Intricacies of statistical inference and teachers’ understandings of them

Thinking with Data

Volumn , Issue , 2012, Pages 207-231

  Thompson, Patrick W ^a   Liu, Yan ^b   Saldanha, Luis A ^c  

^a ARIZONA STATE UNIVERSITY   (United States)

^b NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^c PORTLAND STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84920386673     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.4324/9780203810057     Document Type: Chapter

References (29)

1. Batanero, C., & Serrano, L. (1999). The meaning of randomness for secondary school students. Journal for Research in Mathematics Education, 30(5), 558–567.
2. Chance B. L., delMas, R. C., & Garfield, J. (in press). Reasoning about sampling distributions. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking. Dordrecht, The Netherlands: Kluwer.
3. delMas, R. C., Garfield, J., & Chance B. L. (1999, April). Exploring the role of computer simulations in developing understanding of sampling distributions. Paper presented at the Annual Meeting of the American Educational Research Association. Montreal, Canada.
4. delMas, R. C., Garfield, J., & Chance B. L. (2004, April). Using assessment to study the development of students’ reasoning about sampling distributions. Paper presented at the annual meeting of the American Educational Research Association. San Diego, CA.
5. Earley, M. A. (2001). Investigating the development of knowledge structures in introductory statistics. Unpublished doctoral dissertation, University of Toledo, Toledo, OH.
6. Earley, M. A. (2004). Overcoming the complexity of the sampling distribution concept in introductory statistics courses. San Diego, CA: Annual Meeting of the American Educational Research Association.
7. Falk, R., & Konold, C. C. (1994). Random means hard to digest. Focus on Learning Problems in Mathematics, 16(1), 2–12.
8. Falk, R., & Konold, C. C. (1997). Making sense of randomness: Implicit encoding as a basis for judgment. Psychological Review, 104, 301–318.
9. Glasersfeld, E. v. (1972). Semantic analysis of verbs in terms of conceptual situations. Linguistics, 94, 90–107.
10. Glasersfeld, E. v. (1995). Radical constructivism: A way of knowing and learning. London: Falmer Press.
11. Horvath, J. K., & Lehrer, R. (1998). A model-based perspective on the development of children’s understanding of chance and uncertainty. In S. P. Lojoie (Ed.), Reflections on statistics: Learning, teaching, and assessment in grades K–12 (pp. 121–148). Mahwah, NJ: Lawrence Erlbaum Associates.
12. Konold, C. C. (1994). Datascope user manual. Palo Alto, CA: Intellimation.
13. Konold, C. C., & Pollatsek, A. (2002). Data Analysis as the search for signals in noisy processes. Journal for Research in Mathematics Education, 33(4), 259–289.
14. Metz, K. E. (1998). Emergent understanding and attribution of randomness: Comparative analysis of the reasoning of primary grade children and undergraduates. Cognition and Instruction, 16(3), 285–365.
15. 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: ISI Publications in Statistical Education.
16. 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, Nashville, TN.
17. Saldanha, L. A., & Thompson, P. W. (2002). Conceptions of sample and their relationship to statistical inference. Educational Studies in Mathematics, 51(3), 257–270.
18. 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. Lojoie (Ed.), Reflections on statistics: Learning, teaching, and assessment in grades K–12 (pp. 233–274). Mahwah, NJ: Lawrence Erlbaum Associates.
19. Steffe, L. P. (1991). The constructivist teaching experiment: Illustrations and implications. In E. von Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 177–194). Dordrecht, The Netherlands: Kluwer.
20. Steffe, L. P. (1996). Radical constructivism: A way of knowing and learning [Review of the same title, by Ernst von Glasersfeld]. Zentralblatt für Didaktik der Mathematik [International reviews on Mathematical Education], 96(6), 202–204.
21. Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In R. Lesh & A. E. Kelly (Eds.), Research design in mathematics and science education (pp. 267–307). Mahwah, NJ: Lawrence Erlbaum Associates.
22. Thompson, P. W. (2000). Radical constructivism: Reflections and directions. In L. P. Steffe & P. W. Thompson (Eds.), Radical constructivism in action: Building on the pioneering work of Ernst von Glasersfeld (pp. 412–448). London: Falmer Press.
23. Thompson, P. W., & Saldanha, L. A. (2000). Conceptual issues in understanding sampling distributions and margins of error. In M. Fernandez (Ed.), Proceedings of the 22nd Annual meeting of the International Group for the Psychology of Mathematics Education. Athens, GA: University of Georgia.
24. Thompson, P. W., Saldanha, L. A., & Liu,Y. (2004). Why statistical inference is hard to understand. San Diego, CA: Annual Meeting of the American Educational Research Association.
25. Velleman, P. F. (1997). Data desk statistics guide. Ithaca, NY: Data Description, Inc.
26. Watson, J. M. (2001). Longitudinal development of inferential reasoning by school students. Educational Studies in Mathematics, 47(3), 337–372.
27. Watson, J. M. (2002). Inferential reasoning and the influence of cognitive conflict. Educational Studies in Mathematics, 51(3), 225–256.
28. Watson, J. M., & Moritz, J. B. (2000). Developing concepts of sampling. Journal for Research in Mathematics Education, 31(1), 44–70.
29. 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.