The relationships among working memory, math anxiety, and performance.

Individuals with high math anxiety demonstrated smaller working memory spans, especially when assessed with a computation-based span task. This reduced working memory capacity led to a pronounced increase in reaction time and errors when mental addition was performed concurrently with a memory load task. The effects of the reduction also generalized to a working memory-intensive transformation task. Overall, the results demonstrated that an individual difference variable, math anxiety, affects on-line performance in math-related tasks and that this effect is a transitory disruption of working memory. The authors consider a possible mechanism underlying this effect--disruption of central executive processes--and suggest that individual difference variables like math anxiety deserve greater empirical attention, especially on assessments of working memory capacity and functioning.

Telling stories: the perils and promise of using verbal reports to study math strategies.

The problem size effect in adult arithmetic performance is generally attributed to direct retrieval processes operating on a network representation in long-term memory. J. LeFevre and her colleagues (J. LeFevre, J. Bisanz, et al., 1996; J. LeFevre, G. S. Sadesky, & J. Bisanz, 1996) challenged this explanation using verbal report evidence that adults also use time consuming nonretrieval strategies to solve simple addition and multiplication. The authors replicated J. LeFevre and colleagues' methods, but added instructional biasing and silent control conditions to test these methods. Both reaction time and report results suggest that LeFevre and colleagues' conclusions about nonretrieval frequency may have been influenced by instructions that revealed the experimental hypothesis and affected participants' strategy reports. Obtaining evidence about adult strategy use in simple arithmetic will require understanding instructional demand and appropriate report methodology.

The effects of time pressure on arithmetic performance.

It has recently been demonstrated that highly math-anxious individuals may be less proficient on arithmetic tasks, particularly those that involve complex problems. The processing efficiency theory postulates that in highly anxious individuals, working memory resources are consumed by "worry," thereby leaving fewer resources available for task completion. Although there is some empirical support for this theory, the precise nature of this worry has yet to be identified. We tested the hypothesis that time pressure may be one component contributing to worry, and subsequent performance deficits characteristic of high math-anxious individuals. Thirty participants completed arithmetic problems of varying complexity in both a timed and untimed condition. Although the timing manipulation negatively affected arithmetic performance in both high and low anxious participants, anxiety groups were not differentially affected. Researchers may therefore have to look to other variables to explain the nature of worrisome thoughts that are theorized to disrupt the performance of anxious individuals.

Mathematics anxiety and working memory: support for the existence of a deficient inhibition mechanism.

A current theory of anxiety effects in cognition claims that anxiety disrupts normal processing within the working memory system. We examined this theory in the context of a reading task, for participants who were high or low in assessed mathematics anxiety. The task was designed to measure the ability to inhibit attention to distracting information and the effects of this ability on explicit memory performance. The results suggested that math-anxious individuals have a deficient inhibition mechanism whereby working memory resources are consumed by task-irrelevant distracters. A consequence of this deficiency was that explicit memory performance was poorer for high-anxious individuals. Based on these results, the recommendation is made that Eysenck and Calvo's (1992) processing efficiency theory be integrated with Connelly, Hasher, and Zack's (1991) inhibition theory to portray more comprehensively the relation between anxiety and performance.

A personal case history of transient anomia.

The article presents a first-person account of a transient anomia or word-finding deficit; the assumption is that such an account, reported by someone with a professional background in memory, cognition, and language processes, may shed additional light on the nature of an anomic episode and on the subjective experience of memory and language disruption due to brain-related abnormalities. During the 45-min episode, I was unable to retrieve and use specific content words and terms ("data," "experiment," "printout") in overt speech. I was completely conscious of these target concepts, although not of their names, and was aware of my inability to find the words. Neither word finding for "everyday" words nor ongoing thought processes were particularly disrupted. The nature and quality of my thoughts during the episode indicate no loss of awareness of circumstances or "presence of mind," but no genuine awareness of the seriousness of the episode. I briefly consider the implications of my experience and the similarities to another published case history.

On mental multiplication and age.

In 2 experiments, younger and older adults were presented with simple multiplication problems (e.g., 4 x 7 = 28 and 5 x 3 = 10) for their timed, true or false judgments. All of the effects typically obtained in basic research on mental arithmetic were obtained, that is, reaction time (a) increased with the size of the problem, (b) was slowed for answers deviating only a small amount from the correct value, and (c) was slowed when related (e.g., 7 x 4 = 21) versus unrelated (e.g., 7 x 4 = 18) answers were presented. Older adults were slower in their judgments. Most important, age did not interact significantly with problem size or split size. The authors suggest that elderly adults' central processes, such as memory retrieval and decision making, did not demonstrate the typical age deficit because of the skilled nature of these processes in simple arithmetic.

Cognitive arithmetic: a review of data and theory.

The area of cognitive arithmetic is concerned with the mental representation of number and arithmetic, and the processes and procedures that access and use this knowledge. In this article, I provide a tutorial review of the area, first discussing the four basic empirical effects that characterize the evidence on cognitive arithmetic: the effects of problem size or difficulty, errors, relatedness, and strategies of processing. I then review three current models of simple arithmetic processing and the empirical reports that support or challenge their explanations. The third section of the review discusses the relationship between basic fact retrieval and a rule-based component or system, and considers current evidence and proposals on the overall architecture of the cognitive arithmetic system. The review concludes with a final set of speculations about the all-pervasive problem difficulty effect, still a central puzzle in the field.

The methodology of testing naive beliefs in the physics classroom.

Many undergraduates harbor a variety of misbeliefs about physical objects in motion--for instance, that a bomb will fall straight down when dropped from a moving airplane. The evidence that these misbeliefs are resistant to correction by college-level physics courses, however, has often been based on methodologies that lack adequate internal validity. We used a quasi-experimental "before and after" design to assess the impact of two college physics courses, and we examined selection-bias, test-retest, and task-format factors directly. Initial accuracy and significant improvements due to instruction varied considerably by problem category and subject group; thus, in several ways, the results refute the general conclusion that conventional physics instruction does little to correct students' misbeliefs. We conclude by advocating the quasi-experimental approach for studies of naive beliefs in physics as well as for other situations in which the impact of classroom instruction is of interest.

Mathematics performance in left and right brain-lesioned children and adolescents.

Children and adolescents with unilateral left- or right-hemisphere lesions were administered a standardized test of mathematics ability and a battery of experimental tests that examined the components of numerical and arithmetic processing. All lesioned groups showed at least marginally lower scores on the standardized test than the controls. More importantly, lesion-related deficits in performance were observed, especially for younger left-lesioned subjects (ages 7-12), on the verbal counting, digit matching, speeded addition, and written subtraction tasks; deficits among younger right-lesioned subjects were similar in nature, yet less pronounced than in the left-hemisphere group. Older left-lesioned subjects showed differences from their controls only on complex verbal counting and speeded addition. Correlations among the various measures indicated two further points. First, earlier onset of left-hemisphere lesion is associated with more serious disruption of mathematical processing. Second, these disruptions are not well assessed by a typical standardized test of mathematical performance, but are clearly in evidence with more precise, focused tasks.

Priming and property dominance effects in semantic memory.

Retrieval from semantic memory was examined by means of reaction times to property statements (e.g., sparrow has beak). The variables of interest were normatively defined property dominance (frequency), type of priming between related sentences (sparrow-sparrow vs. sparrow-robin), and separation or lag between related sentences. Statements asserting a high-dominant property (1) were verified more quickly than those containing low-dominant properties, (2) were primed by a preceding related sentence of either high or low dominance, and (3) revealed decay of priming from Lag 1 to 4. The differences between priming with and without stimulus repetition were nonsignificant when stimuli were treated as a random effect. In support of the Collins and Quillian (1972) model of semantic memory, the priming and property dominance factors interacted.

Rehearsal and retrieval processes in free recall of categorized lists.

The relationships between rehearsal and subsequent retrieval characteristics were examined in the context of free recall of categorized lists. The results indicated a direct correspondence between the frequency of rehearsal and the order and speed of retrieval within categories. The same relationship obtained for the categories themselves. It was suggested that both retrieval time and order effects can be predicted in terms of the organization of input processing and the resultant repetition frequency of categories and exemplars.