Challenges and Strategies for Assessing Mathematical Knowledge for Teaching

Authors

  • Chandra Orrill University of Massacheutts D
  • Ok-Kyeong Kim Western Michigan University
  • Susan Peters University of Louisville
  • Alyson Lischka Middle Tennessee State University
  • Cindy Jong University of Kentucky
  • Wendy Sanchez Kennesaw State University
  • Jennifer Eli The University of Arizona

Abstract

Developing and writing assessment items that measureteachers' knowledge is an intricate and complex undertaking. In this paper, webegin with an overview of what is known about measuring teacher knowledge. Wethen highlight the challenges inherent in creating assessment items that focusspecifically on measuring teachers’ mathematical knowledge for teaching. Weoffer insights into three practices we have found valuable towards overcomingchallenges in our own cross-disciplinary work to create assessment items formeasuring teachers' mathematical knowledge for teaching.

References

American Educational Research Association, American Psychological Association, & National Council on Measurement in Education. (1999). Standards for educational and psychological testing. Washington, DC: American Educational Research Association.

Ball, D. L., Lubienski, S., & Mewborn, D. S. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teaching (4th ed., pp. 433–456). Washington, DC: American Educational Research Association.

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

Baumert, J., Kunter M., Blum, W., Brunner, M., Voss, T., Jordan, A.,…& Tsai, Y-.M. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom and student progress. American Educational Research Journal, 47(1), 133-180.

Begle, E. G. (1972). Teacher knowledge and student achievement in algebra (School Mathematics Study Group Report No. 9). Palo Alto, CA: Stanford University.

Begle, E. G. (1979). Critical variables in mathematics education: Findings from a survey of the empirical literature. Washington, DC: Mathematical Association of America and National Council of Teachers of Mathematics.

Beswick, K., & Goos, M. (2012). Measuring preservice primary teachers’ knowledge for teaching mathematics. Mathematics Teacher Education and Development, 14(2), 70-90.

Blömeke, S., Houang, R.T., & Shul, 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.

Blömeke, S., Hsieh, F.-J., Kaiser, G., & Schmidt, W. H. (Eds.) (2014). International perspectives on teacher knowledge, beliefs, and opportunities to learn: TEDS-M results. Dordrecht, The Netherlands: Springer.

Boardman, A. E., Davis, O. A., & Sanday, P. R. (1977). A simultaneous equations model of the educational process. Journal of Public Economics, 7, 23–49.

Bradshaw, L. Izsák, A., Templin, J., & Jacobson, E. (2013). Diagnosing teachers’ understanding of rational numbers: Building a multidimensional test within the diagnostic classification framework. Educational Measurement: Issues and Practices. Advance online publication.

Council of Chief State Schools Officers [CCSSO] (2010). Common core state standards for mathematics. Retrieved June 2, 2010, from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf.

Darling-Hammond, L. (2000). Teacher quality and student achievement: A review of state policy evidence. Education Policy Analysis Archives, 8(1), 1-42.

Donoghue, E. F. (2003). The emergence of a profession: Mathematics education in the United States, 1890-1920. In G. M. A. Stanic, & J. Kilpatrick (Eds.), A history of school mathematics (Volume 1, pp. 159-193). Reston, VA: National Council of Teachers of Mathematics.

Educational Testing Service. (2009). ETS international principles for fairness review of assessments: A manual for developing locally appropriate fairness review guidelines in various countries. Educational Testing Service. Available at: www.ets.org/s/about/pdf/fairness_review_international.pdf

Eisenberg, T. A. (1977). Teacher knowledge and student achievement in algebra. Journal for Research in Mathematics Education, 8, 216-222.

Fennema, E., & Franke, M. L. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147-164). Reston, VA: National Council of Teachers of Mathematics.

Ferrini-Mundy, J., McCrory, R., & Senk, S. (2006, March). Knowledge of algebra teaching: Framework, item development, and pilot results. Paper presented Research symposium at the research presession of NCTM annual meeting. St. Louis, MO.

Frey, B. B., Petersen, S., Edwards, L. M., Pedrotti, J. T., & Peyton, V. (2005). Item-writing rules: Collective wisdom. Teaching and Teacher Education, 21, 357-364.

Haladyna, T. M., Downing, S. M., & Rodriguez, M. C. (2002). A review of multiple-choice item-writing guidelines for classroom assessment. Applied Measurement in Education, 15, 309-334.

Hansen, D. T. (2008). Values and purpose in teacher education. In M. Cochran-Smith, K. E. Demers, S. Feiman-Nemser, & D. J. McIntyre (Eds.), Handbook of research on teacher education: Enduring questions in changing contexts (3rd ed., pp. 10-26). New York: Routledge.

Hanushek, E. A. (1972). Education and race: An analysis of the educational production process. Lexington, MA: D. C. Heath.

Hauk, S., Jackson, B., & Noblet, K. (2010, February). No teacher left behind: Assessment of secondary mathematics teachers’ pedagogical content knowledge. In S. Brown (Ed.), Proceedings of the 13th conference on Research in Undergraduate Mathematics Education (Raleigh, NC). Electronic proceedings.

Hill, H. C. (2007). Mathematical knowledge of middle school teachers: Implications for the No Child Left Behind policy initiative. Educational Evaluation and Policy Analysis, 29(2), 95-114.

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, 372-400.

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.

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

Hodgen, J. (2011). Knowing and identity: A situated theory of mathematics knowledge in teaching. In T. Rowland & K. Ruthven (Eds.), Mathematical knowledge in teaching (pp. 27-42). Dordrecht, The Netherlands: Springer.

Kazemi, E., & Stipek, D. (2001). Promoting conceptual thinking in four upper-elementary mathematics classrooms. Elementary School Journal, 102, 59-80.

Kersting, N. B., Givvin, K. B., Sotelo, F. L., & Stigler, J. W. (2002). Teachers’ analyses of classroom video predict student learning of mathematics: Further explorations of a novel measure of teacher knowledge. Journal of Teacher Education, 61(1-2), 172-181.

Kersting, N. (2008). Using video clips of mathematics classroom instruction as item prompts to measure teachers’ knowledge of teaching mathematics. Educational and Psychological Measurement, 68, 845-861.

Kersting, N. B., Givvin, K. B., Sotelo, F. L., & Stigler, J. W. (2010). Teachers’ analyses of classroom video predict student learning of mathematics: Further explorations of a novel measure of teacher knowledge. Journal of Teacher Education, 61, 172-181.

Kersting, N. B., Givvin, K. B., Thompson, B. J., Santagata, R., & Stigler, J. W. (2012). Measuring usable knowledge: Teachers’ analyses of mathematics classroom videos predict teaching quality and student learning. American Educational Research Journal, 49(3), 568-589.

Krauss, S., Baumert, J., & Blum, W. (2008). Secondary mathematics teachers’ pedagogical content knowledge and content knowledge: Validation of the COACTIV constructs. ZDM Mathematics Education, 40, 873-892.

Kunter, M., Baumert, J., Blum, W., Klusmann, U., Krauss, S., & Neubrand, M. (Eds.), (2013). Cognitive activation in the mathematics classroom and professional competence of teachers: Results from the COACTIV Project. New York: Springer.

Learning Mathematics for Teaching Project. (2011). Measuring the mathematical quality of instruction. Journal of Mathematics Teacher Education, 14, 25-47.

Linsell, C., & Anakin, M. (2012). Diagnostic assessment of preservice teachers’ mathematical content knowledge. Mathematics Teacher Education and Development, 14(2), 4-27.

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

Maher, N., & Muir, T. (2013). "I know you have to put down a zero, but I'm not sure why": Exploring the link between pre-service teachers' content and pedagogical content knowledge. Mathematics Teacher Education & Development, 15(1), 72-87.

Manizade, A. G., & Mason, M. M. (2011). Using Delphi methodology to design assessments of teachers’ pedagogical content knowledge. Educational Studies in Mathematics, 76, 183-207.

McCrory, R., Floden, R., Ferrini-Mundy, J., Reckase, M. D., & Senk, S. L. (2012). Knowledge of algebra for teaching: A framework of knowledge and practice. Journal for Research in Mathematics Education, 43, 584-615.

Messick, S. (1989). Meaning and values in test validation: The science and ethics of

assessment. Educational researcher, 18(2), 5-11.

Monk, D. H. (1994). Subject area preparation of secondary mathematics and science teachers and student achievement. Economics of Education Review, 13(2), 125-145.

Moyer-Packenham, P. S., Bolyard, J. J., Kitsantas, A., & Oh, H. (2008). The assessment of mathematics and science teacher quality. Peabody Journal of Education, 83, 562-591. doi: 10.1080/01619560802414940

National Research Council (2001). Knowing what students know: The science and design of educational assessment. Washington, DC.: The National Academies Press.

Petrou, M., & Goulding, M. (2011). Conceptualising teachers’ mathematical knowledge in teaching. In T. Rowland & K. Ruthven (Eds.), Mathematical knowledge in teaching (pp. 9-26). Dordrecht, The Netherlands: Springer.

Post, T. R., Harel, G., Behr, M. J., & Lesh, R. (1988). Intermediate teachers knowledge of rational number concepts. In Fennema, et al. (Eds.), Papers from the First Wisconsin Symposium for Research on Teaching and Learning Mathematics (pp. 194-219). Madison, WI: Wisconsin Center for Educational Research.

Riley, K. R. (2010). Teachers’ understanding of proportional reasoning. In P. Brosnan, D. B. Erchick, & L. Flevares (Eds.), Proceedings of the 32nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1055-1061). Columbus, OH: The Ohio State University.

Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: The knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8, 255-281.

Saderholm, J., Ronau, R., Brown, E. T., & Collins, G. (2010). Validation of the Diagnostic Teacher Assessment of Mathematics and Science (DTAMS) Instrument. School Science and Mathematics, 110, 180 – 192.

Shechtman, N., Roschelle, J., Haertel, G., & Knudsen, J. (2010). Investigating links from teacher knowledge, to classroom practices, to student learning in the instruction system of the middle-school mathematics classroom. Cognition and Instruction, 28(3), 317-359.

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), 1-22.

Silverman, J., & Thompson, P. W. (2008). Towards a framework for the development of mathematical knowledge for teaching. Journal of Mathematics Teacher Education, 11, 499-511.

Simon, M. A. (1997). Developing new models of mathematics teaching: An imperative for research on mathematics teacher development. In E. Fennema & B. S. Nelson (Eds.), Mathematics teachers in transition (pp. 55-86). Mahwah, NJ: Lawrence Erlbaum Associates.

Thompson, A. G., & Thompson, P. W. (1996). Talking about rates conceptually, part II: Mathematical knowledge for teaching. Journal for Research in Mathematics Education, 27, 2–24.

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.

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2015-03-23

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