Abstract

CARVALHO, Maria José  and  FREITAS, Adelaide. Knowledge level in conditional probability and independence of events: a study case in the portuguese high school. Relime [online]. 2016, vol.19, n.1, pp.41-69. ISSN 2007-6819.  https://doi.org/10.12802/relime.13.1912.

Taking two problem-situations involving conditional probability, independence and incompatibility, we suggest the measurements of the performance and the scientific rigor of a response using, in parallel, two ordinal Likert scale measures. Based on the responses given by 43 students in 12th grade (age 17), a descriptive analysis of these measurements was executed in order to evaluate the levels of knowledge of the students in those concepts. The results showed that not always a correct written response comes with rigor. Besides, an interpretative analysis of the same responses confirmed the existence of conflicts in the teaching of those concepts in Portugal. The conflicts are concerning with the interpretation and the calculation of conditional probabilities and the notions of independence and incompatibility. The present study recommends more practice on the mathematical formulation of statements involving conditional probability and more emphasis on the probabilistic feature of the notion of independence.

Keywords : Concept of conditional probability; Concept of independent events; Concept of mutually exclusive events; Degree of performance; Degree of scientific rigor.

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