Student description of
variation while
working with weather data
chris reading
University of New England
creading@metz.une.edu.au
SUMMARY
Variation is a key concept in the
study of statistics and its understanding is a crucial aspect of most
statistically related tasks. This study aimed to extend
and apply a hierarchy for describing students’ understanding of variation that
was developed in a sampling context to the context of a natural event in which
variation occurs. Students aged 13 to 17 engaged in an inference task
that necessitated the description of both rainfall and temperature data. The SOLO
Taxonomy was used as a framework for analyzing student responses. Two cycles of
Unistructural-Multistructural-Relational levels, one for qualitative
descriptions and the other for quantitative descriptions, were identified in
responses. Implications of the extended hierarchy for describing understanding
of variation for research, teaching and assessment are outlined.
Keywords: Describing variation; SOLO Taxonomy; Inference task; Secondary students
__________________________
Statistics Education Research Journal,
3(2), 84-105, http://www.stat.auckland.ac.nz/serj
Ó International Association for Statistical Education (IASE/ISI), November, 2004
REFERENCES
Bakker, A. (2003). Reasoning about shape as a pattern in variability. In C. Lee (Ed.) Proceedings of the Third International Research Forum on Statistical Reasoning, Thinking, and Literacy (SRTL-3). [CDROM, with video segments] Mount Pleasant, Michigan: Central Michigan University.
Ben-Zvi, D. (2003). The emergence of reasoning about variability in comparing distributions: A case study of two seventh grade students. In C. Lee (Ed.) Proceedings of the Third International Research Forum on Statistical Reasoning, Thinking, and Literacy (SRTL-3). [CDROM, with video segments] Mount Pleasant, Michigan: Central Michigan University.
Biggs, J., & Collis, K. (1991). Multimodal learning and the quality of intelligent behaviour. In H. Rowe (Ed.), Intelligence, Reconceptualization and Measurement (pp. 57–76). New Jersey: Laurence Erlbaum Assoc.
DelMas, R.C., & Liu, Y. (2003). Exploring students’ understanding of statistical variation. In C. Lee (Ed.) Proceedings of the Third International Research Forum on Statistical Reasoning, Thinking, and Literacy (SRTL-3). [CDROM, with video segments] Mount Pleasant, Michigan: Central Michigan University.
Jones, G. A., Langrall, C. W., Thornton, C. A., & Mogill, A. T. (1997). A framework for assessing and nurturing young children’s thinking in probability. Educational Studies in Mathematics, 32, 101–125.
Jones, G. A., Mooney, E. S., Langrall, C. W., & Thornton, C. A. (2002). Students’ individual and collective statistical thinking. In B. Phillips (Ed.), Proceedings of the Sixth International Conference on Teaching Statistics: Developing a Statistically Literate Society, Cape Town, South Africa. [CDROM] Voorburg, The Netherlands: International Statistical Institute.
Jones, G. A., Thornton, C. A., Langrall, C. W., Mooney, E. S., Perry, B., & Putt, I. A. (2000). A framework for characterizing children’s statistical thinking. Mathematical Thinking and Learning, 2, 269–307.
Langrall, C. W. & Mooney, E. S. (2002). The development of a framework characterizing middle school students’ statistical thinking. In B. Phillips (Ed.), Proceedings of the Sixth International Conference on Teaching Statistics: Developing a Statistically Literate Society, Cape Town, South Africa. [CDROM] Voorburg, The Netherlands: International Statistical Institute.
Lann, A., & Falk, R. (2003). What are the clues for intuitive assessment of variability? In C. Lee (Ed.) Proceedings of the Third International Research Forum on Statistical Reasoning, Thinking, and Literacy (SRTL-3). [CDROM, with video segments] Mount Pleasant, Michigan: Central Michigan University.
Makar, K., & Confrey, J. (2003). Chunks, clumps, and spread out. In C. Lee (Ed.) Proceedings of the Third International Research Forum on Statistical Reasoning, Thinking, and Literacy (SRTL-3). [CDROM, with video segments] Mount Pleasant, Michigan: Central Michigan University.
Mooney, E. S. (2002). A framework for characterizing middle school students’ statistical thinking. Mathematical Thinking and Learning, 4(1), 23–63.
Pegg, J. (2003). Assessment in mathematics: A developmental approach. In J. M. Royer (Ed.), Advances in Mathematical Cognition (pp. 227–259). Greenwich, CT: Information Age Publishing.
Reading, C. (1998). Reactions to data: Students’ understanding of data interpretation. In L. Pereira-Mendoza, L. Kea, T. Kee & W-K Wong (Eds.), Proceedings of the Fifth International Conference on Teaching Statistics (Vol. 3, pp. 1427–1433). Voorburg, The Netherlands: International Statistical Institute.
Reading, C., & Lawrie, L. (2004). Using SOLO to
analyse group responses. In M. J. Hoines & A. B. Fuglestad (Eds.), Proceedings of the 28th
International Group for the Psychology of Mathematics Education (Vol. 3,
pp. 193–200). Bergen, Norway: Bergen University College.
Reading, C., & Pegg, J. (1996). Exploring
understanding of data reduction. In A. Gutierrez (Ed.), Proceedings of the 20th International Group for the
Psychology of Mathematics Education (Vol. 4, pp. 187–195). Valencia, Spain:
University of Valencia.
Reading, C., & Shaughnessy, J. M. (2000). Student perceptions of variation in a sampling situation. In T. Nakahar & M. Koyama (Eds.), Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 89–96). Hiroshima: Hiroshima University.
Reading, C., & Shaughnessy, M. (2004). Reasoning about variation. In D. Ben-Zvi & J. Garfield (Eds.) The Challenge of Developing Statistical Literacy, Reasoning and Thinking (pp. 201–226). Dordrecht, The Netherlands: Kluwer Academic Publishers.
Shaughnessy, M., & Ciancetta, M. (2002). Students’ understanding of variability in a probability environment. In B. Phillips (Ed.), Proceedings of the Sixth International Conference on Teaching Statistics: Developing a Statistically Literate Society, Cape Town, South Africa. [CDROM] Voorburg, The Netherlands: International Statistical Institute.
Shaughnessy, M., Watson, J., Moritz, J., & Reading, C. (1999). School mathematics students’ acknowledgement of statistical variation. In C.Maher (Chair), There’s more to life than centers, Procession Research Symposium, 77th Annual National Council of Teachers of Mathematics Conference, San Franciso, CA.
Torok,
R., & Watson, J. (2000). Development of the concept of statistical
variation: an exploratory study. Mathematics
Education Research Journal, 12(2),
147–169.
Watson, J. M., & Kelly, B.A. (2003). Developing intuitions about variation: The weather. In C. Lee (Ed.) Proceedings of the Third International Research Forum on Statistical Reasoning, Thinking, and Literacy (SRTL-3). [CDROM, with video segments] Mount Pleasant, Michigan: Central Michigan University.
Watson, J. M., Kelly, B. A., Callingham, R. A., & Shaughnessy, J. M. (2003). The measurement of school students’ understanding of statistical variation. International Journal of Mathematical Education in Science and Technology, 34(1), 1–29.
Wild, C., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223–262.
Chris reading
SiMERR National Centre
Education Building
University of New England
NSW 2351
Australia