本研究旨在以長期追蹤研究探討技術型高級中等學校工業類群科學生數學科自我效能與學習興趣之長期互為消長之關係，及其對數學科學習成效之影響。本研究採調查研究法，使用問卷為調查工具，採用方便取樣，預計邀請技術型高中工業群科學生參與研究。本研究待答問題有三：一、技術型高級中等學校工業類群科學生數學科自我效能與學習興趣如何長期變化？二、技術型高級中等學校工業類群科學生數學科自我效能與學習興趣如何互相影響？三、技術型高級中等學校工業類群科學生之數學科自我效能、學習興趣與學習成效三者之長期縱貫相關情形為何？在進行描述性統計分析、重複量測變異數分析與交叉延宕分析後依據待答問題提出研究結果有三：一、工業類群技高學生數學自我效能表現較數學學習興趣佳。二、工業類群技高學生數學自我效能與數學學習興趣具正向關聯。三、工業類群技高學生數學自我效能對數學學習成效具正向關聯。依研究結論提出建議供技術型高中教師家長參考：一、可藉教學與課堂活動、班級經營、家庭關係，持續增強學生自我效能。二、可於高一藉培養學習興趣提升自我效能與學習意願。

This study examined the longitudinal cross-lagged relationships between math self-efficacy and interest among vocational high school students in industry category. Additionally, it explored the relationship of math self-efficacy and interest to academic performance. The research adopted a survey research method, employing questionnaires as the research tool with convenience sampling. The target population was vocational high school students in the industry category. The study addressed three main questions: 1) How did math self-efficacy and interest change longitudinally, 2) How did math self-efficacy and interest inform each other over time, and 3) How were math self-efficacy and interest related to the academic performance of math associated over time? After conducting descriptive statistical analysis, repeated measures ANOVA, and cross-lagged analysis, the study presented three research findings based on the research questions: 1) Vocational high school students in applied engineering clusters exhibited better math self-efficacy than their interest, 2) There was a positive correlation between math self-efficacy and interest among vocational high school students in applied engineering clusters, and 3) Math self-efficacy among vocational high school students in industry category positively correlated with academic achievement in math. The study concluded with recommendations for teachers and parents of vocational high school students: 1) Teaching activities, classroom management, and family relationships were suggested to be utilized continuously to enhance students’ self-efficacy, and 2) Enhancing self-efficacy and learning motivation by cultivating interest in learning in the first year of high school.

王秀槐、黃金俊（2010）。擇其所愛、愛其所擇：從自我決定理論看大學多元入學制度中學生的科系選擇與學習成果。教育科學研究期刊，55(2)，1–27。
田秀蘭（2003）。社會認知生涯理論之興趣模式驗證研究。教育心理學報，34（2），247–266。
余民寧、趙珮晴、許嘉家（2009）。影響國中小女學生學業成就與學習興趣因素──以臺灣國際數學與科學教育成就趨勢調查（TIMSS）資料為例。教育資料與研究，87，79–104。
余民寧、趙珮晴、陳嘉成（2010）。以社會認知生涯理論探討影響選擇數學職業意圖的因素。教育科學研究期刊，55（3），177–201。
余民寧、韓珮華（2009）。教學方式對數學學習興趣與數學成就之影響：以TIMSS 2003台灣資料爲例。測驗學刊，56（1），19–48。
呂秋萍（2010）。期望─價值理論融入國中英語科教學方案之效果分析〔未出版之碩士論文〕。國立屏東科技大學。
巫博瀚、陸偉明（2010）。延宕交叉相關與二階層線性成長模式在台灣青少年自尊的發現。測驗學刊，57（4），541–565。
技專校院招生策略委員會（2022年7月06日）。四技二專統一入學測驗。 https://www.techadmi.edu.tw/page.php?pid=2
李旻樺、林清文（2003）。高中學生之自我效能、成功期望、學習任務價值與動機調整策略之研究。中華輔導學報，14，117–145。
李勇輝（2017）。學習動機、學習策略與學習成效關係之研究－以數位學習為例。經營管理學刊，14，68–86。
李懿芳、曾璧光、宋修德（2022）。技術型高級中等學校素養導向教學設計與實踐。台灣教育研究期刊，3（1），333–358。
周亞寬（2016）。創意教學數位平台建構及其學習成效之研究〔未出版之碩士論文〕。國立臺北科技大學。
林啟超、謝智玲（2018）。高職學生知覺教師心理支持、情境興趣、個人興趣與課業投入間關係之探究。師資培育與教師專業發展期刊，11（1），123–153。
林貴彬（2019）。運動興趣與足球學習自我效能及學習表現之關係。成大體育學刊，51（1），70–85。
林清山（2013）。多變項分析統計法。東華書局。
林清南（2023）。淺論技術型高中108課綱機械群實施現況與發展。中等教育，74（1），124–130。
郎亞琴、陳彩卿（2008）。國民中學學生之性別、性別角色、數學自我效能與數學成就之研究－以彰化縣國民中學三年級學生為例。立德學報，6（1），44–58。
袁國芝、王子豪、莊委桐（2016）。十二年國教免試入學分發制度之賽局分析。經濟論文叢刊，44（2），215–255。
高級中等教育法（2021）。https://law.moj.gov.tw/LawClass/LawAll.aspx？pcode=h0060043
張玉茹、江芳盛（2013）。師生關係、學習動機與數學學業成就模式之驗證－以PISA 2003資料庫為例。測驗統計年刊，21，91–121。
張宇樑（2011）。國小五年級學生數學自我效能感之調查研究。科學教育學刊，19（6），507–530。
張芳全（2011）。家長教育程度、文化資本、自我抱負、學習興趣與數學成就之關係研究。臺中教育大學學報：教育類，25（1），29–56。
張春興（1991）。現代心理學。東華書局。
張春興（1996）。教育心理學-三化取向的理論與實踐。東華書局。
張春興（2002）。現代心理學。東華書局。
張雅萍（2000）。摘要策略對網路化學習成效之研究〔未出版之碩士論文〕。國立臺灣師範大學。
張鎮華（2017）。數學學科知識也是數學素養。高中數學學科中心。https://mathcenter.ck.tp.edu.tw/Resources/Ctrl/ePaper/ eArticleDetail.aspx?id=1e8e4437-3aae-4718-bccd-c0ebe6e4b2a5
教育部（2018）。十二年國民基本教育課程綱要技術型高級中等學校數學領域。
教育部（2018）。十二年國民基本教育課程綱要總綱。
教育部（2018）。十二年國民基本教育技術型高級中等學校群科課程綱要－電機與電子群。
教育部（2018）。十二年國民基本教育技術型高級中等學校群科課程綱要－動力機械群。
教育部（2018）。十二年國民基本教育技術型高級中等學校群科課程綱要－土木與建築群。
教育部（2018）。十二年國民基本教育技術型高級中等學校群科課程綱要工業類群。
教育部（2018）。十二年國民基本教育技術型高級中等學校群科課程綱要－化工群。
教育部（2018）。十二年國民基本教育技術型高級中等學校群科課程綱要－機械群。
梁麗珍、林恆瑜（2008）。期待─價值學習動機理論模式實證研究─以技職校院統計課程為例。教育理論與實踐學刊，18，73–96。
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。
陳清溪（2013）。十二年國民基本教育政策之探討。教育資料與研究， 109，53–77。
陳舜文、魏嘉瑩（2013）。大學生學習動機之「雙因素模式」：學業認同與角色認同之功能。中華心理學刊，55（1），41–55。
陳逸倩、李怡穎 （2021）。探討數學素養導向試題設計：以四技二專統一入學測驗為例。台灣教育研究期刊，2（2），125–138。
陳意涵（2016）。大學多元入學管道與學生學習成效之研究-以國立宜蘭大學為例〔未出版之碩士論文〕。國立宜蘭大學。
陳瑋婷（2011）。自我效能、學習策略與學業成就之關係研究：結合後設分析與結構方程模式。師資培育與教師專業發展期刊，4（2），83–95。
陳嘉成、洪兆祥（2021）。先有與趣？或是先有自我效能？從社會認知生涯理論檢驗藝術大學師資生興趣發展模式。教育與心理研究，44（4），1–33。
陳瑩（2017）。從期望價值理論探討學業拖延之成因－以碩士在職專班學生為例〔未出版之碩士論文〕。國立中正大學。
黃俊程（2014）。臺北市高職電機與電子群學生學習風格與學習成效之研究〔未出版之碩士論文〕。國立臺灣師範大學。
黃建翔、蔡明學（2016）。影響高中職學生學習成就關鍵因素之研究。教育行政與評鑑學刊，19，73–98。
楊正群、林貴彬（2018）。運動興趣對網球課程自我效能及學習成效之影響。成大體育學刊，50（1），49–64。
楊國樑、王瑞榮、陳錦初（2014）。管道多元與學生多元制度在入學後學業成效差異之比較。樹德科技大學學報，16（2），37–56。
廖錦文、廖興國、陳柏翔、王藝淇、林泓毅 （2022）。自動控制技能領域電工實習素養導向教學命題初探。台灣教育研究期刊，3（2），103–128。
趙珮晴、余民寧（2012）。自律學習策略與自我效能、學習興趣、學業成就的相關研究。教育研究集刊，58（3），1–32。
劉政宏（2009）。對學習動機最有影響力的動機成分？雙核心動機模式之初探。教育心理學報，41（2），361–384。
劉春榮（2011）。我國國民教育議題與發展。載於國家教育研究院（主 編），我國百年教育回顧與展望（67-80頁）。國家教育研究院。
潘道仁（2012）。十二年國民基本教育完全中學優質化課程發展之困境與因應建議。臺灣教育評論月刊，1（10），47–54。
賴英娟（2010）。教師支持、數學自我效能及數學興趣對職業意向之影響。中華輔導與諮商學報，28，1–27。
譚華德、郝永崴、黃明月（2019）。泰文學習拼字系統之創新教學：泰語學習自我效能、學習興趣、學習焦慮及學習成就之相關研究。教育科學研究期刊，64（3），1–29。
Abolghasemi, M., & Nosrati heshi, K. (2024). Investigating the relationship between math, computer and science self-efficacy and the academic performance of engineering students. Iranian Journal of Engineering Education, 25(100), 49–61.
Ashcraft, M. H., & Krause, J. A. (2007). Working memory, math performance, and math anxiety. Psychonomic Bulletin & Review, 14(2), 243–248.
Atkinson, J. W. (1957). Motivational determinants of risk-taking behavior. Psychological Review, 64(6), 359–372.
Atkinson, J. W. (1964). An introduction to motivation. Van Nostrand.
Bandura, A. (1977). Social learning theory. Prentice-Hall.
Bandura, A. (1997). Self-efficacy: The exercise of control. Freeman
Bandura, A., & National Institute of Mental Health. (1986). Social foundations of thought and action: A social cognitive theory. Prentice-Hall.
Baraldi, A. N. & Enders, C. K. (2010). An introduction to modern missing data analyses. Journal of School Psychology, 48(1), 5–37.
Bong, M. (2001). Between- and within-domain relations of academic motivation among middle and high school students: Self-efficacy, task value, and achievement goals. Journal of Educational Psychology, 93(1), 23–34.
Brophy, J. (1998). Motivating students to learning. McGraw-Hill.
Corral, N., & Antia, S. D. (1997). Self-talk: Strategies for success in math. Teaching Exceptional Children, 29(4), 42–45.
Clements, D. H., & Sarama, J. (2016). Math, science, and technology in the early grades. The Future of Children, 26(2), 75–94.
Cole, J. S., Bergin, D. A., & Whittaker, T. A. (2008). Predicting student achievement for low stakes tests with effort and task value. Contemporary Educational Psychology, 33(4), 609–624.
Conley, A. M. (2012). Patterns of motivation beliefs: Combining achievement goal and expectancy-value perspectives. Journal of Educational Psychology, 104(1), 32–47.
Csikszentmihalyi, M., & Csikszentmihalyi, I. S. (Eds.). (1988). Optimal experience: Psychological studies of flow in consciousness. Cambridge University Press.
DeBacker, T. K., & Nelson, R. M. (1999). Variations on an expectancy-value model of motivation in science. Contemporary Educational Psychology, 24, 71–94.
Deci, E. L., & Ryan, R. M. (1985). Intrinsic motivation and self-determination in human behavior. Plenum.
Durik, A. M., Vida, M., & Eccles, J. S. (2006). Task values and ability beliefs as predictors of high school literacy choices: A developmental analysis. Journal of Educational Psychology, 98(2), 382–393.
Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. Annual Review of Psychology, 53(1), 109–132.
Eccles, J., 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 motives (pp. 75–146). Freeman.
Feather, N. T. (1992). Expectancy‐value theory and unemployment effects. Journal of Occupational and Organizational Psychology, 65(4), 315–330.
Fryer, L. K., & Ainley, M. (2019). Supporting interest in a study domain: A longitudinal test of the interplay between interest, utility-value, and competence beliefs. Learning and Instruction, 60, 252–262.
Grigg, S., Perera, H. N., McIlveen, P., & Svetleff, Z. (2018). Relations among math self-efficacy, interest, intentions, and achievement: A social cognitive perspective. Contemporary Educational Psychology, 53, 73－86.
Groenwold, R. H. H., White, I. R., Donders, A. R. T., Carpenter, J. R., Altman, D. G., & Moons, K. G. M. (2012). Missing covariate data in clinical research: When and when not to use the missing-indicator method for analysis. Canadian Medical Association Journal, 184(11), 1265－1269.
Guay, F., Ratelle, C. F., & Chanal, J. (2008). Optimal learning in optimal contexts: The role of self-determination in education. Canadian Psychology/Psychologie Canadienne, 49(3), 233－240.
Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), 81–112.
Hidi, S., Berndorff, D., & Ainley, M. (2002). Children’s argument writing, interest and self-efficacy: An intervention study. Learning and Instruction, 12(4), 429–446.
Hong, J.-C., Hwang, M.-Y., Tai, K.-H., & Lin, P.-H. (2018). Improving cognitive certitude with calibration mediated by cognitive anxiety, online learning self-efficacy and interest in learning Chinese pronunciation. Educational Technology Research and Development, 67(3), 597–615.
Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1–55.
Hulleman, C. S., Durik, A. M., Schweigert, S. A., & Harackiewicz, J. M. (2008). Task values, achievement goals, and interest: An integrative analysis. Journal of Educational Psychology, 100(2), 398–416.
Joo, Y. J., Chung, Y. L., & Lee, Y. K. (2011). The structural relationship and latent means analysis of gender among academic self-efficacy, interest, external motivation and science achievement for high school students. Journal of the Korean Association for Science Education, 31(6), 876–886.
Kahn, W. A. (2010). The essence of engagement: Lessons from the field. In S. L. Albrecht (Ed.), Handbook of employee engagement: Perspectives, issues, research and practice (pp. 20–30). Edward Elgar Publishing.
Kim, S., Jiang, Y., & Song, J. (2015). The effects of interest and utility value on mathematics engagement and achievement. In K. A. Renninger, M. Nieswandt, & S. Hidi (Eds.), Interest in mathematics and science learning (pp. 63–78). American Educational Research Association.
Köller, O., Baumert, J., & Schnabel, K. (2001). Does interest matter? The relationship between academic interest and achievement in mathematics. Journal for Research in Mathematics Education, 32(5), 448–470.
Kpolovie, P. J., Joe, A. I. & Okoto, T. (2014). Academic achievement prediction: role of interest in learning and attitude towards school. International Journal of Humanities, Social Science and Education, 1(11), 73–100.
Krapp, A., Hidi, S., & Renninger, K. A. (1992). Interest, learning, and development. In K. A. Renninger, S. Hidi, & A. Krapp (Eds.), The role of interest in learning and development (pp. 3–25). Erlbaum.
Lent, R. W., Brown, S. D., & Hackett, G. (1994). Toward a unifying social cognitive theory of career and academic interest, choice, and performance. Journal of Vocational Behavior, 45, 79–122.
Lent, R. W., Brown, S. D., Gover, M. R., & Nijer, S. K. (1996). Cognitive assessment of the sources of mathematics self-efficacy: A thought-listing analysis. Journal of Career Assessment, 4(1), 33–46.
Lent, R. W., Larkin, K. C., & Brown, S. D. (1989). Relation of self-efficacy to inventoried vocational interests. Journal of Vocational Behavior, 34(3), 279–288.
Liu, J., Wu, Y., & Zhao, F. (2023). The impact of self-efficacy on mathematics academic performance among Chinese high school students. Lecture Notes in Education Psychology and Public Media, 21, 299–306.
Linnenbrink, E. A., & Pintrich, P. R. (2003). The role of self-efficacy beliefs in student engagement and learning in the classroom. Reading & Writing Quarterly, 19, 119–137.
Locke, E., & Latham, G. (2002). Building a practically useful theory of goal setting and task motivation: A 35 year odyssey. American Psychologist, 57(9), 705–717.
Nauta, M. M., Kahn, J. H., Angell, J. W., & Cantarelli, E. A. (2002). Identifying the antecedent in the relation between career interests and self-efficacy: Is it one, the other, or both? Journal of Counseling Psychology, 49(3), 290–301.
Özdemir, Ş., & Pesen, C. (2024). An investigation into the relationships between 8th-grade students’ mathematics self-efficacy perceptions and their motivation and anxiety levels. European Journal of Education Studies, 11(5), 260－290.
Pintrich, P. R. (1999). The role of motivation in promoting and sustaining self-regulated learning. International Journal of Educational Research, 31(6), 459–470.
Pintrich, P. R., & Schunk, D. H. (2002). Motivation in education: Theory, research and applications. (3rd ed.). Pearson/Merrill Prentice Hall.
Rao, N., Moely, B. E., & Sachs, J. (2000). Motivational beliefs, study strategies, and mathematics attainment in high- and low-achieving Chinese secondary school students. Contemporary Educational Psychology, 25(3), 287–316.
Renninger, K. A. (1992). Individual interest and development: Implications for theory and practice. In K. A. Renninger, S. Hidi, & A. Krapp (Eds.), The role of interest in learning and development (pp. 361–395). Erlbaum.
Rozgonjuk, D., Kraav, T., Mikkor, K., Orav-Puurand, K., & Täht, K. (2020). Mathematics anxiety among STEM and social sciences students: The roles of mathematics self-efficacy, and deep and surface approach to learning. International Journal of STEM Education, 7(46), 1–11.
Ryan, R. M., & Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. American Psychologist, 55(1), 68–78.
Ryan, R. M., & Deci, E. L. (2009). Promoting self-determined school engagement: Motivation, learning, and well-being. In K. R. Wenzel & A. Wigfield (Eds.), Handbook of motivation at school (pp. 171–195). Routledge.
Salili, F., & Hau, K.-T. (1994). The effect of teachers’ evaluative feedback on Chinese students’ perception of ability: A cultural and situational analysis. Educational Studies, 20(2), 223–236.
Schunk, D. H. (1982). Effects of effort attributional feedback on children’s perceived self-efficacy and achievement. Journal of Educational Psychology, 74(4), 548–556.
Specht, D. A. (1975). On the evaluation of causal models. Social Science Research, 4(2), 113––133.
Steinmayr, R., & Spinath, B. (2009). The importance of motivation as a predictor of school achievement. Learning and Individual Differences, 19(1), 80–90.
Stevenson, H. W., & Lee, S.-Y. (1996). The academic achievement of Chinese students. In M. H. Bond (Ed.), The handbook of Chinese psychology (pp. 124–142). Oxford University Press.
Stigler, J. W., Smith, S., & Mao, L.-W. (1985). The self-perception of competence by Chinese children. Child Development, 56, 1259–1270.
Topping, K., & Ferguson, N. (2005). Effective literacy teaching behaviours. Journal of Research in Reading, 28(2), 125–143.
Tracey, T. J. G. (2002). Development of interests and competency beliefs: A 1-year longitudinal study of fifth- to eighth-grade students using the ICA-R and structural equation modeling. Journal of Counseling Psychology, 49(2), 148–163.
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.
Wang, M.-T. (2012). Educational and career interests in math: A longitudinal examination of the links between classroom environment, motivational beliefs, and interests. Developmental Psychology, 48(6), 1643–1657.
Wang, M.-T., & Degol, J. (2013). Motivational pathways to STEM career choices: Using expectancy–-value perspective to understand individual and gender differences in STEM fields. Developmental Review, 33(4), 304–340.
Wang, M.-T., & Eccles, J. S. (2013). School context, achievement motivation, and academic engagement: A longitudinal study of school engagement using a multidimensional perspective. Learning and Instruction, 28, 12–23. Wang, X., & Lee, S. (2019). Investigating the psychometric properties of a new survey instrument measuring factors related to upward transfer in STEM fields. The Review of Higher Education, 42, 339–384.
Wang, X., Houang, R. T., Schmidt, W. H., & Kelly, K. S. (in press). Relationship between opportunity to learn, mathematics self-efficacy, and math performance: Evidence from PISA 2012 in 63 countries and economies. International Journal of Science and Mathematics Education. https://doi.org/10.1007/s10763-024-10446-6
Wentzel, K. R., & Wigfield, A. (1998). Academic and social motivational influences on students’ academic performance. Educational Psychology Review, 10(2), 155–175.
Wigfield, A. (1994). Expectancy-value theory of achievement motivation: A developmental perspective. Educational Psychology Review, 6(1). 49–74.
Wigfield, A., & Cambria, J. (2010). Students’ achievement values, goal orientations, and interest: Definitions, development, and relations to achievement outcomes. Developmental Review, 30(1), 1–35.
Wigfield, A., & Eccles, J. S. (2000). Expectancy-value theory of achievement motivation. Contemporary Educational Psychology, 25(1), 68–81.
Wigfield, A., Tonks, S., & Klauda, S. L. (2009). Expectancy-value theory. In K. R. Wentzel & A. Wigfield (Eds.), Handbook of motivation at school (pp. 55–75). Routledge.
Živković, M., Pellizzoni, S., Doz, E., Cuder, A., Mammarella, I., & Passolunghi, M. C. (2023). Math self-efficacy or anxiety? The role of emotional and motivational contribution in math performance. Social Psychology of Education, 26, 579–601.