The role of response selection and input monitoring in solving simple arithmetical products

Improving mental arithmetic ability of primary school students with schema teaching method: An experimental study

Skillful utilization of mental arithmetic can significantly improve students' mathematical computation ability. However, it was observed that primary school students often resort to reiterating the process of written arithmetic in their minds during mental arithmetic, which is not conducive to their numerical ability improvement. This paper devises a set of graphic teaching aids for primary school students' mental arithmetic improvement based on mental arithmetic strategies, schema theory, and working memory. To validate the effectiveness of schema teaching in enhancing mental arithmetic ability among primary school students, a controlled experiment was conducted with two groups of third-grade students randomly selected from a primary school in Jingshan City. The results, obtained through descriptive statistical analysis and the multitrait-multimethod approach (MTMM), indicated that the experimental group (n = 52) demonstrated significant improvements in speed, accuracy, and stability in mental addition and subtraction after a 14-day instruction period in schema teaching. This study offers a potent mental arithmetic teaching strategy for elementary mathematics education, which can lead to a comprehensive enhancement of students' mental calculation abilities. It also holds promise for inspiring innovative teaching methodologies in primary and secondary mathematics education in the future.

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.

The role of executive control in resolving grammatical number conflict in sentence comprehension

In sentences with a complex subject noun phrase, like "The key to the cabinets is lost", the grammatical number of the head noun (key) may be the same or different from that of the modifier noun phrase (cabinets). When the number is the same, comprehension is usually easier than when it is different. Grammatical number computation may occur while processing the modifier noun (integration phase) or while processing the verb (checking phase). We investigated at which phase number conflict and plausibility of the modifier noun as subject for the verb affect processing, and we imposed a gaze-contingent tone discrimination task in either phase to test whether number computation involves executive control. At both phases, gaze durations were longer when a concurrent tone task was present. Additionally, at the integration phase, gaze durations were longer under number conflict, and this effect was enhanced by the presence of a tone task, whereas no effects of plausibility of the modifier were observed. The finding that the effect of number match was larger under load shows that computation of the grammatical number of the complex noun phrase requires executive control in the integration phase, but not in the checking phase.

Does solution of mental arithmetic problems such as 2 + 6 and 3 x 8 rely on the process of "Memory updating"?

Two experiments are reported that used the selective interference paradigm to study whether, besides response selection, the process of memory updating is involved in simple mental arithmetic. Participants were asked to solve simple sums (e.g., 2 + 6, Experiment 1) or simple products (e.g., 3 X 8, Experiment 2) in a single-task control condition and in three dual-task conditions with a selective interference task, simple reactions, choice reactions, or delayed choice reactions. The role of memory updating was estimated on the basis of the difference in impairment due to the choice reaction time and the delayed choice reaction time task, whereas the difference in impairment between the simple reaction time and the choice reaction time task indicates the role of response selection. While replicating previous results concerning response selection (Deschuyteneer & Vandierendonck, 2005, in press), the study showed that memory updating is strongly involved in solving simple mental arithmetic sums and products.

Input monitoring and response selection as components of executive control in pro-saccades and anti-saccades

Several studies have shown that anti-saccades, more than pro-saccades, are executed under executive control. It is argued that executive control subsumes a variety of controlled processes. The present study tested whether some of these underlying processes are involved in the execution of anti-saccades. An experiment is reported in which two such processes were parametrically varied, namely input monitoring and response selection. This resulted in four selective interference conditions obtained by factorially combining the degree of input monitoring and the presence of response selection in the interference task. The four tasks were combined with a primary task which required the participants to perform either pro-saccades or anti-saccades. By comparison of performance in these dual-task conditions and performance in single-task conditions, it was shown that anti-saccades, but not pro-saccades, were delayed when the secondary task required input monitoring or response selection. The results are discussed with respect to theoretical attempts to deconstruct the concept of executive control.

Do working-memory executive components mediate the effects of age on strategy selection or on strategy execution? Insights from arithmetic problem solving

Younger and older adults performed an inequality verification task (7+6 < 15, Yes/No?) in a control condition and in a dual-task condition where they simultaneously performed an executive-component task. Arithmetic-problem characteristics were manipulated in order to test strategy selection (i.e., choice of appropriate strategies in order to improve performance) and strategy execution (i.e., performance of the cognitive processes involved in each strategy). Results revealed that strategy selection changes with age: Older adults mainly selected one type of strategies in contrast to younger adults who used several types of strategies. These age-related changes were similar in the control and dual-task conditions. Strategy execution also changed with age, as shown by larger age-related differences on hardest problems. These age-related changes were larger in the dual-task condition, compared to the control condition. This impact of executive components as mediator of age-related changes depended on general age-related slowing. We discuss these findings in order to further understand the effects of age on arithmetic performance.