The Probability Knowledge of Secondary School Students After Teaching

Keywords: Probability, Knowledge, Random compound experiments, Secondary school

Abstract

This article studies the knowledge on Probability of Brazilian secondary school students, after having attended Probability classes. 203 students from the 3rd year of secondary school participated in the study, who attended a public school and a private school in the region of Brasília. The students solved several Probability questions, of which we will analyse two here. In both questions, between two events, the students were asked to identify the most likely or whether both were equally likely. In terms of results, there was a poor student performance, clearly worse in the case of public-school students. Fundamentally, students based the correct answers on determining probabilities or comparing the number of favourable cases, while incorrect answers resulted from the equiprobability of getting any side of the die, ignoring the order of results, comparing the number of white and black balls, and comparing simple probabilities.

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Author Biographies

José António Fernandes, Universidade do Minho

Doutor em Educação pela Universidadedo Minho (UMinho). Professor associado aposentado da Universidade do Minho (UMinho), Braga, Portugal.

Bruno Marx Braga, Instituto Federal de Brasília

Mestre profissional em Matemática pela Universidade de Brasília (UnB). Professor do Instituto Federal de Brasília (IFB), Brasília, DF, Brasil.

References

BARDIN, L. Análise de conteúdo. Lisboa: Edições 70, 2002.

BATANERO, Carmen; HENRY, Michel; PARZYSZ, Bernard. The nature of chance and probability. In: Jones, Graham. A. (Ed.). Exploring probability in school: Challenges for teaching and learning. New York, NY: Springer, 2005. p. 15-37.

BATANERO, Carmen.; BOROVCNIK, Manfred. Statistics and probability in high school. Rotterdam, Holanda: Sense Publishers, 2016.

BRASIL. Ministério da Educação. Base Nacional Comum Curricular. Brasília: MEC, 2017. Disponível em: <http://basenacionalcomum.mec.gov.br/>. Acesso em: 30 jan. 2020.

CARDEÑOSO, José María; MORENO, Amable; GARCÍA-GONZÁLES, Esther.; JIMÉNEZ-FONTANA Rocío. El sesgo de equiprobabilidad como dificultad para comprender la incertidumbre en futuros docentes argentinos. Avances de Investigación en Educación Matemática, Badajoz, v.11, p.145-166, 2017.

DÍAZ, Carmen; CONTRERAS, José Miguel; BATANERO, Carmen; ROA, Rafael. Evaluación de sesgos en el razonamiento sobre probabilidad condicional en futuros profesores de educación secundaria. Bolema, Rio Claro, v. 26, n. 22, p. 1207-1226, 2012.

FERNANDES, José António. Concepções erradas na aprendizagem de conceitos probabilísticos. Dissertação (Mestrado em Educação) - Universidade do Minho, Braga, Portugal, 1990.

FERNANDES, José António. Intuições e aprendizagem de probabilidades: uma proposta de ensino de probabilidades no 9.º ano de escolaridade. Tese (Doutorado em Educação) - Universidade do Minho, Braga, Portugal, 2000.

FERNANDES, José António. Intuições probabilísticas em alunos do 8.º e 11.º anos de escolaridade. Quadrante, Lisboa, v. 10, n. 2, p. 3-32, 2001.

FERNANDES, José António; GEA, María Magladena. Conhecimento de futuros professores dos primeiros anos escolares para ensinar probabilidades. Avances de Investigación en Educación Matemática, Badajoz, v. 14, p. 15-30, 2018.

FERNANDES, José António; BATANERO, Carmen; CORREIA, Paulo Ferreira; GEA, María Magladena. Desempenho em probabilidade condicionada e probabilidade conjunta de futuros professores do ensino básico. Quadrante, Lisboa, v. 23, n. 1, p. 43-61, 2014.

FERNANDES, José António; CORREIA, Paulo Ferreira; CONTRERAS, José Miguel. Ideias intuitivas de alunos do 9.º ano em probabilidade condicionada e probabilidade conjunta. Avances de Investigación en Educación Matemática, Badajoz, v. 4, p. 5–26, 2013.

FERNANDES, José António; GONÇALVES, Gabriela; BARROS, Paula Maria. Formato da informação no cálculo de probabilidades por futuros professores dos primeiros anos. HOLOS, Natal, v. 35, n. 2, 2019.

FISCHBEIN, Efraim; BARBAT, Ileana; MÎNZAT, I. Primary and secondary intuitions in the introduction of probability. In: E. Fischbein. The intuitive sources of probabilistic thinking in children (Appendix I). Dordrecht: D. Reidel Publishing Company, 1975. p. 138-155.

FISCHBEIN, Efraim; SCHNARCH, Ditza. The evolution with age of probabilistic, intuitively based misconceptions. Journal for Research in Mathematics Education, Reston, v. 28, n. 1, p. 96-105, 1997.

GREEN, David Robert. Probability concepts in 11-16 year old pupils. Tese (Doutorado em Matemática) - Loughborough University of Technology, Loughborough, Reino Unido, 1982.

LECOUTRE, Marie-Paule; DURANT, Jean-Luc. Jugements probabilistes et modèles cognitifs: étude d'une situation aléatoire. Educational Studies in Mathematics, Dordrecht, v. 19, p. 357-368, 1988.

PIAGET, Jean; INHELDER, Bärbel. La genèse de l'idée de hasard chez l'enfant. Paris: Presses Universitaires de France, 1951.

POLLATSEK, Alexander; WELL, Arnold; KONOLD, Clifford; HARDIMAN, Pamela; COBB, George. Understanding conditional probabilities. Organitation, Behavior and Human Decision Processes, San Diego, v. 40, p. 255-269, 1987.

TVERSKY, Amos; KAHNEMAN, Daniel. Judgment under uncertainty: Heuristics and biases. In: KAHNEMAN, Daniel; SLOVIC, Paul; TVERSKY, Amos (Eds.). Judgment under uncertainty: Heuristics and biases. Cambridge: Cambridge University Press, 1982. p. 3-20.

TVERSKY, Amos; KAHNEMAN, Daniel. Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment. Psychological Review, Washington, v. 90, n. 4, p. 293-315, 1983.

WATSON, Jane. The probabilistic reasoning of middle school students. In: Jones, G. A. (Ed.). Exploring probability in school: Challenges for teaching and learning. New York, NY: Springer, 2005. p. 145-169.

WATSON, Jane; MORITZ, Jonathan. School students’ reasoning about conjunction and conditional events. International Journal of Mathematical Education in Science and Technology, London, v. 33, n. 1, p. 59-84, 2002.

Published
2023-12-21
How to Cite
FERNANDES, J. A.; BRAGA, B. M. The Probability Knowledge of Secondary School Students After Teaching. Revemop, v. 5, p. e202311, 21 Dec. 2023.
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Article