Errors in subtractions: judged and observed frequencies

In a first study 10 adults, aged 24-44 years, solved all 105 subtraction problems in the form M - N = , where 0 < or = M < or = 13, 0 < or = N < or = 13 and N < or = M. Each participant solved every problem 10 times and in total there were 10 500 answers. Answers, response latencies and errors were registered. Retrospective verbal reports were also given, indicating how a solution was reached: (1) via a (conscious) reconstructive cognitive process or (2) via an (unconscious) reproductive (retrieval) process. The participants made 291 errors (2.8%) when solving the subtractions in study 1. The rate of self-correction was very high, 92%. In a second study 27 undergraduate students estimated overall error rates, including self-corrected errors for the 105 subtraction problems used in the first study. Judged and actual error rates were compared. The participants systematically underestimated error rates for error prone problems and overestimated error rates for error free problems. The participants were fairly accurate when they predicted problems that were most error prone, with a hit rate of 0.67 for the (18) problems predicted as the most error prone ones. In contrast, predictions of which problems were error free were very poor with a hit rate of only 0.20 of the problems predicted as error free really having no errors in study 1. The correlation between judged error rates and frequencies for actually made errors was 0.69 for answers belonging to reconstructive solutions. In contrast, there was no significant correlation between judged and actual error rates at all for retrieved solutions, possibly reflecting the inaccessibility to consciousness of quick retrieval processes.     

The use of verbal protocols as data: An analysis of insight in the candle problem

In the present study, we examined the use of verbal protocols as data in the study of the cognitive processes underlying insight. Fifty-eight Temple University undergraduates attempted to solve Duncker's (1945) candle problem either silently or while thinking aloud. Solution rates, solving times, and solution types were comparable between conditions, suggesting that verbal overshadowing (Schooler, Ohlsson, & Brooks, 1993) did not occur when the participants attempted to solve the candle problem. Subsequent analysis of verbal protocols provided a catalogue of solutions generated by the participants, as well as empirical support for the occurrence of impasse and restructuring. Although restructuring was present in the majority of protocols, including those of the participants who later produced the box solution, the presence of impasse occurred with less frequency and was not associated with production of the box solution. These results provide information concerning how the candle problem is solved and suggest that verbalization can be used to examine how individuals solve insight problems and to evaluate existing theories of insight.     

Gender differences in the pathway from adverse life events to adolescent emotional and behavioural problems via negative cognitive errors

The aim of this study was to test for gender differences in how negative cognitive errors (overgeneralizing, catastrophizing, selective abstraction, and personalizing) mediate the association between adverse life events and adolescents’ emotional and behavioural problems (measured with the Strengths and Difficulties Questionnaire). The sample consisted of 202 boys and 227 girls (aged 11–15 years) from three state secondary schools in disadvantaged areas in one county in the South East of England. Control variables were age, ethnicity, special educational needs, exclusion history, family structure, family socio‐economic disadvantage, and verbal cognitive ability. Adverse life events were measured with Tiet et al.'s (1998) Adverse Life Events Scale. For both genders, we assumed a pathway from adverse life events to emotional and behavioural problems via cognitive errors. We found no gender differences in life adversity, cognitive errors, total difficulties, peer problems, or hyperactivity. In both boys and girls, even after adjustment for controls, cognitive errors were related to total difficulties and emotional symptoms, and life adversity was related to total difficulties and conduct problems. The life adversity/conduct problems association was not explained by negative cognitive errors in either gender. However, we found gender differences in how adversity and cognitive errors produced hyperactivity and internalizing problems. In particular, life adversity was not related, after adjustment for controls, to hyperactivity in girls and to peer problems and emotional symptoms in boys. Cognitive errors fully mediated the effect of life adversity on hyperactivity in boys and on peer and emotional problems in girls.     

Sustained attention failures are primarily due to sustained cognitive load not task monotony

We conducted two studies using a modified sustained attention to response task (SART) to investigate the developmental process of SART performance and the role of cognitive load on performance when the speed-accuracy trade-off is controlled experimentally. In study 1, 23 participants completed the modified SART (target stimuli location was not predictable) and a subjective thought content questionnaire 4 times over the span of 4 weeks. As predicted, the influence of speed-accuracy trade-off was significantly mitigated on the modified SART by having target stimuli occur in unpredictable locations. In study 2, 21 of the 23 participants completed an abridged version of the modified SART with a verbal free-recall memory task. Participants performed significantly worse when completing the verbal memory task and SART concurrently. Overall, the results support a resource theory perspective with concern to errors being a result of limited mental resources and not simply mindlessness per se.     

Verbal and nonverbal behaviour as a basis for credibility attribution: The impact of task involvement and cognitive capacity

Three experiments were able to demonstrate the usefulness of dual-process models for the understanding of the process of credibility attribution. According to the assumptions of dual-process models, only high task involvement and high cognitive capacity leads to intensive processing of verbal and nonverbal information when making credibility judgments. Under low task involvement and/or low cognitive capacity, people predominantly use nonverbal information for their credibility attribution. In Experiment 1, participants under low or high task involvement saw a film in which the nonverbal behaviour (fidgety vs. calm) and the verbal information (low versus high credibility) of a source were manipulated. As predicted, when task involvement was low, only the nonverbal behaviour influenced participants’ credibility attribution. Participants with high task involvement also used the verbal information. In Experiment 2 and 3, the cognitive capacity of the participants was manipulated. Participants with high cognitive capacity, in contrast to those of low cognitive capacity, used the verbal information for their credibility attribution.     

Working memory demands in insight versus analytic problem solving

Working memory is one of the cognitive processes thought to differentiate insight and analytic forms of problem solving. The present research examined memory involvement in the solution of insight versus analytic problems. Participants completed verbal and spatial working memory and short-term memory measures and a series of analytic and insight problems. Results demonstrated a relationship between working-memory capacity and the solution of analytic problems and between verbal short-term memory capacity and the solution of insight problems. This distinction was generally though not universally supported when memory was examined in relation to individual problems. Memory involvement in insight problem solving was further examined to clarify whether restructuring in insight is the end result of active memory search or spontaneous processes. The present research supports the theory that differences exist in the cognitive processes underlying insight versus analytic problem solving, and provides support for the spontaneous theory of restructuring in insight.     

Error detection processes in statistical problem solving

Problem solvers' error detection processes were studied by instructing 16 subjects to think aloud when solving two statistical problems. The evaluative episodes occurring in subjects' protocols were analyzed into Affirmative evaluation, Direct error-hypotheses, Error suspicion, and Standard check episodes, the last three of which are assumed to cover all main types of error detection processes. Most errors (78%) were found to have contributed to a solution part that triggered some evaluative episode. However, only one-third of the undetected errors had contributed to such a solution part. The Standard check episodes, seen as centrally-invoked, only led to the detection of few errors in proportion to the number of times they were performed. Evidence was found for two types of spontaneous error detections, one occurring abruptly and the other as a result of a more elaborated error detection process, initiated by the solver perceiving the solution as dissatisfying or strange. The perception of a symptom was a fairly reliable source of information about errors. However, subjects often did not manage to detect the error after having noticed a symptom. The closer a relevant Error suspicion episode followed an error, the greater was the probability of detecting the error. Good problem solvers detected a higher proportion of their errors compared to poor problem solvers, probably due to differences in the processes leading up to the triggering of an evaluative episode rather than to differences after the episode had been triggered.     

Strategies for solving simple addition problems: A comparison of normal and subnormal children

Abstract.— Children in the third grade in a normal class and children poor in mathematics attending special classes solved all additions with the sum of the two positive addends smaller than 10. The cognitive processes leading to the solutions were described in relation to a process model predicting solution times. The general model included a counter with two operations, setting and incrementing by one unit. It is assumed that solutions are obtained either by direct retrieval from memory or by a reconstructive process. The first step in this process is finding the starting point for the counter which is the greater addend. When the problem has been defined and the starting point has been found the generation of the answers starts by the counter stepping the number of units denoted by the smaller addend. The results based mainly on latencies showed that children poor in mathematics, in addition to a slower processing rate, seemed to have difficulties in the choice of strategy for processing the information in a problem.     

The role of information presentation formats in belief updating

The effects of the format by which information is presented on the cognitive processes of belief updating were investigated in the present research. Because of the differences in the affordance of verbal vs. numerical information, it is predicted that the belief updating processes involved in processing verbal and numerical information would be different. Specifically, the additive rule is used to combine information using verbal formats, while the averaging rule is used to combine information using numerical formats. Two experiments were conducted to test these hypotheses. Experiment 1 tested the belief updating process in the positive direction, and Experiment 2 tested the process in the negative direction. Two independent variables were manipulated: information presentation format (verbal vs numerical) and presentation order (strong–weak vs weak–strong). The participants were asked to adjust their purchase likelihood of a consumer product based on the sequential presentations of two experts' opinions. These two opinions varied in their formats (verbal vs. numerical) and strengths (strong vs weak). The two opinions were presented in either the strong–weak order or the weak–strong order. Participants were instructed to first anchor their purchase likelihood at 50%, and then adjust the purchase likelihood, first based on the first expert's opinion, and second based on both experts' opinions. In both experiments the hypotheses that participants employed an additive rule to integrate verbal information and an averaging rule to integrate numerical information were supported.