Researching Conditional Probability Problem Solving

The chapter is organized into two parts. In the first one, the main protagonist is the conditional probability problem. We show a theoretical study about conditional probability problems, identifying a particular family of problems we call ternary problem

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Abstract The chapter is organized into two parts. In the first one, the main protagonist is the conditional probability problem. We show a theoretical study about conditional probability problems, identifying a particular family of problems we call ternary problems of conditional probability. We define the notions of Level, Category and Type of a problem in order to classify them into sub-families and in order to study them better. We also offer a tool we call trinomial graph that functions as a generative model for this family of problems. We show the syntax of the model that allows researchers and teachers to translate a problem in terms of the trinomial graphs language, and the consequences of this translation. In the second part, there are two main related protagonists: ternary problems of conditional probability and students solving them. Thus, the students’ probabilistic thinking is observed in a broader problem-solving context, in relation to the task variables of problems: structure, context and data format variables. We report some of the results of our investigation into students’ behaviours, showing how these depend in any manner on those task variables.

1 Introduction An alternative perspective in which probabilistic thinking could also be considered is offered in this article. This alternative consists in placing probabilistic thinking in a problem solving framework. This article, although implicitly, also formulates an invitation to consider probability problem solving as a research field for the probabilistic educators and researchers community, still not systematically tackled, as we can check, for example, in Jones and Thornton (2005). Basically, researching into probability problem solving should involve three elements, individually and in relation to each other: problems, students solving these problems and teachers teaching students to solve them. About the problems themselves we have very little information. We do not know what problems students M.P. Huerta (B) Departament de Didàctica de la Matemàtica, University of Valencia, Avenida de Tarongers, 4, 46022, Valencia, Spain e-mail: [email protected] E.J. Chernoff, B. Sriraman (eds.), Probabilistic Thinking, Advances in Mathematics Education, DOI 10.1007/978-94-007-7155-0_33, © Springer Science+Business Media Dordrecht 2014

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have to solve, what characteristics problems possess that might have an influence on students’ behaviour and which make them so difficult to solve. We have not yet considered in which direction teaching models should be addressed so that they could help students to become competent and probabilistically literate in the actual uses of the probability. It is hoped that in this chapter researchers and teachers can find hints as to in which direction future approaches to teaching conditional probability could be based, such as, for example, exploring context of uses by means of solving problems (Carles and Huerta 2007; Huerta 2009). In this article, in particular, we talk about conditional probability problem

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