Validation of The Mathematical Knowledge For Teaching Statistics Instrument

Oktay MERCİMEK, Ayhan Kürşat ERBAŞ


The purpose of this study is to assess preservice teachers’ mathematical knowledge for teaching statistics (MKT-S) and identify the relationship between the components of this knowledge. For this purpose, MKT-S instrument consisting of two dimensions, ‘content knowledge’ (CK) and ‘pedagogical content knowledge’ (PCK) was developed, and applied to 659 preservice middle school mathematics teachers (PTs). Confirmatory factor analysis showed that CK and PCK are two different dimensions of mathematical knowledge of teaching statistics. Third year and fourth year preservice teachers’ factor scores were significantly different and fourth year preservice teachers’ factor scores were slightly higher. It was found that CK factor scores were highly correlated with PCK factor scores. The reliability levels were 0.65 for CK factor scores and 0.76 for PCK factor scores. MKT-S instrument developed in this study has several implications for teacher education. MKT-S instrument can be used to evaluate efficiency of PTs’ mathematical knowledge for teaching statistics. Instrument can be adapted for in-service teachers.

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An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school mathematics teachers in China and the U.S. Journal of Mathematics Teacher Education, 7(2), 145–172.

Ball, D. L. (2002). Knowing mathematics for teaching: Relations between research and practice. Mathematics and Education Reform Newsletter, 14(3), 1-5.

Barrett, P. (2007). Structural equation modelling: Adjudging model fit. Personality and Individual Differences, 42, 815-824.

Blömeke, S., Houang, R. T., & Suhl, U. (2011). TEDS-M: Diagnosing teacher knowledge by applying multidimensional item response theory and multiple-group models. IERI Monograph Series: Issues and Methodologies in Large-Scale Assessments, 4, 109-129. Retrieved May 10, 2013, from

Borko, H., Eisenhart, M., Brown, C. A., Underhill, R. G., Jones, D., & Agard, P. C. (1992). Learning to teach hard mathematics: Do novice teachers and their instructors give up too easily?. Journal for Research in Mathematics Education, 194-222.

Cartwright. F., (2013). IATA Manual. Retrieved June 25, 2013, from

Fan, L., & Cheong, N. P. (2002). Investigating the sources of Singaporean mathematics teachers' pedagogical knowledge. In D. Edge & B. H. Yeap (Eds.), Mathematics education for a knowledge-based era : Vol. 2 (pp. 224-23 1). Singapore: AME.

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.

Hill, H.C., Schilling, S.G., & Ball, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching. Elementary School Journal, 105, 11-30.

Hill, H.C., Rowan, B., & Ball, D.L. (2005) Effects of teachers' mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42, 371-406.

Krauss, S., Brunner, M., Kunter, M., Baumert, J., Blum, W., Neubrand, M., & Jordan, A. (2008). Pedagogical content knowledge and content knowledge of secondary mathematics teachers. Journal of Educational Psychology, 100(3), 716-725.

Mercimek, O. (2013). Assessment of Preservice Mathematics Teachers’ Knowledge For Teaching Statistics (Unpublished doctoral thesis). Middle East Technical University, Turkey

Mullis, I. V. S., Martin, M. O., Ruddock, G. J., O’Sullivan C. Y., Arora, A. & Erberber, E.. (2005). TIMSS 2007 assessment frameworks. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College

Muthén, L.K. and Muthén, B.O. (1998-2012). Mplus user’s guide (7th ed.). Los Angeles, CA: Muthén & Muthén

Muthen, L. K., & Muthen, B. O. (2006). IRT in Mplus. Retrieved March 25, 2013, from

OSYM (2008). Table 4: University Student Capacities for Bachelor Degree Level. Retrieved September 23, 2010, from 2008/2008_OSYS_TERCIH_KILAVUZU/6_tablo4.pdf

OSYM (2009). Table 4: University Student Capacities for Bachelor Degree Level. Retrieved September 23, 2010, from

Schmidt, W., Tatto, M.T., Bankov, K., Blomeke, S., Cedillo, T., Cogan, L., Han, S. I., Houang, R., Hsieh, F. J., Paine, L., Santillan, M., & Schwille, J. (2007). The preparation gap: Teacher education for middle school mathematics in six countries (MT21 report). East Lansing, MI: Michigan State University. Retrieved February 25, 2010, from

Shulman, L. S. (1986). Those Who Understand: Knowledge Growth in Teaching. Educational Researcher, 15(2), 4-14

Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard educational review, 57(1), 1-23.

Tatto, M. T., Schwille, J., Senk, S., Ingvarson, L., Peck, R., & Rowley, G. (2008). Teacher Education and Development Study in Mathematics (TEDS-M): Conceptual framework. East Lansing, MI: Teacher Education and Development International Study Center, College of Education, Michigan State University.


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