Dissociable stages of problem solving (II): first evidence for process-contingent temporal order of activation in dorsolateral prefrontal cortex

In a companion study, eye-movement analyses in the Tower of London task (TOL) revealed independent indicators of functionally separable cognitive processes during problem solving, with processes of building up an internal representation of the problem preceding actual planning processes. These results imply that processes of internalization and planning should also be distinguishable in time and space with respect to concomitant brain activation patterns. To investigate this possibility, here we conducted analyses of fMRI data for left and right dorsolateral prefrontal cortex (dlPFC) during problem solving in the TOL task by accounting for the trial-by-trial variability of onsets and durations of the different cognitive processing stages. Comparisons between stimulus-locked and response-locked modeling approaches affirmed that activation in left dlPFC was elicited particularly during early processes of internalization, comprising the extraction of goal information and the generation of an internal problem representation, whereas activation in right dlPFC was predominantly attributable to later processes of mental transformations on this representation, that is planning proper. Thus, present data corroborate the proposal that often observed bilateral dlPFC activation patterns during complex cognitive tasks such as problem solving may reflect functionally and, to some extent, even temporally separable processes with opposing lateralizations.     

Dissociable stages of problem solving (I): temporal characteristics revealed by eye-movement analyses

Understanding the functional neuroanatomy of planning and problem solving may substantially benefit from better insight into the chronology of the cognitive processes involved. Based on the assumption that regularities in cognitive processing are reflected in overtly observable eye-movement patterns, here we recorded eye movements while participants worked on Tower of London (TOL) problems that comprised an experimental manipulation of different task demands. Single-trial saccade-locked analyses revealed that higher demands on forming an internal problem representation were associated with an increased number of gaze alternations between start state and goal state, but did not show any effect on the durations of these inspections of the states. In contrast, higher demands on actual planning in terms of mental manipulations of working memory contents coincided with a prolonged duration of the very last inspection of the start state (i.e., immediately preceding movement execution) but did not show any effect on the number of gaze alterations. Differential task demands on internalization and planning processes during problem solving hence selectively affect different eye-movement parameters. Moreover, these findings complement previous neuroimaging data on dissociable contributions of left and right dorsolateral prefrontal cortex in problem solving with novel evidence for a corresponding dissociation in the eye-movement patterns reflecting the associated cognitive processes.     

Deconstructing the tower: Parameters and predictors of problem difficulty on the Tower of London task

The Tower of London (TOL) task has been widely used in both clinical and research realms. In the current study, 104 healthy participants attempted all possible moderate- to high-difficulty TOL problems in order to determine: (1) optimal measures of problem solving performance, (2) problem characteristics, other than the minimum moves necessary to solve the problem, that determine participants’ difficulty in solving problems successfully, quickly, and efficiently, and (3) effects of increased task experience on which problem characteristics determine problem difficulty. A factor analysis of six performance measures found that, regardless of task experience, problem difficulty could be captured well either by a single factor corresponding to general quality of solution or possibly by three subordinate factors corresponding to solution efficiency, solution speed, and initial planning speed. Regression analyses predicting these performance factors revealed that in addition to a problem’s minimum moves three problem parameters were critical in determining the problem difficulty: goal position hierarchy, start position hierarchy, and number of solution paths available. The relative contributions of each of the characteristics strongly depended on which performance factor defined performance. We conclude that TOL problem performance is multifaceted, and that classifying problem difficulty using only the minimum moves necessary to solve the problem is inadequate.     

A proposed universal model of problem solving for design,science and cognate fields

A modestly generic, innovative, problem solving process with roots in the study of design and scientific research problem solving is presented and motivated. It is argued to be the shared core process of all problem solving. At its heart is a recognition of five foci or nodes of change vital to the process (changes in problem and solution formulation, method, constraints, and partial solution proposals) together with a bootstrap marked by the formation of higher order knowledge about problem solving in the domain in tandem with the solving of specific problems, the essential feature of all learned improvement. None of these elements is entirely original, but the way they are made explicit and developed (rather than folded into fewer, more abstract, boxes) is argued to provide fresh understanding of the organisation and power of the process to deal with complex practical problems.     

问题结构因素对伦敦塔问题解决的影响

以121名2,4,6年级小学生为被试,采用计算机呈现的方式,探讨了子目标和次佳路径这两个问题结构因素对伦敦塔问题解决表现的影响。结果发现：子目标和次佳路径两个因素存在交互作用,解决有子目标－无次佳路径问题时的计划指标要高于其他类型问题。根据被试在伦敦塔任务上的表现,划分为三大类7种表现类型。当存在不同的问题结构因素时,问题解决表现类型体现出差异性。     

Thinking around the corner: the development of planning abilities

The ability to plan and search ahead is essential for problem solving in most situations in everyday life. To investigate the development of planning and related processes, a sample of four- and five-year-old children was examined in a variant of the Tower of London, a frequently used neuropsychological assessment tool of planning abilities. The applied problems either required searching ahead for optimal solution or were solvable by pure step-by-step forward processing. Furthermore, the ambiguity of subgoal ordering was varied.Results revealed an age-related effect of search depth: the four-year olds’ planning accuracy was particularly decreased in problems demanding search ahead, while five-year olds mastered both problem types equally well. Interestingly, this interaction between age and search depth could not be accounted for by measures of working memory and inhibition. Differential effects of age were also found for subgoal ordering with respect to initial planning and movement execution times. In sum, planning abilities showed considerable development during late kindergarten age that appeared to be specifically associated with the integration and back-validation of the anticipated consequences of internally modeled actions. The present study demonstrates that a careful consideration of problem structure may greatly enhance the insights gained from the application of a routinely used assessment tool, the Tower of London. This may be especially advantageous when addressing specific subpopulations such as children or clinical samples.     

Acquisition of hierarchical reactive skills in a unified cognitive architecture

In this paper, we review Icarus, a cognitive architecture that utilizes hierarchical skills and concepts for reactive execution in physical environments. In addition, we present two extensions to the framework. The first involves the incorporation of means-ends analysis, which lets the system compose known skills to solve novel problems. The second involves the storage of new skills that are based on successful means-ends traces. We report experimental studies of these mechanisms on three distinct domains. Our results suggest that the two methods interact to acquire useful skill hierarchies that generalize well and that reduce the effort required to handle new tasks. We conclude with a discussion of related work on learning and prospects for additional research, including extending the framework to cover developmental phenomena.     

Looking ahead from age 6 to 13: A deeper insight into the development of planning ability

Planning ability gradually increases throughout childhood. However, it remains unknown whether this is attributable to global factors such as an increased ability and willingness to inhibit premature, impulsive responding, or due to the availability of specific planning operations, such as being able to mentally plan ahead more steps (‘search depth’) or to derive a clear temporal order of goals by the task layout (‘goal hierarchy’). Here, we studied the development of planning ability with respect to these global and problem‐specific aspects (search depth and goal hierarchy) of performance in 178 children from 6 to 13 years using the Tower of London task. As expected, global performance gradually developed with age. In accordance, planning durations increasingly reflected global problem demands with longer pre‐planning in harder problems. Furthermore, specific planning parameters revealed that children were increasingly capable of mentally searching ahead more steps. In contrast, the ability to derive a goal hierarchy did not show age‐related changes. While the global development of planning performance and adaptive planning durations were proposed to primarily reflect enhanced self‐monitoring, the specific increase in search depth across childhood that most likely proceeds until young adult age represents more directly planning‐related processes. Thus, development of planning ability is supported by multiple contributions.     

An effective metacognitive strategy: learning by doing and explaining with a computer‐based Cognitive Tutor

Recent studies have shown that self‐explanation is an effective metacognitive strategy, but how can it be leveraged to improve students' learning in actual classrooms? How do instructional treatments that emphasizes self‐explanation affect students' learning, as compared to other instructional treatments? We investigated whether self‐explanation can be scaffolded effectively in a classroom environment using a Cognitive Tutor, which is intelligent instructional software that supports guided learning by doing. In two classroom experiments, we found that students who explained their steps during problem‐solving practice with a Cognitive Tutor learned with greater understanding compared to students who did not explain steps. The explainers better explained their solutions steps and were more successful on transfer problems. We interpret these results as follows: By engaging in explanation, students acquired better‐integrated visual and verbal declarative knowledge and acquired less shallow procedural knowledge. The research demonstrates that the benefits of self‐explanation can be achieved in a relatively simple computer‐based approach that scales well for classroom use.     

Educators' implicit perspectives on wisdom: A comparison between interpersonal and intrapersonal perspectives

This research aimed to investigate educators' implicit perspectives on wisdom in order to compare interpersonal and intrapersonal perspectives and to help identify similarities or differences between these two theoretical perspectives. A total of 56 educators in Taiwan were interviewed individually. We utilised the grounded theory method to analyse the qualitative data. Results showed that both interpersonal and intrapersonal perspectives converged on four core components of wisdom: intrapsychic integration, actions in service of problem solving and ideal implementation, positive results and feedback and adjustments. The interpersonal perspective referred to external characteristics, and admiration and influence, whereas the intrapersonal perspective included greater detail about intrapsychic integration and action strategies than did the interpersonal perspective. We close with a discussion both of how wisdom appears to span across different fields and how the present results might feed into the teaching of wisdom in schools.     

Counterintuitive and alternative moves choice in the Water Jug task

MOVE problems, like the Tower of London (TOL) or the Water Jug (WJ) task, are planning tasks that appear structurally similar and are assumed to involve similar cognitive processes. Carder et al. [Carder, H.P., Handley, S.J., & Perfect, T.J. ( 2004). Deconstructing the Tower of London: Alternative moves and conflict resolution as predictors of task performance. The Quarterly Journal of Experimental Psychology 57a, 8, 1459-1483] showed that one predictor of TOL performance was the number of alternative move choices there were at a given point in the solution. In two experiments an individual move experienced on the WJ task was manipulated (perceptually consistent/counterintuitive) along with the number of alternative moves there were to choose between. A verification paradigm was employed in which participants made speeded judgements about the correctness of a move. Results showed performance was consistent with the application of a perceptual strategy accompanied by a process involving the evaluation of non-redundant alternative moves. These are discussed in the context of recent research that has examined the impact of executive dysfunction on Water Jug performance [Colvin, M.K., Dunbar, K., & Grafman, J. (2001). The effects of frontal lobe lesions on goal achievement in the Water Jug task. Journal of Cognitive Neuroscience, 13, 1129-1147].     

Psychological ownership: The implicit association between self and already-owned versus newly-owned objects

Evidence from explicit measures (e.g. favourability ratings, valuations) has led to the prevalent hypothesis that owned objects become cognitively associated with self-concept. Using a novel version of the Implicit Association Test (self-object IAT), wherein participants categorized objects by colour, we evaluated implicit cognitive associations involving self with already-owned and newly-owned objects. We observed faster responses when self-related words required the same response key as the colour that incidentally corresponded to self-owned objects, irrespective of length of ownership. These findings suggest that participants efficiently form cognitive associations between self and self-owned objects within mere minutes of ownership induction and inspire questions about the extent to which length of ownership drives the strength of this association.     

Dual processes,evolution and rationality

In three experiments we tested hypotheses derived from the goal specificity literature using a real-world physics task. In the balance-scale paradigm participants predict the state of the apparatus based on a configuration of weights at various distances from the fulcrum. Non-specific goals (NSG) have been shown to encourage hypothesis testing, which facilitates rule discovery, whereas specific goals (SG) do not. We showed that this goal specificity effect depends on task difficulty. The NSG strategy led to rule induction among some participants. Among non-discoverers, SG participants were faster and more accurate on difficult problems than NSG participants. The use of misleading exemplars (scale configurations that obscured the rule governing outcomes) led to fixation on inappropriate hypotheses for NSG but not SG participants. When more diagnostic learning exemplars were used, NSG non-discoverers still performed worse than SG participants on difficult problems. SG participants also outperformed NSG participants on a post-test of difficult problems. These findings qualify the generality of goal specificity effects.     

Affective and cognitive reactions to subliminal flicker from fluorescent lighting

This study renews the classical concept of subliminal perception (Peirce & Jastrow, 1884) by investigating the impact of subliminal flicker from fluorescent lighting on affect and cognitive performance. It was predicted that low compared to high frequency lighting (latter compared to former emits non-flickering light) would evoke larger changes in affective states and also impair cognitive performance. Subjects reported high rather than low frequency lighting to be more pleasant, which, in turn, enhanced their problem solving performance. This suggests that sensory processing can take place outside of conscious awareness resulting in conscious emotional consequences; indicating a role of affect in subliminal/implicit perception, and that positive affect may facilitate cognitive task performance.     

Use of the mathematical principle of inversion in young children

An important issue in the development of mathematical cognition is the extent to which children use and understand fundamental mathematical concepts. We examined whether young children successfully use the principle of inversion and, if so, whether they do so based on qualitative identity, length, or quantity. Twenty-four preschool children and 24 children in Grade 1 were presented with three-term inversion problems (e.g., 3+2-2) and standard problems of similar magnitude (e.g., 2+4-3). Problems were presented in three conditions to determine whether children used inversion at all and, if so, whether their decisions were based on quantitative or nonquantitative features of the problems. Both preschool and Grade 1 children showed evidence of using inversion in a fully quantitative manner, indicating that this principle is available in some form prior to extensive formal instruction in arithmetic.     

Using FMRI to test models of complex cognition

This article investigates the potential of fMRI to test assumptions about different components in models of complex cognitive tasks. If the components of a model can be associated with specific brain regions, one can make predictions for the temporal course of the BOLD response in these regions. An event-locked procedure is described for dealing with temporal variability and bringing model runs and individual data trials into alignment. Statistical methods for testing the model are described that deal with the scan-to-scan correlations in the errors of measurement of the BOLD signal. This approach is illustrated using a "sacrificial" ACT-R model that involves mapping 6 modules onto 6 brain regions in an experiment from Ravizza, Anderson, and Carter (in press) concerned with equation solving. The model's visual encoding predicted the BOLD response in the fusiform gyrus, its controlled retrieval predicted the BOLD response in the lateral inferior prefrontal cortex, and its subgoal setting predicted the BOLD response in the anterior cingulate cortex. On the other hand, its motor programming failed to predict anticipatory activation in the motor cortex, its representational changes failed to predicted the pattern of activity in the posterior parietal cortex, and its procedural component failed to predict an initial spike in caudate. The results illustrate the power of such data to direct the development of a theory of complex problem solving, both at the level of a specific task model as well as at the level of the cognitive architecture.     

Sequential modulations of poorer-strategy effects during strategy execution: An event-related potential study in arithmetic

When participants accomplish cognitive tasks, they obtain poorer performance if asked to execute a poorer strategy than a better strategy on a given problem. These poorer-strategy effects are smaller following execution of a poorer strategy relative to following a better strategy. To investigate ERP correlates of sequential modulations of poorer-strategy effects, we asked participants (n = 20) to accomplish a computational estimation task (i.e., provide approximate products to two-digit multiplication problems like 38 × 74). For each problem, they were cued to execute a better versus a poorer strategy. We found event-related potentials signatures of sequential modulations of poorer-strategy effects in two crucial windows (i.e., between 200 and 550 ms and between 850 and 1250 ms) associated with executive control mechanisms and allowing conflict monitoring between the better and the cued strategy. These results have important implications on theories of strategies as they suggest that sequential modulations of poorer-strategy effects involve earlier as well as later mechanisms of cognitive control during strategy execution.     

Gesture offers insight into problem‐solving in adults and children

When asked to explain their solutions to a problem, both adults and children gesture as they talk. These gestures at times convey information that is not conveyed in speech and thus reveal thoughts that are distinct from those revealed in speech. In this study, we use the classic Tower of Hanoi puzzle to validate the claim that gesture and speech taken together can reflect the activation of two cognitive strategies within a single response. The Tower of Hanoi is a well‐studied puzzle, known to be most efficiently solved by activating subroutines at theoretically defined choice points. When asked to explain how they solved the Tower of Hanoi puzzle, both adults and children produced significantly more gesture‐speech mismatches—explanations in which speech conveyed one path and gesture another—at these theoretically defined choice points than they produced at non‐choice points. Even when the participants did not solve the problem efficiently, gesture could be used to indicate where the participants were deciding between alternative paths. Gesture can, thus, serve as a useful adjunct to speech when attempting to discover cognitive processes in problem‐solving.     

Discovering the Sequential Structure of Thought

Multi‐voxel pattern recognition techniques combined with Hidden Markov models can be used to discover the mental states that people go through in performing a task. The combined method identifies both the mental states and how their durations vary with experimental conditions. We apply this method to a task where participants solve novel mathematical problems. We identify four states in the solution of these problems: Encoding, Planning, Solving, and Respond. The method allows us to interpret what participants are doing on individual problem‐solving trials. The duration of the planning state varies on a trial‐to‐trial basis with novelty of the problem. The duration of solution stage similarly varies with the amount of computation needed to produce a solution once a plan is devised. The response stage similarly varies with the complexity of the answer produced. In addition, we identified a number of effects that ran counter to a prior model of the task. Thus, we were able to decompose the overall problem‐solving time into estimates of its components and in way that serves to guide theory.     

Distorted estimates of implicit and explicit learning in applications of the process-dissociation procedure to the SRT task

We investigated potential biases affecting the validity of the process-dissociation (PD) procedure when applied to sequence learning. Participants were or were not exposed to a serial reaction time task (SRTT) with two types of pseudo-random materials. Afterwards, participants worked on a free or cued generation task under inclusion and exclusion instructions. Results showed that pre-experimental response tendencies, non-associative learning of location frequencies, and the usage of cue locations introduced bias to PD estimates. These biases may lead to erroneous conclusions regarding the presence of implicit and explicit knowledge. Potential remedies for these problems are discussed.