Prospective Primary School Teachers’ Perception of Randomness

Referencias bibliográficas

• Ayer, A. J. (1974). El azar [Chance]. In M. Kline (Ed.), Matemáticas en el mundo moderno (pp. 171–172). Barcelona: Blume.
• 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.
• 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.
• Bar-Hillel, M., & Wagenaar, W. A. (1991). The perception of randomness. Advances in Applied Mathematics, 12, 428–454.
• 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/.
• Batanero, C., & Díaz, C. (2012). Training teachers to teach probability: reflections and challenges. Chilean Journal of Statistics, 3(1), 3–13.
• 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/.
• 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.
• Batanero, C., & Serrano, L. (1999). The meaning of randomness for secondary school students. Journal for Research in Mathematics Education, 30(5), 558–567.
• 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.
• Bennett, D. J. (1998). Randomness. Cambridge: Harvard University Press.
• 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.
• Borovcnik, M. (2012). Multiple perspectives on the concept of conditional probability. AIEM. Avances de Investigación en Educación Matemática, 2, 5–27.
• 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.
• 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.
• Chernoff, E. (2009a). Subjective probabilities derived from the perceived randomness of sequences of outcomes. Unpublished Ph.D. Thesis, Simon Fraser University.
• Chernoff, E. (2009b). Sample space partitions: an investigative lens. The Journal of Mathematical Behavior, 28, 19–29.
• 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).
• 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.
• 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.
• 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.
• Falk, R., & Konold, C. (1997). Making sense of randomness: implicit encoding as a basis for judgment. Psychological Review, 104, 301–318.
• Fine, T. L. (1973). Theories of probability. An examination of foundations. London: Academic Press.
• Fischbein, E., & Gazit, A. (1984). Does the teaching of probability improve probabilistic intuitions? Educational Studies in Mathematics, 15(1), 1–24.
• Fischbein, E., Nello, M. S., & Marino, M. S. (1991). Factors affecting probabilistic judgements in children and adolescents. Educational Studies in Mathematics, 22, 523–549.
• 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.
• 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.
• 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.
• 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.
• 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.
• Green, D. R. (1991). A longitudinal study of pupil’s probability concepts (Technical Report ME90/91). Loughborough University of Technology.
• Hawkins, A., Jolliffe, F., & Glickman, L. (1991). Teaching statistical concepts. London: Longman.
• 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.
• 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.
• Jones, G. (2005). Introduction. In G. Jones (Ed.), Exploring probability in school: challenges for teaching and learning (pp. 1–12). New York: Springer.
• 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/.
• Konold, C. (1989). Informal conceptions of probability. Cognition and Instruction, 6, 59–98.
• 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.
• Kyburg, H. E. (1974). The logical foundations of statistical inference. Boston: Reidel.
• 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.
• 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.
• Langer, E. J. (1975). The illusion of control. Journal of Personality and Social Psychology, 32, 311–328.
• Laplace, P. S. (1995). Théorie analytique des probabilités (Analytical theory of probabilities). Paris: Jacques Gabay (Original work published 1814).
• 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/.
• Ma, L. P. (1999). Knowing and teaching elementary mathematics. Mahwah: Erlbaum.
• 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.
• Ministério da Educação (1997). Parâmetros curriculares nacionais: Matemática [National curricular parameters Mathematics]. Brasilia: Author.
• NCTM (2000). Principles and standards for school mathematics. Reston: NCTM. Online: standards.nctm.org/.
• Nickerson, R. S. (2002). The production and perception of randomness. Psychological Review, 109, 330–357.
• 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.
• 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.
• Poincaré, H. (1936). Chance. Journal of the American Statistical Association, 31, 10–30.
• Pratt, D. (2000). Making sense of the total of two dice. Journal for Research in Mathematics Education, 31(5), 602–626.
• Toohey, P. G. (1995). Adolescent perceptions of the concept of randomness. Unpublished Master’s Thesis, University of Adelaide.
• 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.
• von Mises, R. (1952). Probability, statistics and truth. London: William Hodge. (Original work published in 1928).
• Wagenaar, W. A. (1972). Generation of random sequences by human subjects: a critical survey of literature. Psychological Bulletin, 77, 65–72.
• Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223–265.
• 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.