成功期望與興趣價值對數學成就的動態影響：動態結構方程模型分析

Dynamic Effect of Success Expectation and Interest Value on Mathematic Achievement: Dynamic Structural Equation Model Analysis

10.6209/JORIES.202106_66(2).0005

曾明基(Ming-Chi Tseng)

期望價值理論 ； 動態結構方程模型 ； 數學成就 ； expectancy-value theory ； dynamic structural equation model ； mathematic achievement

教育科學研究期刊

66卷2期（2021 / 06 / 01）

145 - 173

繁體中文

本研究以期望價值理論為架構，透過動態結構方程模型分析，瞭解成功期望與興趣價值對數學成就的動態影響。本研究透過經驗採樣方法蒐集國小46位高年級學生，在成功期望與興趣價值兩個變項的密集性追蹤資料，總共100波次，並在課程結束後施測標準化數學成就測驗。經由分析發現，在個體內層次成功期望與興趣價值存在一階自我迴歸，且成功期望與興趣價值也存在一階向量自迴歸，而在個體間層次成功期望正向影響數學成就，興趣價值負向影響數學成就，但是興趣價值對成功期望一階向量自迴歸的隨機變異正向影響數學成就。依據研究結果提出建議，供實務應用及未來研究參考。

This research is based on expectancy-value theory. Through an analysis using dynamic structural equation model, we clarified the dynamic effect of success expectation and interest value on mathematic achievement. We employed empirical sampling to collect intensive longitudinal data from 46 elementary school students. A standardized mathematic achievement test was administered after the course. The analysis revealed an autocorrelation and a cross-lagged effect between success expectation and interest value at the within-person level. At the between-person level, success expectation positively affected mathematic achievement, whereas interest value negatively affected mathematic achievement. However, the random slope related to the cross-lag effect of success expectation positively affected mathematic achievement. On the basis of the study results, suggestions were provided for practical application and future research.

1. 林志哲（2007）。以結構方程模式驗證期望、價值與數學成就的關係。教育學刊，29，103-127。 【Lin, C.-C. (2007). The verification of relationship among expectancy, value, and mathematic achievement by structural equation modeling. Educational Review, 29, 103-127. 】
   連結：
2. 陳敏瑜、游錦雲（2013）。以TIMSS資料檢視能力信念與任務價值對臺灣八年級學生數學成就之影響。教育科學研究期刊，58（3），153-186。 【Chen, M.-Y., & Yu, C.-Y. (2013). Using trends in mathematics and science study to investigate the effects of ability beliefs and task values on eighth-grader mathematics achievements in Taiwan. Journal of Research in Education Sciences, 58(3), 153-186. 】
   連結：
3. 陳敏瑜、游錦雲（2017）。學生知覺教師期望、能力信念、實用價值與內在價值對臺灣八年級學生數理成就之影響：以TIMSS 2011多層次結構方程式模型為例。教育科學研究期刊，62（1），59-102。 【Chen, M.-Y., & Yu, C.-Y. (2017). Effects of perception of teachers’ expectations, ability beliefs, utility values, and intrinsic values on math and science achievement among eighth-grade students in Taiwan: A multilevel structural equation model using TIMSS 2011. Journal of Research in Education Sciences, 62(1), 59-102. 】
   連結：
4. Ahmed, W., Minnaert, A., van der Werf, G., & Kuyper, H. (2010). Perceived social support and early adolescents’ achievement: The mediational roles of motivational beliefs and emotions. Journal of Youth and Adolescence, 39, 36-46.
   連結：
5. Asparouhov, T., & Muthén, B. (2019). Latent variable centering of predictors and mediators in multilevel and time-series models. Structural Equation Modeling: A Multidisciplinary Journal, 26(1), 119-142.
   連結：
6. Asparouhov, T., & Muthén, B. (2020). Comparison of models for the analysis of intensive longitudinal data. Structural Equation Modeling: A Multidisciplinary Journal, 27(2), 275-297.
   連結：
7. Asparouhov, T., Hamaker, E. L., & Muthén, B. (2018). Dynamic structural equation models. Structural Equation Modeling: A Multidisciplinary Journal, 25(3), 359-388.
   連結：
8. Bouffard, T., Marcoux, M., Vezeau, C., & Bordeleau, L. (2003). Changes in self-perceptions of competence and intrinsic motivation among elementary schoolchildren. British Journal of Educational Psychology, 73(2), 171-186.
   連結：
9. Chouinard, R., Karsenti, T., & Roy, N. (2007). Relations among competence beliefs, utility value, achievement goals, and effort in mathematics. British Journal of Educational Psychology, 77(3), 501-517.
   連結：
10. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. Annual Review of Psychology, 53, 109-132.
    連結：
11. Frijns, T., Keijsers, L., & Finkenauer, C. (2020). Keeping secrets from parents: On galloping horses, prancing ponies and pink unicorns. Current Opinion in Psychology, 31, 49-54.
    連結：
12. Guo, J., Marsh, H. W., Parker, P. D., Morin, A. J. S., & Yeung, A. S. (2015). Expectancy-value in mathematics, gender and socioeconomic background as predictors of achievement and aspirations: A multi-cohort study. Learning and Individual Differences, 37, 161-168.
    連結：
13. Hamaker, E. L., & Muthén, B. (2020). The fixed versus random effects debate and how it relates to centering in multilevel modeling. Psychological Methods, 25(3), 365-379.
    連結：
14. Hamaker, E. L., Asparouhov, T., Brose, A., Schmiedek, F., & Muthén, B. (2018). At the frontiers of modeling intensive longitudinal data: Dynamic structural equation models for the affective measurements from the COGITO study. Multivariate Behavioral Research, 53(6), 820-841.
    連結：
15. Hedeker, D., Mermelstein, R. J., & Demirtas, H. (2008). An application of a mixed-effects location scale model for analysis of ecological momentary assessment (EMA) data. Biometrics, 64(2), 627-634.
    連結：
16. Hedeker, D., Mermelstein, R. J., & Demirtas, H. (2012). Modeling between-subject and within- subject variances in ecological momentary assessment data using mixed-effects location scale models. Statistics in Medicine, 31(27), 3328-3336.
    連結：
17. Jongerling, J., Laurenceau, J., & Hamaker, E. L. (2015). A multilevel AR (1) model: Allowing for inter-individual differences in trait-scores, inertia, and innovation variance. Multivariate Behavioral Research, 50(3), 334-349.
    連結：
18. Kadijevich, D. (2008). TIMSS 2003: Relating dimensions of mathematics attitude to mathematics achievement. Zbornik Instituta za Pedagoska Istrazivanja, 40(2), 327-346.
    連結：
19. Liu, S., & Meng, L. (2010). Re-examining factor structure of the attitudinal items from TIMSS 2003 in cross-cultural study of mathematics self-concept. Educational Psychology, 30(6), 699-712.
    連結：
20. Marsh, H. W., Trautwein, U., Lüdtke, O., Köller, O., & Baumert, J. (2005). Academic self-concept, interest, grades, and standardized test scores: Reciprocal effects models of causal ordering. Child Development, 76(2), 397-416.
    連結：
21. McNeish, D., & Hamaker, E. L. (2020). A primer on two-level dynamic structural equation models for intensive longitudinal data in Mplus. Psychological Methods, 25(5), 610-635.
    連結：
22. Muthén, B. O. (1994). Multilevel covariance structure analysis. Sociological Methods & Research, 22(3), 376-398.
    連結：
23. Nickell, S. (1981). Biases in dynamic models with fixed effects. Econometrica, 49(6), 1417-1426.
    連結：
24. Schuurman, N. K., Ferrer, E., de Boer-Sonnenschein, M., & Hamaker, E. L. (2016). How to compare cross-lagged associations in a multilevel autoregressive model. Psychological Methods, 21(2), 206-221.
    連結：
25. Song, H., & Zhang, Z. (2014). Analyzing multiple multivariate time series data using multilevel dynamic factor models. Multivariate Behavioral Research, 49(1), 67-77.
    連結：
26. Trautwein, U., Marsh, H. W., Nagengast, B., Lüdtke, O., Nagy, G., & Jonkmann, K. (2012). Probing for the multiplicative term in modern expectancy-value theory: A latent interaction modeling study. Journal of Educational Psychology, 104(3), 763-777.
    連結：
27. Trull, T. J., & Ebner-Priemer, U. (2014). The role of ambulatory assessment in psychological science. Current Directions in Psychological Science, 23(6), 466-470.
    連結：
28. Wang, L., Hamaker, E., & Bergeman, C. S. (2012). Investigating inter-individual differences in short-term intra-individual variability. Psychological Methods, 17(4), 567-581.
    連結：
29. Watt, H. M. G. (2004). Development of adolescents’ self-perceptions, values, and task perceptions according to gender and domain in 7th- through 11th-grade Australian students. Child Development, 75(5), 1556-1574.
    連結：
30. Wigfield, A., & Eccles, J. S. (2000). Expectancy-value theory of achievement motivation. Contemporary Educational Psychology, 25(1), 68-81.
    連結：
31. Wigfield, A., & Eccles, J. S. (2002). The development of competence beliefs, expectancies for success, and achievement values from childhood through adolescence. In A. Wigfield & J. S. Eccles (Eds.), Development of achievement motivation (pp. 91-120). Academic Press.
    連結：
32. Zhu, Y., & Leung, F. K. S. (2011). Motivation and achievement: Is there an East Asian model? International Journal of Science and Mathematics Education, 9, 1189-1212.
    連結：
33. 張俊彥（主編）（2018）。國際數學與科學教育成就趨勢調查2015國家報告。國立臺灣師範大學科學教育中心。 【Chang, C.-Y. (Ed.). (2018). Trends in international mathematics and science study in 2015: National report in Taiwan. Science Education Center, National Taiwan Normal University.】
34. 蕭儒棠、曾建銘、謝佩蓉、黃馨瑩、吳慧珉、陳冠銘、蔡明學、謝名娟、謝進昌（2017）。大型教育調查研究實務：以TASA為例。國家教育研究院。 【Hsiao, J.-T., Cheng, C.-M., Hsieh, P.-J., Huang, H.-Y., Wu, H.-M., Chen, K.-M., Tsai, M.-H., Hsieh, M.-J., & Hsieh, J.-C. (2017). Using large-scale assessment datasets for research: Taiwan Assessment of Student Achievement (TASA). National Academy for Educational Research.】
35. Deci, E. L., & Ryan, R. M. (1985). Intrinsic motivation and self-determination in human behavior. Plenum.
36. Eccles, J. S., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), Achievement and achievement motivation (pp. 75-146). W. H. Freeman.
37. Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2004). Bayesian data analysis (2nd ed.). Chapman & Hall.
38. Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis (3rd ed.). Chapman & Hall.
39. House, J. D. (2007). Effects of science beliefs and instructional strategies on achievement of students in the United States and Korea: Results from the TIMSS 2003 assessment. (ED510139). ERIC. https://files.eric.ed.gov/fulltext/ED510139.pdf
40. Muthén, L. K., & Muthén, B. O. (1998-2021). Mplus Version 8.6, March 22, 2021. https://www. statmodel.com/verhistory.shtml
41. Wigfield, A., Eccles, J. S., Schiefele, U., Roeser, R. W., & Davis-Kean, P. (2006). Development of achievement motivation. In W. Damon & R. M. Lerner (Eds.), Handbook of child psychology: Vol. 3. Social, emotional, and personality development (6th ed., pp. 933-1002). Wiley.

1. 陳佳欣(2023)。臺灣國小數學低成就學生之數學成就影響因素研究。教育學誌，49，107-128。
2. 鄧鈞文,陳俊瑋(2022)。中等學校體育師資生「師資培育學程選擇動機量表」之修訂與信效度檢驗。國立臺灣體育運動大學學報，11(1)，1-26。
3. 李健恆,呂鳳琳,左台益(2022)。體現動態視覺化對中學生學習代數式基本運算的影響。教育科學研究期刊，67(4)，285-318。
4. 張書毓,邱紹群(2022)。疫情來了，你行動支付了沒？。管理資訊計算，11(1)，81-94。
5. (2021)。課中補救教學對學生數學學習動機的動態影響。教育與心理研究，44(4)，71-91。
6. (2022)。師資培育學程選擇動機與學習成就的關係：以教育專業科目在校成績與教師資格考試表現為例。國立臺灣體育運動大學學報，11(2)，21-41。
7. (2024)。筆記撰寫結合學生出題策略對國小生社會領域筆記品質與學習成效之研究。教育科學研究期刊，69(2)，173-208。
8. (2024)。東部某大學的「學生評鑑教師教學量表」分數之排序：貝氏多層次隨機效果模型分析。測驗學刊，71(1)，95-117。