This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aspinwall, L., & Tarr, J. E. (2001). Middle school students' understanding of the role sample size plays in experimental probability. Journal of Mathematical Behavior, 20, 229–245.
Biehler, R. (1994). Probabilistic thinking, statistical reasoning and the search for causes: Do we need a probabilistic revolution after we have taught data analysis? In J. Garfield (Ed.), Research Papers from The Fourth International Conference on Teaching Statistics, Marrakech 1994. Minneapolis, MN: University of Minnesota.
Biehler, R. (1997). Students' difficulties in practicing computer-supported data analysis: Some hypothetical generalizations from results of two exploratory studies. In J. Garfield & G. Burrill (Eds.), Research on the role of technology in teaching and learning statistics (pp. 169–190). Voorburg, The Netherlands: International Statistical Institute.
Biehler, R. (2001, September). “Girls (tend to) watch less television than boys” — Students' hypotheses and data exploration strategies in group comparison tasks. Paper presented at LOGOS #10, Mathematics Education Unit, Department of Mathematics, The University of Auckland, New Zealand.
Biggs, J.B., & Collis, K. F. (1982). Evaluating the quality of learning: The SOLO taxonomy. New York: Academic Press.
Cobb, G., & Moore, D. (1997). Mathematics, statistics and teaching. The American Mathematical Monthly, 104(9), 801–823.
Curcio, F. (1987). Comprehension of mathematical relationships expressed in graphs. Journal for Research in Mathematics Education, 18(5), 382–393.
Davis, P., & Hersh, R. (1986). Descartes' dream. Orlando, FL: Harcourt Brace Jovanovich.
DelMas, R., Garfield, J., & Chance, B. (1999). A model of classroom research in action: Developing simulation activities to improve students' statistical reasoning. Journal of Statistics Education 7(3). [Online: www.amstat.org/publications/jse/v7n3]
Garfield, J., & Ahlgren, A. (1988). Difficulties in learning basic concepts in probability and statistics: Implications for research. Journal for Research in Mathematics Education, 19(1), 44–63.
Gravemeijer, K. (1998). Developmental research as a research method. In A. Sierpinska and J. Kilpatrick (Eds.), Mathematics education as a research domain: A search for identity (Book 2, pp. 277–295). Dordrecht, The Netherlands: Kluwer Academic Publishers.
Joiner, B. (1994). Fourth generation management. New York: McGraw-Hill Inc.
Jones, P., Lipson, K., & Phillips, B. (1994). A role for computer intensive methods in introducing statistical inference. In L. Brunelli & G. Cicchitelli (Eds.), Proceedings of the First Scientific Meeting of the International Association for Statistical Education (pp. 199–211). Perugia, Italy: University of Perugia.
Key Curriculum Press Technologies (2000). Fathom. Emeryville, CA: Author.
Konold, C. (1994). Understanding probability and statistics through resampling. In L. Brunelli & G. Cicchitelli (Eds.), Proceedings of the First Scientific Meeting of the International Association for Statistical Education (pp. 255–263). Perugia, Italy: University of Perugia.
Konold, C., & Miller, C. (1995). Data Scope. Santa Barbara, CA: Intellimation Library for the Macintosh.
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.
Konold, C., Pollatsek, A., Well, A., & Gagnon, A. (1997). Students analyzing data: Research of critical barriers. In J. Garfield & G. Burrill (Eds.), Research on the role of technology in teaching and learning statistics (pp. 151–168). Voorburg, The Netherlands: International Statistical Institute.
Konold, C., Robinson, A., Khalil, K., Pollatsek, A. Well, A., Wing, R., & Mayr, S. (2002). Students' use of modal clumps to summarize data. In B. Phillips (Ed.), Proceedings of the Sixth International Conference on Teaching Statistics: Developing a statistically literate society, Cape Town, South Africa. [CD-ROM]. Voorburg, The Netherlands: International Statistical Institute.
Lightner, J. (1991). A brief look at the history of probability and statistics. Mathematics Teacher, 84(8), 623–630.
Lipson, K. (2002). The role of computer based technology in developing understanding of the concept of sampling distribution. In B. Phillips (Ed.), Proceedings of the Sixth International Conference on Teaching Statistics: Developing a statistically literate society, Cape Town, South Africa. [CD-ROM]. Voorburg, The Netherlands: International Statistical Institute.
Lipson, K., Kokonis, S., & Francis, G. (2003). Investigation of statistics students' experiences with a web-based computer simulation. In Proceedings of the International Association of Statistical Education Satellite Conference on Statistics Education: Statistics education and the internet, Berlin [CD-ROM]. Voorburg, The Netherlands: International Statistical Institute.
McClain, K., Cobb, P., & Gravemeijer, K. (2000). Supporting students' ways of reasoning about data. In M. Burke & F. Curcio (Eds.). Learning mathematics for a new century: 2000 Yearbook (pp. 174–187). Reston, VA: National Council of Teachers of Mathematics.
Metz, K. (1999). Why sampling works or why it can't: ideas of young children engaged in research of their own design. In F. Hitt & M. Santos (Eds.), Proceedings of the 21st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 492–498). Cuernavaca, Mexico: PME.
Moore, D. (1990). Uncertainty. In L. Steen (Ed.), On the shoulders of giants: new approaches to numeracy (pp. 95–137). Washington, D.C.: National Academy Press.
New Zealand Qualifications Authority (2001). Level 1 achievement standards: Mathematic [Online]. Available: http://www.nzqa.govt.nz/ncea/ach/mathematics/index.shtml
Pfannkuch, M., & Horring, J. (2004). Developing statistical thinking in a secondary school: A collaborative curriculum development. Unpublished manuscript, The University of Auckland, New Zealand.
Pfannkuch, M., & Wild, C. J. (2003). Statistical thinking: How can we develop it? In Proceedings of the 54 th International Statistical Institute Conference [CD-ROM]. Voorburg, The Netherlands: International Statistical Institute.
Pfannkuch, M., Rubick, A., & Yoon, C. (2002). Statistical thinking: An exploration into students' variation-type thinking. New England Mathematics Journal, 34(2), 82–98.
Saldanha, L., & Thompson, P. (2001). Students' reasoning about sampling distributions and statistical inference. In J. Garfield, D. Ben-Zvi, & C. Reading (Eds.), Background Readings of the Second International Research Forum on Statistical Reasoning, Thinking, and Literacy, (pp. 291–296). Armidale, Australia: Centre for Cognition Research in Learning and Teaching.
Saldanha, L., & Thompson, P. (2002). Conceptions of sample and their relationship to statistical inference. Educational Studies in Mathematics, 51(3), 257–270.
Scheaffer, R. (1992). Data, discernment and decisions: an empirical approach to introductory statistics. In F. & S. Gordon (Eds.), Statistics for the twenty-first century. (MAA Notes, Number 26, pp. 69–81). Washington, D.C.: The Mathematical Association of America.
Scheaffer, R., Watkins, A., & Landwehr, J. (1998). What every high school graduate should know about statistics. In S. Lajoie (Ed.), Reflections on statistics: learning, teaching, and assessment in Grades K-12 (pp. 3–31). Mahwah, NJ: Lawrence Erlbaum Associates.
Shaughnessy, M. (2003). Research on students' understandings of probability. In J. Kilpatrick, W. G. Martin, & D. Schifter, (Eds.), A research companion to Principles and Standards for School Mathematics (pp. 216–226). Reston, VA: National Council of Teachers of Mathematics.
Simon, J., Atkinson, D., & Shevokas, C. (1976). Probability and statistics: Experimental results of a radically different teaching method. American Mathematical Monthly, 83, 733–739.
Skovsmose, O., & Borba, M. (2000). Research methodology and critical mathematics education (Publication No. 17). Roskilde, Denmark: Centre for Research in Learning Mathematics, Roskilde University.
Stohl, H., & Tarr, J. E. (2002). Developing notions of inference using probability simulation tools. Journal of Mathematical Behavior, 21, 319–337.
Watson, J. M. (2001). Longitudinal development of inferential reasoning by school students. Educational Studies in Mathematics, 47, 337–372.
Watson, J. M. (2002). Inferential reasoning and the influence of cognitive conflict. Educational Studies in Mathematics, 51, 225–256.
Watson, J. M. (2004). Developing reasoning about samples. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 277–294). Dordrecht, The Netherlands: Kluwer Academic Publishers.
Watson, J. M., & Moritz, J. B. (2000). Development of understanding of sampling for statistical literacy. Journal of Mathematical Behavior, 19, 109–136.
Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry (with discussion). International Statistical Review, 67(3), 223–265.
Wild, C. J., & Seber, G. (2000). Chance encounters: A first course in data analysis and inference. New York: John Wiley & Sons, Inc.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer Science+Business Media, Inc.
About this chapter
Cite this chapter
Pfannkuch, M. (2005). Probability and Statistical Inference: How Can Teachers Enable Learners to Make the Connection?. In: Jones, G.A. (eds) Exploring Probability in School. Mathematics Education Library, vol 40. Springer, Boston, MA. https://doi.org/10.1007/0-387-24530-8_12
Download citation
DOI: https://doi.org/10.1007/0-387-24530-8_12
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-24529-4
Online ISBN: 978-0-387-24530-0
eBook Packages: Humanities, Social Sciences and LawEducation (R0)