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Mathematics Education Research Journal

, Volume 27, Issue 3, pp 283–309 | Cite as

Looking at practice: revealing the knowledge demands of teaching data handling in the primary classroom

  • Aisling Leavy
Original Article
First Online:

Abstract

In the evolving field of mathematics education, there is the need to maintain the relationship between what is presented in college level preparation courses and the skills required to teach mathematics in classrooms. This research examines the knowledge demands placed on 73 pre-service primary teachers as they use lesson study to plan and teach data handling in primary classrooms. Pre-service teachers are observed as they plan, teach and re-teach data lessons in classrooms. Problems of practice are identified and categorized using the Ball, Thames and Phelps (2008) subdomains of common content knowledge (CCK), specialized content knowledge (SCK), knowledge of content and students (KCS) and knowledge of content and teaching (KCT). The results provide insights into the specific knowledge demands placed on early career teachers when teaching data and statistics and identifies foci area that can be addressed in teacher preparation programs. The results illustrate that development of understandings in one knowledge subdomain can motivate and impact learning in another subdomain. These interrelationships were found to exist both within and between the domains of content and pedagogical content knowledge.

Keywords

Teaching data and statistics Elementary mathematics Teacher education Teacher knowledge Lesson study Pedagogical knowledge 
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References

  1. Australian Curriculum, Assessment and Reporting Authority (2014). F10 Curriculum: Mathematics. Available at: http://www.australiancurriculum.edu.au/mathematics/Curriculum/F-10?layout=1
  2. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: what makes it special? Journal of Teacher Education, 59(5), 389–407.CrossRefGoogle Scholar
  3. Cobb, P. (1999). Individual and collective mathematical development: the case of statistical data analysis. Mathematical Thinking and Learning, 1(1), 5–43.CrossRefGoogle Scholar
  4. Cochran-Smith, M., & Lytle, S. L. (1999). Relationships of knowledge and practice: teacher learning in communities. Review of Research in Education, 24, 249–305.Google Scholar
  5. Creswell, J. W. (1997). Qualitative inquiry and research designs: Choosing among five traditions. Thousand Oaks, CA: Sage.Google Scholar
  6. Ertle, B., Chokshi, S., & Fernandez, C. (2001). Lesson Planning Tool. Retrieved June 08, 2009, from http://www.tc.columbia.edu/lessonstudy/doc/Lesson_Planning_Tool.pdf.Google Scholar
  7. Fernandez, C., & Yoshida, M. (2004). Lesson study: A Japanese approach to improving mathematics teaching and learning. Mahwah, NJ: Lawrence Erlbaum Associates, Publisher.Google Scholar
  8. Groth, R. E., & Bergner, J. A. (2006). Preservice elementary teachers’ conceptual and procedural knowledge of mean, median, and mode. Mathematical Thinking and Learning, 8, 37–63.CrossRefGoogle Scholar
  9. Hiebert, J., Morris, A. K., Berke, D., & Jansen, A. (2007). Preparing teachers to learn from teaching. Journal of Teacher Education, 58(1), 47–61.CrossRefGoogle Scholar
  10. Konold, C., & Higgins, T. (2003). Reasoning about data. In J. Kilpatrick, G. Martin, & D. Schifter (Eds.), A research companion to NCTM’s standards. NCTM: Reston, VA.Google Scholar
  11. Konold, C., & Pollatsek, A. (2002). Data analysis as the search for signals in noisy processes. Journal for Research in Mathematics Education, 33(4), 259–289.CrossRefGoogle Scholar
  12. Laborde, C., & Perrin-Glorian, M. J. (2005). Teaching situations as object of research: empirical studies within theoretical perspectives. Educational Studies in Mathematics, 59, 1–12.CrossRefGoogle Scholar
  13. Leavy, A. M. (2006). Using data comparison to support a focus on distribution: examining preservice teacher’s understandings of distribution when engaged in statistical inquiry. Statistics Education Research Journal, 5(2), 89–114.Google Scholar
  14. Leavy, A. M. (2010). Preparing preservice teachers to teach informal inferential reasoning. Statistics Education Research Journal, 9(1), 46–67.Google Scholar
  15. Leavy, A. M., & Middleton, J. A. (2011). Middle grades students’ understanding of typicality. Journal of Mathematical Behaviour, 30(3), 235–254.CrossRefGoogle Scholar
  16. Lewis, C., & Tsuchida, I. (1998). A lesson is like a swiftly flowing river: how research lessons improve Japanese education. American Educator, 22(4), 12–17. 50–52.Google Scholar
  17. Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry. Newbury Park, CA: Sage Publications.Google Scholar
  18. 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
  19. Makar, K., & Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1), 82–105.Google Scholar
  20. Makar, K., Bakker, A., & Ben-Zvi, D. (2011). The reasoning behind informal statistical inference. Mathematical Thinking and Learning, 13(1–2), 152–173.CrossRefGoogle Scholar
  21. Mevarech, Z. R. (1983). A deep structure model of students’ statistical misconceptions. Educational Studies in Mathematics, 14, 415–429.CrossRefGoogle Scholar
  22. Ministry of Education. (1992). Mathematics in the New Zealand curriculum. Wellington: Learning Media.Google Scholar
  23. Moore, D. S. (2004). Foreword. In Ben-Zvi, D., & Garfield, J (Eds), The challenge of developing statistical literacy, reasoning, and thinking (pp. ix-x). Kluwer Academic Publishers, Dordrecht.Google Scholar
  24. Murata, A., & Pothen, E. B. (2011). Lesson study in preservice elementary mathematics courses: connecting emerging practice and understanding. In L. Hart, A. Alston, & A. Murata (Eds.), Lesson study research and practice in mathematics education: learning together (pp. 103–116). New York: Springer.CrossRefGoogle Scholar
  25. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.Google Scholar
  26. Nemser, S. F. (1983). Learning to teach. In L. Shulman & G. Sykes (Eds.), Handbook of teaching and policy (pp. 150–170). New York: Longman.Google Scholar
  27. Petrosino, A. J., Lehrer, R., & Schauble, L. (2003). Structuring error and experimental variation as distribution in the fourth grade. Mathematical Thinking and Learning, 5(2&3), 131–156.CrossRefGoogle Scholar
  28. Petrou, M. (2007). ‘Michigan Research on Developing A Practice-Based Theory of Content Knowledge of Teaching’, [Accessed on-line], http://www.mathsed.org.uk/mkit/Petrou_Nuffield_MKiT_270907.pdf.
  29. Pollatsek, S. J., Lima, S., & Well, A. D. (1981). Concept or understanding: students’ understanding of the mean. Educational Studies in Mathematics, 12, 191–204.CrossRefGoogle Scholar
  30. Rock, T. C. (2003). A lesson study model for preservice teacher education. Journal of Research in Education, 13(1), 31–38.Google Scholar
  31. Shulman, L. S. (1986). Those who understand: knowledge growth in teaching. Educational Researcher, 15(2), 4–14.CrossRefGoogle Scholar
  32. Stake, R. E. (1995). The art of case study research. Thousand Oaks, CA: Sage Publications.Google Scholar
  33. Stigler, J. W., & Hiebert, J. (1999). The teaching gap. Chapter 7. New York: Free Press.Google Scholar
  34. Van Es, E. A., & Sherin, M. G. (2002). Learning to notice: scaffolding new teachers’ interpretations of classroom interactions. Journal of Technology and Teacher Education, 10, 571–576.Google Scholar
  35. Yin, R. K. (2009). Case study research: design and methods (4th ed.). Newbury Park, CA: Sage Publications.Google Scholar

Copyright information

© Mathematics Education Research Group of Australasia, Inc. 2014

Authors and Affiliations

  1. 1.Department of Language, Literacy and Mathematics EducationMary Immaculate College—University of LimerickLimerickIreland

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