Approaching the borderlands of statistics and mathematics in the classroom: qualitative analysis engenderING an unexpected journey

Jane M. Watson

University of Tasmania

Jane.Watson@utas.edu.au

Erica L. nathan

University of Tasmania

Erica.Nathan@utas.edu.au

abstract

To capture aspects of pedagogical content knowledge (PCK) not illuminated in an earlier written survey, an interview protocol was used with 40 middle school teachers. The scenarios were intended to elicit teachers' understanding of the big ideas, ability to anticipate students' answers, and intervention strategies for the classroom. This was expected to be a straight-forward journey based on teachers' responses to three context-based scenarios regarding students' answers to questions. Instead we were surprised by teachers' responses that revealed their perceptions that their experiences teaching mathematics and teaching statistics are very different. This led to further analysis of the PCK tasks and a suggestion that the mathematics embedded in the tasks was sometimes an impediment for the teachers, especially in relation to intervention strategies in the classroom.

Keywords: Statistics education research; Teaching statistics; Teaching mathematics; Pedagogical content knowledge; Teacher interviews

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Statistics Education Research Journal, 9(2), 69-87, http://www.stat.auckland.ac.nz/serj

Ó International Association for Statistical Education (IASE/ISI), November, 2010

References

Assessment Qualification Alliance. (2009). GSE A-level statistics. UK: Author.

[Online: web.aqa.org.uk/qual/gce/maths/stats_noticeboard.php?id=01&prev=01]

Bouma, G., & Ling, R. (2004). The research process (5^th ed.). South Melbourne, Victoria: Oxford University Press.

Callingham, R., & Watson J. M. (2008). Overcoming research design issues using Rasch measurement: The StatSmart project. In P. Jeffery (Ed.), Proceedings of the 2007 Australian Association for Research in Education annual conference. Victoria: Australian Association for Research in Education.

[Online: http://www.aare.edu.au/07pap/cal07042.pdf]

Chick, H. L. (2007). Teaching and learning by example. In J. Watson & K. Beswick (Eds.), Mathematics: Essential research, essential practice. Proceedings of the 30^th annual conference of the Mathematics Education Research Group of Australasia (Vol. 1, pp. 3-21). Adelaide, SA: MERGA

Cobb, G. W., & Moore, D. S. (1997). Mathematics, statistics, and teaching. American Mathematical Monthly, 104(9), 801-824.

College Board. (2008). AP Statistics course description. New York: Author.

[Online: apcentral.collegeboard.com/apc/public/repository/ap08_statistics_coursedesc.pdf]

Hill, H. C., Rowan, R., & Ball, D. L. (2005). Effects of teachers' mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406.

Konold, C., & Miller, C. D. (2005). TinkerPlots: Dynamic Data Exploration [Computer software]. Emeryville, CA: Key Curriculum Press.

Lampert, M. (2001). Teaching problems and the problems of teaching. New Haven, CT: Yale University Press.

Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2^nd ed.). Thousand Oaks, CA: Sage Publications.

Ministry of Education. (2007). Draft mathematics and statistics curriculum. Wellington, NZ: Author.

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.

Rasch, G. (1980). Probabilistic models for some intelligence and attainment tests. Chicago: University of Chicago Press. (Original work published 1960)

Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-22.

Watson, J. M., & Callingham, R. A. (2003). Statistical literacy: A complex hierarchical construct. Statistics Education Research Journal, 2(2), 3-46.

[Online: www.stat.auckland.ac.nz/~iase/serj/SERJ2(2)_Watson_Callingham.pdf]

Watson, J., Callingham, R., & Donne, J. (2008a). Establishing PCK for teaching statistics. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (Eds.), Joint ICME/IASE study: Teaching statistics in school mathematics. Challenges for teaching and teacher education. Proceedings of the ICMI Study 18 and the 2008 IASE Round Table Conference. Voorburg, The Netherlands: International Association for Statistical Education.

[Online: http://www.stat.auckland.ac.nz/~iase/publications/rt08/T2P10_Watson.pdf]

Watson, J., Callingham, R., & Donne, J. (2008b). Proportional reasoning: Student knowledge and teachers' pedagogical content knowledge. In M. Goos, R. Brown, & K. Makar (Eds.), Navigating currents and charting directions. Proceedings of the 31^st annual conference of the Mathematics Education Research Group of Australasia (Vol. 2, pp. 555-562). Adelaide, SA: MERGA.

Watson, J., Callingham, R., & Nathan, E. (2009). Probing teachers' pedagogical content knowledge in statistics: “How will Tom get to school tomorrow?” In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing divides (Vol. 2, pp. 563-570). Palmerston North, NZ: MERGA.

Watson, J., & Nathan, E. (2010a). Assessing the interpretation of two-way tables as part of statistical literacy. In C. Reading (Ed.), ICOTS-8 Proceedings: Towards an evidence based society. Voorburg, The Netherlands: International Association for Statistical Education, International Statistical Institute.

[Online: www.stat.auckland.ac.nz/~iase/publications/icots8/ICOTS8_5E1_WATSON.pdf]

Watson, J., & Nathan, E. (2010b). Biased sampling and PCK: The case of the marijuana problem. In L. Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the future of mathematics education. Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia (Vol. 2, pp. 610-617). Fremantle, WA: MERGA.

Jane M. Watson

Faculty of Education, University of Tasmania

Private Bag 66

Hobart, Tasmania 7001

Australia