M. ��llinger et al.: Mental Set and Insight ExperimentalP sychology 2008 Vol. 55(4):269���282 �� 2008 Hogrefe & Huber Publishers Investigating the Effect of Mental Set on Insight Problem Solving Michael ��llinger1, Gary Jones2, and G��nther Knoblich3 1Parmenides Center for the Study of Thinking, Munich, Germany, 2Psychology Department, Nottingham Trent University, UK, 3Psychology Department, Rutgers University, Newark, NJ, USA Abstract. Mental set is the tendency to solve certain problems in a fixed way based on previous solutions to similar problems. The moment of insight occurs when a problem cannot be solved using solution methods suggested by prior experience and the problem solver suddenly realizes that the solution requires different solution methods. Mental set and insight have often been linked together and yet no attempt thus far has systematically examined the interplay between the two. Three experiments are presented that examine the extent to which sets of noninsight and insight problems affect the subsequent solutions of insight test problems. The results indicate a subtle interplay between mental set and insight: when the set involves noninsight problems, no mental set effects are shown for the insight test problems, yet when the set involves insight problems, both facilitation and inhibition can be seen depending on the type of insight problem presented in the set. A two process model is detailed to explain these findings that combines the representational change mechanism with that of proceduralization. Keywords: representational change, insight problem solving, mental set, ACT-R Introduction Mental set and insight are two elementary processes within problem solving. Both concepts are significant for under- standing and explaining a broad range of human problem solving behavior, and yet to date there has been little re- search that examines both within a single problem solving task. Mental set is the tendency to solve certain problems in a fixed way (Luchins & Luchins, 1959) based on previ- ous solutions to similar problems. Insight is when a prob- lem cannot be solved using conventional stepwise methods (Metcalfe, 1986a,b Metcalfe & Wiebe, 1987) and the prob- lem solver suddenly realizes (the ���aha!��� experience, B��h- ler, 1907 Bowden, 1997 Jung-Beeman, Bowden, Haber- man et al., 2004) that the solution involves unconventional methods (the problem solver realizes that the problem needs restructuring, Wertheimer, 1959 Ohlsson, 1984a,b Ohlsson, 1992 Wagner, Gais, Haider, Verleger, & Born, 2004). Insight is often described as a sudden, unconscious (Sternberg & Davidson, 1995 Bowden, 1997) and unin- tended (Wegner, 2002) process. The goal of this paper is to clarify whether there is any interaction between the processes that underlie mental set and insight. First, important studies of mental set and in- sight will be detailed in order to describe the effects of each. Second, the representational change theory of insight will be introduced as this is a necessary precursor to the manip- ulations made in the experiments presented, together with the matchstick arithmetic domain as a problem solving task to explore mental set and insight. Third, three experimental studies will examine the interplay between mental set and insight. Fourth, the results will be discussed with reference to the procedural view of mental set and the representation- al change view of insight. Studies of Mental Set and Insight Insight has been examined using various problems. Per- haps the most famous study of insight comes from Dun- cker���s (1945) candle problem where participants were pre- sented with a box of matches, a candle and some tacks, and were asked to create a ledge on a wall to rest the candle on. Problem solvers became fixated on the ���container��� func- tion of the matchbox and thus reached an impasse on the problem. Subsequent insight only occurred if the problem solver realized that the matchbox could be used in a differ- ent way (i.e., as a ledge). Maier (1931) explained the find- ings of his two-cord problem in a similar way. Two cords hanging from a ceiling had to be tied together but could not actually be held in the hands at the same time. Various im- plements were also provided (e.g., a pair of pliers), the so- lution being to tie the pliers to one of the strings to act as a pendulum. Problem solvers reached an impasse when at- tempting to solve the problem because their prior knowl- edge led them to see the pliers as a cutting and bending tool rather than as a pendulum. Luchins (1942) examined mental set effects using the now famous water jug problems. Each problem usually had three jugs of different capacities with the goal being to measure a specific amount of water (by pouring water be- tween the jugs). For example, given three jugs A, B, and DOI 10.1027/1618-3169.55.4.269 �� 2008 Hogrefe & Huber Publishers Experimental Psychology 2008 Vol. 55(4):269���282

C, having respective capacities of 21, 127, and 3, the goal might be to measure an amount of 100 into one of the jugs. One solution to such a problem would be to pour water into B (127) and then to fill C twice using the water in B, leaving 121 units in B. The final step is then to fill A using the water in B, to leave 100 units in B. Luchins constructed a set of several problems that were all solved by the same solution method (B ��� 2C ��� A), after which participants were pre- sented with a so called test problem which could either be solved by the ���set��� solution or by a simpler alternative so- lution. For example, given the capacities 23, 49, and 3 in jugs A, B, and C, with the goal of attaining 20 units, the ���set��� solution of B ��� 2C ��� A can be used, but a much sim- pler alternative of A ��� C can also be used. Luchins found that the participants under such a set condition hardly ever used the simple method, whereas a control group that only solved the test problems almost always applied the easier solution approach. Luchins proposed that the repeated application of a suc- cessful method makes blind any alternative approach, be- cause of the mechanization of the particular solution meth- od ��� resulting in what he termed mental set. For about two decades cognitive scientists have started to explain mental set by procedures. Procedures are stated as a collection of rules that specify conditions under which an action is carried out, with a procedure becoming strong- er the more often it is used. From a set of procedures that meet a particular condition, the strongest available proce- dure is always selected. Within this framework, mental set is an artifact resulting from selection processes (Anderson, 1982 Newell, 1990 Lovett & Anderson, 1996 Anderson & Lebiere, 1998), and can be interpreted as a temporary by-product of procedural learning (Ohlsson, 1992). Lovett and Anderson (1996) investigated the procedural explanation of set by developing an analog to the Luchins water-jug problems that enabled the examination of the rel- ative influence of the current problem context and the re- peated selection of the same problem solving procedure. The experiments clearly showed that both the current prob- lem situation and the repeated application of the same so- lution method influence the selection of a solution proce- dure. After structural changes to the problem situation, par- ticipants were able to immediately select an alternative procedure. However, when the structure of the problem sit- uation remained the same, problem solvers persisted on the well-learned procedure. That is, the current conditions de- termined the selection of the solution procedure. These re- sults were also successfully simulated in an ACT-R model of the task. The procedural account does not give a clear indication regarding explanations of insight, but the assumption can be made that prior knowledge makes some procedures more likely for selection than others based on (for example) the usual function of an object. The procedures required for solving insight problems therefore begin with a very low probability of selection. It is through the repeated failure of more high probability solution attempts (and thus a reduc- tion in their probability of selection) that some time later an appropriate solution procedure is selected. Mental set increases the likelihood of a procedure being selected because it has repeatedly been successful in the immediate past. Prior knowledge, on the other hand, is con- cerned with the initial likelihood of a procedure being se- lected, and is thus independent from the effect of set. The concepts of mental set and insight should be seen as different factors that impinge on problem solving behav- ior. For mental set, problem solving behavior is affected by factors relating to the given situation e.g., seeing previous problems that can only be solved using a complex proce- dure and then seeing a problem that can be solved by both a complex and a simple procedure leads the problem solver to continue to use the complex procedure. Thus there has been an external influence involving the previous problems given to the problem solver who accommodates her solu- tion procedures to the invariants of those problems. For insight, problem solving behavior is driven by internal fac- tors e.g., the problem solver restricting the function of an object to what is known from their prior knowledge. In this case there is no pure adjustment of the solution procedure, but a fundamental change of the given knowledge structure is necessary ��� a new solution is searched and has to be established. Furthermore, mental set effects involve short- term memory processes, because they are created from ex- ternal factors in the current problem solving scenario, whereas insight effects involve long-term memory process- es, because they are created from the problem solver���s prior conceptions of the components of the problem. Under these definitions (which fit in with the Gestaltists view of insight and with Luchins��� [1942] view of mental set), mental set and insight are two independent processes. However, the two are likely to interact in circumstances where several problems are presented to the problem solver that have both a mental set and an insight nature to them. Birch and Rabinowitz (1951) were virtually the only Ge- staltists to examine mental set and insight together. In a pretest, participants had to complete electric circuits whereby one group repeatedly added a switch and the other group always added a relay. In the test phase, the partici- pants were confronted with the two-cord-problem. In the testing room, participants find the two cords and both the switch and the relay (either can be used as pendulum weights). The group that added switches in the pretest was more likely to select the relay as a pendulum weight ��� and vice versa for the other group. A control group on the other hand, who did not take part in the pretest, showed no pref- erence for using either the switch or the relay as the pen- dulum weight. Thus, participants show mental set effects for the insight problem ��� they do not consider the compo- nent that they had used for completing electric circuits in the ���set��� pretest. Birch and Rabinowitz hence concluded that the perceived function of objects (i.e., prior knowl- edge) can be influenced by the current problem solving context (i.e., set). The Gestaltists therefore showed that both long-term 270 M. ��llinger et al.: Mental Set and Insight Experimental Psychology 2008 Vol. 55(4):269���282 �� 2008 Hogrefe & Huber Publishers