The effect of conscious controlled verbalization cognitive strategy on transfer in problem solving

The effect of controlled verbalization on learning to solve complex problems was investigated. Fifty participants individually solved the six-disk Tower of Hanoi problem as a criterion task, following one of the five treatments represented in a 2 × 2 factorial design with an appended control group. One factor was the presence or absence of a practice series which required participants to provide verbal rationales for their moves. The other was the presence or absence of verbalization on the six-disk criterion task. The control participants performed the practice tasks and the criterion task without verbalization. Although practice tended to be more effective than no practice for improving performance, its strongest effect occurred when it was coupled with controlled verbalization. Controlled verbalization during the criterion task facilitated performance, but only for subjects who received no prior practice. It was concluded that verbalization was most helpful during the initial flexible stages of learning to solve problems before the skill had become organized. The discussion indicated that performance is facilitated by the quality and timing of the use of verbalizations rather than by the mere activity of verbalizing.     

Enabling spontaneous analogy through heuristic change

Despite analogy playing a central role in theories of problem solving, learning and education, demonstrations of spontaneous analogical transfer are rare. Here, we present a theory of heuristic change for spontaneous analogical transfer, tested in four experiments that manipulated the experience of failure to solve a source problem prior to attempting a target problem. In Experiment 1, participants solved more source problems that contained an additional financial constraint designed to signal the inappropriateness of moves that maximized progress towards the goal. This constraint also led to higher rates of spontaneous analogical transfer to a superficially similar problem. Experiments 2 and 3 showed that the effects of this constraint extend to superficially and structurally different analogs. Experiment 4 generalized the finding to a non-analogous target problem that also benefitted from inhibiting maximizing moves. The results indicate that spontaneous transfer can arise through experience during the solution of a source problem that alters the heuristic chosen for solving both analogical and non-analogical target problems.     

Testing two cognitive theories of insight

Insight in problem solving occurs when the problem solver fails to see how to solve a problem and then--"aha!"--there is a sudden realization how to solve it. Two contemporary theories have been proposed to explain insight. The representational change theory (e.g., G. Knoblich, S. Ohlsson, & G. E. Rainey, 2001) proposes that insight occurs through relaxing self-imposed constraints on a problem and by decomposing chunked items in the problem. The progress monitoring theory (e.g., J. N. MacGregor, T. C. Ormerod, & E. P. Chronicle, 2001) proposes that insight is only sought once it becomes apparent that the distance to the goal is unachievable in the moves remaining. These 2 theories are tested in an unlimited move problem, to which neither theory has previously been applied. The results lend support to both, but experimental manipulations to the problem suggest that the representational change theory is the better indicator of performance. The findings suggest that testable opposing predictions can be made to examine theories of insight and that the use of eye movement data is a fruitful method of both examining insight and testing theories of insight.     

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.     

Using another's gaze as an explicit aid to insight problem solving

Research has shown that implicitly guiding attention via visual cues or unrelated tasks can increase the likelihood of solving insight problems. We examined whether following another person making specific skin-crossing saccades could induce similar attentional shifts and increase solution rates for Duncker's ((1945) Duncker, K. 1945. On problem solving. Psychological Monographs, 58 (5, Whole No. 270)[Crossref] , [Google Scholar]) radiation problem. We presented 150 participants with one of three 30-s eye movement patterns from another problem solver: (a) focusing solely on the central tumour; (b) naturally making skin-crossing saccades between the outside area and the tumour from multiple angles; or (c) making deliberate skin-crossing saccades between the outside area and the tumour from multiple angles. Following another person making skin-crossing saccades increased the likelihood of solving the radiation problem. Our results demonstrate that another person's eye movements can promote attentional shifts that trigger insight problem solving.     

Developing a plan for solving a problem: A representational shift

Research analyzing transitions from lower to higher levels of problem solving has focused either on quantitative increments in processing demands (Case, 1984; Klahr & Robinson, 1981) or on qualitative shifts in the organization of representations (Fischer & Pipp, 1984; Piaget, 1976). This study is concerned with distinguishing the value of these two approaches to problem solving through a microgenetic analysis of children's initial attempts to solve the Tower of Hanoi problem. As suggested by Siegler and Crowley (1991), a microgenetic approach is particularly useful in determining the process of cognitive change. One-hundred and thirty-six children, ages 6 through 8 years, were presented with the standard three-disc problem and allowed 3 minutes to complete it. The quality of the children's performance was analyzed by noting the positioning of the first move, the number and location of illegal moves, and the frequency and location of optimal moves. The results indicate that qualitative shifts in children's representation of the problem space are a crucial aspect of successful performance.     

PROBLEM‐SOLVING SCHEMATA FOR TEXT TYPES: A COMPARISON OF NARRATIVE AND EXPOSITORY TEXT STRUCTURES

In this paper we argue that comprehension is a problem solving activity and that different problem solving schemata exist for different types of texts, both narrative and expository. When processing the text, the reader uses these problem solving schemata to construct meaning of the context and to satisfy personal reading goals. For instance, comprehension of a text, such as a short story, a folk tale, or even a passage from a science book, can be viewed as a problem solving activity. Bransford and Stein's (1984) IDEAL model identifies the problem solver as one who (I) identifies problems, (D) defines and represents problems, (E) explores possible strategies for solving the problem, (A) acts on those strategies, and (L) looks back and evaluates the effects of those strategies. This problem solving model aptly describes what readers as problem solvers do when comprehending a text. The reader as a problem solver identifies and defines specific reading goals. To understand the content of the passage, the reader as a problem solver uses domain‐specific knowledge about the topic, prior experience in reading that type of text to explore a multitude of strategies. While reading the text, the reader uses those strategies to construct meaning about the text. After reading a passage, the proficient reader as a problem solver evaluates what has been read and checks to see if one's reading goals have been met.     

A computational model of frontal lobe dysfunction: working memory and the Tower of Hanoi task

A symbolic computer model, employing the perceptual strategy, is presented for solving Tower of Hanoi problems. The model is calibrated—in terms of the number of problems solved, time taken, and number of moves made—to the performance of 20 normal subjects. It is then "lesioned" by increasing the decay rate of elements in working memory to model the performance of 20 patients with lesions to the prefrontal cortex. The model captures both the main effects of subject groups (patients and normal controls) performance, and the subject groups (patients and normal controls) by problem difficulty interactions. This leads us to support the working memory hypothesis of frontal lobe functions, but for a narrow range of problems.     

Self-observation and learning: the effect of watching oneself on problem solving performance

Two experiments examined the effects of videotape feedback and self-observation on children’s problem solving. The first experiment examined children’s performance on the Tower of Hanoi problem, and demonstrated that video self-observation promotes the acquisition and transfer of procedural knowledge necessary for problem solving. The study also found that specific information presented during the video presentation was not as important as the children seeing their actual prior performance on the problem. The second experiment examined the type of information that may be operative during self-observation. These findings narrow the range of possible explanations for learning through self-observation and, in general, suggest that the positive effect of self-observation is due to active observation of one’s own actual performance.     

Move evaluationasa predictor and moderator of success in solutions to well-structured problems

This paper presents three studies concerned with the evaluation of moves in solutions to Tower of Hanoi problems and the effect that such evaluation processes have on solution success. The existing literature on problem solving suggests that verbalizing whilst solving a problemcan havea positive effect upon performance. However,such verbalization has to be directed toward an explicit evaluation of particular moves. What remains unclear is whether evaluation without verbalization has the same effects or whether some characteristic of the process of verbalization gives rise to improved performance on such tasks. For example, the act of verbalizing per se may simply mean that more processing time is directed toward the problem-solving process. The studies reported in this paper suggest that the process of evaluation may be independent of verbalization processes and that non-verbal evaluation of moves (indicated by a key press) produces the same effects as a verbal evaluation of such moves. Moreover, the process of evaluating moves appears to producea form of behaviour that is prone to disruption via the administration of secondary tasks, whereas non-evaluated solutions are not. This may suggest that problem solvers who engage in evaluation processes develop an explicit representation of the strategies used to solve the problem.     

application of the social marketing model to unemployment counseling: a theoretical perspective

A. R. Andreasen's (1995) social marketing model (SMM) is applied to structure feedback counseling for individuals who are unemployed. The authors discuss techniques used in commercial marketing and how they are equally applicable to solving societal problems; SMM and its application to social interventions; and structured feedback that moves a person from contemplating change to sustained behavioral modification, which can facilitate attitudinal and behavioral change. The relationship of SMM to motivational theories that support the potential of SMM for unemployment counseling is also discussed. The article concludes with a review of the integration of SMM by the New Zealand Employment Service.     

Analogy Events: How Examples are Used During Problem Solving

In attempting to fit a model of analogical problem solving to protocol data of students solving physics problems, several unexpected observations were made. Analogies between examples and exercises (a form of case-based reasoning) consisted of two distinct types of events. During an initialization event, the solver retrieved an example, set up a mapping between it and the problem, and decided whether the example was useful. During a transfer event, the solver inferred something about the problem's solution. Many different types of initialization and transfer events were observed. Poor solvers tended to follow the example verbatim, copying each solution line over to the problem. Good solvers tried to solve the problem themselves, but referred to the example when they got stuck, or wanted to check a step, or wanted to avoid a detailed calculation. Rather than learn from analogies, both Good and Poor solvers tended to repeat analogies at subsequent similar situations. A revised version of the model is proposed (but not yet implemented) that appears to be consistent with all the findings observed in this and other studies of the same subjects.     

The effect of semantics on problem solving is to reduce relational complexity

This article reports a study carried out in order to measure how semantic factors affect reductions in the difficulty of the Chinese Ring Puzzle (CRP) that involves removing five objects according to a recursive rule. We hypothesised that semantics would guide inferences about action decision making. The study involved a comparison of problem solving for two semantic isomorphic variants of the CRP ( fish and fleas ) with problem solving for the puzzle's classic variant (the Balls and Boxes problem; Kotovsky & Simon, 1990 Kotovsky, K. and Simon, H. A. 1990. What makes some problems really hard: Exploration in the problem space difficulty. Cognitive Psychology, 22: 143–183. [Crossref], [Web of Science ®] , [Google Scholar]). Our results showed that the number of moves was reduced by 47% in the fish version and by 51% in the flea version. We discuss these results in terms of semantic inferences and reductions in relational complexity. During the exploratory stage of problem solving participants discover the dependent relations between elements in the puzzle. Initially these relations are processed separately; learning involves generalising the relations within a coherent, interconnected whole that makes up the puzzle's rules. It seems that semantics make it easier for the puzzle's elements to be grouped together within coherent, meaningful wholes, which reduces relational complexity and facilitates problem solving.     

Mathematical model building in the solution of mechanics problems: Human protocols and the MECHO trace

This paper describes model building and manipulation in the solution of problems in mechanics. An automatic problem solver, MECHO, solving problems in several areas of mechanics, employs (1) a knowledge base representing the semantic content of the particular problem area, (2) a means-ends search strategy similar to GPS to produce sets of simultaneous equations and (3) a “focusing” technique, based on the data within the knowledge base, to guide the GSP-like search through possible equation instantiations. Sets of predicate logic statements are employed to describe this model building activity. These clauses are used to give information content to the knowledge base and provide both basis and guidance for the goal driven search. It is hypothesized that humon subjects solving mechanics problems employ similar model building techniques. Protocols of several subjects are presented and comparisons are drawn with the traces of the automated problem solver. Adjustments are made to the program to provide a better fit of traces to protocols. Some implications are presented for using a rule based model for describing human problem solving performance in solving mechanics problems.     

Tower of Hanoi performance of retarded young adults and nonretarded children as a function of solution length and goal state

Three experiments were conducted with the Tower of Hanoi task to assess problem solving ability in 6-, 7-, 8-, and 10-year-old nonretarded children and mentally retarded young adults of varying maturational ages. In Experiment 1 we gradually reduced the number of moves required for solution until subjects could solve the 3-disk tower-ending problem. Although all groups experienced difficulty with the standard 7-move problem, all but the trainable retarded group readily solved the 6-move problem. The trainable group did not reach a comparable level of success until the 4-move problem. On the 7-move problem the retarded groups performed at the level of nonretarded groups that were maturationally $\text{1}\text{1}\text{2}$ to 3 years younger. An analysis of first moves indicated that subject groups differed in the strategies they used to solve the problems. In Experiment 2, practice effects were ruled out as a source of the superior performance on the 6- than on the 7-move problem. In Experiment 3, 7- and 10-year-old nonretarded children and mentally retarded young adults did not differ on 5-move problems in which configuration of the goal states was varied. A comparison of all 5-move problems judged to have the same depth of search requirements indicated that the tower-ending problems were significantly easier to solve than the partial-tower-ending problems, which in turn were easier than the flat-ending problems. A limited depth of search capacity sets boundaries on the use of sophisticated strategies and, to a large extent, accounts for the retarded groups' maturational lag.     

Planning and Problem solving Using the Five disc Tower of London Task

This paper investigates the planning and problem-solving abilities of normal adult subjects using a complex version of Shallice's (1982, 1988) Tower of London (TOL) task. Subjects were required to plan a fluent solution to a range of 5-disc TOL puzzles and then execute their formulated plans as fast as possible. The number of errors and the times taken to prepare the most efficient solutions increased monotonically with the number of chunks of subgoal moves. A subgoal move is a move that is essential for the solution of the puzzle, but which does not place a disc into its goal position. A subgoal chunk is a consecutive series of subgoal moves that all transfer discs to and from the same pegs. Furthermore, preparation time was found to be sensitive to a manipulation that increased the number of competing alternative choices, at critical steps in move selection. When subjects planned their action sequences 'on-line', analyses of individual moves and individual move latencies suggested that planning TOL solutions was limited by the difficulty in evaluating and selecting one action (or one subgoal chunk) from the set of competing potential actions at each step in the course of problem solving.     

Tower of Hanoi: evidence for the cost of goal retrieval.

Past research on the Tower of Hanoi problem has provided clear evidence for the importance of goal-subgoal structures in problem solving. However, the nature of the traditional Tower of Hanoi problem makes it impossible to determine whether there is any special cost associated with storing or retrieving goals. A variation of the Tower of Hanoi problem is described that allows one to determine separately if there is an effect of how long a goal has to be retained on storage time or how long ago it was formed on retrieval time. This paradigm provides evidence for an effect of retention interval on retrieval time and not on storage time. An ACT-R (Adaptive Control of Thought-Rational) simulation of these data is described, which treats goal memory as no different from other memories.     

Meditation and flexibility of visual perception and verbal problem solving

This study investigates the effects of the regular practice of the Transcendental Meditation (TM) technique on habitual patterns of visual perception and verbal problem solving. The study’s predictions were expressed in the context of Norman’s model, which suggests that meditation reduces conceptually driven processes. It was specifically hypothesized that the TM technique involves a reduction of habitual patterns of perceptual and conceptual activation, resulting in (1) more effective application of schemata to new information and (2) less distracting mental activity during performance. This was predicted to result in improved task performance on task conditions in which either (1) habitual patterns of performance hinder or do not aid performance or (2) habitual patterns aid performance. Subjects began the TM technique, relaxed, or added nothing to their daily schedule for 2-week periods. In addition to generalized effects of the interventions, the immediate effects of the TM technique, relaxation, and reading were compared on a letter perception task. The general hypothesis was supported for tasks of tachistoscopic identification of card and letter-sequence stimuli, but not for the verbal problem solving task of anagram solution.     

Combining Item Response Theory and Diagnostic Classification Models: A Psychometric Model for Scaling Ability and Diagnosing Misconceptions

Traditional testing procedures typically utilize unidimensional item response theory (IRT) models to provide a single, continuous estimate of a student’s overall ability. Advances in psychometrics have focused on measuring multiple dimensions of ability to provide more detailed feedback for students, teachers, and other stakeholders. Diagnostic classification models (DCMs) provide multidimensional feedback by using categorical latent variables that represent distinct skills underlying a test that students may or may not have mastered. The Scaling Individuals and Classifying Misconceptions (SICM) model is presented as a combination of a unidimensional IRT model and a DCM where the categorical latent variables represent misconceptions instead of skills. In addition to an estimate of ability along a latent continuum, the SICM model provides multidimensional, diagnostic feedback in the form of statistical estimates of probabilities that students have certain misconceptions. Through an empirical data analysis, we show how this additional feedback can be used by stakeholders to tailor instruction for students’ needs. We also provide results from a simulation study that demonstrate that the SICM MCMC estimation algorithm yields reasonably accurate estimates under large-scale testing conditions.