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The nature and development of middle school mathematics teachers’ knowledge

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Abstract

In this article, we report on the use of a teacher profiling instrument with 62 middle school teachers at the start of a 3-year professional learning programme. The instrument was designed to assess the aspects of teachers’ knowledge identified by Shulman (1987) refined by Ball et al. (2008) and extended to include teachers’ confidence to use and teach various topics in the middle school mathematics curriculum and their beliefs about mathematics teaching and learning. Based on a hierarchical coding of items, the application of the partial credit Rasch model revealed that the profile items were measuring a single underlying construct and suggested that the various facets of teacher knowledge develop together. We describe the characteristics of four levels of the hierarchical construct measuring teacher knowledge and understanding for teaching mathematics in the middle years of schooling, and discuss the unique affordances of a holistic view of teacher knowledge in contrast to considerations of multiple knowledge categories.

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References

  • Adams, R. J., & Khoo, S. T. (1996). Quest: Interactive item analysis system. Version 2.1 [computer software]. Melbourne: Australian Council for Educational Research.

    Google Scholar 

  • Andrich, D. (1978). A rating scale formulation for ordered response categories. Psychometrika, 43, 561–573.

    Article  Google Scholar 

  • Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 83–104). Westport, CT: Ablex.

    Google Scholar 

  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it so special? Journal of Teacher Education, 59(5), 389–407.

    Article  Google Scholar 

  • Beswick, K. (2005). The beliefs/practice connection in broadly defined contexts. Mathematics Education Research Journal, 17(2), 39–68.

    Article  Google Scholar 

  • Beswick, K. (2007). Teachers’ beliefs that matter in secondary mathematics classrooms. Educational Studies in Mathematics, 65(1), 95–120.

    Article  Google Scholar 

  • Beswick, K. (2009). School mathematics and mathematicians’ mathematics: Teachers’ beliefs about mathematics. In M. Tzekaki, M. Kaldrimidou, & S. Haralambos (Eds.), Proceedings of the 33rd conference of the international group for the psychology of mathematics education (Vol. 2, pp. 153–160). Thessaloniki: IGPME.

    Google Scholar 

  • Beswick, K., Watson, J., & Brown, N. (2006). Teachers’ confidence and beliefs and their students’ attitudes to mathematics. In P. Grootenboer, R. Zevenbergen, & M. Chinnappan (Eds.), Identities, cultures and learning spaces: Proceedings of the 29th annual conference of the mathematics education research group of Australasia (Vol. 1, pp. 68–75). Adelaide: Mathematics Education Research Group of Australasia.

    Google Scholar 

  • Bond, T. G., & Fox, C. M. (2007). Applying the Rasch model: Fundamental measurement in the human sciences (2nd ed.). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Callingham, R., & Watson, J. (2004). A developmental scale of mental computation with part-whole numbers. Mathematics Education Research Journal, 16(2), 69–86.

    Article  Google Scholar 

  • Callingham, R., & Watson, J. (2005). Measuring statistical literacy. Journal of Applied Measurement, 6(1), 19–47.

    Google Scholar 

  • Chick, H. L., & Pierce, R. (2008). Issues associated with using examples in teaching statistics. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano, & A. Sepulveda (Eds.), Proceedings of the joint meeting of PME 32 and PME-NA XXX (Vol. 2, pp. 321–328). Mexico: Cinvestav-UMSNH.

    Google Scholar 

  • Chick, H. L., Baker, M., Pham, T., & Cheng, H. (2006). Aspects of teachers’ pedagogical content knowledge for decimals. In J. Novotná, H. Moraová, M. Ktátká, & N. Stehlíková (Eds.), Proceedings of the 30th annual conference of the international group for the psychology of mathematics education (Vol. 2, pp. 297–304). Prague: PME.

    Google Scholar 

  • Ernest, P. (1989). The knowledge, beliefs and attitudes of the mathematics teacher: A model. Journal of Education for Teaching, 15(1), 13–33.

    Article  Google Scholar 

  • Farmer, J. D., Gerretson, H., & Lassak, M. (2003). What teachers take from professional development. Journal of Mathematics Teacher Education, 6, 331–360.

    Article  Google Scholar 

  • Fisher, W. P. (1994). The Rasch debate: Validity and revolution in educational measurement. In M. Wilson (Ed.), Objective measurement (Vol. 2, pp. 36–72). Norwood, NJ: Ablex.

    Google Scholar 

  • Graven, M. (2004). Investigating mathematics teacher learning within an in-service community of practice: The centrality of confidence. Educational Studies in Mathematics, 57, 177–211.

    Article  Google Scholar 

  • Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406.

    Article  Google Scholar 

  • Hill, H. C., Sleep, L., Lewis, J. M., & Ball, D. L. (2007). Assessing teachers’ mathematical knowledge: What knowledge matters and what evidence counts? In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 111–155). Charlotte, NC: Information Age Publishing.

    Google Scholar 

  • Kanes, C., & Nisbet, S. (1996). Mathematics teachers’ knowledge bases: Implications for teacher education. Asia-Pacific Journal of Teacher Education, 24(2), 159–171.

    Article  Google Scholar 

  • Keeves, J. P., & Alagumalai, S. (1999). New approaches to measurement. In G. N. Masters & J. P. Keeves (Eds.), Advances in measurement in educational research and assessment (pp. 23–42). Oxford: Pergamon.

    Google Scholar 

  • Linacre, J. M. (1991). Winsteps Rasch measurement users guide. Chicago: MESA Press. From http://www.winsteps.com/aftp/winsteps.pdf. Retrieved 14 Dec 2007.

  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149–174.

    Article  Google Scholar 

  • Messick, S. (1989). Validity. In R. Linn (Ed.), Educational measurement (3rd ed., pp. 13–103). New York: American Council on Education and Macmillan Publishing Company.

    Google Scholar 

  • Mewborn, D. S. (2001). Teachers’ content knowledge, teacher education, and their effects on the preparation of elementary teachers in the United States. Mathematics Teacher Education and Development, 3, 28–36.

    Google Scholar 

  • Organisation for Economic Co-operation, Development. (2004). Learning for tomorrow’s world: First results from PISA 2003. Paris: Author.

    Google Scholar 

  • Rasch, G. (1980). Probabilistic models for some intelligence and attainment tests. Chicago: University of Chicago Press. (original work published 1960).

    Google Scholar 

  • Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1–22.

    Google Scholar 

  • Stocking, M. L. (1999). Item response theory. In G. N. Masters & J. P. Keeves (Eds.), Advances in measurement in educational research and assessment (pp. 55–63). Oxford: Pergamon.

    Google Scholar 

  • Watson, J. (2001). Profiling teachers’ competence and confidence to teach particular mathematics topics: The case of chance and data. Journal of Mathematics Teacher Education, 4, 305–337.

    Article  Google Scholar 

  • Watson, J., & Callingham, R. (2004). Statistical literacy: From idiosyncratic to critical thinking. In G. Burrill & M. Camden (Eds.), Curricular development in statistics education: International Association for Statistical Education roundtable (pp. 116–137). Lund: IASE.

    Google Scholar 

  • Watson, A., & De Geest, E. (2005). Principled teaching for deep progress: Improving mathematical learning beyond methods and materials. Educational Studies in Mathematics, 58(2), 209–234.

    Article  Google Scholar 

  • Watson, J. M., Beswick, K., & Brown, N. (2006a). Teacher’s knowledge of their students as learners and how to intervene. In P. Grootenboer, R. Zevenbergen, & M. Chinnappan (Eds.), Identities, cultures and learning spaces: Proceedings of the 29th annual conference of the mathematics education research group of Australasia (Vol. 2). Adelaide: MERGA.

    Google Scholar 

  • Watson, J. M., Beswick, K., Caney, A., & Skalicky, J. (2006b). Profiling teacher change resulting from a professional learning program in middle school numeracy. Mathematics Teacher Education and Development, 7, 3–17.

    Google Scholar 

  • Watson, J. M., Beswick, K., Brown, N., & Callingham, R. (2007). Student change associated with teachers’ professional learning. In J. M. Watson & K. Beswick (Eds.), Mathematics, essential research, essential practice: Proceedings of the 30th annual conference of the mathematics education research group of Australasia (Vol. 2, pp. 785–794). Adelaide: MERGA.

    Google Scholar 

  • Watson, J., Callingham, R., & Donne, J. (2008). Establishing PCK for teaching statistics. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (Eds.), Joint ICME/IASE study: Teaching statistics in school mathematics. Challenges for teaching and teacher education. Proceedings of the ICMI study 18 and the 2008 IASE round table conference. Monterrey, Mexico, July, 2008.

  • Waugh, R. F. (2002). Creating a scale to measure motivation to achieve academically: Linking attitudes and behaviours using Rasch measurement. British Journal of Educational Psychology, 72, 65–86.

    Article  Google Scholar 

  • Wilson, M. S., & Cooney, T. J. (2002). Mathematics teacher change and development. In G. C. Leder, E. Pehkonen, & G. Torner (Eds.), Beliefs: A hidden variable in mathematics education (pp. 127–147). Dordrecht: Kluwer.

    Google Scholar 

  • Wood, T., Williams, G., & McNeal, B. (2006). Children’s mathematical thinking in different classroom cultures. Journal for Research in Mathematics Education, 37(3), 222–255.

    Google Scholar 

  • Wright, B. (1991). Diagnosing misfit. Rasch Measurement Transactions, 5(2), 156. From http://www.rasch.org/rmt/rmt52k.htm. Accessed 28 June 2009.

  • Wright, B. D., & Masters, G. N. (1982). Rating scale analysis: Rasch measurement. Chicago: MESA Press.

    Google Scholar 

  • Zhou, Z., Peverly, S. T., & Xin, T. (2006). Knowing and teaching fractions: A cross-cultural study of American and Chinese mathematics teachers. Contemporary Educational Psychology, 31(4), 438–457.

    Article  Google Scholar 

Download references

Acknowledgments

The authors would like to thank Natalie Brown for her valuable contribution to initial discussions of the delineation and naming of levels on the teacher knowledge scale, and Suzie Wright for her assistance with the coding and analysis of the data. This research was funded by Australian Research Council Linkage Grant No. LP0560543.

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Correspondence to Kim Beswick.

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Beswick, K., Callingham, R. & Watson, J. The nature and development of middle school mathematics teachers’ knowledge. J Math Teacher Educ 15, 131–157 (2012). https://doi.org/10.1007/s10857-011-9177-9

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