There is no evidence for order mattering; therefore, order does not matter: An appeal to ignorance

Referencias

Abrahamson, D. (2009). 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. Batanero, C., Chernoff, E., Engel, J. Lee, H., & Sánchez, E. (2016). Research on Teaching and Learning Probability. ICME-13. Topical Survey series. New York: Springer. Borovcnik, M. (2012). Multiple perspectives on the concept of conditional probability. Avances de Investigación en Educación Matemática 2, 5-27. Chernoff, E. J. (2009a). Explicating the multivalence of a probability task. In S. L. Swars, D.W. Stinson, & S. Lemons-Smith (Eds.), Proceedings of the Thirty-First Annual Meeting of the North-American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 653–661). Atlanta, GA: Georgia State University. Chernoff, E. J. (2009b). Sample space partitions: An investigative lens. Journal of Mathematical Behavior, 28(1), 19–29. Chernoff, E. J. (2009c). The subjective-sample-space. In S. L. Swars, D. W. Stinson, & S. Lemons-Smith (Eds.), Proceedings of the Thirty-First Annual Meeting of the NorthAmerican Chapter of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 628–635). Atlanta, GA: Georgia State University. Chernoff, E. J. (2011). Investigating relative likelihood comparisons of multinomial, contextual sequences. In D. Pratt (Ed.), Proceedings of Working Group 5: Stochastic Thinking of the Seventh Congress of the European Society for Research in Mathematics Education. Rzeszów, Poland: University of Rzeszów. Retrieved from http://www.cerme7.univ.rzeszow.pl/WG/5/CERME_Chernoff.pdf Chernoff, E. J. (2012a). Logically fallacious relative likelihood comparisons: The fallacy of composition. Experiments in Education, 40(4), 77–84. Chernoff, E. J. (2012b). Providing answers to a question that was not asked. Proceedings of the Fifteenth Annual Conference of the Special Interest Group of the Mathematical Association of American on Research in Undergraduate Mathematics Education (SIGMAA on RUME). Portland, Oregon. Chernoff, E. J., & Russell, G. L. (2011a). An informal fallacy in teachers’ reasoning about probability. In L. R. Wiest & T. Lamberg (Eds.), Proceedings of the 33rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 241–249). Reno, NV: University of Nevada, Reno. Chernoff, E. J., & Russell, G. L. (2011b). An investigation of relative likelihood comparisons: the composition fallacy. In B. Ubuz (Ed.), Proceedings of the Thirty-fifth annual meeting of the International Group for the Psychology of Mathematics Education (Vol. II, pp. 225–232). Ankara, Turkey: Middle East Technical University. Chernoff, E. J., & Russell, G. L. (2012a). The fallacy of composition: Prospective mathematics teachers’ use of logical fallacies. Canadian Journal for Science, Mathematics and Technology Education, 12(3), 259-271. Chernoff, E. J., & Russell, G. L. (2012b). Why order does not matter: An appeal to ignorance. In Van Zoest, L. R., Lo, J. J., & Kratky, J. L. (Eds.), Proceedings of the 34th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1045–1052). Kalamazoo, MI: Western Michigan University. Chernoff, E. J., & Zazkis, R. (2010). A problem with the problem of points. In P. Brosnan, D. Erchick, & L. Flevares (Eds.), Proceedings of the Thirty-Second Annual Meeting of the North-American Chapter of the International Group for the Psychology of Mathematics Education (Vol. VI, pp. 969–977). Columbus, OH: Ohio State University. 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. Curtis, G. N. (2011). Fallacy files: Appeal to ignorance. Retrieved from http://www.fallacyfiles.org/ignorant.html. Evans, J. S. B. T., & Pollard, P. (1981). Statistical judgment: A further test of the representativeness heuristic. Acta Psychologica, 51, 91–103. Gómez, E., Batanero, C., & Contreras, C. (2013). Conocimiento matemático de futuros profesores para la enseñanza de la probabilidad desde el enfoque frecuencial. Bolema 28(48), 209-229. Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers' topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372-400. Jones, G. A., Langrall, C. W., & Mooney, E. S. (2007). Research in probability: Responding to classroom realties. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 909–955). New York: Macmillan. Kahneman, D. (2011). Thinking, fast and slow. New York: Farrar, Straus and Giroux. Kahneman, D., & Tversky, A. (1972). Subjective probability: A judgment of representativeness. Cognitive Psychology, 3, 430–454. Konold, C. (1989). Informal conceptions of probability. Cognition and Instruction, 6(1), 59–98. 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), 392–414. Kunda, Z., & Nisbett, R. E. (1986). Prediction and partial understanding of the law of large numbers. Journal of Experimental Social Psychology, 22(4), 339–354. Lecoutre, M.-P. (1992). Cognitive models and problem spaces in “purely random” situations. Educational Studies in Mathematics, 23(6), 557–569. Peirce, C. S. (1931). Principles of philosophy. In C. Hartshorne, & P. Weiss (Eds.), Collected papers of Charles Sanders Peirce (Vol. 1). Cambridge, MA: Harvard University Press. Shaughnessy, J. M. (1977). Misconceptions of probability: An experiment with a small group, activity-based, model building approach to introductory probability at the college level. Educational Studies in Mathematics, 8, 285–316. Shaughnessy, J. M. (1992). Research in probability and statistics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 465-494). New York: Macmillan. Stohl, H. (2005). Probability in teacher education and development. In G. A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 345-366). New York: Springer. Strauss & Corbin. (1998). Basics of qualitative research techniques and procedures for developing grounded theory (2nd ed.). London: Sage. Thompson, P. W. (2008). Conceptual analysis of mathematical ideas: Some spadework at the foundations of mathematics education. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano, & A. Sépulveda (Eds.), Plenary paper presented at the annual meeting of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 45–64). Morélia, Mexico: PME. Retrieved from http://pat-thompson.net/PDFversions/ 2008ConceptualAnalysis.pdf Tversky, A., & Kahneman, D. (1971). Belief in the law of small numbers. Psychological Bulletin, 76, 105-110. Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185, 1124–1131. Von Glaserveld, E. (1995). Radical constructivism: a way of knowing and learning. Florence, KY: Psychology Press. Von Glaserveld, E. (1995). Radical constructivism: A way of knowing and learning. Florence, KY: Psychology Press. Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458-477. Yackel, E., Rasmussen, C., & King, K. (2000). Social and sociomathematical norms in an advanced undergraduate mathematics course. Journal of Mathematics Behavior, 19(3), 275-287.