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Enhancing prospective secondary teachers’ potential competence for enacting core teaching practices—through experiences in university mathematics and statistics courses

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Abstract

In 1908, Felix Klein suggested that to mend the discontinuity that prospective secondary teachers face, university instruction must account for teachers’ needs. More than a century later, problems of discontinuity remain. Our project addresses the dilemma of discontinuity in university mathematics courses through simulating core teaching practices in mathematically intensive ways. In other words, we interpret teachers’ needs to include integrating content and pedagogy. We argue that doing so has the potential to impact teachers’ competence. To make this argument, we report findings from the Mathematics of Doing, Understanding, Learning, and Educating for Secondary Schools (MODULE(S2)) project. The results are based on data from 324 prospective secondary mathematics teachers (PSMTs) enrolled in courses using curricular materials developed by the project in four content areas (algebra, geometry, modeling, and statistics). We operationalized competence in terms of PSMTs’ content knowledge for teaching and their motivation for enacting core teaching practices. We examined pre- and post-term data addressing these constructs. We found mean increases in PSMTs’ outcomes in content knowledge for teaching and aspects of motivation.

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References

  • Álvarez, J. A., Arnold, E. G., Burroughs, E. A., Fulton, E. W., & Kercher, A. (2020). The design of tasks that address applications to teaching secondary mathematics for use in undergraduate mathematics courses. The Journal of Mathematical Behavior, 60, 100814.

    Article  Google Scholar 

  • Anhalt, C. O., & Cortez, R. (2016). Developing understanding of mathematical modeling in secondary teacher preparation. Journal of Mathematics Teacher Education, 19, 523–545.

    Article  Google Scholar 

  • Bass, H. (2005). Mathematics, mathematicians, and mathematics education. Bulletin of the American Mathematical Society, 42(4), 417–430.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Blömeke, S., Gustafsson, J. E., & Shavelson, R. J. (2015). Approaches to competence measurement in higher education. Zeitschrift für Psychologie, 223(1), 3–13.

    Article  Google Scholar 

  • Buchholtz, N., & Kaiser, G. (2013). Improving mathematics teacher education in Germany: Empirical results from a longitudinal evaluation of innovative programs. International Journal of Science and Mathematics Education, 11, 949–977. https://doi.org/10.1007/s10763-013-9427-7

    Article  Google Scholar 

  • Burroughs, E. A., Arnold, E. G., Álvarez, J. A., Kercher, A., Tremaine, R., Fulton, E., & Turner, K. (2023). Encountering ideas about teaching and learning mathematics in undergraduate mathematics courses. ZDM – Mathematics Education. https://doi.org/10.1007/s11858-022-01454-3

    Article  Google Scholar 

  • Casey, S., Ross, A., & Strayer, J. (2022). Development and measurement of statistical knowledge for teaching. In A. E. Lischka, E. B. Dyer, R. S. Jones, J. N. Lovett, J. Strayer, & S. Drown (Eds.), Proceedings of the forth-fourth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 615–619). Middle Tennessee State University.

    Google Scholar 

  • Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.

    Google Scholar 

  • Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). Lawrence Erlbaum Associates.

    Google Scholar 

  • Eccles, J. S., & Wigfield, A. (2020). From expectancy-value theory to situated expectancy-value theory: a developmental, social cognitive, and sociocultural perspective on motivation. Contemporary Educational Psychology, 61, 101859.

    Article  Google Scholar 

  • Groth, R. E. (2013). Characterizing key developmental understandings and pedagogically powerful ideas within a statistical knowledge for teaching framework. Mathematical, Thinking and Learning, 15, 121–145.

    Article  Google Scholar 

  • Gueudet, G., Bosch, M., diSessa, A. A., Kwon, O. N., & Verschaffel, L. (2016). Transitions in mathematics education. Springer.

    Book  Google Scholar 

  • Herbst, P., & Kosko, K. (2014). Mathematical knowledge for teaching and its specificity to high school geometry instruction. In J.-J. Lo, K. R. Leatham, & L. R. Van Zoest (Eds.), Research trends in mathematics teacher education (pp. 23–45). Springer.

    Chapter  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Holzberger, D., Philipp, A., & Kunter, M. (2014). Predicting teachers’ instructional behaviors: The interplay between self-efficacy and intrinsic needs. Contemporary Educational Psychology, 39(2), 100–111.

    Article  Google Scholar 

  • Howard, G. S. (1980). Response-shift bias: A problem in evaluating interventions with pre/post self-reports. Evaluation Review, 4(1), 93–106.

    Article  Google Scholar 

  • Howell, H., Lai, Y., & Phelps, G. (2016). Challenges in assessing mathematical knowledge for secondary teaching: Do elementary models extend? [Paper presentation]. 13th International Congress in Mathematics Education, Hamburg, Germany.

  • Kane, M. (2004). Certification testing as an illustration of argument-based approach validation. Measurement: Interdisciplinary Research and Perspectives, 2(3), 135–170.

    Google Scholar 

  • Klein, F. (1908). Elementarmathematik vom höheren Standpunkte aus, I. (B. G. Leubner, English translation in 1932). Macmillan.

  • Lai, Y., Wasserman, N., Strayer, J., Casey, S., Weber, K., Fukawa-Connelly, T., & Lischka, A. (in press). Making advanced mathematics work in secondary teacher education. In B. M. Benken (Ed.), AMTE Professional Book Series (Vol. 5): Reflection on past, present and future: Paving the way for the future of mathematics teacher education (Chapter 6). Association of Mathematics Teacher Educators.

  • LOCUS (n.d.). LOCUS: Levels of conceptual understanding in statistics. https://locus.statisticseducation.org/

  • Milewski, A., Lai, Y., Prasad, P.V., Akbuga, E., & Shultz, M. (2019). Improving teaching and learning in undergraduate geometry courses for secondary teachers [Presentation]. Annual Conference of the Special Interest Group of the Mathematical Association of America on Research in Undergraduate Education.

  • Mohr-Schroeder, M., Ronau, R. N., Peters, S., Lee, C. W., & Bush, W. S. (2017). Predicting student achievement using measures of teachers’ knowledge for teaching geometry. Journal for Research in Mathematics Education, 48(5), 520–566.

    Article  Google Scholar 

  • Murray, E., & Star, J. R. (2013). What do secondary preservice mathematics teachers need to know? Notices of the AMS, 60(10), 1297–1299.

    Google Scholar 

  • National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Authors.

  • Nunnally, J. C. (1978). Psychometric theory (2nd ed.). McGraw-Hill.

    Google Scholar 

  • Schmidt, W. H., Houang, R. T., Cogan, L., Blömeke, S., Tatto, M. T., Hsieh, F. J., Santillan, M., Bankov, K., Han, S. I., Cedillo, T., Schwille, J., & Paine, L. (2008). Opportunity to learn in the preparation of mathematics teachers: Its structure and how it varies across six countries. ZDM - The International Journal on Mathematics Education, 40(5), 735–747. https://doi.org/10.1007/s11858-008-0115-y

    Article  Google Scholar 

  • Stylianides, G. J., & Stylianides, A. J. (2010). Mathematics for teaching: A form of applied mathematics. Teaching and Teacher Education, 26(2), 161–172.

    Article  Google Scholar 

  • Sullivan, G. M., & Feinn, R. (2012). Using effect size—Or why the p value is not enough. Journal of Graduate Medical Education, 4(3), 279–282. https://doi.org/10.4300/JGME-D-12-00156.1

    Article  Google Scholar 

  • Tatto, M. T. (2013). The teacher education and development study in mathematics Policy, practice, and readiness to teach primary and secondary mathematics in 17 countries. Technical report. International Association for the Evaluation of Educational Achievement. https://files.eric.ed.gov/fulltext/ED545287.pdf

  • Tatto, M. T., Lerman, S., & Novotna, J. (2010). The organization of the mathematics preparation and development of teachers: A report from the ICMI Study 15. Journal of Mathematics Teacher Education, 13(4), 313–324.

    Article  Google Scholar 

  • Tatto, M. T., Rodriguez, M. C., Smith, W. M., Reckase, M. D., & Bankov, K. (2018). Exploring the mathematical education of teachers using TEDS-M data. Springer.

    Book  Google Scholar 

  • Wasserman, N. H., & McGuffey, W. (2021). Opportunities to learn from (advanced) mathematical coursework: A teacher perspective on observed classroom practice. Journal for Research in Mathematics Education, 52(4), 370–406.

    Article  Google Scholar 

  • Werler, T. C., & Tahirsylaj, A. (2020). Differences in teacher education programmes and their outcomes across Didaktik and curriculum traditions. European Journal of Teacher Education, 45(2), 154–172.

    Article  Google Scholar 

  • Wigfield, A., & Eccles, J. S. (2000). Expectancy-value theory of motivation. Contemporary Educational Psychology, 25, 68–81.

    Article  Google Scholar 

  • Winsløw, C., & Grønbæk, N. (2014). Klein’s double discontinuity revisited: Contemporary challenges for universities preparing teachers to teach calculus. Recherches en Didactique des Mathématiques, 34(1), 59–86.

    Google Scholar 

  • Zazkis, R., & Leikin, R. (2010). Advanced mathematical knowledge in teaching practice: Perceptions of secondary mathematics teachers. Mathematical Thinking and Learning, 12(4), 263–281.

    Article  Google Scholar 

  • Zee, M., & Koomen, H. M. (2016). Teacher self-efficacy and its effects on classroom processes, student academic adjustment, and teacher well-being: A synthesis of 40 years of research. Review of Educational Research, 86(4), 981–1015.

    Article  Google Scholar 

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Acknowledgements

We are grateful to our advisory board, external evaluators, prior data manager Lindsay Czap, undergraduate student Cleve Young who sharpened the qualitative analysis, and numerous graduate students who assisted in the scoring and analysis of this data. We thank our piloting instructors for their willingness to join us in improving the MODULE(S2) materials through their thoughtful insights, contributions, and conversations. Finally, we appreciate the PSMTs who agreed to help us learn how to better prepare secondary mathematics teachers through sharing their work and thinking with us. This project is partially supported by a multi-institutional collaborative National Science Foundation grant for Improving Undergraduate STEM Education #DUE-1726707, #1726098, #1726252, #1726723, #1726744, and #1726804. The views expressed here are those of the authors and do not necessarily represent those of the National Science Foundation.

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Correspondence to Jeremy F. Strayer.

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Lai, Y., Strayer, J.F., Ross, A. et al. Enhancing prospective secondary teachers’ potential competence for enacting core teaching practices—through experiences in university mathematics and statistics courses. ZDM Mathematics Education 55, 867–881 (2023). https://doi.org/10.1007/s11858-023-01485-4

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