Intuition in Mathematical and Probabilistic Reasoning Page 1 of 18 PRINTED FROM OXFORD HANDBOOKS ONLINE (www.oxfordhandbooks.com). (c) Oxford University Press, 2014. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a title in Oxford Handbooks Online for personal use (for details see Privacy Policy ). Subscriber: Oxford University Press - Master Gratis Access; date: 03 July 2014 Subject: Psychology, Cognitive Psychology, Developmental Psychology Online Publication Date: Mar 2014 DOI: 10.1093/oxfordhb/9780199642342.013.016 Intuition in Mathematical and Probabilistic Reasoning Kinga Morsanyi and Denes Szucs Oxford Handbooks Online Abstract and Keywords Many people have a fragmented knowledge and understanding of the rules of mathematics and probability. As a consequence, they struggle with selecting the appropriate strategies to solve problems, and they often rely on intuitive solutions instead of normative rules. The purpose of this chapter is to introduce some typical intuitive strategies that people might apply when they solve mathematical or probability problems. Then the chapter describes the notions of primary and secondary intuitions, and gives an overview of the factors that might affect the selection of a particular intuitive strategy (such as certain individual differences variables and task characteristics). Finally, the chapter discusses the implications of these findings for researchers and educators. Keywords: fluency, heuristics, biases, individual differences, intuitive rules, primary and secondary intuitions, probabilistic reasoning, randomness, saliency, thinking dispositions Introduction Mathematics, similarly to other scientific subjects, is based on a complex system of interrelated concepts, principles, and procedures. Although most people study mathematics at school for many years, it is only a small minority who feel comfortable with the subject. Indeed, mathematics is notorious for eliciting feelings of anxiety and ‘threat’ (see, e.g., Moore, Rudig, & Ashcraft (in press) for a review). In order to explore the origins of people’s difficulty with understanding different forms of numerical information, we will first give an overview of some typical errors that people make when they try to solve mathematical or probabilistic reasoning problems. We will argue that most people have fragmented knowledge of the rules, procedures, and concepts of mathematics, and, as a result, they are susceptible to use inappropriate strategies to approach problems. In particular, we will focus on the inappropriate use of intuitive strategies (i.e. responses or procedures that come quickly and easily to mind, and which are usually accompanied by feelings of ease and confidence—see, e.g., Fischbein, 1987; Thompson & Morsanyi, 2012). Intuitive strategies are usually very simple, and can be applied automatically, without much conscious reflection. These strategies might be based on personal experiences in real-life settings (i.e. primary intuitions—cf. Fischbein, 1987) or they might develop as a result of formal education (i.e. secondary intuitions). Although intuitive responses are often correct or, at least, satisfactory, here we will focus on the cases where intuition leads to systematic error and bias. Understanding the intuitive sources of typical errors is essential for educators working in the areas of mathematics and probability, as mistaken intuitions can make it hard for students to grasp certain concepts. After reviewing some of the typical intuitive strategies that people tend to adopt, we will explore the cognitive and contextual factors that affect the choice between different strategies to solve problems and, ultimately, the likelihood that a person will be able to find the correct solution. Finally, we will discuss the relevance of these findings for educators and researchers. As described above, mathematics is considered to be a difficult subject, and people are often confused when they are confronted with numerical information in everyday settings. For example, Gigerenzer, Hertwig, Van den Broek, Fasolo, and Katsikopoulos (2005) asked pedestrians in a number of big cities in Europe and the USA what it means