PRESERVICE ELEMENTARY TEACHERS AND THE FUNDAMENTALS OF PROBABILITY

CLARK DOLLARD

Metropolitan State College of Denver

cdollard@mscd.edu

ABSTRACT

This study examined how preservice elementary teachers think about situations involving probability. Twenty-four preservice elementary teachers who had not yet studied probability as part of their preservice elementary mathematics coursework were interviewed using a task-based interview. The participants’ responses showed a wide variety of misconceptions about the meaning of probability. In particular, when they were asked to think about the probability of an irregularly shaped object, many participants had misconceptions about the classical and frequentist interpretations of probability. These findings suggest that instruction for preservice elementary teachers should address the meaning of probability, including the subjective, classical, and frequentist interpretations of probability.

Keywords: Statistics education research; Preservice teacher; Teacher education

__________________________

Statistics Education Research Journal, 10(2), 27-47, http://www.stat.auckland.ac.nz/serj

(c) International Association for Statistical Education (IASE/ISI), November, 2011

REFERENCES

Ball, D. L. (1988). Knowledge and reasoning in mathematical pedagogy: Examining what prospective teachers bring to teacher education. Unpublished doctoral dissertation, Michigan State University, East Lansing, MI.

Bassarear, T. (2005). Mathematics for elementary school teachers (3rd ed.). Boston: Houghton Mifflin.

Batanero, C., Henry, M., & Parzysz, B. (2005). The nature of chance and probability. In G. A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 15-37). New York: Springer.

Beckmann, S. (2005). Mathematics for elementary teachers. Boston: Pearson Education.

Bennett, A. B., Jr., & Nelson, L. T. (2004). Mathematics for elementary teachers: A conceptual approach (6th ed.). Boston: McGraw-Hill.

Billstein, R., Libeskind, S., & Lott, J. W. (2001). A problem solving approach to mathematics for elementary teachers (7th ed.). Boston: Addison Wesley.

Bright, G. W., Frierson, D., Jr., Tarr, J. E., & Thomas, C. (2003). Navigating through probability in grades 6-8. Reston, VA: National Council of Teachers of Mathematics.

Canada, D. L. (2004). Elementary preservice teachers' conceptions of variation. Unpublished doctoral dissertation. Portland State University.

[Online: www.stat.auckland.ac.nz/~iase/publications/dissertations/04.Canada.Dissertation.pdf ]

Canada, D. L. (2006). Elementary pre-service teachers' conceptions of variation in a probability context. Statistics Education Research Journal, 5(1), 36-63.

[Online: http://www.stat.auckland.ac.nz/~iase/serj/SERJ_5%281%29_Canada.pdf ]

Fischbein, E. (1975). The intuitive sources of probabilistic thinking in children. Dordrecht-Holland: D. Reidel.

Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., & Schaeffer, R. (2007). Guidelines for assessment and instruction in statistics education (GAISE) Report: A pre-K-12 curriculum framework. Alexandria, VA: American Statistical Association.

[Online: http://www.amstat.org/education/gaise/GAISEPreK-12_Full.pdf ]

Gigerenzer, G., & Edwards, A. (2003). Simple tools for understanding risks: From innumeracy to insight. British Medical Journal, 327(7417), 741-744.

Gigerenzer, G., Hoffrage, U., & Kleinbolting, H. (1991). Probabilistic mental models: A Brunswikian theory of confidence. Psychological Review, 98(4), 506-528.

Greer, G., & Mukhopadhyay, S. (2005). Teaching and learning the mathematization of uncertainty: Historical, cultural, social and political contexts. In G. A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 297-324). New York: Springer.

Groth, R. E., & Bergner, J. A. (2005). Pre-service elementary school teachers' metaphors for the concept of statistical sample. Statistics Education Research Journal, 4(2), 27-42.

[Online: http://www.stat.auckland.ac.nz/~iase/serj/SERJ4%282%29_groth_bergner.pdf ]

Horvath, J. K., & Lehrer, R. (1998). A model-based perspective on the development of children's understanding of chance and uncertainty. In S. P. Lajoie (Ed.), Reflections in statistics: Learning, teaching, and assessment in grades K-12 (pp. 121-148), Mahwah, NJ: Lawrence Erlbaum.

Jones, G. A. (Ed.). (2005). Exploring probability in school: Challenges for teaching and learning. New York: Springer.

Jones, G. A., Langrall, C. W., Thornton, C. A., & Mogill, A. T. (1999). Students' probabilistic thinking in instruction. Journal for Research in Mathematics Education, 30, 487-519.

Jones, D. L., & Tarr, J. E. (2007). An examination of the levels of cognitive demand required by probability tasks in middle grades mathematics textbooks. Statistics Education Research Journal, 6(2), 4-27.

[Online: http://www.stat.auckland.ac.nz/~iase/serj/SERJ6%282%29_Jones_Tarr.pdf ]

Kahneman, D., Slovic, P., & Tversky, A. (1982). Judgment under uncertainty: Heuristics and biases. Cambridge, UK: Cambridge University Press.

Konold, C. (1989). Informal conceptions of probability. Cognition and Instruction, 6(1), 59-98.

Konold, C. (1991). Understanding students' beliefs about probability. In E. von Glasersfeld (Ed.), Constructivism in mathematics education (pp. 139-156). Dordrecht, The Netherlands: Kluwer.

Lecoutre, M. P. (1992). Cognitive models and problem spaces in "purely random" situations. Educational Studies in Mathematics, 23(6), 557-568.

Lindley, D. (1994). Foundations. In G. Wright & P. Ayton (Eds.), Subjective probability (pp. 3-15). Chichester, UK: John Wiley & Sons.

Metz, K. E. (1998). Emergent understanding and attribution of randomness: Comparative analysis of reasoning of primary grade children and undergraduates. Cognition and Instruction, 16(3), 285-365.

Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis. Thousand Oaks, CA: Sage Publications.

O’Daffer, P., Charles, R., Cooney, T., Dossey, J., & Schielack, J. (2002). Mathematics for elementary school teachers (2nd ed.). Boston: Addison Wesley.

Pratt, D. (2000). Making sense of the total of two dice. Journal for Research in Mathematics Education, 31(5), 602-625.

Shaughnessy, J. M. (1977). Misconceptions of probability: An experiment with a small-group, activity-based, model building approach to introductory probability at the college level. Educational Studies in Mathematics, 8(3), 295-316.

Shaughnessy, J. M. (1992). Research in probability and statistics: Reflections and directions. In D. Grouws (Ed.) Handbook of research on mathematics teaching and learning (pp. 465-494). New York: Macmillan.

Steinbring, H. (1991). The theoretical nature of probability in the classroom. In R. Kapadia & M. Borovcnik (Eds.), Chance encounters: Probability in education. Dordrecht, The Netherlands: Kluwer.

Stohl, H. (2005). Probability in teacher education and development. In G. A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 297-324). New York: Springer.

Watson, J. D., & Moritz, J. B. (2003). Fairness of dice: A longitudinal study of students' beliefs and strategies for making judgments. Journal for Research in Mathematics Education, 34(4), 270-304.

CLARK DOLLARD

Metropolitan State College of Denver

Department of Mathematical and Computer Sciences

Campus Box 38, P.O. Box 173362

Denver, CO 80217

USA