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研究生: 文郁棋
WEN, Yu-Chi
論文名稱: 探討高一學生的數學推理表現特徵
Exploring Characteristics of Tenth Graders’Performance on Mathematical Reasoning
指導教授: 楊凱琳
Yang, Kai-Lin
口試委員: 左台益
Tso, Tai-Yih
林勇吉
Lin, Yung-Chi
楊凱琳
Yang, Kai-Lin
口試日期: 2023/06/29
學位類別: 碩士
Master
系所名稱: 數學系
Department of Mathematics
論文出版年: 2023
畢業學年度: 111
語文別: 中文
論文頁數: 94
中文關鍵詞: 數學推理評量SOLO分類法
研究方法: 內容分析法
DOI URL: http://doi.org/10.6345/NTNU202300916
論文種類: 學術論文
相關次數: 點閱:97下載:47
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  • 本研究旨在透過發展數學推理評量架構設計評量試題,評估試題品質與檢驗此評量架構,並且進一步探討高一學生數學推理之表現特徵。其中根據文獻探討最後結論以Herbert (2021)的三大推理元素作為本研究之推理三元素,分別為分析(Analysing)、推論(Generalising),與驗證(Justifying),並根據本研究有其名詞釋義。進一步以數列級數、排列組合與數據分析的部分數學內容,設計其評量試題,進行前置研究後最終確立正式試題共9題。便利取樣兩所公立高中的高一學生,總共回收604份試題,並將學生回答內容進行編碼與資料分析。
    資料結果顯示,此架構有不錯的試題信度與鑑別度,試題難度上整體來說推論元素較分析元素容易,於試題設計與評分標準上可能尚有討論之處;而構念效度尚未達到標準門檻,可見以此三推理元素發展之架構上還有討論的空間;而不同推理元素與不同數學內容交互作用之下,學生的表現均為顯著;最後則以SOLO分類法探討學生在作答特徵的表現,期許有利於實務面上老師有一基準作為參考,進而針對學生所需加強其數學推理的能力。

    第壹章 緒論 1 第一節 研究動機 1 第二節 研究目的與問題 5 第三節 名詞釋義 6 第貳章 文獻探討 7 第一節 數學推理 7 第二節 數學推理相關實徵研究 19 第參章 研究方法 25 第一節 研究流程 25 第二節 前置研究 26 第三節 正式研究 33 第四節 資料分析 46 第肆章 研究結果 52 第一節 數學推理評量試題 52 第二節 學生在不同推理元素與內容表現 60 第三節 學生在不同推理元素下的作答特徵 62 第伍章 討論與結論 75 第一節 研究結論 75 第二節 研究建議與限制 76 參考文獻 78 附錄 82

    邱皓政(2022)。量化研究與統計分析:SPSS與R資料分析範例解析(第六版四刷)。五南圖書出版股份有限公司。(原著出版年:2009)
    教育部國民與學前教育署(2013)。修正普通高級中學課程綱要。臺北市,教育部。
    教育部(2014)。十二年國民基本教育課程綱要總綱。臺北市,教育部。
    Anderson, J. C., & Gerbing, D. W. (1988). Structural equation modeling in practice: A review and recommended two-step approach. Psychological bulletin, 103(3), 411.
    Australian Curriculum, Assessment and Reporting Authority [ACARA]. Foundation to year 10 curriculum: Mathematics for Key ideas. https://shorturl.at/ansUZ
    Ball, D. L., & Bass, H. (2003). Making mathematics reasonable in school. A research companion to principles and standards for school mathematics, 27-44.
    Bentler, P. M. (1982). Confirmatory factor analysis via noniterative estimation: A fast, inexpensive method. Journal of Marketing Research, 19(4), 417-424.
    Bentler, P. M., & Bonett, D. G. (1980). Significance tests and goodness of fit in the analysis of covariance structures. Psychological bulletin, 88(3), 588.
    Biggs, J. B., & Collis, K. F. (1982). The psychological structure of creative writing. Australian Journal of Education, 26(1), 59-70.
    Boesen, J., Lithner, J., & Palm, T. (2006). The relation between test task requirements and the reasoning used by students.
    Department of Mathematics and Mathemical Statistics, Umeå universitet.
    Brodie, K. (2009). Teaching mathematical reasoning in secondary school classrooms (Vol. 775).Springer Science & Business Media.
    Christou, C., & Papageorgiou, E. (2007). A framework of mathematics inductive reasoning. Learning and Instruction, 17(1), 55-66.
    Davidson, A., Herbert, S., & Bragg, L. A. (2019). Supporting elementary teachers’planning and assessing of mathematical reasoning. International Journal of Science and Mathematics Education, 17, 1151-1171.
    Department for Education (2021). National curriculum in England: mathematics programmes of study. https://shorturl.at/oGSZ0
    Doll, W. J., Xia, W., & Torkzadeh, G. (1994). A confirmatory factor analysis of the end-user computing satisfaction instrument. MIS quarterly, 453-461.
    Hee, O. C. (2014). Validity and Reliability of the Customer-Oriented Behaviour Scale in the Health Tourism Hospitals in Malaysia. International Journal of Caring Sciences, 7(3).
    Herbert, S. (2021). Overcoming challenges in assessing mathematical reasoning. Australian Journal of Teacher Education (Online), 46(8), 17-30.
    Herbert, S., Vale, C., Bragg, L. A., Loong, E., & Widjaja, W. (2015). A framework for primary teachers’ perceptions of mathematical reasoning. International Journal of Educational Research, 74, 26-37.
    Hu, L. T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis:Conventional criteria versus new alternatives. Structural equation modeling: a multidisciplinary journal, 6(1), 1-55.
    Jeannotte, D., & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics, 96, 1-16.
    Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics (Vol. 2101). National research council (Ed.). Washington, DC: National Academy Press.
    Lannin, J., Ellis, A. B., & Elliot, R. (2011). Developing essential understanding of mathematical reasoning. NCTM.
    Lestary, R., & Rahardi, R. (2019, October). An analysis of students’ mathematical reasoning ability in statistic problem solving based on structure of the observed learning outcome taxonomy. In Journal of Physics: Conference Series (Vol. 1320, No. 1, p. 012055). IOP Publishing.
    Lithner, J. (2000). Mathematical reasoning in task solving. Educational studies in mathematics, 165-190.
    Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in mathematics, 67, 255-276.
    Marsh, H. W., Balla, J. R., & McDonald, R. P. (1988). Goodness-of-fit indexes in confirmatory factor analysis: The effect of sample size. Psychological bulletin, 103(3), 391.
    Mata-Pereira, J., & da Ponte, J. P. (2017). Enhancing students’ mathematical reasoning in the classroom: teacher actions facilitating generalization and justification. Educational Studies in Mathematics, 96(2), 169-186.
    McDonald, R. P., & Ho, M. H. R. (2002). Principles and practice in reporting structural equation analyses. Psychological methods, 7(1), 64.
    McDonald, R. P., & Marsh, H. W. (1990). Choosing a multivariate model: Noncentrality and goodness of fit. Psychological bulletin, 107(2), 247.
    Mullis, I. V., Martin, M. O., & von Davier, M. (2021). TIMSS 2023 Assessment Frameworks. International Association for the Evaluation of Educational Achievement.
    National Council of Teachers of Mathematics. (n,d) Common Core State Standards for Mathematics. https://www.nctm.org/ccssm/
    Niiniluoto, I. (1999). Defending abduction. Philosophy of science, 66(S3), S436-S451.
    Niss, M. (2003, January). Mathematical competencies and the learning of mathematics: The Danish KOM project. In 3rd Mediterranean conference on mathematical education (pp. 115-124).
    Peirce, C. S. (1878b). Deduction, induction, and hypothesis. Popular Science Monthly,12, 470-482.
    Pisa, O. E. C. D. (2022). Mathematics Framework (Draft). Retrieved from PISA. https://shorturl.at/xQSV3
    Potter, M. K., & Kustra, E. (2012). A primer on learning outcomes and the SOLO taxonomy. Course Design for Constructive Alignment,(Winter 2012), 1-22.
    Raines-Eudy, R. (2000). Using structural equation modeling to test for differential reliability and validity: An empirical demonstration. Structural equation modeling, 7(1), 124-141.
    Rohati, R., Kusumah, Y. S., & Kusnandi, K. (2022). The development of analytical rubrics: An avenue to assess students’ mathematical reasoning behavior. Cypriot J. Educ. Sci, 17, 2553-2566.
    RUSSELL, J. S. (1999). Mathematical Reasoning in the Elementary Grades. Developing Mathematical Reasoning in Grades K-12. 1999Yearbook, NCTM, 1-12.
    Sari, Y. M., Kartowagiran, B., & Retnawati, H. (2020). Mathematics teachers’challenges in implementing reasoning and proof assessment a case of Indonesian teachers. Universal Journal of Educational Research, 8(7), 3287-3293.
    Singapore Ministry of Education (2020). Mathematics Syllabuses. Ministry of Education, Singapore. https://shorturl.at/zHYZ2
    Steen, L. A. (1999). Twenty Questions about Mathematical Reasoning. In Stiff, L. V., & Curcio, F. R. (Eds.), Developing Mathematical Reasoning in Grades K-12 (pp. 270-285). National Council of Teachers of Mathematics.
    Tabachnick, B. G., Fidell, L. S., & Ullman, J. B. (2013). Using multivariate statistics (Vol. 6, pp. 497-516). Boston, MA: pearson.
    Ho, Yu Chong. (1994, April 4-8). Abduction? Deduction? Induction? Is There a Logic of Exploratory Data Analysis? [Paper presentation].Annual Meeting of the American Educational Research Association 1994, New Orleans, Louisiana.

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