International Electronic Journal of Mathematics Education

International Electronic Journal of Mathematics Education Indexed in ESCI
Exploring Connections between Sampling Distributions and Statistical Inference: an Analysis of Students’ Engagement and Thinking in the Context of Instruction Involving Repeated Sampling
APA
In-text citation: (Saldanha & Thompson, 2007)
Reference: Saldanha, L. A., & Thompson, P. W. (2007). Exploring Connections between Sampling Distributions and Statistical Inference: an Analysis of Students’ Engagement and Thinking in the Context of Instruction Involving Repeated Sampling. International Electronic Journal of Mathematics Education, 2(3), 270-297. https://doi.org/10.29333/iejme/213
AMA
In-text citation: (1), (2), (3), etc.
Reference: Saldanha LA, Thompson PW. Exploring Connections between Sampling Distributions and Statistical Inference: an Analysis of Students’ Engagement and Thinking in the Context of Instruction Involving Repeated Sampling. INT ELECT J MATH ED. 2007;2(3), 270-297. https://doi.org/10.29333/iejme/213
Chicago
In-text citation: (Saldanha and Thompson, 2007)
Reference: Saldanha, Luis A., and Patrick W. Thompson. "Exploring Connections between Sampling Distributions and Statistical Inference: an Analysis of Students’ Engagement and Thinking in the Context of Instruction Involving Repeated Sampling". International Electronic Journal of Mathematics Education 2007 2 no. 3 (2007): 270-297. https://doi.org/10.29333/iejme/213
Harvard
In-text citation: (Saldanha and Thompson, 2007)
Reference: Saldanha, L. A., and Thompson, P. W. (2007). Exploring Connections between Sampling Distributions and Statistical Inference: an Analysis of Students’ Engagement and Thinking in the Context of Instruction Involving Repeated Sampling. International Electronic Journal of Mathematics Education, 2(3), pp. 270-297. https://doi.org/10.29333/iejme/213
MLA
In-text citation: (Saldanha and Thompson, 2007)
Reference: Saldanha, Luis A. et al. "Exploring Connections between Sampling Distributions and Statistical Inference: an Analysis of Students’ Engagement and Thinking in the Context of Instruction Involving Repeated Sampling". International Electronic Journal of Mathematics Education, vol. 2, no. 3, 2007, pp. 270-297. https://doi.org/10.29333/iejme/213
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Saldanha LA, Thompson PW. Exploring Connections between Sampling Distributions and Statistical Inference: an Analysis of Students’ Engagement and Thinking in the Context of Instruction Involving Repeated Sampling. INT ELECT J MATH ED. 2007;2(3):270-97. https://doi.org/10.29333/iejme/213

Abstract

Construing a collection of values of a sample statistic as a distribution is central to developing a coherent understanding of statistical inference. This paper discusses key developments that unfolded over three consecutive lessons in a classroom teaching experiment designed to support a group of high school students in developing such a construal. Instruction began by engaging students in activities that focused their attention on the variability among values of a common sample statistic. There occurred a critical shift in students’ attention and discourse away from individual values of the statistic and toward a collection of such values as a basis for inferring the value of a population parameter. This was followed by their comparisons of such collections and by the emergence and application of a rule for deciding whether two such collections were similar. In the repeated application of their decision rule students structured these collections as distributions. We characterize aspects of these developments in relation to students’ classroom engagement, and we explore evidence in students’ written work that points to how instruction shaped their conceptions.

References

  • Cobb, G. W., & Moore, D. S. (1997). Mathematics, statistics, and teaching. American Mathematical Monthly, 104, 801-823.
  • delMas, R. C., Garfield, J., & Chance, B. L. (1999). Exploring the role of computer simulations in developing understanding of sampling distributions. Paper presented at the American Educational Research Association Conference, Montreal.
  • Glasersfeld, E. v. (1995). Radical constructivism: A way of knowing and learning. London: Falmer Press.
  • Kahneman, D., & Tversky, A. (1982). Variants of uncertainty. In D. Kahneman, P. Slovic, & A. Tversky (Eds.), Judgment under uncertainty: Heuristics and biases (pp. 509-521). New York: Cambridge University Press.
  • Kahneman, D., & Tversky, A. (1972). Subjective probability: A judgment of representativeness. Cognitive Psycholog, 3, 430-454.
  • Konold, C. (1989). Informal conceptions of probability. Cognition and Instruction, 6(1), 59-98.
  • Konold, C., & Miller, C. (1996). Prob Sim. Computer Program. Amherst, MA.
  • 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.
  • NCTM. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
  • Piaget, J., & Inhelder, B. (1951). La genèse de l’idée de hasard chez l’enfant (The origin of chance in children). Paris: Presses Universitaires de France.
  • Rubin, A., Bruce, B., & Tenney, Y. (1991). Learning about sampling: Trouble at the core of statistics. In D. Vere-Jones (Ed), Proceedings of the Third International Conference on Teaching Statistics (Vol. 1, pp. 314-319). Dunedin, New Zealand: International Statistical Institute.
  • Saldanha, L. A. (2004). “Is this sample unusual?”: An investigation of students exploring connections between sampling distributions and statistical inference. Unpublished Doctoral Dissertation.Vanderbilt University.
  • Saldanha, L. A. & Thompson, P. W. (2002). Conceptions of sample and their relationship to statistical inference. Educational Studies in Mathematics, 51, 257-270.
  • Schwartz, D. L., Goldman, S. R., Vye, N. J., & Barron, B. J. (1998). Aligning everyday and mathematical reasoning: The case of sampling assumptions. In S. P. Lajoie (Ed.), Reflections on statistics: learning, teaching, and assessment in grades K-12 (pp. 233-273). Mahwah, NJ: Lawrence Erlbaum.
  • Sedlmeier, P. (1999). Improving statistical reasoning: Theoretical models and practical implications. Mahwah, NJ: Lawrence Erlbaum.
  • Sedlmeier, P., & Gigerenzer, G. (1997). Intuitions about sample size: The empirical law of large numbers. Journal of Behavioral Decision Making, 10, 33-51.
  • Shaughnessy, J. M., Watson, J., Moritz, J., & Reading, C. (1999). School students’ acknowledgment of statistical variation. Paper presented at the Research Pre- session Symposium of the 77th Annual NCTM Conference, San Francisco,CA.
  • Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In A. E. Kelly, & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 267-306). Mahwah, NJ: Lawrence Erlbaum.
  • Thompson, P. W., Saldanha, L. A., & Liu. Y. (2004). Why statistical inference is hard to understand. Paper presented at the Annual Meeting of the American Educational Research Association, San Diego, April 2004.
  • Thompson, P. W., & Saldanha, L. A. (2003). Fractions and multiplicative reasoning. In J. Kilpatrick, G. Martin, & D. Schifter (Eds.), Research companion to the principles and standards for school mathematics (pp. 95- 113). Reston, VA: NCTM.
  • Thompson, P. W., & Saldanha, L. A. (2000). Epistemological analyses of mathematical ideas: A research methodology. In M. L. Fernandez (Ed.), Proceedings of the Twenty Second Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 403- 408), Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.
  • Vygotsky, L. S. (1986). Thought and language. Cambridge, MA: MIT Press.
  • Watson, J. M., & Moritz, J. B. (2000). Developing concepts of sampling. Journal for Research in Mathematics Education, 31 (1), 44-70.
  • Well, A. D., Pollatsek, A., & Boyce, S. J. (1990). Understanding the effects of sample size on the variability of the mean. Journal of Organizational Behavior and Human Decision Processes, 47, 289-312.

License

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