The impact of perceived teachers’ autonomy support on students’ mathematics achievement: evidences based on latent growth curve modelling

  • Dan Wei
  • Danhui ZhangEmail author
  • Jingwen He
  • Janette Bobis


According to the self-determination theory, autonomy-supportive teaching is considered an effective approach to motivate students to learn. The present study investigates the effect of students’ perceived autonomy support on math achievement over time, i.e. from grades 4 to 6, using a longitudinal survey administered in Chinese elementary schools. A total of 1624 participants were assessed over four waves. Autonomy need satisfaction and classroom engagement were included as predictors of achievement growth. Latent growth curve modelling (LGCM) indicated that perceived autonomy support accounted for more variance in mathematics achievement among 4th- and 5th-grade students than it did for 6th-grade students. Furthermore, student autonomy need satisfaction positively predicted the growth rate of their achievement, while behavioural engagement significantly and positively predicted both the growth rate and the average initial level of mathematics achievement.


Perceived autonomy support Autonomy need satisfaction Engagement Mathematics achievement Latent growth curve modelling 



  1. Alexander, K. L., Entwisle, D. R., & Dauber, S. L. (1993). First-grade classroom behavior: its short- and long-term consequences for school performance. Child Development, 64(3), 801–814.CrossRefGoogle Scholar
  2. Archambault, I., Janosz, M., Fallu, J.-S., & Pagani, L. S. (2009). Student engagement and its relationship with early high school dropout. Journal of Adolescence, 32(3), 651–670.CrossRefGoogle Scholar
  3. Assor, A., Kaplan, H., & Roth, G. (2002). Choice is good, but relevance is excellent: autonomy-enhancing and suppressing teacher behaviours predicting students’ engagement in schoolwork. British Journal of Educational Psychology, 72(2), 261–278.CrossRefGoogle Scholar
  4. Bentler, P., Bonett, D., & Hernstein, R. J. (1980). Significance tests and goodness of fit in the analysis of covariance structures. Psychological Bulletin, 88(3), 588–606.CrossRefGoogle Scholar
  5. Black, A. E., & Deci, E. L. (2000). The effects of instructors’ autonomy support and students’ autonomous motivation on learning organic chemistry: a self-determination theory perspective. Science Education, 84(6), 740–756.CrossRefGoogle Scholar
  6. Bradley, R., & Corwyn, R. (2002). Socioeconomic status and child development. Annual Review of Psychology, 53(1), 371–399.CrossRefGoogle Scholar
  7. Browne, M., & Cudeck, R. (1993). Alternative ways of assessing model fit. In K. Bollen & J. Long (Eds.), Testing structural equation models (pp. 136–162). Newbury Park, CA: Sage.Google Scholar
  8. Byrne, B. M. (1998). Structural equation modeling with LISREL, PRELIS and SIMPLIS: basic concepts, applications and programming. Mahwah: Lawrence Erlbaum Associates.Google Scholar
  9. Carreira, J. M. (2012). Motivational orienations and psychological needs in EFL learning among elementary school students in Japan. System, 40(2), 191–202.CrossRefGoogle Scholar
  10. Carreira, J. M., Ozaki, K., & Maeda, T. (2013). Motivational model of English learning among elementary school students in Japan. System, 41(3), 706–719.CrossRefGoogle Scholar
  11. Cheng, L., Dou, D., Feng, C., Qi, C. X., & Martin, V. (2013). The relationship between learning motivation and mathematics literacy of 11-year old and 15-year-old students. Studies of Psychology and Behavior (Pin Yin: Xin Li Yu Xing Wei Yan Jiu), 11(1), 84–89.Google Scholar
  12. Chirkov, V. I., & Ryan, R. M. (2001). Parent and teacher autonomy-support in Russian and U.S. adolescents: common effects on well-being and academic motivation. Journal of Cross-Cultural Psychology, 32(5), 618–635.CrossRefGoogle Scholar
  13. Connell, J. P., & Wellborn, J. G. (1991). Competence, autonomy, and relatedness - a motivational analysis of self-system processes. Minnesota Symposia on Child Psychology, 23, 43–77.Google Scholar
  14. Deci, E. L., & Ryan, R. M. (1985). Intrinsic motivation and self-determination in human behavior. New York: Plenum.CrossRefGoogle Scholar
  15. Deci, E. L., & Ryan, R. M. (2000). The ‘what’ and ‘why’ of goal pursuits: human needs and the self determination of behavior. Psychological Inquiry, 11(4), 227–268.CrossRefGoogle Scholar
  16. Deci, E. L., Schwartz, A., Sheinman, L., & Ryan, R. M. (1981). An instrument to assess adult’s orientations toward control versus autonomy in children: reflections on intrinsic motivation and perceived competence. Journal of Educational Psychology, 73(5), 642–650.CrossRefGoogle Scholar
  17. Deci, E., Eghrari, H., Patrick, B., & Leone, D. (1994). Facilitating internalization: the self-determination theory perspective. Journal of Personality, 62(1), 119–142.CrossRefGoogle Scholar
  18. Diseth, A., Breidablik, H. J., & Meland, E. (2018). Longitudinal relations between perceived autonomy support and basic need satisfaction in two student cohorts. Educational Psychology, 38(1), 99–115.CrossRefGoogle Scholar
  19. Dupont, S., Galand, B., Nils, F., & Hospel, V. (2014). Social context, self-perceptions and student engagement: a SEM investigation of the self-system model of motivational development (SSMMD). Electronic Journal of Research in Educational Psychology, 12(1), 5–32.Google Scholar
  20. Entwistle, N. (1991). Approaches to learning and perceptions of the learning environment. Higher Education, 22(3), 201–204.CrossRefGoogle Scholar
  21. Fortus, D., & Vedder-Weiss, D. (2014). Measuring students’ continuing motivation for science learning. Journal of Research in Science Teaching, 51(4), 497–522.CrossRefGoogle Scholar
  22. Fredricks, J. A., & McColskey, W. (2012). The measurement of student engagement: a comparative analysis of various methods and student self-report instruments. In S. L. Christenson, A. L. Reschly, & C. Wylie (Eds.), Handbook of research on student engagement (p. 763e782). US: Springer.Google Scholar
  23. Fredricks, J. A., Blumenfeld, P. C., & Paris, A. H. (2004). School engagement: potential of the concept, state of the evidence. Review of Educational Research, 74(1), 59–109.CrossRefGoogle Scholar
  24. Grimm, K. J., Kuhl, A. P., & Zhang, Z. (2013). Measurement models, estimation, and the study of change. Structural Equation Modeling, 20(3), 504–517.CrossRefGoogle Scholar
  25. Gagné, M. (2003). The role of autonomy support and autonomy orientation in prosocial behavior engagement. Motivation and Emotion, 27(3), 199–223.CrossRefGoogle Scholar
  26. Hancock, G. R., & Choi, J. (2006). A vernacular for linear latent growth models. Structural Equation Modeling, 13(3), 352–377.CrossRefGoogle Scholar
  27. Hardré, P. L., & Reeve, J. (2003). A motivational model of rural students’ intentions to persist in, versus drop out of, high school. Journal of Educational Psychology, 95(2), 347–356.CrossRefGoogle Scholar
  28. Hooper, D., Coughlan, J., & Mullen, M. R. (2008). Structural equation modelling: guidelines for determining model fit. Electronic Journal of Business Research Methods, 6(1), 53–60.Google Scholar
  29. Hospel, & Galand. (2016). Are both classroom autonomy support and structure equally important for students’ engagement? A multilevel analysis. Learning and Instruction, 41, 1–10.CrossRefGoogle Scholar
  30. Hu, L. T., & Bentler, P. M. (1998). Fit indices in covariance structure modeling: sensitivity to underparameterized model misspecification. Psychological Methods, 3(4), 424–453.CrossRefGoogle Scholar
  31. Jang, H., Kim, E. J., & Reeve, J. (2012). Longitudinal test of self-determination theory’s motivation mediation model in a naturally occurring classroom context. Journal of Educational Psychology, 104(4), 1175–1188.CrossRefGoogle Scholar
  32. Jang, H., Kim, E. J., & Reeve, J. (2016). Why students become more engaged or more disengaged during the semester: a self-determination theory dual-process model. Learning and Instruction, 1–12.Google Scholar
  33. Jang, H., Reeve, J., & Deci, E. L. (2010). Engaging students in learning activities: it is not autonomy support or structure but autonomy support and structure. Journal of Educational Psychology, 102(3), 588–600.CrossRefGoogle Scholar
  34. Jang, H., Reeve, J., Ryan, R. M., & Kim, A. (2009). Can self-determination theory explain what underlies the productive, satisfying learning experiences of collectivistically oriented Korean students? Journal of Educational Psychology, 101(3), 644–661.CrossRefGoogle Scholar
  35. Ladd, G. W., & Dinella, L. M. (2009). Continuity and change in early school engagement: predictive of children’s achievement trajectories from first to eighth grade? Journal of Educational Psychology, 101(1), 190–206.CrossRefGoogle Scholar
  36. Lai, M. H. C., Richardson, G. B., & Mak, H. W. (2018). Quantifying the impact of partial measurement invariance in diagnostic research: an application to addiction research. Addictive Behaviors, 94, 50–56.CrossRefGoogle Scholar
  37. Laursen, B., & Little, T. D. (2012). Handbook of developmental research methods. Guilford Press.Google Scholar
  38. Lee, V. E. (2000). Using hierarchical linear modeling to study social contexts: the case of school effects. Educational Psychologist, 35(2), 125–141.CrossRefGoogle Scholar
  39. Masters, G. N. (1982). A rasch model for partial credit scoring. Psychometrika, 47(2), 149–174.CrossRefGoogle Scholar
  40. Maydeu-Olivares, A., Shi, D., & Rosseel, Y. (2018). Assessing fit in structural equation models: a Monte-Carlo evaluation of RMSEA versus SRMR confidence intervals and tests of close fit. Structural Equation Modeling: A Multidisciplinary Journal, 25(3), 389–402.CrossRefGoogle Scholar
  41. McArdle, J. J. (2009). Latent variable modeling of differences and changes with longitudinal data. Annual Review of Psychology, 33, 577–605.CrossRefGoogle Scholar
  42. Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55(1), 107–122.CrossRefGoogle Scholar
  43. Muthén, B. O. (1991). Analysis of longitudinal data using latent variable models with varying parameters. In L. M. Collins & J. L. Horn (Eds.), Best methods for the analysis of change: recent advances, unanswered questions, future directions (pp. 1–17). Washington DC: American Psychological Association.Google Scholar
  44. Muthén, L.K. and Muthén, B.O. (1998-2007). Mplus user’s guide. Seventh Edition. Los Angeles, CA: Muthén & Muthén.Google Scholar
  45. Noels, K. A. (2013). Promoting the motivation of Japanese learners of English through autonomy, competence, and relatedness. In M. T. Apple, D. Da Silva, & T. Fellner (Eds.), Language learning motivation in Japan (pp. 15–34). Bristol: Multilingual Matters.CrossRefGoogle Scholar
  46. Noels, K. A., Pelletier, L. G., Clément, R., & Vallerand, R. J. (2000). Why are you learning a second language? Motivational orientations and self-determination theory. Language Learning, 50(1), 57–85.CrossRefGoogle Scholar
  47. Ntoumanis, N. (2001). A self-determination approach to the understanding of motivation in physical education. British Journal of Educational Psychology, 71(2), 225–242.CrossRefGoogle Scholar
  48. Oga-Baldwin, W. L. Q., & Nakata, Y. (2017). Engagement, gender, and motivation: a predictive model for Japanese young language learners. System, 65, 151–163.CrossRefGoogle Scholar
  49. Oga-Baldwin, W. L. Q., Nakata, Y., Parker, P., & Ryan, R. M. (2017). Motivating young language learners: a longitudinal model of self-determined motivation in elementary school foreign language classes. Contemporary Educational Psychology, 49(C), 140–150.CrossRefGoogle Scholar
  50. Olsen, R., Prenzel, M., & Martin, R. (2011). Interest in science: a many-faceted picture painted by data from the OECD PISA study. International Journal of Science Education, 33(1), 1–6.CrossRefGoogle Scholar
  51. Pintrich, P. R. (2000). Multiple goal, multiple pathways: the role of goal orientation in learning and achievement. Journal of Educational Psychology, 92(3), 544–555.CrossRefGoogle Scholar
  52. Pintrich, P., & Harris, K. R. (2003). A motivational science perspective on the role of student motivation in learning and teaching contexts. Journal of Educational Psychology, 95(4), 667–686.CrossRefGoogle Scholar
  53. Polyhart, R. E., & Vandenberg, R. J. (2010). Longitudinal research: the theory, design, and analysis of change. Journal of Management, 36(1), 413–422.Google Scholar
  54. Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. (Copenhagen, Danish Institute for Educational Research). Expanded edition (1980), with foreword and afterword by B. D. Wright. Chicago, The University of Chicago Press.Google Scholar
  55. Reeve, J. (2009). Why teachers adopt a controlling motivating style toward students and how they can become more autonomy supportive. Educational Psychologist, 44(3), 159–175.CrossRefGoogle Scholar
  56. Reeve, J., Jang, H., & Harris, K. R. (2006). What teachers say and do to support students’ autonomy during a learning activity. Journal of Educational Psychology, 98(1), 209–218.CrossRefGoogle Scholar
  57. Reeve, J., & Tseng, C. (2011). Agency as a fourth aspect of students’ engagement during learning activities. Contemporary Educational Psychology, 36(4), 257–267.CrossRefGoogle Scholar
  58. Reeve, J., Jang, H., Carrell, D., Jeon, S., & Barch, J. (2004). Enhancing students’ engagement by increasing teachers’ autonomy support. Motivation and Emotion, 28(2), 147–169.Google Scholar
  59. Reeve, J., Nix, G., & Hamm, D. (2003). Testing models of the experience of self-determination in intrinsic motivation and the conundrum of choice. Journal of Educational Psychology, 95(2), 375–392.CrossRefGoogle Scholar
  60. Ryan, R. M., & Deci, E. L. (2000). Intrinsic and extrinsic motivations: classic definitions and new directions. Contemporary Educational Psychology, 25(1), 54–67.CrossRefGoogle Scholar
  61. Schimitt, N., & Kuljanin, G. (2008). Measurement invariance: review of practice an implications. Human Rescource Management Review, 8(4), 210–222.Google Scholar
  62. Schuitema, J., Peetsma, T., & Van Der Veen, I. (2016). Longitudinal relations between perceived autonomy and social support from teachers and students' self-regulated learning and achievement. Learning and Individual Differences, 49, 32–45.CrossRefGoogle Scholar
  63. Senécal, C., Julien, E., & Guay, F. (2003). Role conflict and academic procrastination: a self-determination perspective. European Journal of Social Psychology, 33(2), 135–145.CrossRefGoogle Scholar
  64. Shernoff, D. (2013). Optimal learning environments to promote student engagement (Vol. 8167, Advancing responsible adolescent development). New York, NY: Springer New York.Google Scholar
  65. Shih, S. S. (2009). An examination of factors related to Taiwanese adolescents’ reports of avoidance strategies. Journal of Educational Research, 102(5), 377–388.CrossRefGoogle Scholar
  66. Skinner, E. A., & Belmont, M. J. (1993). Motivation in the classroom: reciprocal effects of teacher behavior and student engagement across the school year. Journal of Educational Psychology, 85(4), 571–581.CrossRefGoogle Scholar
  67. Skinner, E., Furrer, C., Marchand, G., & Kindermann, T. (2008). Engagement and disaffection in the classroom: part of a larger motivational dynamic? Journal of Educational Psychology, 100(4), 765–781.CrossRefGoogle Scholar
  68. Soenens, B., & Vansteenkiste, M. (2005). Antecedents and outcomes of selfdetermination in 3 life domains: the role of parents’ and teachers’ autonomy support. Journal of Youth and Adolescence, 34(6), 589–604.CrossRefGoogle Scholar
  69. Standage, M., & Gillison, F. (2007). Students’ motivational responses toward school physical education and their relationship to general self-esteem and health-related quality of life. Psychology of Sport and Exercise, 8(5), 704–721.CrossRefGoogle Scholar
  70. Stroet, K., Opdenakker, M.-C., & Minnaert, A. (2013). Effects of need supportive teaching on early adolescents’ motivation and engagement: a review of the literature. Educational Research Review, 9(0), 65–87.Google Scholar
  71. Sun, L., (2012). Primary school students’ mathematics learning motivation current situation and strategy research. Northeast Normal University, Jilin, China, 2012.Google Scholar
  72. Tong, X. (2014). A review on academic overburden among Chinese primary and middle school students. Education Science Forum, 7, 73–75.Google Scholar
  73. Vansteenkiste, M., Niemiec, C. P., & Soenens, B. (2010). The development of the five mini-theories of self-determination theory: an historical overview, emerging trends, and future directions. In T. C. Urdan & S. A. Karabenick (Eds.), Advances in motivation and achievement (The decade ahead: theoretical perspectives on motivation and achievement) (Vol. 16, pp. 105–167). Bingley: Emerald Group.Google Scholar
  74. Vansteenkiste, M., Sierens, E., Soenens, B., Luyckx, K., & Lens, W. (2009). Motivational profiles from a self-determination perspective: the quality of motivation matters. Journal of Educational Psychology, 101(3), 671–688.CrossRefGoogle Scholar
  75. Vansteenkiste, M., Zhou, M., Lens, W., & Soenens, B. (2005). Experiences of autonomy and control among Chinese learners: vitalizing or immobilizing? Journal of Educational Psychology, 97(3), 468–483.Google Scholar
  76. White, R. W. (1959). Motivation reconsidered: the concept of competence. Psychological Review, 66(5), 297–333.CrossRefGoogle Scholar
  77. Williams, G. C., & Deci, E. L. (1996). Internalization of biopsychosocial values by medical students: a test of self-determination theory. Journal of Personality and Social Psychology, 70(4), 767–779.CrossRefGoogle Scholar
  78. Wu, W., & Wu, X. (2007). Zhong Xiao Xue Sheng Xue Xi Dong Ji De Fa Zhan Qu Shi Ji Qi Dui Xue Ye Cheng Ji De Ying Xiang (Pin Yin). Chinese Psychological Society (Abstract).Google Scholar
  79. Zhang, D., Bobis, J., Wu, X., & Cui, Y. (2018). Research in Science Education,
  80. Zhang, D. H., Fu, D. M., Liu, H. Y., & Liu, L. M. (2018). Effect of Perceived Teacher's Autonomy Support on Students' Achievement: The mediating Role of Autonomy Psychological Need and Intrinsic Motivation. Teacher Education Research (Pin Yin:Jiao Shi Jiao Yu Yan Jiu), 30(1):79-86.Google Scholar
  81. Zhen, R., Liu, R.-D., Ding, Y., Liu, Y., Wang, J., & Xu, L. (2018). The moderating role of intrinsic value in the relation between psychological needs support and academic engagement in mathematics among Chinese adolescent students. International Journal of Psychology, 53(4), 313–320.CrossRefGoogle Scholar
  82. Zhou, M. M., Ma, W. J., & Deci, E. (2009). The importance of autonomy for rural Chinese children's motivation for learning. Learning and Individual Differences, 19(4), 492–498.CrossRefGoogle Scholar

Copyright information

© Instituto Superior de Psicologia Aplicada, Lisboa and Springer Nature B.V. 2019

Authors and Affiliations

  • Dan Wei
    • 1
  • Danhui Zhang
    • 2
    Email author
  • Jingwen He
    • 2
  • Janette Bobis
    • 3
  1. 1.Faculty of PsychologyBeijing Normal UniversityBeijingChina
  2. 2.Collaborative Innovation Center of Assessment Toward Basic Education QualityBeijing Normal UniversityBeijingChina
  3. 3.The University of SydneySydneyAustralia

Personalised recommendations