he acquisition of structural knowledge in the exploration phase, whereas problem-solving performance has been deﬁned in terms of a deviation from a speciﬁed goal state in the system control phase. One might argue that these measures are reasonably independent, as are the various other measures employed. Also, in the Vollmeyer et al. ( 1996 ) study, strategies have been operational- ized independently of structural knowledge and performance measures. As for the theoretical overlap, one may object that it is a truism that one needs structural knowledge in order to control a complex system. How- ever, given the dissociations between the quality of structural knowledge and problem-solving performance in some studies (e.g., Beckmann, 1995 ; Funke & M ¨uller, 1988 ; also see next section), we believe that it is an empir- ical question worthy of pursuing. It is somewhat disappointing that none of the studies reviewed in this section reports any reliabilities. Thus, we have some concerns regarding the reliability and validity of structural knowledge assessment, particularly for semantically rich problems. As has been pointed out by Funke ( 1991 ; see also Shanks & St. John, 1994 ), it may well be that problem solvers apply or develop “incorrect” models that can nevertheless be useful for successful problem solving within a restricted range of values. criterion 2. The presumed relation between intellectual ability and problem- solving competence must have a theoretical explanation . Funke’s approach is to derive hypotheses about mental representations on the basis of formal task analyses. As Buchner ( 1995 ) has argued, this approach is very similar to early experimental work on deductive reasoning that rested heavily on Is Problem Solving Related to Intellectual Ability? 109 the assumption that human deductive reasoning could best be described and explained in close analogy to formal logic. While such an approach demonstrates that system knowledge is a predictor of problem-solving performance, and helps us to understand how certain task characteristics constrain the process of knowledge acquisition, it does not tell us much about the underlying abilities leading to adequate structural knowledge and successful problem solving. As already mentioned earlier, knowledge by itself is not an intellectual ability. Things are somewhat different with regard to Vollmeyer’s approach, however. In our view, Vollmeyer et al. ( 1996 ) were indeed able to identify intellectual abilities involved in acquiring mental models of a task. It would be interesting to see whether problem solvers who differ in terms of certain cognitive characteristics (e.g., working memory capacity or learning abil- ity) would also be able to learn and use systematic strategies to different degrees (see Fritz & Funke, 1988 , for a promising start on this particular line of research). criterion 3. The direction of the presumed causality must be demonstrated empirically . The only causal inﬂuence that has been demonstrated thus far is the link from task characteristics to structural knowledge. This assertion holds also for the Vollmeyer et al. study (but see their Experiment 2 , next section), in which strategies have been identiﬁed in a post hoc manner. To demonstrate a causal inﬂuence, experimental manipulation of strategy use would be necessary, possibly in combination with between-group compar- isons and training. implicit problem solving Some ﬁndings in the domains of artiﬁcial grammar learning, sequence learning, and complex problem solving suggest that people acquire knowl- edge that allows them to successfully solve problems, although they are not able to express their knowledge. Such ﬁndings have led some researchers (e.g., Berry & Broadbent, 1984 , 1987 ; Nissen & Bullemer, 1987 ; Reber, 1967 , 1969 ) to propose independent learning systems, namely, explicit and im- plicit learning. The former is thought to be based on deliberate hypothesis testing, is selective with respect to what is being learned, and leads to con- sciously accessible and verbalizable knowledge. Implicit learning, 7 on the other hand, has been characterized as involving “the unselective and pas- sive aggregation of information about the co-occurrence of environmental events and features” (Hayes & Broadbent, 1988,p. 251 ). Thus, it has been assumed that implicit learning takes place irrespective of the intention to learn, does not rely on hypothesis testing, and leads to implicit (tacit) 7 This is only one characterization of implicit learning. For a collection of deﬁnitions, see, e.g., Frensch ( 1998 ). 110 Wenke and Frensch knowledge that cannot or can be only partially accessed. Furthermore, it has been argued (Reber, Walkenﬁeld, & Hernstadt, 1991 ; see also Anderson, 1998 ) that implicit learning shows less interindividual variability because it is an evolutionary older, less variable, and more robust ability. In this section, we review empirical ﬁndings concerning the existence and the potential characteristics of such an implicit learning ability in the domain of complex problem solving. To this end, we ﬁrst describe the tasks that are typically used in this type of research. We then highlight some of the results that have initially led researchers to propose two differing learning mechanisms, as well as research that relates implicit learning to intellectual ability. Next, we turn to results that question the original assumptions, and discuss alternative accounts of the main ﬁndings. Finally, we consider factors that might mediate the acquisition of different (e.g., explicit and implicit) types of knowledge. The Tasks The dynamic system most often used in the studies reported below con- sists of a simple linear equation relating one input variable to an out- put variable, also taking into account the previous output. In addition, in most studies a random component is added on two thirds of the tri- als, such that on these trials the system changes to a state one unit above or below the state that would be correct according to the deterministic equation. The system is frequently used in one or both of two semantic versions: the SUGAR FACTORY and the COMPUTER PERSON. When con- trolling the SUGAR FACTORY, problem solvers are required to reach and maintain speciﬁed levels of sugar output by varying the number of work- ers employed. In case of the COMPUTER PERSON, problem solvers enter attitude adjectives (e.g., “friendly” or “polite”) from a ﬁxed adjective set in order to get the computer person to display a speciﬁed behavior (e.g., “very friendly”). A second frequently used task is the CITY TRANSPORTATION system. This task is similar to the linear equation systems described in the previ- ous section in that two variables (free parking slots and number of people taking the bus) need to be adjusted by varying two exogenous variables (time schedule for buses and parking fee). In the majority of studies prob- lem solvers are asked to control the system from the beginning (i.e., there is no exploration phase). In addition, instructions and/or system features are varied. After controlling the system for a while, problem solvers are probed for their structural knowledge. This is usually done with the help of multiple-choice questionnaires that require problem solvers to predict outcomes, given a speciﬁed previous output and novel input. The exper- imental approach thus differs from the standard procedure of the studies discussed in the previous section in that (a) the systems are usually less Is Problem Solving Related to Intellectual Ability? 111 complex in terms of the underlying variables and relations, (b) problem solvers are typically not allowed to explore the system before they are asked to reach speciﬁed target values, and © problem solvers are usually not probed for their structural knowledge before they have completed the experiment. Empirical Evidence Empirical evidence supporting the existence of two independent learning systems mainly comes from two types of dissociations, namely, (a) dissoci- ations between problem-solving performance and questionnaire answers, and (b) differential effects on problem-solving performance when systems are controlled that are assumed to engage the different learning systems. For instance, Berry and Broadbent ( 1984 ), using both the SUGAR FACTORY and the COMPUTER PERSON task, found that problem-solving performance improved with practice (two vs. one block of practice), but that structural knowledge was unaffected. Furthermore, correlations between problem-solving performance and knowledge tended to be negative. In contrast, informing problem solvers about the principles of the system after the ﬁrst practice block improved structural knowledge but did not affect performance. Again, no positive correlations between problem-solving performance and knowledge emerged. Berry and Broadbent ( 1987 , 1988 ) demonstrated that this type of disso- ciation critically depends on the salience of the relations among variables. In their 1988 study, salience was manipulated by varying feedback de- lay in the COMPUTER PERSON task. In the salient version, the output depended on the input of the current trial. In contrast, in the nonsalient version, the output was determined by the problem solver’s input on the preceding trial. Berry and Broadbent assumed that nonsalient tasks would induce implicit learning, whereas the easier salient task would be learned explicitly. The authors reported that performance improved with prac- tice for both task versions, although performance on the salient task was generally better than on the nonsalient task. More interesting is that in- structions to search for systematic relations between variables improved performance for the group working on the salient task, but impaired per- formance in the nonsalient group. Moreover, structural knowledge scores were higher in the salient group than in the nonsalient group, and correla- tions between knowledge and problem-solving performance tended to be somewhat higher in the salient group (yet none of the correlations reached signiﬁcance). The nature of the underlying relations also seems to affect the ability to transfer knowledge to novel situations (Berry & Broadbent, 1988 ; Hayes & Broadbent, 1988 ). Hayes and Broadbent found that a change of the equa- tion after an initial learning phase impaired problem-solving performance 112 Wenke and Frensch in the nonsalient condition of the COMPUTER PERSON, but not in the salient condition. More dramatic, however, is that this pattern of results reversed when problem solvers worked under dual-task conditions (i.e., when they performed a concurrent random-letter generation task). That is, when a secondary task had to be performed concurrently, relearning was impaired in the salient, but not in the nonsalient condition. Based on these and similar results, Berry and Broadbent concluded that two inde- pendent learning systems exist, and that the unselective and unintentional implicit-learning mechanism is particularly well suited to dealing with highly complex situations in which deliberate hypothesis testing has little chance to be successful. Implicit Learning and Intellectual Ability If indeed an unintentional implicit-learning mechanism exists that might affect complex problem-solving performance, then it is at least conceivable that the efﬁciency with which this mechanism operates might be related to intellectual ability (e.g., IQ). In short, implicit learning might be related to intellectual ability. Unfortunately, there do not seem to exist any empirical studies that have explored this potential relation directly. However, there exist at least two studies that have explored the relation in a somewhat indirect manner. Reber et al. ( 1991 ), for example, compared participants’ performance on an “explicit” letter series completion task (i.e., requiring an explicit search for underlying rules) with implicit learning (i.e., a well-formedness judg- ment) following an artiﬁcial grammar learning task. During the learning phase of the artiﬁcial grammar learning task, participants were instructed to memorize letter strings produced by a ﬁnite state grammar. They were informed about the existence of rules underlying the strings only after the learning phase had ended, that is, before the test phase took place. During the test phase, participants were asked to judge whether a given string cor- responded to the rules or not (i.e., well-formedness task). To ensure a com- mon metric for the series completion task and the well-formedness task, performance on the series completion task was assessed via two-choice response alternatives. In addition, participants were required to explain their choices. Reber et al. found relatively small individual differences on the well- formedness task as compared with much larger individual differences on the series completion task. This result could be corroborated by a reanalysis of former studies (e.g., Reber, 1976 ) in which implicit versus explicit learn- ing was manipulated by varying the instruction for the artiﬁcial grammar task. More to the point and much more interesting (although perhaps little surprising given that variance was lower in the implicit task) was the fact Is Problem Solving Related to Intellectual Ability? 113 that Reber et al. ( 1991 ) could show that participants’ WAIS scores corre- lated strongly with performance on the series completion task ( r = . 69 ), but only weakly and nonsigniﬁcantly with performance on the well- formedness task ( r = . 25 ). Thus, implicit learning did not correlate sig- niﬁcantly with IQ. A similar result was obtained by Zacks, Hasher, and Sanft ( 1982 ), who reported no differences in frequency encoding (an implicit-learning type test) between students from a university with median Scholastic Aptitude Test (SAT) scores of 610 and those from a school with median SAT scores of 471 . Although the implicit-learning task used by Reber and colleagues can- not be considered a complex problem-solving task, the null ﬁndings are nevertheless interesting because they point to the possibility that implicit and explicit problem-solving competence might rely on different intellec- tual abilities. Clearly, much research is needed in this particular area to explore the relation between cognitive abilities, on the one hand, and com- plex problem solving under different task conditions and instructions, on the other hand. Doubts and Alternative Accounts Unfortunately, not all researchers have empirically obtained such clear- cut dissociations between problem-solving performance and questionnaire answers supporting the existence of two independent learning systems as have Berry and Broadbent ( 1987 , 1988 ), nor do all researchers agree with Berry and Broadbent’s interpretation. For example, Green and Shanks ( 1993 ), in an attempt to replicate Hayes and Broadbent ( 1988 ), found that problem solvers in the salient and nonsalient conditions were similarly im- paired by an equation reversal (transfer), as well as by an equation change under dual-task conditions. Moreover, under dual-task conditions, initial learning was better in the salient than in the nonsalient group. Green and Shanks concluded that feedback delay may simply inﬂuence task difﬁculty and hence the amount of knowledge acquired, instead of tapping into two functionally distinct learning systems. When problem solvers who learned nothing or very little during the initial learning phase were included in the analysis, Green and Shanks found that performance of nonlearners in the nonsalient/dual-task condition improved after the equation change. How- ever, Berry and Broadbent ( 1995 ) reanalyzed the Hayes and Broadbent data and could not conﬁrm this latter pattern in their data analysis. Instead, they raised the possibility that differences in instructions 8 may have contributed to these obviously contradictory results. 8 Green and Shanks’s ( 1993 ) instructions to both the salient and the nonsalient group included a search instruction similar to that used by Berry and Broadbent ( 1988 ). 114 Wenke and Frensch Other studies, using slightly different manipulations and/or different indicators of verbalizable knowledge, also failed to ﬁnd dissociations. For example, Stanley, Mathews, Buss, and Kotler-Cope ( 1989 ), who used both the original SUGAR FACTORY and the COMPUTER PERSON task, found that informing problem solvers about the underlying principles of the system did improve their performance relative to controls, which had not been the case in the Berry and Broadbent ( 1984 ) study. It is interesting, however, that other types of instructions, such as a memorization instruc- tion (consisting of concrete examples), a simple heuristic instruction (e.g., “always select the response level half-way between the current produc- tion level and the target level”), or a pooled transcript of skilled problem solvers’ explanations, all led to similar performance improvements, as did the “principles” instruction, suggesting that different kinds of strategies may lead to comparable levels of performance. Their explanation condition was derived froma different experiment, in which a separate group of prob- lem solvers was asked to provide instructions on how to deal with the sys- tem after each block of practice. The informativeness of these instructions was assessed by the performance of yoked subjects requested to follow the transcribed instructions. Stanley et al.’s original learners’ performance improved well before they were able to provide helpful instructions. This suggests that performance improves before helpful verbalizable knowl- edge emerges and that extended practice is needed to develop verbalizable structural knowledge (for a similar view, see Squire & Frambach, 1990 ). On the other hand, Sanderson ( 1989 ) argued that high levels of prac- tice might be necessary for verbal knowledge to show up because par- tially incorrect mental models that are induced by the semantic context need to be overcome. Sanderson, using mental model analysis techniques and questionnaires to assess verbal knowledge, found that verbalizable knowledge was associated with problem-solving performance on the CITY TRANSPORTATION system, and that changes in mental models preceded questionnaire improvement and accompanied performance improvement. However, the association between verbalizable knowledge and perfor- mance depended on the task demands. More speciﬁcally, the dissociation showed only after much practice when the solution space was enlarged by requiring problem solvers to enter decimal values instead of integer val- ues. Sanderson argued that enlarging the problem space might render rule induction strategies more advantageous. Results such as these have led researchers to doubt the existence of two truly independent and possibly antagonistic learning systems, and instead to focus more on describing the nature of the knowledge that is acquired and used under certain task demands, and to devise more reﬁned measures of verbalizable knowledge. Most researchers (e.g., Berry & Broadbent, 1988 ; Buchner, Funke, & Berry, 1995 ; Dienes & Fahey, 1995 , 1998 ; Stanley et al., 1989 ) now seem Is Problem Solving Related to Intellectual Ability? 115 to agree that complete and adequate structural knowledge (i.e., rule-based mental models) is not a necessary condition for successful problem solving in complex systems. Rather, in some conditions, problem solving may be predominantly memory-based. For instance, Dienes and Fahey ( 1995 ), using a posttask prediction ques- tionnaire that required problem solvers to determine the required input for unrelated new situations or old situations under a given target level with- out receiving feedback, demonstrated that problem solvers are better at answering posttask prediction questions consisting of old situations they have encountered when controlling the original SUGAR FACTORY or the nonsalient version of the COMPUTER PERSON task (especially those sit- uations on which they have been correct) than answering questions that consist of novel situations. However, problem solvers who performed in the salient COMPUTER PERSON condition were also able to correctly an- swer novel-situation questions. Dienes and Fahey therefore concluded that problem solvers control nonsalient systems by retrieving old similar situ- ations instead of by predicting subsequent states on the basis of abstract rules. In contrast, problem solvers in the salient condition may abstract rules that enabled them to successfully predict in novel situations. Buchner et al. ( 1995 ) provided a similar account of the dissociation be- tween problem-solving performance and performance on the traditional prediction task. The authors reasoned that good problem solvers (partic- ipants with many trials on target) experience fewer system transitions (situations) than do poor problem solvers who experience more speciﬁc situations, and are thus more likely to correctly answer more questions on the posttask questionnaire. As expected, Buchner et al. found that the number of trials necessary to “move” the system to a speciﬁed target state was negatively correlated with trials on targets, but was positively corre- lated with questionnaire performance. However, this correlational pattern emerged only when problem solvers had to reach one and the same target state in successive blocks. When problem solvers had to adjust the SUGAR FACTORY to a different target state in successive blocks and thus experi- enced a large number of different situations, then performance as well as questionnaire answering deteriorated. Furthermore, both problem-solving performance and prediction ability correlated negatively with the number of encountered state transitions. These results point to the possibility that under varied target conditions, reliance on a memory-based performance strategy is not effective, leading to a rule search strategy for some prob- lem solvers. As pointed out by Sanderson ( 1989 , see above), changes in learning-based mental models show up in questionnaire raw scores only after extended practice. The studies reviewed thus far indicate that task demands and, possibly, strategies determine what is learned and how ﬂexibly the acquired knowl- edge can be transferred to novel situations. 116 Wenke and Frensch Vollmeyer et al. ( 1996 ) and Geddes and Stevenson ( 1997 ) investigated in more detail the mediating role of strategies adopted under different task demands. Vollmeyer et al. ( 1996 ) had their participants work on the linear equation system BIOLOGY LAB described in the previous section for three practice phases. In a ﬁrst phase, participants were told to explore the system and to learn as much about it as possible, either under a nonspeciﬁc-goal condition (see previous section) or under a speciﬁc-goal condition in which they had to reach speciﬁc target states on several variables. Half of the participants in both groups were, in addition, instructed on how to use the optimal systematic strategy of varying only one variable at a time while holding the other variables constant. When the exploration phase had been completed, system knowl- edge was assessed via causal diagram analysis. Based on Sweller’s (e.g., Mawer & Sweller, 1982 ; Sweller, 1983 , 1988 ) ﬁndings of impoverished rule knowledge in problem solvers who work under speciﬁc-goal instructions, Vollmeyer et al. expected that participants in the speciﬁc-goal condition would use a difference reduction strategy (i.e., reducing the distance be- tween current state and goal state) and predominantly search instance space (Klahr & Dunbar, 1988 ; Simon & Lea, 1974 ; see previous section), leading to poor abstract system knowledge. In contrast, participants in the unspeciﬁc-goal condition do not have a speciﬁc target state for which a dif- ference reduction strategy would be effective. Accordingly, Vollmeyer et al. expected participants in the nonspeciﬁc-goal condition to also search rule space and to proceedby hypothesis testing. This in turn should lead to a bet- ter understanding of the rules underlying system behavior, at least for those participants using systematic hypothesis-testing strategies. Vollmeyer et al. hypothesized that both groups of participants would be able to control the system in a subsequent experimental phase (phase 2 ) with comparable suc- cess in which the target states were the same as those given to the speciﬁc- goal group in the exploration phase. However, because knowledge in the speciﬁc-goal group should be tied to the goal participants had worked with in the exploration phase, the speciﬁc-goal group was expected to perform worse when transferred to a novel goal state (phase 3 ). The nonspeciﬁc- goal participants, on the other hand, should be able to use their system knowledge to perform reasonably well on the transfer task. After ﬁnishing the control task, all participants received a prediction task that was similar to that used by Berry and colleagues. The results can be summarized as follows: (a) Exploring the system with an unspeciﬁc goal led to signiﬁcantly better structural knowledge (causal diagram and prediction); (b) nonspeciﬁc-goal and speciﬁc-goal participants performed comparably well when controlling the system in the second phase, but © only nonspeciﬁc-goal participants were able to keep performance at a high level when the goal state was changed. Perfor- mance of the speciﬁc-goal group deteriorated considerably in the transfer Is Problem Solving Related to Intellectual Ability? 117 phase; (d) both initial problem-solving performance and transfer as well as structural knowledge were affected by the strategy instruction, whereby separate strategy analyses show that instructed speciﬁc-goal participants tended to switch to a difference reduction strategy in the course of the ex- ploration phase, whereas the nonspeciﬁc-goal participants beneﬁted from the strategy instruction and stayed with their strategy throughout the ex- ploration phase. These results illustrate that strategies are powerful media- tors of what is learned under different task demands, and that comparable performance in some conditions (i.e., phase 2 ) may be achieved by differ- ent types of knowledge, namely, rule knowledge versus knowledge about speciﬁc transitions (see also Stanley et al., 1989 ). Geddes and Stevenson ( 1997 ), following a line of reasoning similar to that of Vollmeyer et al., investigated the inﬂuence of goal speciﬁcity on in- stance versus rule learning using the nonsalient version of the COMPUTER PERSON task. In their study, there were three groups of participants: ( 1 ) those who explored the system without a speciﬁc goal (nonspeciﬁc- goal group working under search instruction), ( 2 ) a group with a speciﬁc goal but without the instruction to discover underlying rules (speciﬁc-goal group), and ( 3 ) a group with both a search instruction and a speciﬁc goal (dual group). All participants were then given a goal state different from that of the speciﬁc goal groups in the exploration phase (i.e., a transfer test in Vollmeyer et al.’s sense) before they were asked to answer post- task prediction questions of the kind used by Dienes and Fahey ( 1995 , see above). Transfer performance was best in the nonspeciﬁc-goal group, second best in the speciﬁc-goal group, and worst in the dual group. Moreover, participants in the speciﬁc-goal group and the dual group were better at predicting old than novel situations on the posttask questionnaire, whereas the nonspeciﬁc-goal group also correctly predicted novel situations, indi- cating that only the nonspeciﬁc-goal group acquired abstract rule knowl- edge. In addition, the quality of performance correlated with prediction scores only in the nonspeciﬁc-goal group, suggesting that they could use their knowledge to control the system. It is interesting, however, that the dual group was even worse than the speciﬁc-goal group on the prediction task in that the dual group could master only old correct situations (see Dienes & Fahey, 1995 ), whereas the speciﬁc-goal group was good at predicting previously correct as well as incorrect situations. Geddes and Stevenson interpret this result as indicating that problem solvers in the speciﬁc-goal condition might have engaged in some sort of goal-oriented hypotheses testing. However, because strategies have not been assessed directly, this conclusion is rather speculative. Whereas Geddes and Stevenson replicated the Vollmeyer et al. result that speciﬁc- goal groups are impaired on transfer tests involving novel goal states, 118 Wenke and Frensch a study by Haider ( 1992 ) also showed that the purely speciﬁc-goal and purely nonspeciﬁc-goal problem solvers do not necessarily differ when re- quired to adjust the system to the “old” goal state. In her study, too, system knowledge was correlated with performance in the nonspeciﬁc-goal group only. Taken together, these studies provide convincing illustrations of how task demands determine the way problem solvers approach a complex problem-solvingtask and what they learn while controlling the system. The studies do not, however, address the issue of whether and how problem solvers become aware of underlying rules when salient rules are used (e.g., Dienes & Fahey, 1995 ), when solution space is enlarged (e.g., Buchner et al., 1995 ; Sanderson, 1989 ), and/or after extended periods of practice (e.g., Sanderson, 1989 ; Stanley et al., 1989 ). What are the implications of all this with regard to the effect of intellec- tual ability on complex problem-solving competence? We believe that the studies discussed do not provide ﬁrm evidence in support of two func- tionally dissociable learning systems, one being selective and intentional, resulting in explicit verbalizable knowledge, the other being passive, un- conscious and leading to nonverbalizable knowledge. Rather, we agree with Whittlesea (e.g., Whittlesea & Dorken, 1993 ; Wright & Whittlesea, 1998 ) that people simply adapt to task demands and that learning is a con- sequence of the processing engaged in when trying to meet task demands. As Wright and Whittlesea propose, this may have little to do with uncon- sciousness about what is being learned (but see Dienes & Fahey, 1998 ): We claim that people directly acquire information only about those stimulus aspects they are required to process, under the demands of the task, but in doing so acquire the potential to respond along unanticipated dimensions. They are learning without awareness, but without awareness of the consequences of their current behavior, not of what they are currently learning, or their current intentions, or the demands under which they learn. They have learned something that makes them sensitive to implicit properties, but to call that “implicit learning” is parallel to referring to the act of winning a lottery as “implicit spending.” (Wright & Whittlesea, 1998,p. 418 ) We do not mean to say, however, that the processing, and hence the required intellectual abilities, are identical under different task conditions and instructions. Rather, we believe that the strategies employed to meet particular task demands play a major role with respect to what is learned and how ﬂexibly this knowledge can be applied to novel situations. Fur- thermore, different strategies may be associated with different levels of interindividual variability, as was demonstrated by Reber et al. ( 1991)in the study discussed above in which problem solvers’ performance on an “explicit” letter series completion task was comparedwith implicit learning Is Problem Solving Related to Intellectual Ability? 119 on a different implicit learning task (artiﬁcial grammar learning). Reber et al. were able to show that series completion, but not implicit learning, was associated with global intelligence. While goal speciﬁcity has been shown to be associated with different strategies, the role of semantic context (and, consequently, of activated prior knowledge), as well as of salience of underlying rules and practice, needs to be investigated further, possibly using mental model analysis techniques (e.g., Sanderson, 1989 ) and more reﬁned assessments of verbal- izable knowledge (e.g., Dienes & Fahey, 1995 ). Evaluation of Approach criterion 1. Both the intellectual ability presumably underlying problem- solving competence and problem-solving competence itself need to be explicitly deﬁned and must not overlap at theoretical and/or operational levels . In most studies, structural knowledge has been assessed separately from problem- solving performance. However, using more sensitive measures of explicit knowledge (e.g., Dienes & Fahey, 1995 ) also renders the prediction task more similar to the problem-solving task. Especially when subjects are asked to predict old situations, the two tests can be regarded as overlap- ping, although the format of the tasks differs. Nevertheless, the systematic use of prediction tasks has led to insights about the ﬂexibility of the appli- cation of acquired knowledge (i.e., whether knowledge can be transferred to novel situations), thus theoretically justifying this type of explicit test. Also, the mental model analysis techniques used by Sanderson ( 1989)are promising and appear to have little empirical overlap with the problem- solving task. Concerning theoretical independence, the concepts of implicit and explicit learning have been deﬁned independently of each other; thus, one may argue that – at least according to the original assumptions – no theoretical overlap exists. Unfortunately, none of the studies reviewed in the present section re- ports any reliabilities, neither for performance indicators nor for the ques- tionnaires. Given the assumptions regarding the nature of the two learning mechanisms and the evidence regarding changes in learning/knowledge with practice, it would not make much sense to assess retest reliability. There is indirect evidence, however, that parallel-test reliability may not be very high. For example, several researchers (e.g., Stanley et al., 1989 ) have reported that problem solvers were better at controlling the COM- PUTER PERSON than the SUGAR FACTORY task, although the structure of the two tasks is identical. This again points to the impact of semantic embedding and of prior knowledge that is brought to the task, which may differ across individuals and domains. criterion 2. The presumed relation between intellectual ability and problem- solving competence must have a theoretical explanation . The proposal that an implicit learning mechanism might contribute to complex problem 120 Wenke and Frensch solving and is functionally dissociable from explicit learning is an exciting one because most work on abilities and individual differences has exclusively concentrated on explicit/conscious cognition. Unfortunately, however, convincing evidence for truly independent learning mechanisms does not exist. Rather, recent work on task demands and strategy use sug- gests that what differs is not learning per se, but the processing of study episodes when working with particular systems. It may well be the case that different strategies are associated with different levels of interindivid- ual variability (e.g., Reber et al., 1991 ) and that the processing induced by different task demands correlates with different subtests of traditional in- telligence tests and/or learning tests. Clearly, better deﬁnitions of critical task-related concepts such as “salience” and more thorough accounts of which processing requirements and abilities are afforded by certain task characteristics are needed in order to gain a better understanding of the abilities underlying implicit complex problem solving. Vollmeyer et al.’s as well as Geddes and Stevenson’s work on strategies can be regarded as a ﬁrst step in the right direction. criterion 3. The direction of the presumed causality must be demonstrated empirically . Evidence for a causal inﬂuence of an implicit learning mech- anism on complex problem solving is weak. However, some work (e.g., Geddes & Stevenson, 1997 ; Stanley et al., 1989 ; Vollmeyer et al., 1996 ) sug- gests that task demands encourage use of particular strategies, which in turn affect what is being learned. Particularly noteworthy in this regard is the study by Vollmeyer et al., who directly manipulated strategy use. Of course, more work including experimental strategy induction as well as training, in combination with between group designs, is necessary to gain a more complete understanding of strategic abilities. In addition, these stud- ies should address the issues of (a) semantic embeddedness and its inﬂu- ence on the mental models problem solvers bring to the task, and (b) factors that lead to potential strategy shifts in the course of practice (e.g., chunking) or when working with enlarged solution spaces. summary and conclusions The main goal of the present chapter was to discuss to what extent, if indeed at all, differences in complex problem-solving competence can be traced to differences in an individual’s intellectual ability. In the ﬁrst section of the chapter we provided deﬁnitions of complex problem solving and of in- tellectual ability and described what it means to state that an individual’s problem-solving competence is due to intellectual ability. In the second and third sections, we evaluated much of the empirical work that relates complex problem-solving competence to some measure of intellectual abil- ity with regard to three evaluation criteria. Two forms of problem solving were distinguished. In the second section, we focused on explicit problem Is Problem Solving Related to Intellectual Ability? 121 solving, that is, problem solving that is controlled by a problem solver’s intentions. In the third section, our focus was on implicit, that is, automatic or nonconscious complex problem solving. Our two main conclusions are as follows: First, there exists no con- vincing empirical evidence that would support a causal relation between any intellectual ability, on the one hand, and complex explicit or implicit problem-solving competence, on the other hand. It is important to em- phasize, again, that this conclusion is one that is based on a lack of evi- dence, not necessarily a lack of theoretical relation. That is, we do not deny the possibility that a causal relation between intellectual ability and com- plex problem-solving competence might exist; we argue only that there exists no convincing empirical evidence as yet that would support such a relation. The conclusion has two important consequences. First, because the in- tellectual abilities investigated thus far are much too coarse, general, and abstract to allow a prediction of interindividual differences in complex problem-solving competence, what is clearly needed in future research is a focus on much more speciﬁc and narrow intellectual abilities (e.g., working-memory capacity) that more closely capture the cognitive sys- tem’s architecture and functioning. Second, from the empirical evidence that is currently available it ap- pears that the relation between intellectual ability and complex problem- solving performance might be moderated by a complex interaction among subjects, tasks, and situations. With restricted range in subjects, the empir- ically obtained correlations attenuate. With unreliable measurement, the correlations attenuate. With certain kinds of problem-solving tasks, the correlations attenuate. Thus, the future task may be to ﬁnd not whether there is a correlation, but when. Our second main conclusion is that there does, however, exist good evidence that differences in complex problem-solving competence, both explicit and implicit, are tied to differences in task knowledge and strategy. Whether or not differences in strategy and in the structure and acquisition of task knowledge may, in turn, be due to differences in speciﬁc intellectual abilities is, as yet, an open empirical question. references Amthauer, R., Brocke, B., Liepmann, D. & Beauducel, A. ( 1973 ). Intelligence Structure Test (IST 70) .G¨ ottingen: Hogrefe. Anderson, M. ( 1998 ). Individual differences in intelligence. In K. Kirsner, C. Speelman, M. Maybery, A. O’Brien-Malone, M. Anderson, & C. 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Such problems are the bread and butter of problem solving; from kindergarten to the university, students accumulate a great deal of experience with these “canned” problems. Difﬁculties arise, however, when people need to solve problems that do not ﬁt the mold, that require some innovative thinking. Guilford ( 1967 ) proposed that “real” problem solving involved actively seeking, constructing new ideas that ﬁt with constraints imposed by a task or more generally by the environment. In other words, in most instances “real” problem solving involves creative thinking (see Mayer, 1983 ). One well-known example of an unpredictable yet vital problem that was solved successfully is illustrated by the epic return ﬂight of the Apollo 13 space mission (King, 1997 ). Preserving the lives of the crew members required a cascade of operations, each involving creative thinking, as the explosion of the ship’s main oxygen supply was not the kind of problem that the ﬂight crew expected to encounter, and thus they had no speciﬁc training, no preestablished procedure to follow. necessity is the mother of invention The world in which we live can be characterized as a rapidly evolving, technology- and information-oriented one in which creative problem solv- ing skills are increasingly valued (Sternberg & Lubart, 1996 ). According to some theorists, such as Romer ( 1994 ), future economic growth will be driven by innovative products and services that respond to societal needs and problems rather than by providing established products and services more efﬁciently (see Getz & Lubart, 2001 ). We would argue, therefore, that “real” problem solving as opposed to “canned” problem solving is a topic of growing interest. A “problem” can be conceived broadly as encompassing any task that an individual seeks 127 128 Lubart and Mouchiroud to accomplish in which one’s goal state is not equal to one’s current state. Thus, scientists who seek to understand a complex phenomenon, artists who seek to express an idea, and people who seek to solve conﬂicts in their everyday lives can all be considered to be engaged in problem solving (see Runco & Dow, 1999 ). Finding solutions to “real” problems – new ideas that ﬁt with task con- straints – is difﬁcult for two main reasons. First, a diverse set of cognitive and conative factors is necessary. Second, in order to be effective, these abilities and traits must be called into play at appropriate points in the problem-solving process. We consider each of these points. Finally, we dis- cuss a rather different (and even opposite) point of view on the relation between problem solving and creativity. cognitive and conative factors for creative thought During the last twenty years, a multivariate approach to creativity has developed. In this perspective, creativity requires a particular combina- tion of cognitive and conative factors whose expression is inﬂuenced by environmental conditions. The nature of the proposed factors and their interaction varies according to different theorists (see Feldhusen, 1995 ; Lubart, 1999 a, 2000 – 2001 ; Runco, Nemiro, & Walberg, 1998 ). For exam- ple, Amabile ( 1996 ) proposed a componential model in which creativ- ity stems from domain-relevant skills (e.g., knowledge, technical skills), creativity-relevant skills (e.g., ability to break mental set, heuristics for idea generation, and conducive work style), and task motivation (interest and commitment to the task). Feldman, Csikszentmihalyi, and Gardner ( 1994 ; Csikszentmihalyi, 1988 , 1999 ) advanced a systems approach that focuses on interactions between individuals (with their cognitive and conative fac- tors), domains (culturally deﬁned bodies of knowledge), and ﬁelds (e.g., people who control or inﬂuence a domain by evaluating and selecting novel ideas). Other proposals include Woodman and Schoenfeldt’s ( 1990 ) interactionist model and Runco and Chand’s ( 1995 ) two-tier componen- tial model. We base our presentation on Sternberg and Lubart’s ( 1991 , 1995 ) multivariate model, which proposes that creativity draws on spe- ciﬁc aspects of intelligence, knowledge, cognitive styles, personality, and motivation operating within an environmental context.