Abstract
The aim of this research was to assess the common knowledge of elementary probability in a sample of 183 prospective primary school teachers using and open-ended task, where teachers had to compute simple, compound and conditional probability from data presented in a two-way table. We base on theoretical ideas from the onto-semiotic approach to perform a semiotic analysis, in which we describe the mathematical objects and processes involved in the solutions of the tasks. Participants in the sample showed a weak common knowledge to compute simple, compound and conditional probabilities from a two-way table: they confused simple, compound and conditional probability; exchanged condition and event in conditional probabilities; confused probability and frequency or the union of events with the intersection. The semiotic analysis is used to provide and explanation for these errors in terms of semiotic conflicts. This list of difficulties expands what was found in previous research and may be used to reinforcing the preparation of prospective teachers to teach probability.
Highlights
Probability has been included in the primary school curriculum in many countries due to the usefulness of probability for daily life, the way in which probability reasoning support decision making and the instrumental role of probability in various curricular areas and professional work (Gal, 2005; Jones, 2005)
Our results suggest that computing simple, compound and conditional probabilities from a two-way table was not easy for participants in the sample who showed a weak common knowledge of probability to solve this task
Many teachers were unable to provide a correct answer to the problems, in agreement with Estrada and Díaz’s (2006) research, or made errors reported in previous research, by Falk (1986)
Summary
Probability has been included in the primary school curriculum in many countries due to the usefulness of probability for daily life, the way in which probability reasoning support decision making and the instrumental role of probability in various curricular areas and professional work (Gal, 2005; Jones, 2005). C. Batanero et al school levels, where students are expected to perform experiments or simulations, formulate questions or predictions, collect and analyze data from these experiments, propose and justify conclusions and predictions that are based on data (Franklin et al, 2007; NCTM, 2000). Batanero et al school levels, where students are expected to perform experiments or simulations, formulate questions or predictions, collect and analyze data from these experiments, propose and justify conclusions and predictions that are based on data (Franklin et al, 2007; NCTM, 2000) The success of these curricula will depend on the extent to which we can educate these teachers to teach probability. The above reasons suggest to us the relevance of assessing the teachers’ educational needs in probability in order to reinforce the specific and the didactic preparation of primary school statistics teachers, when needed
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