Probabilistic thinking and probability literacy in the context of risk
Pensamento probabilístico e alfabetização em probabilidade no contexto do risco

Manfred Borovcnik

Resumo


Abstract

The aim of this paper is to develop and synthesise ideas about probabilistic thinking and highlight the considerations by illustrating how the concept of probability is entrenched with the concept of risk. We use a hermeneutic way of argument, relate the ideas to the mathematical and philosophical background of probability, and illustrate our ideas by examples that relate probability considerations to risk. Special features of competing intuitions and strategies link probabilistic thinking to its roots in psychology, to the paradigm of causality, to its empirical expressions, and to thinking and decisions. Higher-ordered probabilistic thinking is described by the categories of the theoretical character of probability, conditional probability, and by the construct of probabilistic evidence. The robustness of probabilistic misconceptions is explained by an archetypical way of thinking. The peculiar logic of decisions adds to probabilistic thinking. Finally, the purpose of probability is declared as central issue for teaching and understanding probability. Throughout, the connection of probability to risk enhances probabilistic concepts and reveals a twin-character of probability and risk.


Resumo

O objetivo deste artigo é desenvolver e sintetizar ideias sobre o pensamento probabilístico e destacar as considerações apresentadas ilustrando como o conceito de probabilidade está enraizado no conceito de risco. Utilizamos argumentação hermenêutica, articulando as ideas com o quadro teórico matemático e filosófico da probabilidade, e ilustramos nossas ideas por meio de exemplos que relacionam probabilidade e risco. Características especiais de intuições e estratégias concorrentes ligam o pensamento probabilístico às suas raízes na psicologia, ao paradigma da causalidade, às suas expressões empíricas, ao pensamento e às decisões. O pensamento probabilístico de ordem superior é descrito pelas categorias de caráter teórico da probabilidade, probabilidade condicional e pela construção da evidência probabilística. A robustez dos equívocos probabilísticos é explicada por um modo de pensar arquetípico. A lógica peculiar das decisões é adicionada ao pensamento probabilístico. Finalmente, o propósito da probabilidade é declarado como questão central para o seu ensino e compreensão. Assim, a conexão da probabilidade ao risco realça conceitos probabilisticos e revela um caráter dialético da probabilidade e do risco.


Palavras-chave


Probabilistic thinking, Probability literacy, Risk literacy, Mathematical thinking, Theoretical character of probability, Probabilistic evidence, Conditional probability, Archetypical strategies, Logic of decisions, Insurance contract

Texto completo:

PDF

Referências


BATANERO, C.; HENRY, M.; PARZYSZ, B. The nature of chance and probability. In: A. G. Jones (Ed.), Exploring probability in school: challenges for teaching and learning, p. 15–37. New York: Springer, 2005.

BATANERO, C.; BOROVCNIK, M. Statistics and probability in high school. Rotterdam: Sense Publishers, 2016.

BOROVCNIK, M. Fundamentale Ideen als Organisationsprinzip in der Mathematik-Didaktik. In: Schriftenreihe zur Didaktik der Mathematik der Österreichischen Mathematischen Gesellschaft (ÖMG), v. 27, p. 17-32, 1997.

BOROVCNIK, M. Probabilistic and statistical thinking. In: M. Bosch (Ed.): Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education. Barcelona: European Society for Research in Mathematics Education, p. 484-506, 2006.

BOROVCNIK, M. Strengthening the role of probability within statistics curricula. In: C. Batanero, G. Burrill, C. Reading, & A. Rossman (Eds.), Statistics in School Mathematics. Challenges for Teaching and Teacher Education, p. 71-84. New York: Springer, 2011.

BOROVCNIK, M. Multiple perspectives on the concept of conditional probability. In: Avances de Investigación en Didactica de la Matemática, v.1, n.2, p. 5-27, 2012.

BOROVCNIK, M. Risk and decision making: The “logic” of probability. In: The Mathematics Enthusiast, v.12, n.1-3, p. 113-139, 2015.

BOROVCNIK, M.; KAPADIA, R. Risk in health: more information and more uncertainty. In: Proceedings of IASE Satellite on “Statistics Education and Outreach”. Voorburg: ISI, 6 pp, 2011a.

BOROVCNIK, M.; KAPADIA, R. Determinants of decision-making in risky situations. In: Proceedings of the 58th World Statistics Congress. Voorburg: ISI, 6 pp, 2011b.

BOROVCNIK, M.; KAPADIA, R. Modelling in probability and statistics – Key ideas and innovative examples. In J. Maaß; J. O’Donoghue (Eds.), Real-world problems for secondary school students, pp. 1-44. Rotterdam: Sense Publishers, 2011c.

BOROVCNIK, M.; KAPADIA, R. A historical and philosophical perspective on probability. In: E. J. Chernoff, & B. Sriraman (Eds.), Probabilistic thinking: presenting plural perspectives, p. 7-34. Berlin: Springer, 2014.

BOROVCNIK, M.; KAPADIA, R. Reasoning with risk – A survival guide. In C. Batanero; E. Chernoff; J. Engel; H. Lee; E. Sánchez. Research on teaching and learning probability. New York: Springer, 2017, to appear.

DUBBEN, H.-H.; BECK-BORNHOLDT, H.-P. Mit an Sicherheit grenzender Wahrscheinlichkeit (With a probability that comes close to certainty). Logisches Denken und Zufall. Reinbek: Rowohlt, 2010.

DÜRR, D.; GOLDSTEIN, S.; TUMULKA, R.; ZANGHI, N. Bohmian mechanics and quantum field theory. In: Physical Review Letters, v.93, n.9, 2004.

FINETTI, B. de, La prévision: ses lois logiques, ses sources subjectives. In: Annales Institut Henri Poincaré, v.7, p. 1-68. Foresight: Its logical laws, its subjective sources in: S. Kotz; N. L. Johnson, Breakthroughs in statistics. v1, p. 134-174. New York: Springer, 1937/1992.

FISCHBEIN, E. The intuitive sources of probabilistic thinking in children. Dordrecht: Reidel, 1975.

FISCHBEIN, E. Intuition in science and mathematics. An educational approach. Dordrecht: Reidel, 1987.

GIGERENZER, G. Calculated risks: how to know when numbers deceive you. New York: Simon & Schuster, 2002.

HEITELE, D. An epistemological view on fundamental stochastic ideas. In: Educational Studies in Mathematics v.6, p. 187-205, 1975.

KAHNEMAN, D; TVERSKY, A. Subjective probability. A judgment of representativeness. In: Cognitive Psychology v.3, n.3, p. 430-454, 1972.

KAHNEMAN, D.; TVERSKY, A. Prospect theory: an analysis of decision under risk. In: Econometrica, v.47, n.2, p. 263-292, 1979.

KAPADIA, R.; BOROVCNIK, M. (Eds.) Chance encounters: probability in education. Dordrecht: Kluwer, 1991.

KOLMOGOROV, A. N. Foundations of the theory of probability. New York: Chelsea, 1933/1956.

KONOLD, C. Informal conceptions of probability. In: Cognition and Instruction, v.6, n.1, p. 59-98, 1989.

LECOUTRE, M. P. Cognitive models and problem spaces in “purely random” situations. In: Educational Studies in Mathematics v.23, n.6, p. 557-568, 1992.

PIAGET, J.; INHELDER, B. La genèse de l’idée de hasard chez l’enfant (The origin of the idea of chance in children). Paris: Presses Universitaires de France, 1951.

SPIEGELHALTER, D. Comments on probabilistic thinking. In: E. J. Chernoff; B. Sriraman (Eds.), Probabilistic thinking: presenting plural perspectives (Backcover). New York: Springer, 2014.

SPIEGELHALTER, D.; GAGE, J. What can education learn from real-world communication of risk and uncertainty? In: The Mathematics Enthusiast, v.12, n.1-3, p. 4-10, 2015.

STYER, D. F. The strange world of quantum mechanics. Cambridge: Cambridge University Press, 2000.


Métricas do artigo

Carregando Métricas ...

Metrics powered by PLOS ALM


INDEXADORES DA REVISTA