Learning subgoals and methods for solving probability problems

We hypothesize that typical example problems used in quantitative domains such as algebra and probability can be represented in terms of subgoals and methods that these problems teach learners. The "quality" of these subgoals and methods can vary, depending on the features of the examples. In addition, the likelihood of these subgoal's being recognized in novel problems and the likelihood of learners' being able to modify an old method for a new problem may be functions of the training examples learners study. In Experiment 1, subjects who studied examples predicted to teach certain subgoals were often able to recognize those subgoals in nonisomorphic transfer problems. Subjects who studied examples demonstrating two methods rather than one exhibited no advantages in transfer. Experiment 2 demonstrated that if the conditions for applying a method are highlighted in examples, learners are more likely to appropriately adapt that method in a novel problem, perhaps because they recognize that the conditions do not fully match those required for any of the old methods. Overall, the results indicate that the subgoal/method representational scheme may be useful in predicting transfer performance.     

A process model for water jug problems

We develop and evaluate a model for the water jug task in which a subject is required to find a sequence of moves (pouring operations) which produce a specified amount of water in each jug. Experiment 1 was designed to evaluate the meansends, move selection heuristics that are assumed by the model. Experiment 2 tested the model's predictions concerning those aspects of the water jug task that determine problem difficulty.A three stage process model incorporating GPS-like, means-ends heuristics and assumptions concerning the utilization of short- and long-term memory was able to account for differences across problems as well as details of the performance of subjects solving a given problem. We conclude that a GPS-like model that only selects one move at a time (no forward planning of move sequences or setting up of subgoals) can provide a good account of solution behavior in the water jug task.     

Improving examples to improve transfer to novel problems

People often memorize a set of steps for solving problems when they study worked-out examples in domains such as math and physics without learning what domain-relevant subgoals or subtasks these steps achieve. As a result, they have trouble solving novel problems that contain the same structural elements but require different, lower-level steps. In three experiments, subjects who studied example solutions that emphasized a needed subgoal were more likely to solve novel problems that required a new approach for achieving this subgoal than were subjects who did not learn this subgoal. This result suggests that research aimed at determining the factors that influence subgoal learning may be valuable in improving transfer from examples to novel problems.     

Effects of interpolating a secondary task during the intertrial interval of a concept identification problem

Several tasks were interpolated during the intertrial interval (ITI) of a concept identification (CI) task. In Experiment I, 234 subjects were required to count backwards by threes, emit a sibilant, or to refrain from thinking after all responses, after correct responses, or after errors. Counting backwards interfered with performance, but only if it occurred after errors. Stimulus and feedback information was either withheld, as in Experiment I, or made available during the ITI in Experiment II. Results of the data from 280 subjects indicated that counting backwards interfered with performance only when interpolated after errors, when stimulus-feedback information was withheld, but had an equivalent effect after errors and correct responses when stimulus-feedback information was available during ITI, indicating that different strategies were induced by the presence of such information.     

Hobbits and orcs: Acquisition of a sequential concept

Subjects solved the hobbits-orcs problem repeatedly until they made no errors on two successive solutions. Groups varied in the kind of feedback given after errors. Further support was obtained for Thomas' (this journal) conclusion that subjects organize the sequence of moves in small subsequences, rather than individual moves. Differences between feedback groups suggested that the organization is oriented forward in the problem, and this contrasts with GPS' retroactive organization of this problem. Comparison between feedback groups also leads to the conclusion that subjects learned from positive information indicating which response is correct, rather than by a process of eliminating errors or sampling new strategies after errors. Analysis of acquisition data agreed with the hypothesis of all-or-none learning at individual states, except for one state where the additional complexity was related to an ambiguity about backward moves. The general pattern of results was invariant over a change in the characters of the problem (men and elves) designed to produce a reversal of relationship between the characters concerning who was prevented from outnumbering whom.     

Individual differences that moderate the effectiveness of relational reasons for self-improvement

Two studies tested the hypotheses that relationally-autonomous reasons (RARs) for goals predict attainment, and that this relationship is stronger among highly relational and agreeable people than others. Study 1 (n = 134) assessed participants’ self-construal and Agreeableness, and their tendency to pursue subgoals for RARs, relationally-controlled reasons (RCRs), and personally-controlled reasons (PARs). One month later, they indicated the number of subgoals they had attained. RARs were positively correlated with attainment, and this relationship was stronger among highly relational and agreeable people than others. In Study 2 (n = 74), self-construal and Agreeableness were assessed then participants generated possible outcomes of 3 subgoals using a Goal Attainment Scale. They were then randomly assigned to a goal program that either emphasized RARs, RCRs, or PARs. One week later, participants indicated their level of attainment. Highly relational and agreeable people had higher levels of attainment than others in the program emphasizing RARs.     

Planning times during traveling salesman's problem: differences between closed head injury and normal subjects

We studied planning behavior in a group of normal subjects and a group of closed head injury patients (CHI). A computerized version of the traveling salesman's problem was used as a visuospatial planning ability task. The program collected measurements of partial times, number of moves, and number of skipped subgoals. These measures allow us to calculate a "planning index" of subjects' planning ability. Results show that CHI patients present limitations in the planning process due to the lack of ongoing planning.     

Suggestions for revised scoring of the Tower of Hanoi test

Detailed time and error analyses of the Tower of Hanoi (TOH) test was performed using four repeated assessments of eight children (ages 9-12 years), who had perceptual and problem solving deficits. The time before each move was measured. In addition to the traditionally counted time scores, new, relative time scores were computed in order to separate the planning time from the general reaction speed. New error scores were defined and sum scores of serious errors (perserative moves, illegal moves, and wrong results) and mild errors (self-corrected moves, almost performed moves, and interrupted trials) were computed. The relative planning time correlated positively with the achieved score, and negatively with the serious errors. The serious errors correlated negatively with the achieved score. The relative planning time seems to measure the quality of planning better than does the raw planning time, and it is a recommended score for TOH analysis. The value of new error scores requires additional research.     

The Effects of Ratee Prototypicality on Rater Observation and Accuracy1

Social cognition theory asserts that perceivers (raters) assign stimulus persons (ratees) to social categories. These categories help the raters encode, store, and recall information. In a longitudinal design that represented a performance appraisal situation, this study examined the effects of information about a ratee's category membership on the amount of information that raters collected about the ratee prior to rating. One hundred fourteen subjects participated in three separate experimental sessions which spanned a 3-week time period. Among other tasks, subjects were required to rate a subordinate who was described in a manner which made it either difficult or easy to assign the subordinate to a social category. It was predicted and found that raters of ratees who were easily categoriezed spent less time observing the ratees' performance than raters of ratees who were less easily classified. Furthermore, results indicated that it was the effect of rater categorization on observation time that was critical to rating accuracy.     

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.     

The role of semantic knowledge and working memory in everyday tasks

We present a single case study of a patient, HG, who was severely impaired on routine everyday tasks, such as cleaning his teeth and preparing a cup of tea. We used the Action Coding System developed by Schwartz et al. (1991) to provide quantitative and qualitative measures of his performance in a number of experimental manipulations: (a) with task-congruent objects only, (b) with task-congruent objects and semantic distractors, (c) with a set of written commands to follow, (d) when he was given one command at a time, (e) when he was shown how the task should be performed before starting himself, and (f) when the task was divided into smaller subgoals. In general, the majority of HG's errors were step omissions, perseverations, sequence errors, and semantic errors. These semantic errors are particularly interesting since HG was able to name, gesture to, and define all the objects when they were presented in isolation or in task-congruent arrays. We suggest that semantic errors may arise for a number of reasons: (1) impaired access from semantic memory to a network representing action schema, (2) degradation of stored schema, and (3) behavior that is abnormally driven by the goal, by preceding actions, or by salient objects rather than by an appropriate association between these elements in working memory.     

Implicit memory for textual materials

As a word moves from isolation in a list to being contextually bound in meaningful discourse, its probability of priming in tests of implicit memory decreases. The present experiments explore whether considerable priming effects can be revealed with conceptual tests of implicit memory as compared to perceptual tests. In the study phase, meaningful actions were described within a coherent text. In Experiment 1 subjects elaborated half of the actions by visual imagery. In Experiment 2, subjects elaborated the actions by enacting them symbolically. In both experiments, subjects in a control condition were simply required to read the same activities. In Experiment 2, a further group of subjects had to detect orthographic errors. The results demonstrated reliable effects of implicit memory in terms of associations with verbs repeated from the studied text. This form of repetition priming for textual materials in a conceptual test of implicit memory was enhanced by both types of elaboration. A word-stem completion task for the same targets revealed a less pronounced and inconsistent priming effect, uninfluenced by both types of elaboration. But the latter form of perceptual priming was found to be more pronounced within the error-detection condition. Measures of explicit memory showed similar effects of elaborative encoding conditions but there were some dissimilarities to measures of implicit memory, too. In general and in accordance with a transfer-appropriate processing view, conceptual tests rather than perceptual tests may be more suitable for detecting effects of implicit memory within the domain of text processing.     

The Influence of Indirect Knowledge of Previous Performance on Ratings of Present Performance: The Effects of Job Familiarity and Rater Training

In a 2 × 2 × 2 crossed factorial design, trained or untrained subjects viewed a videotape and evaluated performance on either a familiar (college lecturer) or unfamiliar (salesperson) job. Prior to viewing the videotape, some subjects reviewed positive information about the ratee's prior performance, whereas other subjects did not review any prior performance information. To determine whether assimilation or contrast effects occurred, we compared ratings provided by subjects who reviewed positive information about prior performance with ratings provided by subjects who did not review any prior performance information. A three-way interaction was obtained. Ratings of performance on the familiar job by untrained or trained subjects revealed only a small assimilation effect. However, when rating performance on the unfamiliar job, a large assimilation effect was observed among untrained subjects, whereas a large contrast effect was observed among trained subjects. The results indicate that rater error training may reverse, rather than reduce or eliminate, rating errors that arise from knowledge of a ratee's prior performance. Implications for further understanding and reducing assimilation and contrast effects are discussed.     

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.     

Grip morphology and hand use in chimpanzees (Pan troglodytes): evidence of a left hemisphere specialization in motor skill

Three experiments on grip morphology and hand use were conducted in a sample of chimpanzees. In Experiment 1, grip morphology when grasping food items was recorded, and it was found that subjects who adopted a precision grip were more right-handed than chimpanzees using other grips. In Experiment 2, the effect of food type on grasping was assessed. Smaller food items elicited significantly more precision grips for the right hand. In Experiment 3, error rates in grasping foods were compared between the left and right hands. Significantly more errors were made for the left compared with the right hand. The cumulative results indicate that chimpanzees show a left-hemisphere asymmetry in motor skill that is associated with the use of precision grips.     

Age and prospective memory

This paper reports an investigation into the effects of age, intelligence, and retrospective memory on performance in a prospective memory task in which subjects aged between 52 and 95 were required to telephone once a day either between two times or at an exact time. The most important influence on performance was how subjects chose to remember to make the telephone calls. The best performance was from subjects who telephoned either in conjunction with another routine event or engaged in some form of advanced planning of the daily schedule. The worst performance was from those who relied on internal cues from their own memory. Performance was intermediate from those who used external cues such as notes or diary entries. Subjects in the between condition were less likely to choose internal cues than those in the exact condition, possibly because the task appeared more difficult, and this resulted in their showing superior performance. The effect of age was influenced by the cue used. For subjects using internal cues, those who forgot were older than those who remembered, whereas for subjects using the other cues, those who forgot were younger than those who remembered. Regardless of cue, self-ratings of cognitive failures were related to performance such that those who reported more minor everyday mistakes were indeed more likely to forget to telephone. While there was some indirect effect of general intelligence on performance in the task, there was no relationship between retrospective memory scores and whether or not subjects remembered to telephone.     

The role of subvocalisation in reading

A series of experiments explored the role of subvocalisation in fluent reading. Experiment I showed that when subjects were required to suppress articulation while reading, their ability to detect anomalous words or errors of word order in prose was markedly impaired although speed of reading was unaffected. Experiment II showed that this decrement was not a general effect due to performing a secondary task, since a concurrent tapping task did not impair detection accuracy. A third study explored the role of acoustic interference in reading by requiring subjects to detect errors in prose while attempting to ignore irrelevant speech, with or without articulatory suppression. Once again articulatory suppression led to a clear decrement in the subject's ability to detect errors, while unattended speech had no effect on performance. None of the manipulations influenced the speed with which the subjects performed the reading task. It is concluded that subvocalisation allows the creation of a supplementary articulatory code which is produced and utilised in parallel with other aspects of reading. Such a code seems particularly suitable for monitoring order information.     

The relation between horizontality and rod-and-frame and vestibular navigational performance

Sex differences on Piaget's water-level (horizontality) test are well established but poorly understood. In this article, correlates of female horizontality performance are systematically explored. Across the five experiments reported, it was found that female subjects who failed the water-level test (poor-horizontality female subjects) were selectively impaired on tasks that required processing information from the otolith organs. In Experiment 1, poor-horizontality female subjects were found to be impaired relative to good-horizontality subjects on the rod-and-frame test. In Experiment 2, a relation was found between female horizontality performance and the ability to process vestibular information in a passive transport task. Experiment 3 ruled out poor spatial updating as a mediating factor in this relation. The results of Experiments 4 and 5 indicated that poor-horizontality female subjects perform randomly on vestibular navigation because they cannot judge linear displacement under conditions of passive transport. The linear transport task is similar to the rod-and-frame task in that both require the central processing of otolith signals. It is proposed that one way to solve the water-level test is to imagine, on the basis of prior perceptual experiences, what the water level looks like inside tilted containers. Because of complex visual-otolith interactions, poor-horizontality female subjects may experience these events differently than good-horizontality subjects.     

Rate of imagery processing in two versus three dimensions

A series of five experiments was conducted to test the optimal speed for performing two- and three-dimensional imagery tasks. Subjects were required to keep track of the location of a pathway in an imagined matrix, as the directions of its successive movements were described verbally. Matrices varied in size and in number of spatial dimensions, with two-dimensional matrices drawn on cardboard and three-dimensional ones built from wooden blocks. When subjects were able to dictate the rate of presentation of the terms describing the pathway, they preferred slower rates for three-dimensional than for two-dimensional stimuli. In subsequent experiments, very fast presentation rates had a larger detrimental effect on performance with three-dimensional matrices than with two-dimensional matrices. A comparison of the patterns of performance for subjects who generally scored high with the patterns for those who scored low showed a stronger effect of dimensionality for poor performers, suggesting that individual differences mediate performance on the task.