New insights in the role of working memory in carry and borrow operations

The present paper provides a state-of-the-art overview concerning the role of working mem-ory in carry and borrow operations in metal arithmetic. The role of the executive working-memory component is discussed, alongside the contribution of the phonological and visuo-spatial working-memory components. Moreover, a broad view on various carry characteristics (such as the number of carry/borrow operations and the value of the carry) and various operations (addition, subtraction, and multiplication) is provided. Finally, some ideas for fur-ther research are offered

Sequential Neural Processes in Abacus Mental Addition: An EEG and fMRI Case Study

Abacus experts are able to mentally calculate multi-digit numbers rapidly. Some behavioral and neuroimaging studies have suggested a visuospatial and visuomotor strategy during abacus mental calculation. However, no study up to now has attempted to dissociate temporally the visuospatial neural process from the visuomotor neural process during abacus mental calculation. In the present study, an abacus expert performed the mental addition tasks (8-digit and 4-digit addends presented in visual or auditory modes) swiftly and accurately. The 100% correct rates in this expert’s task performance were significantly higher than those of ordinary subjects performing 1-digit and 2-digit addition tasks. ERPs, EEG source localizations, and fMRI results taken together suggested visuospatial and visuomotor processes were sequentially arranged during the abacus mental addition with visual addends and could be dissociated from each other temporally. The visuospatial transformation of the numbers, in which the superior parietal lobule was most likely involved, might occur first (around 380 ms) after the onset of the stimuli. The visuomotor processing, in which the superior/middle frontal gyri were most likely involved, might occur later (around 440 ms). Meanwhile, fMRI results suggested that neural networks involved in the abacus mental addition with auditory stimuli were similar to those in the visual abacus mental addition. The most prominently activated brain areas in both conditions included the bilateral superior parietal lobules (BA 7) and bilateral middle frontal gyri (BA 6). These results suggest a supra-modal brain network in abacus mental addition, which may develop from normal mental calculation networks

When is working memory important for arithmetic?: the impact of strategy and age

Our ability to perform arithmetic relies heavily on working memory, the manipulation and maintenance of information in mind. Previous research has found that in adults, procedural strategies, particularly counting, rely on working memory to a greater extent than retrieval strategies. During childhood there are changes in the types of strategies employed, as well as an increase in the accuracy and efficiency of strategy execution. As such it seems likely that the role of working memory in arithmetic may also change, however children and adults have never been directly compared. This study used traditional dual-task methodology, with the addition of a control load condition, to investigate the extent to which working memory requirements for different arithmetic strategies change with age between 9-11 years, 12-14 years and young adulthood. We showed that both children and adults employ working memory when solving arithmetic problems, no matter what strategy they choose. This study highlights the importance of considering working memory in understanding the difficulties that some children and adults have with mathematics, as well as the need to include working memory in theoretical models of mathematical cognition

The role of working memory in the carry operation of mental arithmetic: Number and value of the carry

Two experiments were conducted to investigate the role of phonological and executive working memory components in the carry operation in mental arithmetic. We manipulated the number of carry operations, as previous research had done, but also the value that had to be carried. Results of these experiments show that in addition to the number of carry operations, the value of the carry is also an important variable determining the difficulty of arithmetical sums. Furthermore, both variables (number and value) interacted with each other in such a way that the combination of multiple carries and values of carries larger than one resulted in more difficult problems irrespective of the presence of a working-memory load. The findings with respect to working-memory load suggest that mainly the central executive is important in handling the number of carry operations as well as the value that has to be carried. The implications of the present findings for our views on mental arithmetic and its reliance on working memory are discussed