?: An Overview[J/OL]. Universal Journal of Educational Research, 2020, 8(5A): 34-39.
[24] XENOFONTOS C, MOUROUTSOU S. Resilience in mathematics education research: a systematic review of empirical studies[J/OL]. Scandinavian Journal of Educational Research, 2023[2026-01-01]. https://www.tandfonline.com/doi/abs/10.1080/00313831.2022.2115132.
[25] ATIT K, POWER J R, VEURINK N, 等. Examining the role of spatial skills and mathematics motivation on middle school mathematics achievement[J/OL]. International Journal of STEM Education, 2020, 7(1): 38.
[26] MERCADER J, MIRANDA A, PRESENTACIÓN M J, 等. Contributions of Motivation, Early Numeracy Skills, and Executive Functioning to Mathematical Performance. A Longitudinal Study[J/OL]. Frontiers in Psychology, 2017, 8: 2375.
[27] CHANG I. Early numeracy and literacy skills and their influences on fourth-grade mathematics achievement: a moderated mediation model[J/OL]. Large-scale Assessments in Education, 2023, 11(1): 18.
[28] BORMAN G D, OVERMAN L T. Academic Resilience in Mathematics among Poor and Minority Students[J/OL]. The Elementary School Journal, 2004, 104(3): 177-195.
[29] DWECK C. What having a “growth mindset” actually means[J]. Harvard business review, 2016, 13(2): 2-5.
[30] DONG L, JIA X, FEI Y. How growth mindset influences mathematics achievements: A study of Chinese middle school students[J/OL]. Frontiers in Psychology, 2023, 14: 1148754.
[31] BLACKWELL L S, TRZESNIEWSKI K H, DWECK C S. Implicit Theories of Intelligence Predict Achievement Across an Adolescent Transition: A Longitudinal Study and an Intervention[J/OL]. Child Development, 2007, 78(1): 246-263.
[32] YEAGER D S, DWECK C S. What can be learned from growth mindset controversies?[J]. American psychologist, 2020, 75(9): 1269.
[33] BENNETT-PIERRE G, CHERNUTA T, ALTAMIMI R, 等. Effects of praise and “easy” feedback on children’s persistence and self-evaluations[J/OL]. Journal of Experimental Child Psychology, 2024, 247: 106032.
[34] 谢铭立, 程凤农. 挫折情境下小班幼儿情绪调节策略研究[J]. 教育导刊(下半月), 2018(6): 43-48.
[35] SHARABI Y, ROTH G. Emotion regulation styles and the tendency to learn from academic failures[J/OL]. The British Journal of Educational Psychology, 2025, 95(1): 162-179.
[36] SILKENBEUMER J R, SCHILLER E M, KÄRTNER J. Co- and self-regulation of emotions in the preschool setting[J/OL]. Early Childhood Research Quarterly, 2018, 44: 72-81.
[37] PIZZIE R G, MCDERMOTT C L, SALEM T G. Neural evidence for cognitive reappraisal as a strategy to alleviate the effects of math anxiety[J]. Social Cognitive and Affective Neuroscience, 2020, 15(12): 1271-1287.
[38] EGARA F O, MOSIMEGE M. Effect of blended learning approach on secondary school learners’ mathematics achievement and retention[J/OL]. Education and Information Technologies, 2024, 29(15): 19863-19888.
[39] MUFIT F, FAUZAN A. The Effect of Cognitive Conflict-Based Learning (CCBL) Model on Remediation of Misconceptions.[J]. Journal of Turkish Science Education, 2023, 20(1): 26-49.
[40] WANG C, XU Q, FEI W qun. The effect of student-perceived teacher support on math anxiety: chain mediation of teacher–student relationship and math self-efficacy[J]. Frontiers in Psychology, 2024, 15: 1333012.
[41] 詹雅滢, 晏 宁. 基于自我决定理论的支持性课堂气氛营造策略[J/OL]. Advances in Education, 2024, 14: 1372.
[42] İLTER İ, AKSOY N C, CEYLAN M. The relationships between parental involvement, teacher support, and mathematics performance: mediating roles of academic self-efficacy and academic buoyancy[J/OL]. BMC Psychology, 2025, 13(1): 1222.
[43] HAWROT A, ZHOU J. Parent-child school-related interactions and helplessness in maths: the role of maths self-efficacy[J/OL]. European Journal of Psychology of Education, 2024, 39(2): 1353-1370.
[44] WANG C, LI X yue, LIN X yi. Peer support as a buffer: reducing math anxiety through psychological resilience in left-behind rural students[J]. Humanities and Social Sciences Communications, 2025, 12(1): 1-10.
[45] CROPP I. Using peer mentoring to reduce mathematical anxiety[J/OL]. Research Papers in Education, 2017, 32(4): 481-500.
[46] MIZUHARA M S, TOMS K, WILLIAMS M. A bounded confidence model to predict how group work affects student math anxiety[J/OL]. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2025, 35(6)[2025-12-17]. https://pubs.aip.org/aip/cha/article/35/6/063131/3350443.
[47] STEELE C M, ARONSON J. Stereotype threat and the intellectual test performance of African Americans.[J]. Journal of personality and social psychology, 1995, 69(5): 797.
[48] TOTONCHI D A, PEREZ T, LEE Y kyung. The role of stereotype threat in ethnically minoritized students’ science motivation: A four-year longitudinal study of achievement and persistence in STEM[J]. Contemporary educational psychology, 2021, 67: 102015.
[49] SPENCER S L. Stereotype threat and women’s math performance: The possible mediating factors of test anxiety, test motivation and self-efficacy[D/OL]. Rutgers The State University of New Jersey, School of Graduate Studies, 2005[2025-12-17]. https://search.proquest.com/openview/275044cab5979c420842e0975594ead1/1?pq-origsite=gscholar&cbl=18750&diss=y.
[50] ESCOBAR-SOLER C, BERRIOS R, PEÑALOZA-DÍAZ G. Effectiveness of Self-Affirmation interventions in Educational settings: a Meta-analysis[C/OL]//Healthcare: 12. MDPI, 2023: 3[2025-12-17]. https://www.mdpi.com/2227-9032/12/1/3.
[51] JIANPING G, ROSLAN S, SOH K G. Effects of positive education intervention on growth mindset and resilience among boarding middle school adolescents in China: a randomized controlled trial[J]. Frontiers in Psychology, 2024, 15: 1446260.
[52] MEYER H H, STUTTS L A. The Effect of Mindset Interventions on Stress and Academic Motivation in College Students[J/OL]. Innovative Higher Education, 2024, 49(4): 783-798.
[53] XENOFONTOS C, MOUROUTSOU S. Resilience in mathematics education research: a systematic review of empirical studies[J/OL]. Scandinavian Journal of Educational Research, 2023, 67(7): 1041-1055. DOI:10.1080/00313831.2022.2115132.
[54] DURU D C, OBASI C V, OGUOMA C. Predictive Analysis: Academic Resilience as a Determinant of Mathematics Achievement among Senior Secondary School Students in Nigeria[J]. Brillo Journal, 2024, 3(2): 72-82.
[55] SHEEHAN J, HADFIELD K. Overcoming socioeconomic adversity: Academic resilience in mathematics achievement among children and adolescents in Ireland[J/OL]. British Journal of Developmental Psychology, 2024, 42(4): 524-545.
[56] DOZ E, CUDER A, PELLIZZONI S. The interplay between ego-resiliency, math anxiety and working memory in math achievement[J/OL]. Psychological Research, 2024, 88(8): 2401-2415.
[57] ATTAMI D, INDRIATI D. Mathematical resilience and mathematical problem-solving ability in Junior High School[C/OL]//Journal of Physics: Conference Series: 1613. IOP Publishing, 2020:012028[2025-12-18]. https://iopscience.iop.org/article/10.1088/1742-6596/1613/1/012028/meta.
[58] AMOADU M, HAGAN JR J E, OBENG P. Academic resilience and motivation as predictors of academic engagement among rural and urban high school students in Ghana[J]. Youth, 2025, 5(1): 11.
[59] SUN Y, LIU L. Structural equation modeling of university students’ academic resilience academic well-being, personality and educational attainment in online classes with Tencent Meeting application in China: investigating the role of student engagement[J/OL]. BMC Psychology, 2023, 11(1): 347.
[60] WIXCEY H, CROPLEY B, SHEARER D. An examination of the influence of mental well-being and resilience on academic outcomes in Further Education learners in Wales[J/OL]. Journal of Further and Higher Education, 2025[2025-12-19]. https://www.tandfonline.com/doi/abs/10.1080/0309877X.2024.2440501.
[61] MARTIN A J, MARSH H W. Academic resilience and its psychological and educational correlates: A construct validity approach[J/OL]. Psychology in the Schools, 2006, 43(3): 267-281.
[62] MARTIN A J, MARSH H W. Academic buoyancy: Towards an understanding of students’ everyday academic resilience[J]. Journal of school psychology, 2008, 46(1): 53-83.
[63] WANG M T, ECCLES J S. Social support matters: Longitudinal effects of social support on three dimensions of school engagement from middle to high school[J]. Child development, 2012, 83(3): 877-895.
[64] PAUNESKU D, WALTON G M, ROMERO C. Mind-set interventions are a scalable treatment for academic underachievement[J]. Psychological science, 2015, 26(6): 784-793.
[65] LUTHAR S S, CICCHETTI D, BECKER B. The Construct of Resilience: A Critical Evaluation and Guidelines for Future Work[J/OL]. Child Development, 2000, 71(3): 543-562.
[66] MARTIN A J, MARSH H W. Academic resilience and academic buoyancy: multidimensional and hierarchical conceptual framing of causes, correlates and cognate constructs[J/OL]. Oxford Review of Education, 2009, 35(3): 353-370.
[67] JOHNSTON-WILDER S, LEE C, MACKRELL K. Addressing mathematics anxiety through developing resilience: Building on self-determination theory[J]. Creative education, 2021, 12: 2098-2115.
[68] MACKRELL K, JOHNSTON-WILDER S. The mathematics resilience approach to mathematics anxiety: Is this supported by self-determination theory?[J/OL]. Proceedings of the British Society for Research into Learning Mathematics, 2020, 40(1)[2026-01-01]. https://wrap.warwick.ac.uk/id/eprint/134909/.
[69] BLASCOVICH J. The biopsychosocial model of challenge and threat: Reflections, theoretical ubiquity, and new directions[M/OL]//Neuroscience of prejudice and intergroup relations. Psychology Press, 2013: 229-242[2026-01-01]. https://www.taylorfrancis.com/chapters/edit/10.4324/9780203124635-16/biopsychosocial-model-challenge-threat-jim-blascovich.
[70] ASHCRAFT M H, KRAUSE J A. Working memory, math performance, and math anxiety[J/OL]. Psychonomic Bulletin & Review, 2007, 14(2): 243-248.
[71] KOOKEN J, WELSH M E, MCCOACH D B. Development and Validation of the Mathematical Resilience Scale[J/OL]. Measurement and Evaluation in Counseling and Development, 2016, 49(3): 217-242.
[72] SONCINI A, VISINTIN E P, MATTEUCCI M C. Positive error climate promotes learning outcomes through students’ adaptive reactions towards errors[J]. Learning and Instruction, 2022, 80: 101627.
[73] JAMES-BRABHAM E, VON BASTIAN C C, BROUGH C. Do home mathematical activities relate to early mathematical skills? A systematic review and meta-analysis[J]. Child Development, 2025, 96(1): 451-468.
[74] 张美蓉, 陈惠勇, MUSTAFA Z. 数学韧性量表在中国青年学生中的信度和效度研究[J]. 数学教育学报, 2025, 34(6): 84-90.
[75] 韦嘉, 贺慧, 唐槐, 等. 数学韧性量表在小学高年级学生中的信效度检验[J]. 中国临床心理学杂志, 2024, 32(3): 595-600.
[76] GÜREFE N, AKÇAKIN V. The Turkish Adaptation of the Mathematical Resilience Scale: Validity and Reliability Study[J/OL]. Journal of Education and Training Studies, 2018, 6(4): 38.
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