數學建模評量規準之研究__臺灣人文及社會科學引文索引資料庫

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題名：	數學建模評量規準之研究
書刊名：	科學教育學刊
作者：	楊凱琳／林福來／蕭志如
作者(外文)：	Yang, Kai-lin／Lin, Fou-lai／Hsiao, Chih-ru
出版日期：	2012
卷期：	20:4
頁次：	頁319-342
主題關鍵詞：	概化理論；實作評量；數學建模；Generalizability；Performance assessment；Mathematical modeling
原始連結：	連回原系統網址
相關次數：	被引用次數:期刊(3) 博士論文(0) 專書(0) 專書論文(0) 排除自我引用:3 共同引用:13 點閱:73

數學建模問題是一種具有真實或逼真的情境問題，不同的解題者可能會有不同的考量和方法完成這樣複雜的任務。因此，數學建模問題也是一種能啟發學生主動學習的開放性任務。此外，在考量給予適當的評量規準有助於促進學生的數學學習之下，本研究想藉由實作評量與概化理論來探討評量數學建模表現的評量規準。首先，參考文獻上提出的建模歷程共同元素，再透過數學建模專家與國中數學教師的意見調整元素及其內涵，希望此規準能夠涵蓋數學建模中各種想法的共同元素，以完整地評量各種想法的長處與不足。形成數學建模表現評量規準後，基於概化理論檢驗此評量規準的變異來源並計算不同評分人數的概化係數和可靠性係數。最後，以準實驗研究檢驗其對學生數學建模表現的影響。結果顯示，在引模、探模和展模問題中，評分者在各個面向給分的一致性還不錯，而且如果有兩位評分者時，概化係數和可靠度係數皆能達至 .86的水準。另外，在學生尚未參與建構本評量規準的情況下，提供實驗組評量規準的學生數學建模表現仍顯著優於未提供本評量規準的對照組學生。

以文找文

Mathematical modeling problems are problems with real or realistic situations. Different problem solvers may use diverse methods to solve the same modeling problems, and thus we assumed that modeling problems are the type of tasks that can elicit students’ active learning. Moreover, taking into account that providing appropriate assessment is helpful to facilitate students’ learning of mathematics, this study aimed at constructing a rubric for assessing mathematical modeling performance based on generalizability theory and performance assessment. In order to construct a complete rubric which could be used to assess the strength and weakness of varied ideas for solving modeling problems, we firstly referred to the elements of modeling process in literature. Next, we modified the elements and their content according to a mathematics modeling expert and mathematics teachers’ opinions. After formulating the rubric, its generalizability and dependability was evaluated by the generalizability theory, and a quasi-experimental study was implemented to assess its effect on students’ performance in mathematical modeling. The results show that the agreement among the raters was good and both the generalizability coefficient and the dependability index with two raters were above .86 for each rating facet of each modeling task. Moreover, students who were provided this rubric performed better on the modeling task than students who were not provided this rubric.

以文找文

期刊論文
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2.	Meyer, C. A.(1992)。What's the difference between authentic and performance assessment。Educational Leadership，49(8)，39-41。
3.	Black, P.、Wiliam, D.(1998)。Inside the black box: Raising standards through classroom assessment。Phi Delta Kappan，80(2)，139-148。
4.	楊凱琳、林福來(20061000)。探討高中數學教學融入建模活動的支撐策略及促進參與教師反思的潛在機制。科學教育學刊，14(5)，517-543。延伸查詢
5.	Messick, S.(1995)。Validity of Psychological Assessment: Validation of Inferences from Persons' Responses and Performances as Scientific Inquiry into Score Meaning。American Psychologist，50(9)，741-749。
6.	English, L. D.(2006)。Mathematical modeling in the primary school: Children’s construction of a consumer guide。Educational Studies in Mathematics，63(3)，303-323。
7.	Ferri, R. B.(2006)。Theoretical and empirical differentiations of phases in the modelling process。Zentralblatt fur Didaktik der Mathematik，38(2)，86-95。
8.	Fuchs, L. S.、Fuchs, D.、Karns, K.、Hamlett, B. L.、ICatzaroff, M.(1999)。Mathematics performance assessment in the classroom: Effects on teacher planning and student problem solving。American Educational Research Journal，36(3)，609-646。
9.	Galbraith, P.、Stillman, G.(2006)。A framework for identifying student blockages during transitions in the modelling process。Zentralblatt fur Didaktik der Mathematik，38(2)，143-162。
10.	Haines, C.、Crouch, R.(2005)。Applying mathematics: Making multiple-choice questions work。Teaching Mathematics and its Applications，24(2/3)，107-113。
11.	Haynes, S. N.、Richard, D. C. S.、Kubany, E. S.(1995)。Content validity in psychological assessment: A functional approach to concepts and methods。Psychological Assessment，7(3)，238-247。
12.	Kilfeather, P.、O’Leary, M.、Varley, J.(2006)。Adapting science performance tasks developed in different countries for use in Irish primary schools。Irish Educational Studies，25(1)，3-33。
13.	Leahy, S.、Lyon, C.、Thompson, M.、Wiliam, D.(2005)。Classroom assessment: Minute by minute, day by day。Educational Leadership，63(3)，18-24。
14.	Baghaei, P.、Amrahi, N.(2011)。The effects of the number of options on the psychometric characteristics of multiple choice items。Psychological Test and Assessment Modeling，53(2)，192-211。
15.	Brennan, R. L.、Johnson, E. G.(1995)。Generalizability of performance assessment。Educational Measurement: Issues and Practices，14(4)，9-12。
16.	Brookhart, S. M.(1997)。Effects of the classroom assessment environment on mathematics and science achievement。The Journal of Educational Research，90(6)，323-330。
17.	Lin, F. L.、Yang, K. L.(2005)。Distinctive characteristics of mathematical thinking in non-modelling friendly environment。Teaching Mathematics and Its Applications，24(2/3)，97-106。
18.	Miller, M. D.、Linn, R. L.(2000)。Validation of performance-based assessments。Applied Psychological Measurement，24(4)，367-378。
19.	Mousoulides., N.、Sriraman, B.、Christou, C.(2007)。From problem solving to modelling: The emergence of models and modelling perspectives。Nordic Studies in Mathematics Education，12(1)，23-47。
20.	Shepard, L. A.(1993)。Evaluating test validity。Review of Research in Education，19，405-450。
21.	Sriraman, B.、Lesh, R.(2006)。Modeling conceptions revisited。Zentralblatt fur Didaktik der Mathematik，38(3)，247-254。
22.	Stillman, G.、Brown, J.、Galbraith, P.(2010)。Researching applications and mathematical modeling in mathematics learning and teaching。Mathematics Education Research Journal，22(2)，1-6。
23.	Sun, A.、Valiga, M. J.、Gao, X.(1997)。Using generalizability theory to assess the reliability of student ratings of academic advising。The Journal of Experimental Education，65(4)，367-379。
24.	Trevisan, M. S.、Davis, D. C.、Calkins, D. E.、Gentili, K. L.(1999)。Designing sound scoring criteria for assessing student performance。Journal of Engineering Education，55(1)，79-85。
25.	Van Leeuwen, D. M.(1997)。Assessing reliability with generalizability theory: An application to inter-rater reliability。Journal of Agricultural Education，38(3)，36-42。
26.	Zbiek, R. M.、Conner, A.(2006)。Beyond motivation: Exploring mathematical modeling as a context for deepening students’ understandings of curricular mathematics。Educational Studies in Mathematics，63(1)，89-112。

會議論文
1.	楊凱琳、林福來、蕭志如(2008)。概念化數學建模表現的評量規準。彰化市。延伸查詢
2.	楊凱琳、楊子錕(2008)。在數學建模問題脈絡下探討個案學生的思維特徵。中華民國第24屆科學教育年會。彰化市：國立彰化師範大學。延伸查詢

學位論文
1.	Hjalmarson, M. A.(2004)。Designing presentation tools: A window into mathematics teacher practice。Purdue University，West Lafayette, IN。

圖書
1.	Organization for Economic Cooperation and Development(2006)。Assessing scientific, reading and mathematical literacy: A framework for PISA 2006。OECD。
2.	Mason, J.、Johnston-Wilder, S.(2004)。Fundamental Constructs in Mathematics Education。Routledge Falmer。
3.	Earl, Lorna M.、Marzano, Robert J.、Guskey, Thomas R.(2003)。Assessment as learning: using classroom assessment to maximize student learning。Thousand Oaks, Calif.：Corwin Press。
4.	Brennan, R. L.(2001)。Generalizability Theory。New York, NY：Springer-Verlag。
5.	Shavelson, Richard J.、Webb, Noreen M.(1991)。Generalizability Theory: A Primer。Newbury Park, California：Sage。
6.	Stiggins, Richard J.(1994)。Student-centered classroom assessment。New York, NY：Macmillan Publishing Company。
7.	Linn, R. L.、Miller, M. D.(2005)。Measurement and assessment in teaching。Upper Saddle River, NJ：Merrill。
8.	Freudenthal, H.(1991)。Revisiting Mathematics Education: China Lectures。Dordrecht。
9.	李坤崇(2006)。教學評量。台北：心理。延伸查詢
10.	Nunnally, Jum C.(1967)。Psychometric Theory。McGraw-Hill。
11.	Ellerton, N. F.、Clarkson, P. C.(1996)。Language factors in mathematics teaching and learning。International handbook of mathematics education \\ A. J. Bishop (Ed.)。Dordrecht, The Netherlands。
12.	Glickman-Bond, J.、Rose, K.(2006)。Creating and using rubrics in today’s classrooms。Norwood, MA。
13.	Lesh, R.、Doerr, H. M,(2003)。Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching。Mahwah, NJ。
14.	Lesh, R.、Zawojewski, J. S.(2007)。Problem solving and modeling。Second handbook of research on mathematics teaching and learning \\ F. K. Lester (Ed.)。Greenwich, CT。
15.	Bell, A.、Burkhardt, H.、Swan, M.(1992)。Balanced, assessment of mathematical performance。Assessment of authentic performance in school mathematics \\ R. Lesh ; S. J. Lamon (Eds.)。Washington, DC。
16.	Blum, W.(1993)。Mathematical modelling in mathematics education and instruction。Teaching and learning mathematics in context \\ T. Breiteig ; I. Huntley ; G. KaiserMessmer (Eds.)。London。
17.	Mason, J.、Davis, J.(1991)。Modelling with mathematics in primaiy and secondaiy schools。Geelong, Australia。
18.	Messick, S.(1996)。Validity of performance assessments。Technical issues in large-scale performance assessment \\ G. W. Phillips (Ed.)。Washington DC。
19.	Niss, M.(2001)。Issues and problems of research on the teaching and learning of applications and modelling。Modelling and mathematics education: ICTMA 9: Applications in science and technology \\ J. F. Matos ; S. K. Houston ; W. Blum ; S. P. Carreira (Eds.)。Chichester, UK。
20.	Reddy, V.(2007)。Mathematics and science achievement at South African schools in TIMSS 2003。Cape Town, South Africa。
21.	Stiggins, R. J.(2005)。Student-involved assessment for learning。Upper Saddle River, NJ。
22.	Turner, R.(2007)。Modelling and applications in PISA。Modelling and applications in mathematics education: The 14th ICMI study \\ W. Blum ; P. L. Galbraith ; H.-W. Henn ; M. Niss (Eds.)。New York。

其他
1.	黃榮村(2003)。國民中小學九年一貫課程之問題與檢討(中華民國九十二年十月十三日立法院第五屆第四會期)，0。延伸查詢
2.	Niss, M.(2002)。Mathematical competencies and the learning of mathematics: The Danish KOM project，http://www7.nationalacademies.orgmseb/mathematicalcompetencies_and_the_leaming_of_mathematics.pdf， 2004/10/15。
3.	Liang, X.，Creasy, K.(2004)。Classroom assessment in web-bqsed instructional environment: Instructors' experience。
4.	Dickinson, W. B.，Onwuegbuzie, A. J.，Hines, C.，Hall, B. W.(2007)。Summalive assessment strategies for statistical learning: Development, administration, and scoring of authentic and performance assessments。

圖書論文
1.	Resnick, Lauren B.、Resnick, Daniel P.(1992)。Assessing the Thinking Curriculum: New Tools for Educational Reform。Changing Assessments: Alternative Views of Aptitude, Achievement and Instruction。Kluwer Academic Publishers。
2.	Lange, J. D.(1996)。Using and Applying Mathematics in Education。International Handbook of Mathematics Education。Dordrecht：Kluwer Academic Publishers。
3.	Schoenfeld, A. H.(1992)。Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics。Handbook of research on mathematics teaching and learning: A project of the national council of teachers of mathematics。New York：Macmillan。
4.	Baron, J. B.(1991)。Performance assessment: Blurring the edges of assessment, curriculum, and instruction。Science assessment in the service of reform。Washington, DC：American Association for the Advancement of Science。

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