Abstract
The Mathematics Scan (M-Scan), a content-specific observational measure, was utilized to examine the extent to which standards-based mathematics teaching practices were present in three focal lessons. While previous studies have provided evidence of validity of the inferences drawn from M-Scan data, no prior work has investigated the affordances and limitations of the M-Scan in capturing standards-based mathematics teaching. We organize the affordances and limitations into three categories: the operationalization of the M-Scan, the organization of the M-Scan, and the M-Scan within the larger ecology of instruction. Our analysis indicates the M-Scan differentiates among lessons in their use of standards-based mathematics teaching practices by operationalizing the M-Scan dimensions at the lesson level, sometimes at the expense of capturing the peaks and valleys within a single lesson. Simultaneously, the analysis revealed how the application of the rubrics may be impacted by lesson transcripts. We discuss the theoretical organization of the M-Scan and its implications for researchers and practitioners applying the rubrics. Finally, we point to the affordances and limitations of the M-Scan within the larger ecology of instruction by considering curricular issues and two dimensions of instruction not highlighted by the M-Scan.
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References
American Educational Research Association, American Psychological Association, & National Council on Measurement in Education. (2014). Standards for educational and psychological testing. Washington, DC: AERA.
Berry, R. Q., Rimm-Kaufman, S. E., Ottmar, E. M., Walkowiak, T. A., Merritt, E., & Pinter, H. H. (2013). The Mathematics Scan (M-Scan): A measure of standards-based mathematics teaching practices (Unpublished measure). Charlottesville, VA: University of Virginia.
Borko, H., Stecher, B., & Kuffner, K. (2007). Using artifacts to characterize reform-oriented instruction: The Scoop Notebook and rating guide. Los Angeles: Center for Research on Evaluation, Standards, and Student Testing.
Borko, H., Stecher, B. M., Alonzo, A. C., Moncure, S., & McClam, S. (2005). Artifact packages for characterizing classroom practice: A pilot study. Educational Assessment, 10(2), 73–104. https://doi.org/10.1207/s15326977ea1002_1.
Bruner, J. S. (1966). Toward a theory of instruction. Cambridge, MA: Harvard University Press.
Center for Responsive Schools. (2017). Principles and practices of responsive classroom. Retrieved May 28, 2017 from https://www.responsiveclassroom.org/about/principles-practices/.
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1–2), 103–131.
Faulkner, V. N. (2013). Why the Common Core changes math instruction. Phi Delta Kappan, ‘95(2), 59–63.
Gainsburg, J. (2008). Real-world connections in secondary mathematics teaching. Journal of Mathematics Teacher Education, 11(3), 199–219.
Hiebert, J., Stigler, J. W., Jacobs, J. K., Givvin, K. B., Garnier, H., Smith, M.,.. .Gallimore, R. (2005). Mathematics teaching in the United States today (and tomorrow): Results from the TIMSS 1999 video study. Educational Evaluation and Policy Analysis, 27(2), 111–132.
Hill, H. C., Blunk, M. L., Charalambous, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L., & Ball, D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430–511. https://doi.org/10.1080/07370000802177235.
Hill, H. C., Charalambous, C. Y., & Kraft, M. A. (2012). When rater reliability is not enough teacher observation systems and a case for the generalizability study. Educational Researcher, 41(2), 56–64.
Hufferd-Ackles, K., Fuson, K. C., & Sherin, M. G. (2004). Describing levels and components of a math-talk learning community. Journal for Research in Mathematics Education, 35(2), 81–116. https://doi.org/10.2307/30034933.
Jackson, K., & Cobb, P. (2010). Refining a vision of ambitious mathematics instruction to address issues of equity. Paper presented at the annual meeting of the American Educational Research Association, Denver, CO.
Kane, M. T. (2013). The argument-based approach to validation. School Psychology Review, 42(4), 448–457.
Karp, K. S., Bush, S. B., & Dougherty, B. J. (2014). 13 rules that expire. Teaching Children Mathematics, 21(1), 18–25.
Lampert, M., Beasley, H., Ghousseini, H., Kazemi, E., & Franke, M. L. (2010). Using designed instructional activities to enable novices to manage ambitious mathematics teaching. In M. K. Stein & L. Kucan (Eds.), Instructional explanations in the disciplines (pp. 129–141). New York: Springer.
Lehrer, R., & Schauble, L. (2004). Modeling natural variation through distribution. American Educational Research Journal, 41(3), 635–679.
Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 33–40). Hillsdale: Lawrence Erlbaum.
Mashburn, A. J., Meyer, J. P., Allen, J. P., & Pianta, R. C. (2014). The effect of observation length and presentation order on the reliability and validity of an observational measure of teaching quality. Educational and Psychological Measurement, 74(3), 400–422.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston: NCTM.
National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston: NCTM.
National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, DC: Common Core State Standards Initiative.
Ottmar, E. R., Rimm-Kaufman, S. E., Berry, R. Q., & Larsen, R. A. (2013). Does the responsive classroom approach affect the use of standards-based mathematics teaching practices? Results from a randomized controlled trial. The Elementary School Journal, 113(3), 434–457. https://doi.org/10.1086/668768.
Ottmar, E. R., Rimm-Kaufman, S. E., Larsen, R. A., & Berry, R. Q. (2015). Mathematical knowledge for teaching, standards-based mathematics teaching practices, and student achievement in the context of the Responsive Classroom approach. American Educational Research Journal, 52(4), 787–821.
Pianta, R. C., La Paro, K. M., & Hamre, B. K. (2008). Classroom assessment scoring system manual, K-3. Baltimore, MD: Brookes Publishing Co.
Piburn, M., Sawada, D., Turley, J., Falconer, K., Benford, R., Bloom, I., & Judson, E. (2000). Reformed teaching observation protocol (RTOP): Reference manual. ACEPT Technical Report No. IN00-3). Tempe, AZ: Arizona Collaborative for Excellence in the Preparation of Teachers.
Praetorius, A. K., Pauli, C., Reusser, K., Rakoczy, K., & Klieme, E. (2014). One lesson is all you need? Stability of instructional quality across lessons. Learning and Instruction, 31, 2–12.
Rimm-Kaufman, S. E., Larsen, R. A., Baroody, A. E., Curby, T. W., Ko, M., Thomas, J. B., Merritt, E. G., Abry, T., & DeCoster, J. (2014). Efficacy of the Responsive Classroom approach: Results from a 3-year, longitudinal randomized controlled trial. American Educational Research Journal, 51(3), 567–603.
Schoenfeld, A. H. (2013). Reflections on problem solving theory and practice. The Mathematics Enthusiast, 10(1/2), 9.
Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2009). Implementing standards-based mathematics instruction: A casebook for professional development. New York: Teachers College Press.
Walkowiak, T. A. (2018). Utilizing confirmatory factor analysis to confirm the theoretical structure of measures of mathematics instruction: The case of the M-Scan (Manuscript in preparation).
Walkowiak, T. A., Berry, R. Q., Meyer, J. P., Rimm-Kaufman, S. E., & Ottmar, E. R. (2014). Introducing an observational measure of standards-based mathematics teaching practices: Evidence of validity and score reliability. Educational Studies in Mathematics, 85(1), 109–128.
Walkowiak, T. A., Pinter, H. H., & Berry, R. Q. (2017). A reconceptualized framework for ‘opportunity to learn’ in school mathematics. Journal of Mathematics Education at Teachers College, 8(1), 7–18.
Webb, N. M., Franke, M. L., Ing, M., Wong, J., Fernandez, C. H., Shin, N., & Turrou, A. C. (2014). Engaging with others’ mathematical ideas: Interrelationships among student participation, teachers’ instructional practices, and learning. International Journal of Educational Research, 63, 79–93.
Acknowledgements
This work was supported by the National Science Foundation under Award #1561453 and by the Institute of Education Sciences, US Department of Education, under grant R305A070063. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of NSF or the US Department of Education.
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Walkowiak, T.A., Berry, R.Q., Pinter, H.H. et al. Utilizing the M-Scan to measure standards-based mathematics teaching practices: affordances and limitations. ZDM Mathematics Education 50, 461–474 (2018). https://doi.org/10.1007/s11858-018-0931-7
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DOI: https://doi.org/10.1007/s11858-018-0931-7