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.

» More

1. Ball, D. L., & Bass, H. (2009, March) With an eye on the mathematical horizon: Knowing mathematics for teaching to learners’ mathematical futures. Paper presented at the 43rd Jahrestagung der Gesellschaft für Didaktik der Mathematik, Oldenburg, Germany. 
2. Ball, D. L., Thames, M. H., Bass, H., Sleep, L., Lewis, J., & Phelps, G. (2009). A practice-based theory of mathematical knowledge for teaching. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33rd conference of the international group for the psychology of mathematics education (Vol. 1; pp. 95-98). Thessaloniki, Greece: PME. 
3. 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.  doi:10.1177/0022487108324554
4. 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.  
5. Borasi, R. (1996). Reconceiving mathematics instruction: A focus on errors. Santa Barbara, CA: Greenwood Publishing Group.
6. Chazan, D., Herbst, P., & Sela., H (2011). Instructional alternatives via a virtual setting: Rich media supports for teacher development. In O. Zaslavsky & P. Sullivan (Eds.), Constructing knowledge for teaching secondary mathematics: Tasks to enhance prospective and practicing teacher learning (pp. 23-37). New York, NY: Springer. doi:10.1007/978-0-387-09812-8_2
7. Figueiras, L., & Deulofeu, J. (2005). Visualising and conjecturing solutions for Heron’s problem. In M. Bosch (Ed.), Proceedings of the CERME 4 international conference (pp. 420-427). Sant Feliu de Guixols, Spain: CERME. 
8. Heath, T. L. (1921). A history of Greek mathematics (Vols. I&II). New York, NY: Dover. 
9. Herbst, P., & Kosko, K. (2012, November). Mathematical knowledge for teaching high school geometry. Paper presented at the Proceedings of the 34th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Kalamazoo, MI. 
10. 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.  
11. 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. 
12. 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. doi:10.1086/428763
13. Hill, H. C., Sleep, L., Lewis, J., & Ball, D. L. (2007). Assessing teachers’ mathematical knowledge: What knowledge matters and what evidence counts. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 111-156). Charlotte, NC: Information Age. 
14. Jakobsen, A., Thames, M. H., Ribeiro, C. M., & Delaney, S. (2012, July). Using practice to define and distinguish horizon content knowledge. Paper presented at 12th International Congress on Mathematics Education, Seoul, South Korea.  
15. Kersting, N. (2008). Using video clips as item prompts to measure teachers’ knowledge of teaching mathematics. Educational and Psychological Measurement, 68(5), 845-861. doi:10.1177/ 001316 4407313369
16. 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. doi:10.1177/0022487109347875
17. Lin, Y.-C., & Chin, C. (in press). Extending the conception of Horizon Content Knowledge: Fundamental mathematical knowledge and a sample assessment item. Chinese Journal of Science Education.  
18. 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. doi:10.1007/s10649-010-9276-z
19. 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. doi:10.1007/s10857-006-4084-1

APA Format	Lin, Y.-C., & Chin, C. (2014). Developing an Instrument for Capturing High School Teachers’ Mathematics Knowledge for Teaching: An Exploratory Study. Journal of Research in Education Sciences, 59(3), 133-160. doi:10.6209/JORIES.2014.59(3).05