comparing box plot distributions:
A teacherís reasoning
The University of
Drawing conclusions from the comparison of datasets using informal statistical inference is a challenging task since the nature and type of reasoning expected is not fully understood. In this paper a secondary teacherís reasoning from the comparison of box plot distributions during the teaching of a Year 11 (15-year-old) class is analyzed. From the analysis a model incorporating ten distinguishable elements is established to describe her reasoning. The model highlights that reasoning in the sampling and referent elements is ill formed. The methods of instruction, and the difficulties and richness of verbalizing from the comparison of box plot distributions are discussed. Implications for research and educational practice are drawn.
Keywords: Statistics education research; Box plots; Distributional reasoning; Secondary statistics teaching; Informal statistical inference
Statistics Education Research Journal, 5(2), 27-45, http://www.stat.auckland.ac.nz/serj
” International Association for Statistical Education (IASE/ISI), November, 2006
Bakker, A. (2004). Design
research in statistics education: On symbolizing and computer tools.
Bakker, A., Biehler, R., & Konold, C. (2005).
Should young students learn about box plots? In G. Burrill & M. Camden
(Eds.), Curricular Development in
Statistics Education: International
Association for Statistical Education (IASE) Roundtable,
Bakker, A., & Gravemeijer, K. (2004). Learning to
reason about distribution. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical
literacy, reasoning, and thinking (pp. 147-168).
Ball, D., & Cohen, D. (1999). Developing practice,
developing practitioners. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the learning profession:
Handbook of policy and practice (pp. 3-32).
Ben-Zvi, D. (2004). Reasoning about variability in comparing distributions. Statistics Education Research Journal, 3(2), 42-63.
Biehler, R. (1997). Studentsí difficulties in
practicing computer-supported data analysis: Some hypothetical generalizations
from results of two exploratory studies. In J. Garfield & G. Burrill
(Eds.), Research on the role of
technology in teaching and learning statistics (pp. 169-190). Voorburg, The
Biehler, R. (2004, July). Variation, Co-Variation, and Statistical Group Comparison: Some Results
from Epistemological and Empirical Research on Technology Supported Statistics
Education. Paper presented at the 10th International Congress on
Carr, J., & Begg, A. (1994). Introducing box and
whisker plots. In J. Garfield (Ed.), Research
papers from the Fourth International Conference on Teaching Statistics (ICOTS
Friel, S. (1998). Comparing data sets: How do students
interpret information displayed using box plots? In S. Berenson, K. Dawkins, M.
Blanton, W. Coulombe, J. Kolb, K. Norwood, & L. Stiff (Eds.), Proceedings of the Twentieth Annual Meeting,
North American Chapter of the International Group for the Psychology of
Mathematics Education (Vol. 1, pp. 365-370).
Friel, S., Curcio, F., & Bright, G. (2001). Making sense of graphs: Critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 32(2), 124-159.
Hill, H., Rowan, B., & Ball, D. (2005). Effects of teachersí mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406.
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.
Konold, C., Pollatsek, A., Well, A., & Gagnon, A.
(1997). Students analyzing data: Research of critical barriers. In J. Garfield
& G. Burrill (Eds.), Research on the
role of technology in teaching and learning statistics (pp. 151-168).
Konold, C., Robinson, A., Khalil, K., Pollatsek, A.
Well, A., Wing, R., & Mayr, S. (2002). Studentsí use of modal clumps to
summarize data. In B. Phillips (Ed.), Proceedings
of the Sixth International Conference on Teaching Statistics: Developing a
statistically literate society, Cape
Town, South Africa, July, 2002 [CD-ROM.] Voorburg, The
Moore, D. (1990). Uncertainty. In L. Steen (Ed.) On the shoulders of giants: New approaches
to numeracy (pp. 95-137).
Pfannkuch, M. (2005). Probability and statistical
inference: How can teachers enable learners to make the connection? In G. Jones
(Ed.), Exploring probability in school:
Challenges for teaching and learning (pp. 267-294).
Pfannkuch, M. (2006). Informal inferential reasoning. Proceedings of the Seventh International
Conference on Teaching Statistics: Working cooperatively in statistics
Pfannkuch, M., Budgett, S., Parsonage, R., &
Horring, J. (2004). Comparison of data
plots: building a pedagogical framework. Paper presented at ICME-10,
[Online at: http://www.stat.auckland.ac.nz/~iase/publications.php]
Pfannkuch, M., & Horring, J. (2005). Developing
statistical thinking in a secondary school: A collaborative curriculum
development. In G. Burrill & M. Camden (Eds.), Curricular Development in Statistics Education: International Association for Statistical
Education (IASE) Roundtable,
Tukey, J. (1977). Exploratory
Watson, J. (2004). Developing reasoning about samples.
In D. Ben-Zvi and J. Garfield (Eds.), The
challenge of developing statistical literacy, reasoning and thinking (pp.
Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry (with discussion). International Statistical Review, 67(3), 223-265.
Department of Statistics
Private Bag 92019
Auckland, New Zealand