2013. In Lindmeier, A. M. & Heinze, A. (Eds.). Proceedings of the 37 th Conference of the International 4 - 113 Group for the Psychology of Mathematics Education, Vol. 4, pp. 113-120. Kiel, Germany: PME. COMPARISON OF EXPERT AND NOVICE PROBLEM SOLVING AT GRADES FIVE AND SIX Benjamin Rott Leibniz University of Hanover Comparing expert and novice performance is a fruitful approach in research on mathematical problem solving, but is there something like expertise in children aged 10 – 12? The problem solving processes of 10 “pupil experts” (successful participants of mathematical competitions) are compared to those of 45 “novices” (regular pupils). The “experts” show superior performance in all of the three tasks that were chosen for this study as well as higher “mental flexibility” in executing the processes which seems to distinguish them from the novices beyond advance in practice. BACKGROUND Problem Solving: As an important part of mathematics, problem solving is fundamental for school mathematics (cf. Schoenfeld 1992, p. 334 ff.). The terms “problem” and “problem solving” have differing meanings ranging from working routine tasks to solving perplexing or difficult situations (ibid., p. 337 ff.) of which I refer to the latter interpretation as in the following definition: “When you are faced with a problem and you are not aware of any obvious solution method, you must engage in a form of cognitive processing called problem solving. Problem solving is cognitive processing directed at achieving a goal when no solution method is obvious to the problem solver […]” (Mayer & Wittrock 2006, p. 287) It is important to note that the attribute “problem” does not depend on the task itself but on the solver. A perplexing situation (sensu Schoenfeld) for one pupil or student can be a routine task for another (e.g., more experienced) one. Thus, research on problem solving should focus on processes. Important factors in such processes are control and heuristics (resources and beliefs being other factors, cf. Schoenfeld 1985, p. 44 f.). The term “control” refers to “the question of resource management and allocation […] [specifically] major decisions regarding planning, monitoring, and assessing solutions on-line” (ibid.). Whereas “heuristics” are “rules of thumb for effective problem solving” (ibid.) or “methods and rules of discovery and invention” (Pólya 1945, p. 112) like working backward or looking for a related problem. Bruder and Collet (2011, p. 34 ff.) 1 claim that successful problem solvers often show intuition and mental flexibility and that a lack of such flexibility can be compensated (up to a certain degree) by learning heuristics. Research results show that missing control leads to failure in problem solving attempts. Schoenfeld (1985, ch. 9), for example, shows in a study with more than 100 students, that successful problem processes contained a significant amount of self-regulation, 1 See Bruder (2003) for an English version: http://www.math-learning.com/files/learnmethod.pdf (12.12.2012).