Vol. 30 No. 2 (2022)
Articles

Scholarly Practice and Inquiry: Dynamic Interactions in an Elementary Mathematics Methods Course

Andrew Tyminski
Clemson University
Bio
McKenzie H. Brittain
Marshall University

Published 2022-03-04

Keywords

  • elementary,
  • preservice teachers,
  • teacher knowledge,
  • Methods course

Abstract

This paper presents research that exists at the crossroad of scholarly practice and scholarly inquiry. We outline the process in the design, enactment, and empirical examination of an elementary methods course activity, Exploring and Supporting Student Thinking (ESST), which engaged 18 elementary prospective teachers (PTs) in two sessions of one-on-one problem posing with 3rd grade students.  Our results mirror outcomes from existing literature focused on student interviews and letter exchanges as well as reveal other potential PTs experiences from such interactions. We end by describing implications for future activity design and with a call for researchers to continue to contribute to scholarly inquiry in this area.

References

  1. Ambrose, R. C. (2004). Initiating change in prospective elementary school teachers' orientations to mathematics teaching by building on beliefs. Journal of Mathematics Teacher Education, 7, 91-119.
  2. Brown, C. A., & Borko, H. (1992). Becoming a mathematics teacher. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 209–239). National Council of Teachers of Mathematics.
  3. Carpenter, T. P., & Fennema, E. (1992). Cognitively guided instruction: Building on the knowledge of students and teachers. International Journal of Educational Research, 17, 457-470.
  4. Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (1999). Children’s mathematics: Cognitively guided instruction. Heinemann.
  5. Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (2000). Cognitively guided instruction: A research-based teacher professional development program for elementary school mathematics. National Center for Improving Student Learning and Achievement in Mathematics and Science, Report, (003).
  6. CCSSO & National Governors Association. (2010). Common Core State Standards for Mathematics. http://www.corestandards.org/the-standards/mathematics
  7. Crespo, S. (2000). Seeing more than right and wrong answers: Prospective teachers' interpretations of students' mathematical work. Journal of Mathematics Teacher Education, 3, 155-181.
  8. Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers' practices. Educational Studies in Mathematics, 52, 243–270.
  9. Dewey, J. (1938). Logic: The theory of inquiry. New York: Holt.
  10. Drake, C., Land, T. J., Franke, N., Johnson, J., & Sweeney, M. (forthcoming). Teaching elementary mathematics for understanding. National Council of Teachers of Mathematics.
  11. Edthena, [web-based computer platform]. (2017). Retrieved from https://www.edthena.com/
  12. Ernest, P. (1994). Social constructivism and the psychology of mathematics education. Constructing mathematical knowledge: Epistemology and mathematical education, 62-71.
  13. 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). National Council of Teachers of Mathematics.
  14. González, G., & Eli, J. A. (2017). Prospective and in-service teachers’ perspectives about launching a problem. Journal of Mathematics Teacher Education, 20(2), 159-201.
  15. Grossman, P., Compton, C., Igra, D., Ronfeldt, M., Shahan, E., & Williamson, P. W. (2009). Teaching practice: A cross-professional perspective. Teachers college record, 111(9), 2055-2100.
  16. 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.
  17. Jacobs, V. R., & Ambrose, R. C. (2008). Making the most of story problems. Teaching children mathematics, 15(5), 260-266.
  18. Jacobs, V. R., & Empson, S. B. (2016). Responding to children’s mathematical thinking in the moment: An emerging framework of teaching moves. ZDM, 48(1), 185-197.
  19. Jacobs, V. R., Lamb, L. L., & Philipp, R. A. (2010). Professional noticing of children's mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169-202.
  20. Jenkins, O. F. (2010). Developing teachers' knowledge of students as learners of mathematics through structured interviews. Journal of Mathematics Teacher Education, 13, 141-154.
  21. Land, T. J, Drake, C., Sweeney, M., Franke, N., & Johnson, J. (2014). Number choice: building children’s mathematical understanding. National Council of Teachers of Mathematics.
  22. Lee, H., & Mewborn, D. (2009). Mathematics teacher educators engaging in scholarly practices and inquiry. In D. Mewborn & H. Lee (Eds.), Scholarly practices and inquiry in the preparation of mathematics teachers, (pp. 1-6). Association of Mathematics Teacher Educators.
  23. Mewborn, D. S. (1999). Reflective thinking among preservice elementary mathematics teachers. Journal for Research in Mathematics Education, 30(3), 316-341.
  24. Moyer, P. S., & Milewicz, E. (2002). Learning to question: Categories of questioning used by teachers during diagnostic mathematics interviews. Journal of Mathematics Teacher Education, 5, 293-315.
  25. National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. National Council of Teachers of Mathematics.
  26. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
  27. Nicol, C. (1998). Learning to teach mathematics: Questioning, listening, and responding. Educational Studies in Mathematics, 37(1), 45-66.
  28. Norton, A., & Kastberg, S. (2012). Learning to pose cognitively demanding tasks through letter writing. Journal of Mathematics Teacher Education, 15(2), 109-130.
  29. Parrish, S. (2010). Number talks: Helping children build mental math and computation strategies, grades K-5. Math Solutions.
  30. Smith, M. S., Bill, V., & Hughes, E. K. (2008). Thinking through a lesson: Successfully implementing high-level tasks. Mathematics Teaching in the Middle School, 14(3), 132-138.
  31. Smith, M., & Stein, M. K. (2011). Five practices for orchestrating productive mathematics discussions. Corwin Press SC Department of Education (2015). South Carolina College and Career Readiness Standards – Mathematics. Retrieved from http://ed.sc.gov/instruction/standards-learning/mathematics/standards/scccr-standards-for-mathematics-final-print-on-one-side/
  32. Strauss, A., & Corbin, J. (1998). Basics of qualitative research: Grounded theory procedures and techniques. Sage.
  33. TERC (2008). Investigations. Pearson/Scott Foresman.
  34. Tyminski, A. M., Land, T. J., Drake, C., Zambak, V. S., & Simpson, A. (2014). Preservice elementary mathematics teachers’ emerging ability to write problems to build on children’s mathematics. In Research trends in mathematics teacher education (pp. 193-218). Springer.
  35. UCSMP (2007). Everyday Mathematics. McGraw Hill.
  36. UIC (2008). Math Trailblazers (3rd ed.). Kendall Hunt.
  37. Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2016). Elementary and middle school mathematics. London: Pearson Education UK.