Conceptos fundamentales y sus propiedades clave en probabilidad: cómo identificarlos y proporcionar intuiciones que los sostengan

Referencias

Batanero, C. (2016). Understanding randomness: Challenges for research and teaching. In K. Krainer and N. Vondrová (Eds.), Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education (pp. 34-49). Prague: ERME. Batanero, C. & Borovcnik, M. (2016). Statistics and probability in high school. Rotterdam: Sense. Batanero, C., Chernoff, E., Engel, J. Lee, H., & Sánchez, E. (2016). Research on teaching and learning probability. ICME-13 Topical Surveys. Cham, Switzerland: Springer. Batanero, C., Henry, M., & Parzysz, B. (2005). The nature of chance and probability. In: A. G. Jones (Ed.), Exploring probability in school (pp. 15-37). New York: Springer. Bennett, D. J. (1999). Randomness. Cambridge, MA: Harvard University Press. Borovcnik, M. (1992). Stochastik im Wechselspiel von Intuitionen und Mathematik (Stochastics in the interplay between intuitions and mathematics). Mannheim: Bibliographisches Institut. 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. 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. (pp. 71-83). New York: Springer. Borovcnik, M. (2012). Multiple perspectives on the concept of conditional probability. Avances de Investigación en Didactica de la Matemática, 1(2), 5-27. Borovcnik, M. (2015a). Central theorems of probability theory and their impact on probabilistic intuitions. In J. M. Contreras, et al. (Eds.), Didáctica de la Estadística, Probabilidad y Combinatoria, 2 (pp. 15-35). Granada, Universidad de Granada. Borovcnik, M. (2015b). Risk and decision making: The “logic” of probability. The Mathematics Enthusiast, 12(1, 2 & 3), 113-139. Borovcnik, M., & Bentz, H. J. (1990, 2003). Intuitive Vorstellungen von Wahrscheinlichkeits- konzepten: Fragebögen und Tiefeninterviews (Intuitive conceptions of probability: Questionnaire and in-depth interviews). Technical Reports. Klagenfurt University. Borovcnik, M., Kapadia, R. (2011). Modelling in probability and statistics – Key ideas and innovative examples. In J. Maaß, & J. O‘Donoghue (Eds.), Real-World Problems for Secondary School Students–Case Studies (pp. 1-44). Rotterdam: Sense Publishers. Borovcnik, M., & Kapadia, R. (2014). A historical and philosophical perspective on probability. In E. J. Chernoff & B. Sriraman (Eds.), Probabilistic thinking: presenting plural perspectives (pp. 7-34). New York: Springer. Borovcnik, M. & Kapadia, R. (2018). Reasoning with risk: Teaching probability and risk as twin concepts. In C. Batanero & E. J. Chernoff (Eds.), Teaching and Learning Stochastics – Advances in Probability Education Research (pp. 3-22). ICME 13 Topic Series. Cham, Switzerland: Springer International Publishing. Carranza, P. & Kuzniak, A. (2008). Duality of probability and statistics teaching in French education. 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. Monterrey: ICMI and IASE. Chernoff, E. J. (2013). Probabilistic relativism: A multivalentological investigation of normatively incorrect relative likelihood comparisons. Philosophy of Mathematics Education Journal, 27, 1-30. Chernoff, E. & Sriraman, B. (Eds.) (2014). Probabilistic thinking: presenting plural perspectives. Advances in Mathematics Education (Vol. 7). New York: Springer. de Finetti, B. (1937/1992). La prévision: ses lois logiques, ses sources subjectives. Annales Institut Henri Poincaré, 7, 1-68 (1937); English translation: Foresight: Its logical laws, its subjective sources. In S. Kotz, & N. L. Johnson (Eds.), Breakthroughs in statistics. (pp. 134-174). New York, Berlin: Springer Finetti, B. (1974). Theory of probability. New York: Wiley (Translated by A. Machi & A. Smith). David, F. N. (1962). Games, gods and gambling. London: Griffin. Dubben, H.-H., & Beck-Bornholdt, H.-P. (2010). Mit an Sicherheit grenzender Wahrscheinlichkeit. Logisches Denken und Zufall. Reinbek: Rowohlt. Dürr, D., Goldstein, S., Tumulka, R., & Zanghi, N. (2004). Bohmian mechanics and quantum field theory. In: Physical Review Letters, 93(9). Fischbein, E. (1975). The intuitive sources of probabilistic thinking in children. Dordrecht: Reidel. Fischbein, E. (1987). Intuition in science and mathematics. Dordrecht: Reidel. Gal, I. (2002). Adults’ statistical literacy: Meanings, components, responsibilities (with discussion). International Statistical Review, 70(1), 1-51. Gal, I. (2005). Towards “probability literacy” for all citizens: Building blocks and instructional dilemmas. In G.A. Jones (Ed.), Exploring probability in school (pp. 39-63). Dordrecht: Kluwer. Gigerenzer, G. (2002). Calculated risks: How to know when numbers deceive you. New York: Simon & Schuster. Hacking, I. (1975). The emergence of probability. Cambridge: Cambridge University Press. Heitele, D. (1975). An epistemological view on fundamental stochastic ideas. Educational Studies in Mathematics, 6, 187-205. Jones, G. A., Langrall, C.W., & Mooney, E. S. (2007). Research in probability: Responding to classroom realities. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning, Vol. 2 (pp. 909-956). Greenwich, CT: Information Age Publishing. Kahneman, D. & Tversky, A. (1972). Subjective probability. A judgment of representativeness. Cognitive Psychology 3(3), 430-454. Kahneman, D. & Tversky, A. (1973). Availability: A heuristic for judging frequency and probability. Cognitive Psychology, 5(2), 207-232 Kahneman, D. & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263-292. Kahneman, D., Slovic, P., & Tversky, A. (1982). Judgment under uncertainty: Heuristics and biases. Cambridge: Cambridge University Press. Kapadia, R., Borovcnik, M. (Eds.) (1991). Chance encounters. Probability in education. Dordrecht: Kluwer. Kolmogorov, A. N. (1933/1956). Grundbegriffe der Wahrscheinlichkeitsrechnung. Berlin; English translation: Foundations of the theory of probability. New York: Chelsea. Konold, C. (1989). Informal conceptions of probability. Cognition and Instruction, 6(1), 59-98. Laplace, P. S. de (1814/1995). Théorie analytique des probabilités, 2nd ed. Paris: Courcier; 1st ed. 1812; reprinted 1995. Paris: Jacques Gabay. Lecoutre, M. P. (1992). Cognitive models and problem spaces in “purely random” situations. Educational Studies in Mathematics, 23(6), 557-568. Mises, R. v. (1919). Grundlagen der Wahrscheinlichkeitsrechnung. Mathematische Zeitschrift, 5, 52–99. Piaget, J. & Inhelder, B. (1951). La genèse de l’idée de hasard chez l’enfant (The origin of the idea of chance in children). Paris: Presses Universitaires de France. Simons, P. R. (1984). Instructing with analogies. Journal of Educational Psychology, 76(3), 513–527. Spiegelhalter, D. (2014a). Probabilistic thinking. In: E. J. Chernoff & B. Sriraman (Eds.), Probabilistic thinking: presenting plural perspectives (Back cover). New York: Springer. Spiegelhalter, D. (2014b, April). What can education learn from real-world communication of risk and uncertainty? Eight British Congress on Mathematical Education, Nottingham. Steinbring, H. (1991). The theoretical nature of probability in the classroom. In: R. Kapadia & M. Borovcnik (Eds.). Chance encounters (pp. 135-167). Dordrecht: Kluwer. Styer, D. F. (2000). The strange world of quantum mechanics. Cambridge: Cambridge University Press. Székely, G.J. (1986). Paradoxes in probability and mathematical statistics. Dordrecht: Reidel. Tversky, A. & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185, 1124- 1130. von Plato, J. (1994). Creating modern probability: its mathematics, physics and philosophy in historical perspective. Cambridge: Cambridge University Press.