Developing an Instrument for Capturing High School Teachers' Mathematics Knowledge for Teaching: An Exploratory Study

發展高中教師教數學所需的知識之問卷：探索性研究

10.6209/JORIES.2014.59(3).05

林勇吉(Yung-Chi Lin)；金鈐(Chien Chin)

高中數學 ； 評量工具 ； 問卷發展 ； 教數學所需的知識 ； 教師知識 ； high school mathematics ； instrument ； item development ； mathematics knowledge for teaching (MKT) ； teacher knowledge

教育科學研究期刊

59卷3期（2014 / 09 / 01）

133 - 160

英文

本研究旨在描述如何發展高中教師「教數學所需的知識」（MKT）問卷。研究結果以一個具代表性的問題為例。呈現這個代表性問題如何發展與不斷精緻，最後報導本問卷的前導測驗結果。本研究發現三個有效的創造問卷的策略：一、使用具有「關鍵」教學知識的數學問題（教導這個數學問題，需要一個基礎、重要且不能忽略的核心知識）。二、使用學生非例行性解法。三、使用教師在實際教學上的錯誤。本研究希望提供相關領域研究者，如何設計MKT問卷的參考依據。

This paper addresses an effort to design and test a set of items for assessing the mathematics knowledge for teaching. The paper begins by describing how a representative item was developed based on three experienced high school teachers' analyzing classroom instruction. Subsequently, item refinement by two experts is documented. Finally, the initial results of a pilot-test of a focus group of 11 high school mathematics teachers are reported. This study revealed three useful methods for creating items for assessment: (1) using mathematics problems containing certain key mathematical ideas; (2) using nonstandard approaches of students that are unfamiliar to the teachers; and (3) using the errors of teachers.

1. Heath, T. L. (1921). A history of Greek mathematics (Vols. I&II). New York, NY: Dover
2. Ball, D. L.,Bass, H.(2009).With an eye on the mathematical horizon: Knowing mathematics for teaching to learners' mathematical futures.43rd Jahrestagung der Gesellschaft für Didaktik der Mathematik,Oldenburg, Germany:
3. Ball, D. L.,Thames, M. H.,Bass, H.,Sleep, L.,Lewis, J.,Phelps, G.(2009).A practice-based theory of mathematical knowledge for teaching.Proceedings of the 33rd conference of the international group for the psychology of mathematics education,Thessaloniki, Greece:
4. Ball, D. L.,Thames, M. H.,Phelps, G.(2008).Content knowledge for teaching: What makes it special?.Journal of Teacher Education,59(5),389-407.
5. Bell, C. A.,Wilson, S. M.,Higgins, T.,McCoach, D. B.(2010).Measuring the effects of professional development on teacher knowledge: The case of developing mathematical ideas.Journal for Research in Mathematics Education,41(5),479-512.
6. Borasi, R.(1996).Reconceiving mathematics instruction: A focus on errors.Santa Barbara, CA:Greenwood Publishing Group.
7. Figueiras, L.,Deulofeu, J.(2005).Visualising and conjecturing solutions for Heron's problem.Proceedings of the CERME 4 international conference,Sant Feliu de Guixols, Spain:
8. Herbst, P.,Kosko, K.(2012).Mathematical knowledge for teaching high school geometry.Proceedings of the 34th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education,Kalamazoo, MI.:
9. Hill, H. C.(2010).The nature and predictors of elementary teachers' mathematical knowledge for teaching.Journal for Research in Mathematics Education,41(5),513-545.
10. Hill, H. C.,Ball, D. L.,Schilling, S. G.(2008).Unpacking "pedagogical content knowledge": Conceptualizing and measuring teachers' topic-specific knowledge of students.Journal for Research in Mathematics Education,39(4),372-400.
11. Hill, H. C.,Schilling, S. G.,Ball, D. L.(2004).Developing measures of teachers' mathematics knowledge for teaching.The Elementary School Journal,105(1),11-30.
12. Jakobsen, A.,Thames, M. H.,Ribeiro, C. M.,Delaney, S.(2012).Using practice to define and distinguish horizon content knowledge.12th International Congress on Mathematics Education,Seoul, South Korea:
13. Kersting, N.(2008).Using video clips as item prompts to measure teachers' knowledge of teaching mathematics.Educational and Psychological Measurement,68(5),845-861.
14. Kersting, N. B.,Givvin, K. B.,Sotelo, F. L.,Stigler, J. W.(2010).Teachers' analyses of classroom video predict student learning: Further explorations of a novel measure of teacher knowledge.Journal of Teacher Education,61(1-2),172-181.
15. Lester, F. K.(Ed.)(2007).Second handbook of research on mathematics teaching and learning.Charlotte, NC:Information Age.
16. Lin, Y.-C.,Chin, C..Extending the conception of Horizon Content Knowledge: Fundamental mathematical knowledge and a sample assessment item.Chinese Journal of Science Education
17. Manizade, A. G.,Mason, M. M.(2011).Using Delphi methodology to design assessments of teachers' pedagogical content knowledge.Educational Studies in Mathematics,76(2),183-207.
18. Osana, H. P.,Lacroix, G. L.,Tucker, B. J.,Desrosiers, C.(2006).The role of content knowledge and problem features on preservice teachers' appraisal of elementary mathematics tasks.Journal of Mathematics Teacher Education,9(4),347-380.
19. Zaslavsky, O.(Ed.),Sullivan, P.(Ed.)(2011).Constructing knowledge for teaching secondary mathematics: Tasks to enhance prospective and practicing teacher learning.New York, NY:Springer.

1. Lin, Yung-Chi,Chin, Chien(2015).Extending the Conception of Horizon Content Knowledge: Fundamental Mathematical Knowledge and Its Sample Assessment Item.科學教育學刊,23(1),1-22.