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Prospective Primary School Teachers’ Perception of Randomness

  • Chapter
Probabilistic Thinking

Part of the book series: Advances in Mathematics Education ((AME))

Abstract

Subjective perception of randomness has been researched by psychologists and mathematics educators, using a variety of tasks, resulting in a number of different descriptions for the biases that characterize people’s performances. Analysing prospective teachers’ possible biases concerning randomness is highly relevant as new mathematics curricula for compulsory teaching levels are being proposed that incorporate increased study of random phenomena. In this chapter, we present results of assessing perception of randomness in a sample of 208 prospective primary school teachers in Spain. We first compare three pairs of random variables deduced from a classical task in perception of randomness and deduce the mathematical properties these prospective teachers assign to sequences of random experiments. Then, the written reports, where prospective teachers analyse the same variables and explicitly conclude about their own intuitions are also studied. Results show a good perception of the expected value and poor conception of both independence and variation as well as some views of randomness that parallel some naïve conceptions on randomness held at different historic periods.

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References

  • Ayer, A. J. (1974). El azar [Chance]. In M. Kline (Ed.), Matemáticas en el mundo moderno (pp. 171–172). Barcelona: Blume.

    Google Scholar 

  • Azcárate, P., Cardeñoso, J. M., & Porlánd, R. (1998). Concepciones de futuros profesores de educación primaria sobre la noción de aleatoriedad [Prospective primary school teachers’ conceptions on the notion of randomness]. Enseñanza de las Ciencias, 16(1), 85–97.

    Google Scholar 

  • Ball, D. L., Lubienski, S. T., & Mewborn, D. S. (2001). Research on teaching mathematics: the unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teaching (pp. 433–456). Washington: American Educational Research Association.

    Google Scholar 

  • Bar-Hillel, M., & Wagenaar, W. A. (1991). The perception of randomness. Advances in Applied Mathematics, 12, 428–454.

    Article  Google Scholar 

  • Batanero, C., Arteaga, P., & Ruiz, B. (2010). Statistical graphs produced by prospective teachers in comparing two distributions. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of the sixth European conference of research in mathematics education, CERME-6 conference. Lyon: ERME. Online: www.inrp.fr/editions/editions-electroniques/cerme6/.

    Google Scholar 

  • Batanero, C., & Díaz, C. (2012). Training teachers to teach probability: reflections and challenges. Chilean Journal of Statistics, 3(1), 3–13.

    Google Scholar 

  • Batanero, C., Godino, J. D., & Roa, R. (2004). Training teachers to teach probability. In Journal of Statistics Education (Vol. 12). Online: www.amstat.org/publications/jse/.

    Google Scholar 

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

    Chapter  Google Scholar 

  • Batanero, C., & Serrano, L. (1999). The meaning of randomness for secondary school students. Journal for Research in Mathematics Education, 30(5), 558–567.

    Article  Google Scholar 

  • Batanero, C., Serrano, L., & Green, D. R. (1998). Randomness, its meanings and implications for teaching probability. International Journal of Mathematical Education in Science and Technology, 29(1), 113–123.

    Article  Google Scholar 

  • Bennett, D. J. (1998). Randomness. Cambridge: Harvard University Press.

    Google Scholar 

  • Borovcnik, M. (2011). Strengthening the role of probability within statistics curricula. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics—challenges for teaching and teacher education. A joint ICMI/IASE study (pp. 71–83). New York: Springer.

    Chapter  Google Scholar 

  • Borovcnik, M. (2012). Multiple perspectives on the concept of conditional probability. AIEM. Avances de Investigación en Educación Matemática, 2, 5–27.

    Google Scholar 

  • Chadjipadelis, T., Meletiou, M., & Paparistodemou, E. (2010). Statistics teacher of the new era: another specialized mathematician or a totally different person? In C. Reading (Ed.), Proceedings of the eight international conference on teaching statistics. Lubjana: International Association for Statistical Education. Online: www.stat.auckland.ac.nz/~iase/publications/icots8.

    Google Scholar 

  • Chaput, B., Girard, J. C., & Henry, M. (2011). Modeling and simulations in statistics education. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics—challenges for teaching and teacher education. A joint ICMI/IASE study (pp. 85–95). New York: Springer.

    Chapter  Google Scholar 

  • Chernoff, E. (2009a). Subjective probabilities derived from the perceived randomness of sequences of outcomes. Unpublished Ph.D. Thesis, Simon Fraser University.

    Google Scholar 

  • Chernoff, E. (2009b). Sample space partitions: an investigative lens. The Journal of Mathematical Behavior, 28, 19–29.

    Article  Google Scholar 

  • Dantal, B. (1997). Les enjeux de la modélisation en probabilité. In M. Henry (Coord.), Enseigner les probabilités au lycée (pp. 57–59). Reims: Commission Inter-IREM (The betting of modelling in probability).

    Google Scholar 

  • Engel, J., & Sedlmeier, P. (2005). On middle-school students’ comprehension of randomness and chance variability in data. ZDM. Zentralblatt für Didaktik der Mathematik, 37(3), 168–177.

    Article  Google Scholar 

  • Falk, R. (1981). The perception of randomness. In C. Laborde (Ed.), Proceedings of the fifth international conference for the psychology of mathematics education (pp. 222–229). Grenoble: University of Grenoble.

    Google Scholar 

  • Falk, R., Falk, R., & Ayton, P. (2009). Subjective patterns of randomness and choice: some consequences of collective responses. Journal of Experimental Psychology. Human Perception and Performance, 35(1), 203–224.

    Article  Google Scholar 

  • Falk, R., & Konold, C. (1997). Making sense of randomness: implicit encoding as a basis for judgment. Psychological Review, 104, 301–318.

    Article  Google Scholar 

  • Fine, T. L. (1973). Theories of probability. An examination of foundations. London: Academic Press.

    Google Scholar 

  • Fischbein, E., & Gazit, A. (1984). Does the teaching of probability improve probabilistic intuitions? Educational Studies in Mathematics, 15(1), 1–24.

    Article  Google Scholar 

  • Fischbein, E., Nello, M. S., & Marino, M. S. (1991). Factors affecting probabilistic judgements in children and adolescents. Educational Studies in Mathematics, 22, 523–549.

    Article  Google Scholar 

  • Franklin, C., Kader, G., Mewborn, D. S., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2005). A curriculum framework for K-12 statistics education (GAISE report). American Statistical Association. Online www.amstat.org/education/gaise/.

  • Franklin, C., & Mewborn, D. (2006). The statistical education of pre-K-12 teachers: a shared responsibility. In G. Burrill (Ed.), NCTM 2006 yearbook: thinking and reasoning with data and chance (pp. 335–344). Reston: NCTM.

    Google Scholar 

  • Gal, I. (2005). Towards “probability literacy” for all citizens: building blocks and instructional dilemas. In G. Jones (Ed.), Exploring probability in schools: challenges for teaching and learning (pp. 39–63). New York: Springer.

    Chapter  Google Scholar 

  • Godino, J. D., Batanero, C., Roa, R., & Wilhelmi, M. R. (2008). Assessing and developing pedagogical content and statistical knowledge of primary school teachers through project work. In C. Batanero, G. Burrill, C. Reading, & 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. Monterrey: ICMI and IASE. Online: www.stat.auckland.ac.nz/~iase/publications.

    Google Scholar 

  • Green, D. R. (1983). A survey of probabilistic concepts in 3000 students aged 11–16 years. In D. R. Grey et al. (Eds.), Proceedings of the first international conference on teaching statistics (v.2) (pp. 766–783). Sheffield: University of Sheffield.

    Google Scholar 

  • Green, D. R. (1989). Schools students’ understanding of randomness. In R. Morris (Ed.), Studies in mathematics education: Vol. 7. The teaching of statistics (pp. 27–39). Paris: Unesco.

    Google Scholar 

  • Green, D. R. (1991). A longitudinal study of pupil’s probability concepts (Technical Report ME90/91). Loughborough University of Technology.

    Google Scholar 

  • Hawkins, A., Jolliffe, F., & Glickman, L. (1991). Teaching statistical concepts. London: Longman.

    Google Scholar 

  • Harten, G., & Steinbring, H. (1983). Randomness and stochastic independence. On the relationship between intuitive and mathematical definition. In R. W. Scholz (Ed.), Decision making under uncertainty (pp. 363–373). Amsterdam: Reidel.

    Google Scholar 

  • Jacobbe, T. (2010). Preparing elementary school teachers to teach statistics: an international dilemma. In C. Reading (Ed.), Proceedings of the eight international conference on teaching statistics. Ljubljana: International Association for Statistical Education. Online: www.stat.auckland.ac.nz/~iase/publications/icots8.

    Google Scholar 

  • Jones, G. (2005). Introduction. In G. Jones (Ed.), Exploring probability in school: challenges for teaching and learning (pp. 1–12). New York: Springer.

    Chapter  Google Scholar 

  • Johnston-Wilder, P., & Pratt, D. (2007). The relationship between local and global perspectives on randomness. In D. Pitta & G. Philippou (Eds.), Proceedings of the fifth European conference on research in mathematics education. Lamarca: ERME. Online: www.erme.unito.it/CERME5b/.

    Google Scholar 

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

    Article  Google Scholar 

  • Konold, C., Lohmeier, J., Pollatsek, A., Well, A. D., Falk, R., & Lipson, A. (1991). Novice Views on Randomness. In R. G. Underhill (Ed.), Proceedings of the thirteenth annual meeting of the North American chapter of the international group for the psychology of mathematics education (pp. 167–173). Blacksburg: Virginia Polytechnic Institute and State University.

    Google Scholar 

  • Kyburg, H. E. (1974). The logical foundations of statistical inference. Boston: Reidel.

    Book  Google Scholar 

  • Lahanier-Reuter, D. (1999). Conceptions du hasard et enseignement des probabilités statistiques [Conceptions of chance and teaching of statistics and probability]. París: Presses Universitaires de France.

    Google Scholar 

  • Liu, Y., & Thompson, P. (2002). Randomness: rethinking the foundation of probability. In D. Mewborn, P. Sztajn, E. White, H. Wiegel, R. Bryant, & K. Nooney (Eds.), Proceedings of the twenty fourth annual meeting of the North American chapter of the International Group for the Psychology of Mathematics Education, Athens, GA (Vol. 3, pp. 1331–1334). Columbus. Eric Clearinghouse.

    Google Scholar 

  • Langer, E. J. (1975). The illusion of control. Journal of Personality and Social Psychology, 32, 311–328.

    Article  Google Scholar 

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

    Google Scholar 

  • Lecoutre, M. P., Rovira, K., Lecoutre, B., & Poitevineau, J. (2006). People’s intuitions about randomness and probability: an empirical study. Statistics Education Research Journal, 5, 20–35. Online: www.stat.auckland.ac.nz/~iase/serj/.

    Google Scholar 

  • Ma, L. P. (1999). Knowing and teaching elementary mathematics. Mahwah: Erlbaum.

    Google Scholar 

  • MEC (2006). Real Decreto 1513/2006, de 7 de diciembre, por el que se establecen las enseñanzas mínimas correspondientes a la Educación primaria. Madrid: Author.

    Google Scholar 

  • Ministério da Educação (1997). Parâmetros curriculares nacionais: Matemática [National curricular parameters Mathematics]. Brasilia: Author.

    Google Scholar 

  • NCTM (2000). Principles and standards for school mathematics. Reston: NCTM. Online: standards.nctm.org/.

    Google Scholar 

  • Nickerson, R. S. (2002). The production and perception of randomness. Psychological Review, 109, 330–357.

    Article  Google Scholar 

  • Piaget, J., & Inhelder, B. (1951). La genése de l’idée de hasard chez l’enfant [The origin of the idea of chance in children]. Paris: Presses Universitaires de France.

    Google Scholar 

  • Stohl, H. (2005). Probability in teacher education and development. In G. Jones (Ed.), Exploring probability in schools: challenges for teaching and learning (pp. 345–366). New York: Springer.

    Chapter  Google Scholar 

  • Poincaré, H. (1936). Chance. Journal of the American Statistical Association, 31, 10–30.

    Article  Google Scholar 

  • Pratt, D. (2000). Making sense of the total of two dice. Journal for Research in Mathematics Education, 31(5), 602–626.

    Article  Google Scholar 

  • Toohey, P. G. (1995). Adolescent perceptions of the concept of randomness. Unpublished Master’s Thesis, University of Adelaide.

    Google Scholar 

  • Tversky, A., & Kahneman, D. (1982). Judgement of and by representativeness. In D. Kahneman, P. Slovic y, & A. Tversky (Eds.), Judgement under uncertainty: heuristics and biases (pp. 84–98). Cambridge: Cambridge University Press.

    Chapter  Google Scholar 

  • von Mises, R. (1952). Probability, statistics and truth. London: William Hodge. (Original work published in 1928).

    Google Scholar 

  • Wagenaar, W. A. (1972). Generation of random sequences by human subjects: a critical survey of literature. Psychological Bulletin, 77, 65–72.

    Article  Google Scholar 

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

    Google Scholar 

  • Zabell, S. L. (1992). The quest for randomness and statistical applications. In F. Gordon & S. Gordon (Eds.), Statistics for the XXI Century (pp. 139–150). Washington: Math. Assoc. of America.

    Google Scholar 

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Acknowledgements

Research supported by the project: EDU2010-14947 (MCINN-FEDER) and Group FQM196 (Junta de Andalucía).

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Authors and Affiliations

  1. University of Granada, Granada, Spain

    Carmen Batanero, Pedro Arteaga & Luis Serrano

  2. ITESM, Monterrey, Mexico

    Blanca Ruiz

Authors
  1. Carmen Batanero
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  2. Pedro Arteaga
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  3. Luis Serrano
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  4. Blanca Ruiz
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Correspondence to Carmen Batanero .

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Editors and Affiliations

  1. University of Saskatchewan College of Education, Saskatoon, Saskatchewan, Canada

    Egan J. Chernoff

  2. Dept of Mathematical Sciences, The University of Montana, Montana, Montana, USA

    Bharath Sriraman

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Batanero, C., Arteaga, P., Serrano, L., Ruiz, B. (2014). Prospective Primary School Teachers’ Perception of Randomness. In: Chernoff, E., Sriraman, B. (eds) Probabilistic Thinking. Advances in Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7155-0_19

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