ELEMENTARY PRE-SERVICE
TEACHERS’ CONCEPTIONS
OF VARIATION IN A
PROBABILITY CONTEXT
DANIEL
Eastern
dcanada@mail.ewu.edu
ABSTRACT
While other research has begun to contribute to our understanding of how pre-college students reason about variation, little has been published regarding pre-service teachers’ statistical conceptions. This paper summarizes a framework useful in examining elementary pre-service teachers’ conceptions of variation, and investigates the question of how a class of pre-service teachers’ responses concerning variation in a probability context compare from before to after class interventions. The interventions comprised hands-on activities, computer simulations, and discussions that provided multiple opportunities to attend to variation. Results showed that there was overall class improvement regarding what subjects expected and why, in that more responses after the interventions included appropriate balancing of proportional thinking along with an appreciation of variation in expressing what was likely or probable.
Keywords: Statistics Education Research; Teacher Education; Variation; Probability
__________________________
Statistics Education Research
Journal, 5(1), 36-63, http://www.stat.auckland.ac.nz/serj
Ó International Association for Statistical Education (IASE/ISI), May, 2006
REFERENCES
[Online: www.stat.auckland
ac.nz/~iase/publications/dissertations/dissertations.php]
Cobb, G., &
Moore, D. (1997). Mathematics, statistics, and teaching. American
Mathematics Monthly, 104(9), 801-824.
Finzer, W. (2001). Fathom™ Dynamic Statistics [Computer
software, v. 1.1].
[Online: http://www.stat.auckland.ac.nz/~iase/serj/SERJ4(1)_Garfield_BenZvi.pdf]
Hammerman, J., & Rubin, A. (2004). Strategies for managing statistical complexity with new software tools. Statistics Education Research Journal, 3(2), 17-41.
[Online: www.stat.auckland.ac.nz/~iase/serj/SERJ3(2)_Hammerman_Rubin.pdf]
Jolliffe, F., & Gal,
[Online: www.stat.auckland.ac.nz/~iase/serj/SERJ3(2).pdf]
Jones, G., Mooney, E., Langrall, C., & Thornton, C.
(2002). Students’ individual and collective statistical thinking. In B. Philips
(Ed.), Proceedings of the Sixth International Conference on Teaching
Statistics: Developing a Statistically Literate Society,
Kahneman, D., & Tversky, A. (1972). Subjective probability: A judgment of representativeness. Cognitive Psychology, 3, 430-451.
Konold, C. (1989). Informal conceptions of probability. Cognition and Instruction, 6(1), 59-98.
Konold, C., & Miller, C. (1994). ProbSim: A
Probability Simulation Program.
Makar, K., &
Makar, K., & Confrey, J. (2005). “Variation-talk”: Articulating meaning in statistics. Statistics Education Research Journal, 4(1), 27-54.
[Online: http://www.stat.auckland.ac.nz/~iase/serj/SERJ4(1)_Makar_Confrey.pdf]
Meletiou, M., & Lee, C. (2002). Student
understanding of histograms: A stumbling stone to the development of intuitions
about variation. In B. Philips (Ed.), Proceedings of the Sixth International
Conference on Teaching Statistics: Developing a Statistically Literate Society,
National Council of
Teachers of Mathematics. (1991). Professional standards for teaching mathematics.
[Online: http://www.stat.auckland.ac.nz/~iase/serj/SERJ3(2)_Reading.pdf]
Shaughnessy, J. (1997). Missed opportunities in
research on the teaching and learning of data and chance. In F. Bidduch &
K. Carr (Eds.), Proceedings of the 20th Annual Conference of the
Mathematics Education Research Group of
Shaughnessy, M.,
& Arcidiacono, M. (1993). Visual encounters with chance (Unit VIII, Math
and the mind’s eye).
Shaughnessy, J.M., & Ciancetta, M. (2002).
Students’ understanding of variability in a probability environment. In B.
Philips (Ed.), Proceedings of the Sixth International Conference on Teaching
Statistics: Developing a Statistically Literate Society,
Shaughnessy, J. M., Ciancetta, M. & Canada, D.
(2004). Types of student reasoning on sampling tasks. In the Proceedings
of the 28th Conference of the International Group for the Psychology
of Mathematics Education.
Shaughnessy, J., Watson, J., Moritz, J., &
Shulman, L. (1986).
Those who understand: Knowledge growth in teaching. Educational Researcher,
15, 4-14.
Torok, R., & Watson, J. (2000). Development of the concept of statistical variation: An exploratory study. Mathematics Education Research Journal, 12(2), 147-169.
Truran, J. (1994). Children’s intuitive understanding
of variance. In J. Garfield (Ed.), Research Papers from the 4th
International Conference on Teaching Statistics (ICOTS 4).
Watson, J., Kelly, B., Callingham, R., & Shaughnessy, J. (2002). The measurement of school students’ understanding of statistical variation. The International Journal of Mathematical Education in Science and Technology, 34, 1-29.
Watson, J., & Moritz, J. (1999). The beginning of statistical inference: Comparing two data sets. Educational Studies in Mathematics, 37(2), 145-168.
Wild, C., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67, 233-265.
DANIEL L. CANADA
Eastern
203