Abstracts - Earli

intuition was conducted by Fischbein (1987), resulting in the intuitive rules theory (Stavy &Tirosh, 2000). Recently, intuitively-rooted mathematical knowledge is studied from conceptualchangeperspectives (Vosniadou & Verschaffel, 2004), and intuitive/analytic distinctions are madefrom situated-cognition viewpoints (Vinner, 1997). Parallelled by this dualism, dual-processingaccounts originated in (cognitive) psychological research, including decision making (Kahneman,2002), social cognition (Chaiken & Trope, 1999), and reasoning (Evans, 2003). Roughly, suchaccounts contrast heuristic processes (associative, rapid, automatic, effortless) with analyticprocesses (rule-based, slow, sequential, controlled). Both may compete for the control ofbehaviour. The symposium aims at discussing how recent dualist cognitive-psychological theoriesand methodologies can deepen our understanding of problem-solving processes, and considerspossible instructional outcomes of such findings. Inglis et al. found that mathematicians respondbetter to a classical logic task than the general well-educated population. Their inspection-timeeye-movement data showed that mathematical education correlates with the use of analyticalprocesses that can override preconscious attention biases. Three other contributions use recentmethodologies – so far applied in cognitive psychology and neuroscience – to address the intuitiveand analytical reasoning processes related to problem solving. Gillard et al. characterisedproportional reasoning as intuitively-based, by experimentally restricting students’ reaction timeswhile solving word problems. Stavy et al. used reaction time and fMRI measurements to showhow participants reason when overcoming intuitive interference and addressed the role of salienceand working memory. Babai el al. showed that conflict training activates control mechanisms toovercome intuitive problem-solving interference, but elongated reaction times indicated that thesereasoning processes were effortful. The symposium shows that such methodologies could deepenour understanding of students’ reasoning processes, enabling to develop and to evaluateinstruction.Studying advanced mathematics is correlated with analytical reasoning on the Wason SelectionTaskMatthew Inglis, Institute of Education, University of Warwick, United KingdomDerrick G. Watson, Department of Psychology, University of Warwick, United KingdomAdrian Simpson, School of Education, University of Durham, United KingdomTwo experiments are reported that examine successful mathematicians’ responses to the WasonSelection Task, a classic logic task designed to interrogate reasoning behaviour (Wason, 1968).Experiment 1 found that the range of answers given by mathematics undergraduates andresearchers was different to the typical range of answers made by the general well-educatedpopulation, both in terms of the proportion selecting the logically correct answer, and in terms ofthe non-logical responses that they made. In Experiment 2 these differences were investigatedfurther using an inspection time eye-movement methodology. It was found that mathematiciansspend longer inspecting the cards mentioned in the rule that they reject (the rejected matchingcards) than the general population. These findings are analysed in terms of the heuristic-analyticdual process theory (Evans, 2006). It is argued that studying advanced mathematics is correlatedwith the use of analytical processes on the Wason Selection Task.– 132 –