Procedural knowledge versus fact retrieval in mental arithmetic: A reply to Baroody

Based on a review of reaction time studies, a model of mental arithmetic performance which emphasizes the process of fact retrieval from organized memory representations was proposed (M. H. Ashcraft, Developmental Review, 1982, 2, 213–236). In contrast to this view A. J. Baroody (Developmental Review, 1983, 3, 225–230) proposes that most mental arithmetic performance depends on procedural knowledge such as rules, heuristics, and principles. While Baroody's idea is both intriguing and potentially important, its exposition is quite vague and speculative. Without concrete suggestions as to the nature of the proposed rules and heuristics, especially for routine problems like 4 + 3 and 8 × 5, Baroody's proposal appears to be pertinent only to special cases like N + 0 and N + 1. Lacking this sort of elaboration, the alternative does not provide a useful or compelling explanation of the existing Chronometric results, and seems, at best, to be premature.     

Deficits in temporal sequencing of verbal material: The effect of laterality of lesion

Temporal sequencing of verbal materials (digits, words, and geometric forms) presented in two sensory modalities (auditory and visual) to three groups of subjects (Broca's with left anterior lesions, patients with right hemisphere lesions, and normals) was examined. Each subject was asked to point to a set of stimuli in the same sequence as presented by the examiner. Results indicated that patients with left hemisphere lesions were more impaired on all tasks than the right hemisphere lesioned patients who, in turn, were impaired compared to normal controls. Response to auditory presentation was superior to response to visual presentation. Also, digits were the easiest for all groups, and words were easier than geometric forms. Of special interest was the finding which suggested that right hemisphere lesions are associated with impairment of verbal temporal sequencing under either auditory or visual presentation.     

Comprehension disorders in aphasia: a historical review.

This paper reviews the clinical reports and theoretical inferences made by early scientists in regard to the impairment of auditory comprehension so often found in aphasics. It first presents an analysis of the literature on and the interpretation of comprehension disorders in aphasia up to the time of Pierre Marie and Arnold Pick. It then reviews early attempts to assess and quantify receptive impairment. Finally, it discusses the historical origin of some of the questions on comprehension currently under investigation by contemporary researchers.     

The production and verification tasks in mental addition: An empirical comparison

We respond to A. Baroody's comment (1984, Developmental Review, 4, 148–156) with an empirical comparison of the production and verification tasks. With the exception of performance at the first grade level, the two tasks yield essentially identical conclusions. The results of an adjunct task, in which the rate of mental counting was assessed, suggest that children as young as second grade are relying on memory retrieval to a significant degree. In contrast to Baroody's speculation, there appear to be no widespread difficulties associated with results from the verification task. Furthermore, the task permits a more analytic examination of performance and underlying mental process than is afforded by the production task. We conclude by reiterating the empirical support for a model of fact retrieval, and suggesting that accessibility of the arithmetic facts is the basic factor which underlies both fact retrieval and procedural knowledge performance.     

Simple and complex mental addition across development

Students in Grades 1, 4, 7, and 10 were timed as they solved simple and complex addition problems, then were presented similar problems in an untimed interview. A manipulation of confusion between addition and multiplication, in which multiplication answers were given to addition problems (3 + 4 = 12), revealed evidence for the hypothesized interrelatedness of these operations in memory only in 10th graders. The overall pattern of results suggests a strong reliance on memory retrieval, even in the first-grade group, with discernible time differences when “procedural” knowledge of carrying is required for problem solution. The results were judged consistent with a fact retrieval model which invokes explicit procedural information when problem difficulty is high or when processes like carrying and estimating magnitudes are required. In agreement with several other reports, the overall slowing of performance to larger problems is best explained in terms of normatively defined problem difficulty or associative strength in memory.     

Mental addition in third,fourth, and sixth graders

Research on mental arithmetic has suggested that young children use a counting algorithm for simple mental addition, but that adults use memory retrieval from an organized representation of addition facts. To determine the age at which performance shifts from counting to retrieval, children in grades 3, 4, and 6 were tested in a true/false verification task. Reaction time patterns suggested that third grade is a transitional age with respect to memory structure for addition—half of these children seemed to be counting and half retrieving from memory. Results from fourth and sixth graders implicated retrieval quite strongly, as their results resembled adult RTs very closely. Fourth graders' processing, however, was easily disrupted when false problems were presented. The third graders' difficulties are not due to an inability to form mental representations of number; all three grades demonstrated a strong split effect, indicative of a simpler mental representation of numerical information than is necessary for addition. The results were discussed in the context of memory retrieval versus counting models of mental arithmetic, and the increase across age in automaticity of retrieval processes.     

Paralinguistic aspects of auditory comprehension in aphasia.

Eight severe aphasics were given sentences with either emotional or neutral content, presented once directly by the examiner and once via a tape recorder. Sentences with emotional content produced a greater number of responses than their neutral counterparts. Sentences spoken by the examiner also produced a significantly greater number of responses than the same items originating from a tape recorder. These results confirm the view that elements not related to the linguistic aspects of a message (and therefore referred to as paralinguistic) play a significant role in auditory comprehension.     

Effect of locus of control,expectancy confirmation-disconfirmation,and type of goal on causal attributions of failure

Two experiments demonstrated interactive effects between locus of control and expectancy confirmation-disconfirmation in determining attribution of failure. Experiencing an expected versus an unexpected failure significantly influenced the performance attributions of internals but not externals. The first experiment also demonstrated an interaction between locus of control and type of performance goal (self-determined versus other-determined) in determining failure attribution. When the performance goal was other-determined, there were significant differences between internals and externals in their attributions of failure, but these differences did not materialize when the performance goals were selfdetermined, in the absence of any externally defined standard. Interpretation of results focused on the differences between internals and externals in regard to information processing and certain cognitive characteristics as they are related to the attribution of outcomes.     

Effects of knowledge that attributions will be observed by others

The current study was conducted to determine if attribution statements would be affected by subjects' knowledge that their attributions of success or failure would be observed by an opposite-sex peer. At the time subjects recorded their attributions, half of them anticipated that their attributions would soon be observed in their presence by an opposite-sex peer, while the other half recorded their attributions anonymously. Results indicated that attributions of success and failure were affected by the social context. Observed subjects evidenced less tendency to attribute their failure to low ability than did nonobserved subjects. Subjects who succeeded on an identity-relevant task reported higher ability attributions under observation conditions than under nonobservation conditions. Observed subjects evidenced significantly greater willingness to attribute failure to lack of effort than did nonobserved subjects. For a task intended to be of minimal relevance to subjects' identities, nonobserved subjects attributed failure to task difficulty to a significantly greater degree than did observed subjects. Results were discussed in relation to Bradley's contention that self-serving biases in attribution can usefully be conceptualized as strategic self-presentations.     

Antecedents of employees' mental health—The role of career and work satisfaction

It was hypothesized that individual and situational variables, as a whole, will show stronger relationships with work-related attitudes than with mental health indices. Work-related attitudes, on the other hand, were expected to contribute more strongly to mental health than the individual and situational variables. Results obtained from two groups of staff professionals and retail store managers, using primarily questionnaire data, supported these hypotheses. Career and work satisfaction emerged as the strongest contributors to mental health. Situational variables such as job characteristics, supervisory style, and pay related more strongly to the attitudinal variables than to mental health. This pattern suggests that career and work satisfaction may serve as intervening variables in the relationship between situational variables and mental health.     

The relationship between vocational interests and job satisfaction: Reconciliation of divergent results

It was hypothesized that congruency of vocational interests with present occupation would be positively related to job satisfaction for long job-tenured employees, and would be unrelated to satisfaction for short job-tenured employees. In two samples of 54 and 47 middle managers, the hypothesis was supported for satisfaction with work and supervision. This differential pattern of correlations may help explain the inconsistent relationship between vocational interests and job satisfaction obtained in past studies.     

The role of analogy in transfer between similar problem states

The study investigated the effect of transfer between two problems having similar (homomorphic) problem states. The results of three experiments revealed that although transfer occurred between repetition of the same problems, transfer occurred between the Jealous Husbands problem and the Missionary—Cannibal problem only when (a) Ss were told the relationship between the two problems and (b) the Jealous Husbands problem was given first. The results are related to the formal structure of the problem space and to alternative explanations of the use of analogy in problem solving. These include memory for individual moves, memory for general strategies, and practice in applying operators.     

Retrieval processes in fifth graders and adults

This research was concerned with retrieval processes which underlie conceptual clustering. In a free recall task with categorized lists, fifth graders' and adults' retrieval was examined temporally by means of interword response times. List organization and retrieval cue factors were manipulated in order to assess the developmental relevance of an hypothesized three component retrieval model. The results indicated that both age groups used a qualitatively similar retrieval strategy, involving search for and decoding of higher-order memory units. Providing retrieval cues eliminated the category search component, but also increased the likelihood of exhaustive recall attempts under random presentation conditions. The results were discussed in terms of the inter-relationships between storage and retrieval strategies. Age-related differences in retrieval time were attributed to insufficient reorganization during input and failure to attempt to recall all of a category's members.     

The effect of attending to feeling on memory for internally generated stimuli

The present experiments examined the effects of self-focus, as produced by focusing on feelings, on memory. In an initial experiment subjects did complex mental arithmetic significantly faster after self-focus. Because complex mental addition involves internally generated stimuli, the remaining experiments compared the effects, on memory, of self-focus on internally generated stimuli to the effect of self-focus on stimuli supplied by the experimenter. In a second experiment, self-focus facilitated memory for digits recalled in reverse order but not for digits when recalled in the given order. In a third experiment, self-focus facilitated the memory for the classification of digits but not for the digits themselves. In a fourth and fifth experiment, self-focus aided memory for classification of objects into categories such as small, medium, or large but did not aid memory for the objects themselves. In general, improved performance due to feeling focus was attributed to the role that self-focus may play in increasing attention to internally generated stimuli.     

A different form of agraphia: Syntactic writing errors in patients with motor speech and movement disorders

Three patients are described who displayed syntactic writing errors in combination with a motor speech disturbance and impaired motor limb function. Two of the patients had bulbar amyotrophic lateral sclerosis (ALS). Agraphia appeared when verbal communication was no longer possible. Autopsy in one patient disclosed only lesions consistent with ALS. The third patient had palilalia and chorea and, although not aphasic, his written language showed persistent syntactic errors. We hypothesize that the agraphia in these patients occurred because of the combination of disordered feedback from the motor speech apparatus and limbs.     

An analysis of neurological soft signs in children with learning problems

Eighty children with learning problems were systematically evaluated for neurological soft signs, general intelligence, scholastic achievement, hyperactivity, and neurocognitive dysfunction. A factor analysis yielded six factors, and a higher order, general ability factor was derived from an orthogonal rotation. Neurocognitive functions appeared in three factors suggesting “types” of dysfunctions. The higher order general ability factor represents a broad range of skills. The two other factors with neurocognitive loads suggest a distinction between verbal-motor integration and visual-motor integration. Age, sex, and hyperactivity formed the remaining clusters.     

Attending to feelings and cognitive performance

The effect on cognitive performance of attending to internally generated stimuli was examined. Specifically, the effect of examining feelings and sensations upon performance in the Stroop test and upon the performance of mental addition was measured. In two initial experiments subjects more quickly named, in the Stroop test, the color of the ink (“red”) in which a color word (“green”) was printed following instructions to attend to their feelings. It was found that this facilitation was due in part to the slowing of the automatic, interfering habit of reading for word meanings. In a third experiment, the effect of attending to physical sensations on the back of the hand was found to have a similar facilitating effect and was seen as resulting from the allocation of attention to internally generated stimuli. In a final experiment, attending to feelings and to the physical sensations on the back of the hand was found to increase speed of mental addition. This effect was attributed to increased attention to internally generated stimuli (here knowledge about the arithmetic performance at the moment).     

A study of hyperlexia

Twelve children with early intense reading and superior word recognition skills coupled with disordered language and cognitive behavior are described. Cognitive, linguistic, and reading measures evidenced a generalized cognitive deficit in forming superordinate schemata which was not specific to visual or auditory modalities. Positive family histories for reading problems were present for 11 of the 12 children, suggesting a relationship between hyperlexia and dyslexia.     

Biasing evaluations to appear unbiased: A self-presentational paradox

Subjects interviewed a confederate posing as a job applicant. In a 2 × 2 factorial design, half the subjects were insulted by the confederate at the end of the interview and half were not insulted. Half the subjects were observed by the experimenter during the final phase of the interview and evaluated the confederate publicly. The remaining subjects were unobserved during the interview and evaluated the confederate anonymously. As predicted, subjects who were publicly insulted were more favorable toward the confederate than were subjects who were privately insulted. Within the public/insult condition, subjects scoring high on Snyder's (1974, Journal of Personality and Social Psychology, 30, 526–537) self-monitoring scale were more favorable toward the confederate than were subjects scoring low on this scale. The positivity bias occurred only on highly subjective ratings, which are most prone to the appearance of bias. The results are discussed in terms of the subjects' desire to avoid the appearance of bias by biasing their evaluations.