本研究探討高中生解數學素養題的成功期望與任務價值的潛在類型及性別在各潛在類型的差異，以及比較不同潛在類型的數學素養表現。同時，也探討不同性別高中生的成功期望及任務價值與數學素養表現之間的關聯性。為了達成研究目的並回答研究問題，本研究針對普通高級中學一年級的三角比學習內容開發數學素養題以評量數學素養表現，並設計李克特4點量表的期望價值問卷，以測量學生對於解數學素養題的成功期望與任務價值。而本研究對普通高級中學二年級與三年級共220位男性學生、175位女性學生進行施測，共獲得216個男性有效樣本與175個女性有效樣本。本研究採用多群組潛在剖面分析(Multiple group Latent Profile Analysis, MgLPA)探討男女學生對於成功期望與任務價值的潛在類型恆等性，並以多組獨立樣本無母數分析(Kruskal-Wallis H test)針對所獲得的各潛在類型，比較各潛在類型之間數學素養表現的差異性。另外，本研究也採用多群組結構方程模型(Multiple group Structural Equation Model, MgSEM)探討男女學生在成功期望及任務價值與數學素養表現之間結構關係的恆等性，並以結構方程模型(Structural Equation Model, SEM)探討結構關係。研究結果顯示：(1)針對成功期望與任務價值的潛在類型，男性可分為低動機組與高動機組，女性則可分為低動機組、中動機組與高動機組；(2)男性的低動機組與高動機組在數學素養表現未達顯著差異，而女性的中動機組與高動機組在數學素養表現皆顯著高於低動機組；(3)全體學生的成功期望對數學素養表現有直接且正向的影響，而任務價值對數學素養表現無直接影響，但會透過成功期望有間接影響。本研究建議現職教師可參考本研究所開發之數學素養題，設計提升數學素養表現的教學活動。針對教學活動施行細節，(1)可根據潛在類型進行分組，針對不同組別學生而有不同的教學策略；(2)可關注低程度期望價值的女性學生，提供解數學素養題相應的輔導與諮詢；(3)設計提升學生解數學素養題自信心與價值的教學活動，以提高學生的數學素養表現。

大學入學考試中心(2017a)。108新課綱與素養導向命題精進方向。https://reurl.cc/37zlEO
大學入學考試中心(2017b)。學測表現，各有所長。https://reurl.cc/bVgQql
大學入學考試中心(2020)。111大考素養導向命題方向與試題示例。https://reurl.cc/G41RyA
大學入學考試中心(2022)。111年學科能力測驗數學B考科。https://reurl.cc/D40Qkd
余民寧、翁雅芸、張靜軒(2018)。數理科學的學習動機有性別差異嗎？一個來自後設分析的證據。當代教育研究季刊，26(1)，45-75。https://doi.org/10.6151/CERQ.201803_26(1).0002
吳正新(2019)。數學素養導向評量試題研發策略[The Approaches of Developing Mathematical Literacy-Based Assessment]。中等教育，70(3)，11-35。https://doi.org/10.6249/se.201909_70(3).0024
吳正新、林裕峯、余陳宗、謝佳叡(2019)。108學年度國中素養導向評量分析報告。https://reurl.cc/xLRjj4
邱皓政(2011)。結構方程模式：LISREL/SIMPLIS原理與應用。臺北市：雙葉。
邱皓政(2023)。潛在異質性分析：潛在結構模式與進階應用。臺北市：五南。
邱皓政(2024)。結構方程模式：原理與應用 使用Mplus, LISREL (SIMPLIS), R, AMOS (三版)。臺北市：雙葉。
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。https://doi.org/10.6450/ER.200712.0103
林素微、林娟如、吳正新、江培銘(2011)。學生PISA素養與基測表現的對照分析。收錄於臺灣PISA國家研究中心(主編)，臺灣PISA 2009結果報告(頁187-194)。臺北市：心理。
國家教育研究院(2018)。素養導向「紙筆測驗」要素與範例試題(定稿版)。https://bit.ly/43A4u62
張偉豪、鄭時宜(2012)。與結構方程模型共舞-曙光初現。新北市：前程。
教育部(2014)。十二年國民基本教育課程綱要總綱。https://bit.ly/3vp99ee
教育部(2018)。十二年國民基本教育課程綱要國民中小學暨普通高級中等學校-數學領域。https://bit.ly/3TRTm17
張雅雲(2019)。宜蘭是一座博物館02》除了蘭陽博物館，更值得你認識的「蘭博家族」。https://reurl.cc/eLr44L
臺灣PISA國家研究中心(2022)。PISA2022數學範例試題。https://reurl.cc/6vX0pM
謝佳叡(2021)。數學領域108課綱PISA素養教學與評量。https://reurl.cc/54myy6
魏如慧(2024)。數學自我效能與數學能力之性別差異：PISA 2022資料分析 [Gender Disparities in Mathematics Self-efficacy and Proficiency: Insights from PISA 2022 Data Analysis]。學校行政，151，118-130。https://doi.org/10.6423/hhhc.202405_(151).0006
Bandura, A. (1997). Self-efficacy: The exercise of control. W H Freeman/Times Books/ Henry Holt & Co.
Bentler, P. M., & Bonett, D. G. (1980). Significance tests and goodness of fit in the analysis of covariance structures. Psychological Bulletin, 88(3), 588-606. https://doi.org/10.1037/0033-2909.88.3.588
Berger, J.-L., & Karabenick, S. A. (2011). Motivation and students’ use of learning strategies: Evidence of unidirectional effects in mathematics classrooms. Learning and Instruction, 21(3), 416-428. https://doi.org/10.1016/j.learninstruc.2010.06.002
Bollen, K. A. (1989). Structural equations with latent variables. John Wiley & Sons. https://doi.org/10.1002/9781118619179
Cheung, G.W., & Rensvold, R.B. (2002). Evaluating Goodness-of-Fit Indexes for Testing Measurement Invariance. Structural Equation Modeling: A Multidisciplinary Journal, 9, 233 - 255. https://doi.org/10.1207/S15328007SEM0902_5
Doz, E., Cuder, A., Pellizzoni, S., Carretti, B., & Passolunghi, M. C. (2023). Arithmetic word problem-solving and math anxiety: The role of perceived difficulty and gender. Journal of Cognition and Development, 24(4), 598–616. https://doi.org/10.1080/15248372.2023.2186692
Eccles, J. S., & Wigfield, A. (1995). In the mind of the actor: The structure of adolescents’ achievement task values and expectancy-related beliefs. Personality and Social Psychology Bulletin, 21(3), 215-225. https://doi.org/10.1177/0146167295213003
Eccles, J. S., & Wigfield, A. (2020). From expectancy-value theory to situated expectancy-value theory: A developmental, social cognitive, and sociocultural perspective on motivation. Contemporary Educational Psychology, 61. https://doi.org/10.1016/j.cedpsych.2020.101859
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, 75–146.
Ferri, R. B. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM, 38(2), 86-95. https://doi.org/10.1007/BF02655883
Fornell, C., & Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research, 18(1), 39-50. https://doi.org/10.2307/3151312
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. https:/doi.org/10.1016/j.lindif.2015.01.008
Hair, J. F., Anderson, R. E., Tatham, R. L., & Black, W. C. (1998). Multivariate data analysis (5th ed.). New York: Macmillan.
Holenstein, M., Bruckmaier, G. & Grob, A. (2021). Transfer effects of mathematical literacy: an integrative longitudinal study. Eur J Psychol Educ 36, 799–825 https://doi.org/10.1007/s10212-020-00491-4
Jiang, Y., & Rosenzweig, E. Q. (2021). Using cost to improve predictions of adolescent students' future choice intentions, avoidance intentions, and course grades in mathematics and English. Learning and Individual Differences, 86, 101978. https://doi.org/10.1016/J.LINDIF.2021.101978
Lazarides, R., Schiepe-Tiska, A., Heine, J.-H., & Buchholz, J. (2022). Expectancy-value profiles in math: How are student-perceived teaching behaviors related to motivational transitions? Learning and Individual Differences, 98, 102198. https:/doi.org/10.1016/j.lindif.2022.102198
Leiss, D., Schukajlow, S., Blum, W., Messner, R., & Pekrun, R. (2010). The role of the situation model in mathematical modelling-task analyses, student competencies, and teacher interventions. Journal fur Mathematik-Didaktik, 31(1), 119-141. https://doi.org/10.1007/s13138-010-0006-y
Marsh, H.W., Balla, J., & Mcdonald, R.P. (1988). Goodness-of-fit indexes in confirmatory factor analysis : The effect of sample size. Psychological Bulletin, 103, 391-410. https://doi.org/10.1037/0033-2909.103.3.391
McDonald, R. P., & Ho, M. R. (2002). Principles and practice in reporting structural equation analysis. Psychological methods, 7, 64-82. https://doi.org/10.1037/1082-989x.7.1.64
Morin, A. J. S., Meyer, J. P., Creusier, J., & Biétry, F. (2016). Multiple-Group Analysis of Similarity in Latent Profile Solutions. Organizational Research Methods, 19(2), 231-254. https://doi.org/10.1177/1094428115621148
Mullis, I. V. S., Martin, M. O., Foy, P., Kelly, D. L., & Fishbein, B. (2020). TIMSS 2019 International Results in Mathematics and Science. Retrieved from Boston College, TIMSS & PIRLS International Study Center website: https://reurl.cc/XqzYoE
Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and Applications in Mathematics Education: New ICMI study series, 10. https://doi.org/10.1007/978-0-387-29822-1_1
OECD. (2018). PISA 2021 Mathematics Framework (Draft). Retrieved from https://bit.ly/43yR8qn
OECD. (2019). PISA 2018 results (Volume I): What students know and can do. Retrieved from https://doi.org/10.1787/5f07c754-en
OECD. (2023). PISA 2022 results (Volume I): The State of Learning and Equity in Education. Retrieved from https://doi.org/10.1787/53f23881-en.
Olson, C. L. (1979). Practical considerations in choosing a MANOVA test statistic: A rejoinder to Stevens. Psychological Bulletin, 86(6), 1350–1352. https://doi.org/10.1037/0033-2909.86.6.1350
Part, R., Perera, H. N., Marchand, G. C., & Bernacki, M. L. (2020). Revisiting the dimensionality of subjective task value: Towards clarification of competing perspectives. Contemporary Educational Psychology, 62, 101875. https://doi.org/10.1016/j.cedpsych.2020.101875
Phan, H. P. (2014). Expectancy-value and cognitive process outcomes in mathematics learning: a structural equation analysis. Higher Education Research & Development, 33(2), 325–340. https://doi.org/10.1080/07294360.2013.832161
Putwain, D. W., Nicholson, L. J., Pekrun, R., Becker, S., & Symes, W. (2019). Expectancy of success, attainment value, engagement, and Achievement: A moderated mediation analysis. Learning and Instruction, 60, 117-125. https:/doi.org/10.1016/j.learninstruc.2018.11.005
Raufelder, D., Hoferichter, F., Hirvonen, R., & Kiuru, N. (2022). How students’ motivational profiles change during the transition from primary to lower secondary school. Contemporary Educational Psychology, 71, 102117. https://doi.org/10.1016/j.cedpsych.2022.102117
Schukajlow, S., Blomberg, J., Rellensmann, J., & Leopold, C. (2022). The role of strategy-based motivation in mathematical problem solving: The case of learner-generated drawings. Learning and Instruction, 80. https://doi.org/10.1016/j.learninstruc.2021.101561
Schukajlow, S., Rakoczy, K., & Pekrun, R. (2023). Emotions and motivation in mathematics education: Where we are today and where we need to go. ZDM, 55(2), 249-267. https://doi.org/10.1007/s11858-022-01463-2
Tuominen, H., Juntunen, H., & Niemivirta, M. (2020). Striving for success but at what cost? Subject-Specific achievement goal orientation profiles, perceived cost, and academic well-being. Frontiers in Psychology, 11:557445. https://doi.org/10.3389/fpsyg.2020.557445
Velayutham, S., Aldridge, J. M., & Fraser, B. (2012). Gender differences in student motivation and self-regulation in science learning: A multi-group structural equation modeling analysis. International journal of science and mathematics education, 10, 1347-1368. https://doi.org/10.1007/s10763-012-9339-y
Vilenius‐Tuohimaa, P. M., Aunola, K., & Nurmi, J. (2008). The association between mathematical word problems and reading comprehension. Educational Psychology, 28(4), 409-426. https://doi.org/10.1080/01443410701708228
Wakhata, R., Balimuttajjo, S., & Mutarutinya, V. (2024). Relationship between students' attitude towards, and performance in mathematics word problems. PloS one, 19(2), e0278593. https://doi.org/10.1371/journal.pone.0278593
Weber, K., Lew, K., & Mejía-Ramos, J. P. (2020). Using expectancy value theory to account for individuals’ mathematical justifications. Cognition and Instruction, 38(1), 27-56. https://doi.org/10.1080/07370008.2019.1636796
Wigfield, A., & Eccles, J. S. (2000). Expectancy-value theory of achievement motivation. Contemp Educ Psychol, 25(1), 68-81. https://doi.org/10.1006/ceps.1999.1015
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. https://doi.org/10.1016/B978-012750053-9/50006-1