Mental Arithmetic Performance Research Articles

Reliability and validity of day-to-day blood flow velocity reactivity in a single subject: an fTCD study

To evaluate the within-subject variability of repeated task-induced blood flow velocity (BFV) change, we measured the haemodynamics of the anterior and middle cerebral arteries of the same volunteer on 20 consecutive working days during the performance of mental arithmetic with transcranial Doppler ultrasonography. BFV changes with the arithmetic condition were compared against a resting and a counting condition. Absolute BFV data showed equally increased velocities during rest and arithmetic activity as compared to counting. The findings suggest that the resting state might not be the ideal reference paradigm to evaluate task-induced haemodynamic changes. Selecting the counting condition as the more valid baseline measure, we obtained relatively stable lateralisation indices for the MCA with 1 of 10 measurements outside the 95% confidence interval. Reproducibility was poorer in the ACA, with 3 outliers. A strategy that calculates the average of multiple short activation epochs within the same session appears to improve the reliability of the lateralisation index. (E-mail: guy.vingerhoets@rug.ac.be)

Adrenocortical stress responses and altered working memory performance

This study examined stress cortisol responses and cognitive performance. We initially measured cortisol responses of 40 right‐handed healthy male volunteers to counterbalanced mental arithmetic and public speaking stressors. We then examined the relationship between cortisol reactivity and dichotic listening and mental arithmetic performance. High cortisol responders made more errors and completed fewer mental arithmetic items than low reactors. On dichotic listening, high responders tended toward better performance in all conditions and to both ears. High responders showed better performance to the right ear in the forced right than in the nonforced condition, whereas no difference between these conditions was found in low responders. High cortisol responders may have an increased focus on sensory stimuli and a decreased allocation of resources to working memory tasks.

Defective alpha reactivity with mental concentration.

We have studied 120 patients with EEGs that show defective reactivity of alpha activity in which one side fails to attenuate during the performance of mental arithmetic. The side of defective reactivity was the right side in 74 patients and the left in 46. A similar asymmetric reactivity of alpha activity to eye opening (Bancaud phenomenon) was seen in 32 patients. Also, 113 patients had lateralized EEG abnormalities on the side of defective reactivity and on the side in which cerebral lesions or disorders of cerebral function were present. The unilateral failure of alpha attenuation with mental concentration represents a subtle lateralized electrographic manifestation of cerebral dysfunction on the side of defective reactivity.

Inhibitory Processes in Sequential Retrieval: Evidence from Variable-Lag Repetition Priming

Performance of simple mental arithmetic provides a sensitive measure of subtle inhibitory and excitatory processes operating in sequential retrieval. Specifically, the probability that an error (e.g., 6 × 7 = 36) matches an earlier answer is below chance for the preceding trial (negative error priming), greater-than-chance for intermediate lags (positive error priming), and returns to chance after about 10 intervening trials (≈60 sec) (Campbell & Clark, 1989). Negative error priming suggests that inhibitory processes initially suppress just-produced items and temporarily mask excitatory effects of recent retrievals. To test further the inhibition hypothesis of negative error priming, we examined repetition priming effects at variable lags. The results demonstrate similar non-monotonic functions for error priming and repetition priming as a function of lag, consistent with the hypothesized decay of inhibitory memory processes.

Topographic EEG Changes across Single-To-Dual Task Performance of Mental Arithmetic and Tracking

Topographic EEG Changes across Single-To-Dual Task Performance of Mental Arithmetic and Tracking

Counting on working memory in arithmetic problem solving.

Mental calculation is an important everyday skill involving access to well-learned procedures, problem solving, and working memory. Although there is an active literature on acquiring concepts and procedures for mental arithmetic, relatively little is known about the role of working memory in this task. This paper reports two experiments in which dual-task methodology is used to study the role of components of working memory in mental addition. In Experiment 1, mental addition of auditorily presented two-digit numbers was significantly disrupted by concurrent random letter generation and, to a lesser extent, by concurrent articulatory suppression, but was unimpaired by concurrent hand movement or by presentation of irrelevant pictures. Although the number of errors increased with two of the dual tasks, the incorrect responses tended to be quite close to the correct answer. In Experiment 2, the numbers for addition were presented visually. Here again, random generation produced the largest disruption of mental arithmetic performance, while a smaller amount of disruption was observed for articulatory suppression, hand movement, and unattended auditorily presented two-digit numbers. The overall levels of performance were better and the absolute size of the disruptive effects shown with visual presentation was very small compared with those found for auditory presentation. This pattern of results is consistent with a role for a central executive component of working memory in performing the calculations required for mental addition and in producing approximately correct answers. Visuospatial resources in working memory may also be involved in approximations. The data support the view that the subvocal rehearsal component of working memory provides a means of maintaining accuracy in mental arithmetic, and this matches a similar conclusion derived from previous work on counting. The general implications for the role of working memory in arithmetic problem solving will be discussed.

Mathematics anxiety and mental arithmetic performance: An exploratory investigation

Abstract Two exploratory studies were conducted to determine if mathematics anxiety, as assessed by the Mathematics Anxiety Rating Scale (MARS), is related to the underlying mental processes of arithmetic performance. MARS scores were higher when the test was administered by computer, vs. the standard paper-and-pencil format, and were higher for female than male college students. Small but significant processing differences in simple addition and multiplication were found when subjects were divided by quartiles into anxiety groups. Much larger differences in processing speed and accuracy were found with complex addition problems and a set of difficult problems (e.g. 9 × 16 = 134, true or false) that tested all four arithmetic operations. Overall, the low anxiety group was consistently the most rapid and accurate, the medium high was consistently the slowest, and the high anxiety group the most prone to errors. The results suggest that genuine performance differences exist among the several levels of mathe...

Localization of activated areas and directional EEG patterns during mental arithmetic

In a search for the physiological correlates of mental activity, localized EEG desynchronization induced by mental arithmetic was assessed by the entropy of the EEG power spectrum (irregularity index, II). The topographic mapping of II can show a localized cortical activation. Directional EEG patterns during mental arithmetic were further examined with a directed mutual information measure (information flow). These two information measures were compared between resting and mental arithmetic conditions in 10 right-handed subjects as well as one left-handed subject. II significantly increased during mental arithmetic in the left temporo-centro-parietal region in right-handed subjects, thus exhibiting its activation. Significant changes in information flow during mental arithmetic were found in the directions mostly from the temporo-centro-parietal region to other areas and within the frontal region in right-handed subjects: information flow from the left temporal and the mid-frontal areas increased and information flow mostly from the left hemisphere decreased. One left-handed subject showed greater II in the right temporo-parietal area and smaller II in the left temporal area during mental arithmetic, together with smaller information flow from the right post-temporal area. These findings suggest that the left temporo-centro-parietal activation is specific to calculation processing, and the frontal information flow is related to the active performance of mental arithmetic.

Mathematical performance before, during, and following cycling at workloads of low and moderate intensity.

Mental arithmetic performance before, during, and following low (40% maximal heart-rate reserve; approximately 90 watts exercise for 15 min.) and moderate (60% maximal heart-rate reserve; approximately 150 watts exercise for 10 min.) intensity cycling by 20 male students (M age = 28.1 yr.) was studied. Subjects were grouped, by using a median-split on their total mathematical performance scores, into a group of 10 low in arithmetic skill and a group of 10 high in arithmetic skill. The numbers and percentages of right answers to 1-min. mathematical problem-sets of either group were not different in the various conditions, suggesting that 25 min. of progressive cycling exercise did not influence mathematical problem-solving efficacy.

Reducing heart rate reactivity to stress with feedback. Generalization across task and time.

Heart rate (HR) reactions to two behavioral stressors (videogame and mental arithmetic) were measured in 8 experimental subjects who received biofeedback training and 8 matched control subjects during three assessment periods: pretraining, posttraining, and one-week follow-up. Experimental subjects exhibited significant reductions in HR following a training session in which they received ongoing HR feedback while playing a videogame. Control subjects, who played the same number of videogames without HR feedback, showed smaller HR reductions. During the training session, all subjects were instructed to reduce HR while maximizing game performance. In comparison to controls, experimental subjects (a) maintained lower HRs during videogame presentations after a one-week period and (b) generalized these HR reductions to the mental arithmetic challenge at follow-up. Performance on the videogame declined from posttraining to follow-up for experimental subjects but not for control subjects. No group difference in mental arithmetic performance was observed.

Psychophysiological responses in women reporting severe premenstrual symptoms.

Sixteen women attending a Premenstrual Tension Clinic and eight control women were tested experimentally in the premenstrual and postmenstrual phases with assessments of heart rate, skin conductance level, and neck electromyogram during rest, relaxation, an emotionally upsetting film, and performance of mental arithmetic and video game tasks. All participants completed daily symptom assessments for two menstrual cycles prior to the study. The clinic attenders were divided into eight (Clinic+) who showed marked increases in symptoms premenstrually, and eight (Clinic-) who recorded only modest changes in symptom severity across the menstrual cycle. There were no marked differences in resting autonomic activity. During relaxation, skin conductance level decreased to a greater extent in the premenstrual than in the postmenstrual phase, while neck electromyogram showed the reverse pattern. Heart rate reactions to the mental arithmetic and video game tasks were smaller in the premenstrual than in the postmenstrual phase in Controls and Clinic- groups, but not in the Clinic+ group. Possible explanations of these results are discussed.

The effects of noise, cognitive set and gender on mental arithmetic performance

Recent research on the effects of moderate noise seems to indicate that the main changes in performance are elicited by shifts in the adopted strategy. The present experiment investigated this effect by directly manipulating the cognitive set and following male and female subjects' performances on an arithmetic task under two levels of noise. The results showed that noise significantly impaired rate of work but has no detrimental effect on accuracy. Noise clearly reduced the pace at which female subjects were working, but it hardly affected that of male subjects. The differential response pattern of men and women in quiet and noise when working under different cognitive sets resulted in a significant interaction between these factors. These findings support the idea that the effects of noise are mediated by a constellation of factors whose control is necessary for a realistic evaluation of performance in noise.

Textbook Presentations of the Basic Addition Facts

Widely usedmathematics textbooks from kindergarten, first, second, and third grades were evaluated both for the frequency and the order of presentation of the basic 100 addition facts 0 + 0 through 9 + 9. A striking result was that the frequency of occurrence distributions for the basic facts were markedly skewed. There were many fewer presentations of large than small problems in the texts, and problems involving the addition of 0 were relatively infrequent at all grades; such was also the case in a similar study conducted in 1924. Correlations among the tabulated variables and a variety of published normative and performance measures are presented. We suggest several possible relationships between these results and the empirical literature on mental arithmetic performance. In particular, reaction time performance across the entire developmental span is closely related to both the frequency of presentation and the order of presentation of the basic facts in elementary texts. Furthermore, both the frequency and order of presentation variables have strong and possibly important relationships to adults' ratings of problem difficulty.

A clinical study of Gilles de la Tourette syndrome in the United Kingdom.

The clinical features of 53 British-born patients with Gilles de la Tourette syndrome are described. The mean age at onset of body tics was seven years and for vocalisations 11 years. Coprolalia was present in 39%, copropraxia in 21%, echolalia in 46% and echopraxia in 21%. Complicated antics and mannerisms were also common, often involving the compulsive touching of objects or self-injurious behaviour. Forty-six per cent of cases had a family history of tics in a single close relative and in two individuals a further member of the family had Gilles de la Tourette syndrome. Focal dystonia was present in four patients who had never received neuroleptics drugs and chorea was seen in two other untreated patients. In three patients acoustic startle consistently induced brief eye blink followed by a whole body jerk or jump. Rapid repetitive movements of the hands increased the frequency and severity of tics in 13 patients, but the performance of mental arithmetic under time pressure had a much more unpredictable effect. Electroencephalographic abnormalities occurred in eight (13%) but no definite CT brain scan abnormalities were detected. The incidence of left handedness did not differ from that in the general population and no evidence to suggest organic impairment was found on neuropsychological testing. This study provides no support for the notion that Gilles de la Tourette syndrome is a degenerative disorder of the central nervous system but provides some evidence for heterogeneity.

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.

Cardiovascular reactivity in mild hypertension

Blood pressure and heart rate were monitored in 18 mild hypertensives and 18 normotensive controls matched for age and sex during rest, isometric exercise, carbon dioxide rebreathing, cold pressor test, head-up tilt, radiant heat, head-back tilt and mental arithmetic. Blood pressure and heart rate were higher in the hypertensive than in the normotensive group at rest. During the instructions prior to the mental arithmetic and head-back tilt tests, heart rate increased more in the hypertensive than in the normotensive group while during mental arithmetic performance, blood pressure levels increased more in hypertensives than in normotensive controls. Diastolic blood pressure levels increased more in hypertensives during head-up tilt. In all other conditions, cardiovascular responses were similar in both groups. The results support the view that the sympathetic nervous system contributes to hypertension since the cardiovasculature of mild hypertensives was hyperreactive during tests where sympathetic activity was likely to predominate.

Instructed heart rate control in the presence and absence of a distracting task: the effects of biofeedback training.

Twenty volunteers participated in a single-session experiment in which bi-directional heart rate (HR) control was assessed before and after brief unidirectional HR biofeedback. Subjects attempted to raise (INC) and lower (DEC) HR while performing mental arithmetic, as well as in no-task conditions. Biofeedback training was also carried out in the presence and absence of mental arithmetic. Subjects were divided into two groups on the basis of initial HR reactivity to mental arithmetic. Group U received feedback and instructions to raise HR during the training period, while group D attempted to lower HR. Significant differences in HR modifications during INC and DEC trials were observed prior to any biofeedback training in no-task conditions. Following training, however, ability to raise HR deteriorated in group D, while HR decelerations were impaired in group U. Unidirectional training in HR control thus handicapped subsequent attempts to modify HR in the reverse direction. The pattern of HR change was generally paralleled by respiration rate. Subjects were also able to influence the cardiac reactions to mental arithmetic even before the administration of biofeedback. The data nevertheless suggest that training affects the magnitude of HR reactions after the biofeedback is withdrawn. In the biofeedback phase itself, the HR increases and decreases produced by groups U and D, respectively, were diminished on simultaneous mental arithmetic performance.

Computer estimated alpha attenuation during problem solving in children with learning disabilities

The parieto-occipital EEG and power spectra were recorded during resting intervals, while listening to instructions on tape, and during active performance of mental arithmetic and immediate recall to determine if 10 boys with learning disabilities (LD) would show less alpha attenuation than 11 normal controls. The LD boys showed less alpha attenuation than the normal control boys. In addition, the control boys responded correctly to more of the problems. Since attention deficits are found in LD children, and attenuation of the parieto-occipital alpha rhythm is correlated with attention, these results show that a deficit of the latter can be associated with disturbances in the former.