Skip to main content

Strengthening the Role of Probability Within Statistics Curricula

  • Chapter
  • First Online:

Part of the book series: New ICMI Study Series ((NISS,volume 14))

Abstract

This chapter illustrates probability as a type of thinking, which has its own existence even without a theoretical study. While such thinking is usually omitted in teaching, it is deep-rooted. The success of probabilistic models as compared to other, possibly primitive approaches is difficult to judge. This might hinder learners in accepting and applying – not to speak of understanding – the concepts. Probabilistic models seem to resemble scenarios more directly than fit perfectly to real situations. This runs contrary to current trends to reduce the link between probability and data to relative frequencies. A wider framework for the interpretation seems to be required. Consequences of such views on randomness and probability for teaching statistics are described.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Albert, J. (1997). Teaching Bayes’ rule: A data-oriented approach. American Statistician, 51(3), 247–253.

    Google Scholar 

  • Barnett, V. (1973). Comparative statistical inference. New York: Wiley.

    Google Scholar 

  • Batanero, C., Burrill, G., Reading, C., & Rossman, A. (Eds.) (2008). Joint ICMI/IASE Study: Teaching Statistics in School Mathematics. Challenges for Teaching and Teacher Education. Proceedings of the ICMI Study 18 and 2008 IASE Round Table Conference. Monterrey, Mexico: International Commission on Mathematical Instruction and International Association for Statistical Education. Online: www.stat.auckland.ac.nz/~iase/publications

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

    Chapter  Google Scholar 

  • Berger, J. O. (1993). Statistical decision theory and Bayesian analysis. New York: Springer.

    Google Scholar 

  • Bernoulli, Jacques (1987). Ars conjectandi4ème partie (N. Meunier, Trans.). Rouen, France: Institut de Recherche sur l’Enseignement Mathematique (Original work published in 1713).

    Google Scholar 

  • Berry, D. A. (1997). Teaching elementary Bayesian statistics with real applications in science. American Statistician, 51(3), 241–246.

    Google Scholar 

  • Borovcnik, M. (1996). Fundamentale Ideen als Organisationsprinzip in der Mathematik-Didaktik (Fundamental ideas as organizing logic in the didactics of mathematics). In K. P. Müller (Ed.), Beiträge zum Mathematikunterricht (pp. 106–109). Hildesheim: Franzbecker.

    Google Scholar 

  • Borovcnik, M. (2006). Probabilistic and statistical thinking. In M. Bosch (Ed.), Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education (pp. 484–506). Barcelona: European Society for Research in Mathematics Education. Online: ermeweb.free.fr/CERME4/

    Google Scholar 

  • Borovcnik, M., & Bentz, H. J. (1990/2003). Intuitive Vorstellungen von Wahrscheinlichkeitskonzepten: Fragebögen und Tiefeninterviews. (Intuitive conceptions of probabilistic concepts: Questionnaire and in-depth interviews.) (Technical Reports). Klagenfurt am Wörthersee: Klagenfurt University.

    Google Scholar 

  • Borovcnik, M., & Peard, R. (1996). Probability. In A. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 239–288). Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Carranza, P., & Kuzniak, A. (2008). Duality of probability and statistics teaching in French education. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (2008).

    Google Scholar 

  • Chaput, B., Girard, J. C., & Henry, M. (2008). Modeling and simulations in statistics education. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (2008).

    Google Scholar 

  • David, F. N. (1962). Games, gods and gambling. London: Charles Griffin.

    Google Scholar 

  • Díaz, C., & Batanero, C. (2009). University Students’ Knowledge and Biases in Conditional Probability Reasoning. International Electronic Journal of Mathematics Education, 4(3), 131–162. Online: www.iejme.com/

    Google Scholar 

  • Diderot, D. (1983). Jacques le Fataliste (Jacques the Fatalist). Paris: Le Livre de Poche (Original work published 1796).

    Google Scholar 

  • Dürr, D., Goldstein, S., Tumulka, R., & Zanghi, N. (2004, August 24). Bohmian mechanics and quantum field theory. Physical Review Letters, 93(9). Online: arxiv.org/abs/quant-ph/0303156v2.

    Google Scholar 

  • Falk, R., & Konold, C. (1992). The psychology of learning probability. In F. Sheldon & G. Sheldon (Eds.), Statistics for the twenty-first century (MAA notes 26, pp. 151–164). Washington, DC: The Mathematical Association of America.

    Google Scholar 

  • Fischbein, E. (1975). The intuitive sources of probabilistic thinking in children. Dordrecht, The Netherlands: Reidel.

    Book  Google Scholar 

  • Fischbein, E. (1987). Intuitions in science and mathematics. An educational approach. Dordrecht, The Netherlands: Reidel.

    Google Scholar 

  • Garuti, R., Orlandoni, A., & Ricci, R. (2008). Which probability do we have to meet? A case study about statistical and classical approach to probability in students’ behaviour. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (2008).

    Google Scholar 

  • Gigerenzer, G. (2002). Calculated risks: How to know when numbers deceive you. New York: Simon & Schuster.

    Google Scholar 

  • Girard, J. C. (2008). The Interplay of probability and statistics in teaching and in training the teachers in France. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (2008).

    Google Scholar 

  • Hacking, I. (1990). The taming of chance. Cambridge, UK: Cambridge University Press.

    Google Scholar 

  • Heitele, D. (1975). An epistemological view on fundamental stochastic ideas. Educational Studies in Mathematics, 6, 187–205.

    Article  Google Scholar 

  • Kahneman, D., & Tversky, A. (1972). Subjective probability: A judgement of representativeness. Cognitive Psychology, 3, 430–454.

    Article  Google Scholar 

  • Kapadia, R., & Borovcnik, M. (1991). Chance encounters: Probability in education. Dordrecht, The Netherlands: Kluwer.

    Book  Google Scholar 

  • Kiaer, A. N. (1899). Die repräsentative Untersuchungsmethode (The representative method of investigation). Allgemeines Statistisches Archiv, 5, 1–22.

    Google Scholar 

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

    Article  Google Scholar 

  • Laplace, P. S. (1995). Théorie analytique des probabilités (Analytical theory of probabilities). Paris: Jacques Gabay. (Original work published 1814).

    Google Scholar 

  • Lysø, K. (2008, July). Strengths and limitations of informal conceptions in introductory probability courses for future lower secondary teachers. Paper presented at the Eleventh International Congress on Mathematics Education (ICME 11), Topic Study Group 13Research and development in the teaching and learning of probability”. Monterrey, Mexico. Online: tsg.icme11.org/tsg/show/14

    Google Scholar 

  • Moore, D. S. (1997). Bayes for beginners? Some reasons to hesitate. American Statistician, 51(3), 254–261.

    Google Scholar 

  • Nemetz, T. (1997). An overview of the teaching of probability in secondary schools. In B. Phillips (Ed.), Papers on statistical education presented at ICME 9 (pp. 75–86). Hawthorn: Swinburne University.

    Google Scholar 

  • Ottaviani, M. G. (2008). The interplay of probability and statistics in teaching and in training the teachers. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (2008).

    Google Scholar 

  • Peters, E. (2008). Numeracy and the perception and communication of risk. Annals of the New York Academy of Science, 1128, 234–267.

    Article  Google Scholar 

  • Styer, D. F. (2000). The strange world of quantum mechanics. Cambridge, UK: Cambridge University Press.

    Google Scholar 

  • Tversky, A., & Kahneman, D. (1980). Causal schemas in judgment under uncertainty. In M. Fishbein (Ed.), Progress in social psychology. Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Tversky, A., & Kahneman, D. (1983). Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment. Psychological Review, 90(4), 293–315.

    Article  Google Scholar 

  • vos Savant, M. (n.d.). Game show problem. Online: www.marilynvossavant.com/articles/gameshow.html

  • Witmer, J., Short, T. H., Lindley, D. V., Freedman, D. A., & Scheaffer, R. L. (1997). Teacher’s corner. Discussion of papers by Berry, Albert, and Moore, with replies from the authors. American Statistician, 51(3), 262–274.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Manfred Borovcnik .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Borovcnik, M. (2011). Strengthening the Role of Probability Within Statistics Curricula. In: Batanero, C., Burrill, G., Reading, C. (eds) Teaching Statistics in School Mathematics-Challenges for Teaching and Teacher Education. New ICMI Study Series, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1131-0_11

Download citation

Publish with us

Policies and ethics