Skip to main content
SpringerLink
Log in

Research on Uncertainty

  • Chapter
  • First Online:
International Handbook of Research in Statistics Education

Part of the book series: Springer International Handbooks of Education ((SIHE))

Abstract

We discuss research on the teaching and learning of uncertainty, with a particular emphasis on quantifiable aspects as might be represented by probability. We acknowledge earlier reviews of the field by integrating research, especially from the last 10 years, with previous studies. In particular, we focus on three issues, which have become increasingly significant: (1) the realignment of previous work on heuristics and biases, (2) conceptual and experiential engagement with uncertainty and (3) adopting a modelling perspective on probability. The role of the teacher in shaping the learning environment in various critical ways emerges as a key finding. In the concluding section, we indicate promising directions for research, including the need for more exploratory research in new areas such as the role of modelling and carefully designed experiments to test hypotheses that are apparent from more established studies.

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

Access this chapter

Log in via an institution

Institutional subscriptions

References

  • Abrahamson, D. (2009a). Orchestrating semiotic leaps from tacit to cultural quantitative reasoning—The case of anticipating experimental outcomes of a quasi-binomial random generator. Cognition and Instruction, 27(3), 175–224.

    Article  Google Scholar 

  • Abrahamson, D. (2009b). A student’s synthesis of tacit and mathematical knowledge as a researcher’s lens on bridging learning theory. In M. Borovcnik and R. Kapadia (Eds.), Research and developments in probability education [Special Issue]. International Electronic Journal of Mathematics Education, 4(3), 195–226.

    Google Scholar 

  • Abrahamson, D., Berland, M., Shapiro, B., Unterman, J., & Wilensky, U. (2006). Leveraging epistemological diversity through computer-based argumentation in the domain of probability. Learning of Mathematics, 26(3), 39–45.

    Google Scholar 

  • Abrahamson, D., Gutiérrez, J. F., & Baddorf, A. K. (2012). Try to see it my way: The discursive function of idiosyncratic mathematical metaphor. Mathematical Thinking and Learning, 14(1), 55–80.

    Article  Google Scholar 

  • Abrahamson, D., & Wilensky, U. (2007). Learning axes and bridging tools in a technology-based design for statistics. International Journal of Computers and Mathematical Learning, 12(1), 23–55.

    Article  Google Scholar 

  • Ainley, J., Pratt, D., & Hansen, A. (2006). Connecting engagement and focus in pedagogic task design. British Educational Research Journal, 32(1), 23–38.

    Article  Google Scholar 

  • Babai, R., Brecher, T., Stavy, S., & Tirosh, D. (2006). Intuitive interference in probabilistic reasoning. International Journal of Science and Mathematics Education, 4(4), 627–639.

    Article  Google Scholar 

  • Bakhtin, M. M. (1986). Speech genres and other late essays (trans: McGee, V. W.). Austin, TX, University of Texas Press.

    Google Scholar 

  • Bennett, D. (2014). Sticking to your guns: A flawed heuristic for probabilistic decision-making. In E. J. Chernoff & B. Sriraman (Eds.), Probabilistic thinking: Presenting plural perspectives (pp. 261–281). Dordrecht: Springer Science+BusinessMedia.

    Chapter  Google Scholar 

  • Ben-Zvi, D., Aridor, K., Makar, K., & Bakker, A. (2012). Students’ emergent articulations of uncertainty while making informal statistical inferences. ZDM: The International Journal on Mathematics Education, 44(7), 913–925.

    Article  Google Scholar 

  • Biehler, R., Ben-Zvi, D., Bakker, A., & Makar, K. (2013). Technologies for enhancing statistical reasoning at the school level. In M. A. Clements, A. Bishop, C. Keitel-Kreidt, & J. Kilpatrick (Eds.), Third international handbook of mathematics education (pp. 643–688). New York: Springer Science+Business Media.

    Google Scholar 

  • Biehler, R., Frischemeier, D., & Podworny, S. (2015). Elementary preservice teachers’ reasoning about modelling a “family factory” with TinkerPlots—A pilot study. Proceedings of the International Collaboration for Research on Statistical Reasoning, Thinking and Learning, SRTL-9 (pp. 146–175). Paderborn, Germany.

    Google Scholar 

  • Bodemer, N., Meder, B., & Gigerenzer, G. (2014). Communicating relative risk changes with baseline risk: Presentation format and numeracy matter. Medical Decision Making, 34(5), 615–627.

    Article  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 

  • Bryant, P., & Nunes, T. (2012). Children’s understanding of probability: A literature review. London: Nuffield Foundation.

    Google Scholar 

  • Canada, D. (2006). Elementary pre-service teachers’ conceptions of variation in a probability context. Statistics Education Research Journal, 5(1), 36–64.

    Google Scholar 

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

    Google Scholar 

  • Chernoff, E. J. (2012). Recognizing revisitation of the representativeness heuristic: An analysis of answer key attributes. ZDM Mathematics Education, 44(7), 941–952.

    Article  Google Scholar 

  • Chernoff, E. J., & Sriraman, B. (2014). Probabilistic thinking: Presenting plural perspectives. New York: Springer.

    Book  Google Scholar 

  • Chernoff, E. J., & Zazkis, R. (2011). From personal to conventional probabilities: From sample set to sample space. Educational Studies in Mathematics, 77(1), 15–33.

    Article  Google Scholar 

  • Chiesi, F., & Primi, C. (2009). Recency effects in primary-age children and college students. International Electronic Journal of Mathematics Education, 4(3), 259–274.

    Google Scholar 

  • Corter, J. E., & Zahner, D. (2007). Use of external visual representations in probability problem solving. Statistics Education Research Journal, 6(1), 22–50.

    Google Scholar 

  • Diaz, C., & Batanero, C. (2009). University students’ knowledge and biases in conditional probability reasoning. International Electronic Journal of Mathematics Education, 4(3), 131–162.

    Google Scholar 

  • English, L. D., & Watson, J. M. (2016). Development of probabilistic understanding in fourth grade. Journal for Research in Mathematics Education, 47(1), 28–62.

    Article  Google Scholar 

  • Fast, G. R. (2007). Analogical reconstruction of the probability knowledge of Zimbabwean female secondary school students. Canadian Journal of Science, Mathematics and Technology Education, 7(2–3), 149–181.

    Article  Google Scholar 

  • Fielding-Wells, J. (2015). Young children’s development and use of models as evidence in support of informal statistical inference. Proceedings of the International Collaboration for Research on Statistical Reasoning, Thinking and Learning, SRTL-9 (pp. 98–106). Paderborn, Germany.

    Google Scholar 

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

    Book  Google Scholar 

  • Francisco, J. M., & Maher, C. A. (2005). Conditions for promoting reasoning in problem solving: Insights from a longitudinal study. Journal of Mathematical Behavior, 24(2–3), 361–372.

    Article  Google Scholar 

  • Gal, I. (2005). Towards ‘probability literacy’ for all citizens. In G. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 39–63). New York: Springer.

    Chapter  Google Scholar 

  • Gigerenzer, G. (1991). How to make cognitive illusions disappear: Beyond heuristics and biases. In W. Stroebe & M. Hewstone (Eds.), European review of social psychology (Vol. Volume 2, pp. 83–115). Chichester, UK: Wiley.

    Google Scholar 

  • Gigerenzer, G. (1993). The bounded rationality of probabilistic mental models. In K. I. Manktelow & D. E. Over (Eds.), Rationality: Psychological and philosophical perspectives (pp. 284–313). London: Routledge.

    Google Scholar 

  • Gigerenzer, G. (1994). Why the distinction between single-event probabilities and frequencies is important for psychology (and vice versa). In G. Wright & P. Ayton (Eds.), Subjective probability (pp. 129–161). Chichester, UK: Wiley.

    Google Scholar 

  • Gigerenzer, G. (2012). Contribution to panel ‘What Can Economists Know: Rethinking the Foundations of Economic Understanding’. The Institute for New Economic Thinking’s (INET) Paradigm Lost Conference, Berlin. Retrieved June 5, 2017, from https://www.youtube.com/watch?v=DdEEwoKkfMA.

  • Gigerenzer, G. (2014). Risk savvy: How to make good decisions. London, UK: Allen Lane.

    Google Scholar 

  • Hacking, I. (1975). The Emergence of Probability: A philosophical Study of Early Ideas about Probability, Induction and Statistical Inference. Cambridge: Cambridge University Press.

    Google Scholar 

  • Ireland, S., & Watson, J. (2009). Building a connection between experimental and theoretical aspects of probability. International Electronic Journal of Mathematics Education, 4(3), 339–370.

    Google Scholar 

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

    Book  Google Scholar 

  • Jones, G. A., Langrall, C., & Mooney, E. S. (2007). Research in probability: Responding to classroom realities. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 909–955). Greenwich, CT: Information Age Publishing, Inc. and NCTM.

    Google Scholar 

  • Jones, G. A., Langrall, C. W., Thornton, C. A., & Mogill, A. T. (1997). A framework for assessing and nurturing young children’s thinking in probability. Educational Studies in Mathematics, 32(2), 101–125.

    Article  Google Scholar 

  • Kafoussi, S. (2004). Can kindergarten children be successfully involved in probabilistic tasks? Statistics Education Research Journal, 3(1), 29–39.

    Google Scholar 

  • Kahneman, D. (1996). On the reality of cognitive illusions. Psychological Review, 103(3), 582–591.

    Article  Google Scholar 

  • Kahneman, D. (2011a). Thinking fast and slow. Farrar, NY: Straus and Giroux.

    Google Scholar 

  • Kahneman, D. (2011b). Thinking fast and slow, Google Talks. Retrieved June 5, 2017, from https://www.youtube.com/watch?v=CjVQJdIrDJ0.

  • Kahneman, D. (1991). Judgment and decision making: A personal view, Psychological Science, 2(3), 12–145.

    Google Scholar 

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

    Book  Google Scholar 

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

    Book  Google Scholar 

  • Kazak, S. (2010). Modeling random binomial rabbit hops. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies: ICTMA 13 (pp. 561–570). New York: Springer.

    Chapter  Google Scholar 

  • Kazak, S. (2015). ‘How confident are you?’: Supporting young students’ reasoning about uncertainty in chance games through students’ talk and computer simulations. In A. Zieffler & E. Fry (Eds.), Reasoning about uncertainty: Learning and teaching informal inferential reasoning (pp. 29–55). Minneapolis, MN: Catalyst Press.

    Google Scholar 

  • Kazak, S., & Pratt, D. (2015). Pre-service mathematics teachers’ informal statistical inference when building probability models for a chance game. Proceedings of the International Collaboration for Research on Statistical Reasoning, Thinking and Learning, SRTL-9 (pp. 138–145). Paderborn, Germany.

    Google Scholar 

  • Kazak, S., Wegerif, R., & Fujita, T. (2015a). Combining scaffolding for content and scaffolding for dialogue to support conceptual breakthroughs in understanding probability. ZDM Mathematics Education, 47(7), 1269–1283.

    Article  Google Scholar 

  • Kazak, S., Wegerif, R., & Fujita, T. (2015b). The importance of dialogic processes to conceptual development in mathematics. Educational Studies in Mathematics, 90(2), 105–120.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Konold, C., Harradine, A., & Kazak, S. (2007). Understanding distributions by modeling them. International Journal of Computers for Mathematical Learning, 12(3), 217–230.

    Article  Google Scholar 

  • Konold, C., & Kazak, S. (2008). Reconnecting data and chance. Technology Innovations in Statistics Education, 2(1), Article 1. Retrieved from http://repositories.cdlib.org/uclastat/cts/tise/vol2/iss1/art1

    Google Scholar 

  • Konold, C., Madden, S., Pollatsek, A., Pfannkuch, M., Wild, C., Ziedins, I., et al. (2011). Conceptual challenges in coordinating theoretical and data-centered estimates of probability. Mathematical Thinking and Learning, 13(1–2), 68–86.

    Article  Google Scholar 

  • Konold, C., & Miller, C. D. (2011). TinkerPlots 2.0: Dynamic data exploration. Emeryville, CA: Key Curriculum.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Konold, C., Pollatsek, A., Well, A., Lohmeier, J., & Lipson, A. (1993). Inconsistencies in students’ reasoning about probability. Journal for Research in Mathematics Education, 24(5), 393–414.

    Article  Google Scholar 

  • Kustos, P., & Zelkowski, J. (2013). Grade-continuum trajectories of four known probabilistic misconceptions: What are students’ perceptions of self-efficacy in completing probability tasks? Journal of Mathematical Behaviour, 32(3), 508–526.

    Article  Google Scholar 

  • Lecoutre, M. P., Rovira, K., Lecoutre, B., & Poitevineau, J. (2006). People’s intuitions about randomness and probability: An empirical approach. Statistics Education Research Journal, 5(1), 20–35.

    Google Scholar 

  • Lee, H. S., Angotti, R. L., & Tarr, J. E. (2010). Making comparisons between observed data and expected outcomes: Students’ informal hypothesis testing with probability simulation tools. Statistics Education Research Journal, 9(1), 68–96.

    Google Scholar 

  • Lee, H. S., & Lee, J. T. (2009). Reasoning about probabilistic phenomena: Lessons learned and applied in software design. Technology Innovations in Statistics Education, 3(2). Retrieved from http://escholarship.org/uc/item/1b54h9s9.

  • Lehrer, R., Kim, M. J., & Schauble, L. (2007). Supporting the development of conceptions of statistics by engaging students in measuring and modeling variability. International Journal of Computers for Mathematical Learning, 12(3), 195–216.

    Article  Google Scholar 

  • Lehrer, R., & Schauble, L. (2010). What kind of explanation is a model? In M. K. Stein & L. Kucan (Eds.), Instructional explanation in the disciplines (pp. 9–22). New York: Springer.

    Chapter  Google Scholar 

  • Liu, Y., & Thompson, P. W. (2007). Teachers’ understandings of probability. Cognition and Instruction, 25(2), 113–160.

    Article  Google Scholar 

  • Meder, B., & Gigerenzer, G. (2014). Statistical thinking: No one left behind. In E. J. Chernoff & B. Sriraman (Eds.), Probabilistic thinking: Presenting plural perspectives (pp. 127–148). Dordrecht: Springer Science+Business Media.

    Chapter  Google Scholar 

  • Mercer, N., & Sams, C. (2006). Teaching children how to use language to solve maths problems. Language and Education, 20(6), 507–528.

    Article  Google Scholar 

  • National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • Nilsson, P. (2007). Different ways in which students handle chance encounters in the explorative setting of a dice game. Educational Studies in Mathematics, 66(3), 293–315.

    Article  Google Scholar 

  • Noll, J., & Shaughnessy, M. (2012). Aspects of students’ reasoning about variation in empirical sampling distributions. Journal for Research in Mathematics Education, 43(5), 509–556.

    Article  Google Scholar 

  • Nunes, T., Bryant, P., Evans, D., Gottardis, L., & Terlektsi, M.-E. (2014). The cognitive demands of understanding the sample space. ZDM Mathematics Education, 46(3), 437–448.

    Article  Google Scholar 

  • Paparistodemou, E. (2014). Children’s constructions of a sample space with respect to the Law of Large Numbers. In E. J. Chernoff & B. Sriraman (Eds.), Probabilistic Thinking: Presenting plural perspectives (pp. 600–611). Dordrecht: Springer Science+Business Media.

    Google Scholar 

  • Paparistodemou, E., Noss, R., & Pratt, D. (2008). The interplay between fairness and randomness in a spatial computer game. International Journal of Computers and Mathematical Learning, 13(2), 89–110.

    Article  Google Scholar 

  • Pfannkuch, M., & Ziedins, I. (2014). A modelling perspective on probability. In E. J. Chernoff & B. Sriraman (Eds.), Probabilistic thinking: Presenting plural perspectives (pp. 101–116). Dordrecht: Springer Science+Business Media.

    Chapter  Google Scholar 

  • Piaget, J., & Inhelder, B. (1951). The origin of the idea of chance in children. New York: Norton.

    Google Scholar 

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

    Article  Google Scholar 

  • Pratt, D., & Noss, R. (2002). The micro-evolution of mathematical knowledge: The case of randomness. Journal of the Learning Sciences, 11(4), 453–488.

    Article  Google Scholar 

  • Pratt, D., & Noss, R. (2010). Designing for mathematical abstraction. International Journal of Computers for Mathematical Learning, 15(2), 81–97.

    Article  Google Scholar 

  • Prediger, S. (2008). Do you want me to do it with probability or with my normal thinking?—Horizontal and vertical views on the formation of stochastic conceptions. International Electronic Journal of Mathematics Education, 3(3), 126–154.

    Google Scholar 

  • Prodromou, T. (2012). Connecting experimental probability and theoretical probability. ZDM Mathematics Education, 44(7), 855–868.

    Article  Google Scholar 

  • Prodromou, T., & Pratt, D. (2006). The role of causality in the co-ordination of two perspectives on distribution within a virtual simulation. Statistics Education Research Journal, 5(2), 69–88.

    Google Scholar 

  • Prodromou, T., & Pratt, D. (2013). Making sense of stochastic variation and causality in a virtual environment. Technology, Knowledge and Learning, 18(3), 121–147.

    Article  Google Scholar 

  • Ruthven, K., & Hofmann, R. (2013). Chance by design: Devising an introductory probability module for implementation at scale in English early-secondary education. ZDM Mathematics Education, 45(3), 409–423.

    Article  Google Scholar 

  • Schnell, S., & Prediger, S. (2012). From “everything changes” to “for high numbers, it changes just a bit”. ZDM Mathematics Education, 44(7), 825–840.

    Article  Google Scholar 

  • Shaughnessy, M. (1992). Research in probability and statistics: Reflections and directions. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 465–494). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Smith, T. M., & Hjalmarson, M. A. (2013). Eliciting and developing teachers’ conceptions of random processes in a probability and statistics course. Mathematical Thinking and Learning, 15(1), 58–82.

    Article  Google Scholar 

  • Stanovich, K. E., & West, R. F. (2000). Individual differences in reasoning: Implications for the rationality debate? Behavioural and Brain Sciences, 23(5), 645–665.

    Article  Google Scholar 

  • Taleb, N. N. (2010). The black swan: The impact of the highly improbable. London: Penguin.

    Google Scholar 

  • Watson, J., & Callingham, R. (2013). Likelihood and sample size: The understandings of students and their teachers. Journal of Mathematical Behavior, 32(3), 660–672.

    Article  Google Scholar 

  • Watson, A., Jones, K., & Pratt, D. (2013). Key ideas in teaching mathematics: Research-based guidance for ages 9–19. Oxford, UK: Oxford University Press.

    Google Scholar 

  • Weisburg, H. I. (2014). Willful ignorance: The mismeasure of uncertainty. Hoboken, NJ: Wiley.

    Book  Google Scholar 

  • Wild, C. J. (2006). The concept of distribution. Statistics Education Research Journal, 5(2), 10–26.

    Google Scholar 

  • Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry (with discussion). International Statistical Review, 67(3), 223–265.

    Article  Google Scholar 

  • Zahner, D., & Corter, J. E. (2010). The process of probability problem solving: use of external visual representations. Mathematical Thinking and Learning, 12(2), 177–204.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Education, University College London, London, UK

    Dave Pratt

  2. Faculty of Education, Pamukkale University, Denizli, Turkey

    Sibel Kazak

Authors
  1. Dave Pratt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sibel Kazak
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dave Pratt .

Editor information

Editors and Affiliations

  1. Faculty of Education, The University of Haifa, Haifa, Israel

    Dani Ben-Zvi

  2. School of Education, University of Queensland, St Lucia, Queensland, Australia

    Katie Makar

  3. Department of Educational Psychology, The University of Minnesota, Minneapolis, Minnesota, USA

    Joan Garfield

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Pratt, D., Kazak, S. (2018). Research on Uncertainty. In: Ben-Zvi, D., Makar, K., Garfield, J. (eds) International Handbook of Research in Statistics Education. Springer International Handbooks of Education. Springer, Cham. https://doi.org/10.1007/978-3-319-66195-7_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-66195-7_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66193-3

  • Online ISBN: 978-3-319-66195-7

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics

Search

Navigation