Abacus Train Sim Modeler Serial Key
Vida Hubbert
Our previous work demonstrated that abacus-based mental calculation (AMC), a traditional Chinese calculation method, could help children improve their math abilities (e.g. basic arithmetical ability) and executive function (e.g. working memory). This study further examined the effects of long-term AMC training on math ability in visual-spatial domain and the task switching component of executive function. More importantly, this study investigated whether AMC training modulated the relationship between math abilities and task switching. The participants were seventy 7-year-old children who were randomly assigned into AMC and control groups at primary school entry. Children in AMC group received 2-hour AMC training every week since primary school entry. On the contrary, children in the control group had never received any AMC training. Math and task switching abilities were measured one year and three years respectively after AMC training began. The results showed that AMC children performed better than their peers on math abilities in arithmetical and visual-spatial domains. In addition, AMC group responded faster than control group in the switching task, while no group difference was found in switch cost. Most interestingly, group difference was present in the relationships between math abilities and switch cost. These results implied the effect of AMC training on math abilities as well as its relationship with executive function.
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Working memory refers to a limited capacity involved in storage, manipulation and retrieval of relevant information [17]. It is assumed that problem-solving processes in arithmetic, algebra and geometry often involve the storage of relevant information and retrieval of partial results, which may rely on working memory resources [18]. Task switching refers to the ability switching back and forth between multiple and conflicting conceptual representations, strategies, and/or mental sets [14, 19]. It may also restrain math abilities because solving math problems requires individuals to switch flexibly between different operations, strategies and problem-solving steps [18]. Past research has showed that working memory is a stable predictor of different math abilities [20, 21], but the findings for the associations between task switching and math abilities are still scarce and inconclusive. For example, several studies have shown that task switching is significantly correlated with math abilities [12, 18, 22], while other studies failed to duplicate such relationship [23, 24]. Thus, further exploring the associations between task switching and math abilities is of great importance, which can help us gain a more comprehensive understanding of the underlying cognitive basis for math success and thus develop more effective math instruction methods.
In summary, the current study attempted to explore the impact of long-term AMC training on math abilities, task switching ability and their relationships. Our first prediction was that long-term AMC training would be associated with better performance in both arithmetical and visual-spatial math abilities. Secondly, we predicted that long-term AMC training would also affect the task switching aspect of executive function. Finally, we predicted that long-term AMC training would modulate the relationship between task switching and math abilities (arithmetical ability and visual-spatial ability).
The study was approved by the Institutional Review Board of Zhejiang University and was conducted in accordance with the guidelines of Helsinki Declaration. Written informed consent was obtained from all participants or their guardians before the implementation of the experiments.
Eighty-two children were recruited from a primary school at school entry and were randomly assigned to either AMC or control groups. All subjects were reported to have no hearing loss, normal or corrected-to-normal visual acuity, no history of neurological disorders and no experience of abacus practice by their parents. We informed all the participants that the study was designed to investigate early child development throughout the whole primary school. Additionally, for participants in the AMC group, we informed them that the study also investigated the developmental effect of AMC training. Thus, we disclosed enough information to the participants and their guardians in order to help them decide if they want to attend our study. Twelve children (10 AMC and 2 control children) were excluded from the study because of their absence in some evaluations and/or school transferring. Hence the AMC group and the control group consisted of 31 (17 boys) and 39 (18 boys) children, respectively.
The baseline evaluation included two questionnaires, a Raven Test and a go/no-go task to measure preschool behaviors, intelligence and inhibition. It was conducted at the start of grade 1 (AMC group: mean age = 6.89 0.41; control group: mean age = 6.90 0.45). Then the AMC group received intensive AMC training for two hours per week at school, while the control children received no physical or mental abacus instruction at or after school. The project was designed to guarantee that both groups had studied the same school curriculum except AMC training. The second and third evaluations were conducted at grade 2 (AMC training length = 9 months; AMC group: mean age = 8.14 0.41; control group: mean age = 8.15 0.45) and at grade 4 (AMC training length = 26 months; AMC group: mean age = 10.22 0.41; control group: mean age = 10.23 0.45) respectively. Both switching task and math test were administrated in these two testing phases. Each evaluation phase lasted approximately two weeks. The go/no-go task and the switching task were tested individually in a quiet room at school, whereas the raven and math tests were administrated in a group.
The Chinese version of Combined Raven Test for Children [43] was a paper-pencil test. Participants had 40 minutes to complete 6 units (with 12 items in each unit). Each item consisted of a series of geometric figures with one of them missing. Children were asked to find a missed figure among several options. Intelligence raw score was computed for each child and then standardized according to the age norm [44].
The subscale of visual-spatial ability included five timed subtests. In the subtest of line estimation, children were required to estimate the length of a series of two-dimensional black lines by comparing them with three presented one-dimensional lines representing length of 1, 5 and 10. In the subtest of pictures counting, children were required to count how many small pictures in each frame. In the subtest of cubes counting, children were required to find out how many small cubes build a three-dimensional figure. In order to give a correct answer, children needed to find out not only the visible cubes, but also the invisible cubes that were completely or partly covered and were necessary to build the figure. In the subtest of number connecting, twenty numbers were randomly presented in each frame and children were required to visually search and connect them with an increasing order of 1 to 20. In the subtest of number sequences, children were required to write three missing numbers in number sequences by deductive reasoning the rule. An additional subtest of copying numbers was first administrated to help children adapt to the other subtests. T scores were computed for these two subscales according to the Chinese adapted city norm in grade 2 and grade 4, respectively.
To investigate if AMC training modulates the relationship between task switching and math abilities, hierarchical regression was conducted separately for arithmetical ability and visual-spatial ability in both grades. As there were significant correlations between pre-training intelligence and the two math subscales, the intelligence score (standardized score) was entered into the models as covariates in step 1 Group (dummy coded: 0 = control, 1 = AMC) was entered into step 2. Switch cost measured by accuracy/RT (standardized score) was entered in step 3 to determine its incremental predictive validity after controlling for the effects of pre-training intelligence and AMC training. Finally, the interaction term between switch cost and group was entered into step 4. A significant increase in the multiple R2 in the last step would indicate moderator effect. In the current study, each switch cost (RT switch cost in grade 2, accuracy switch cost in grade 2, RT switch cost in grade 4 and accuracy switch cost in grade 4) ran a separate analysis in predicting arithmetical ability and visual-spatial ability. The correlation matrix among the study variables were displayed in Table 3.
The criterion on the y-axis was plotted against two levels of the task switching ability: low switching ability (1 SD above the mean of RT switch cost) and high switching ability (1 SD below the mean of RT switch cost). Plotted regression lines represented the correlations in AMC (red line) and control groups (blue line). Each line represented partial correlations between task switching and math abilities for each group after controlling for pre-training intelligence.
This study investigated how AMC training affected math abilities and executive functions and modulated their relationships. The results demonstrated that long-term AMC training was associated with better arithmetical and visual-spatial abilities. An interaction between training and switch cost was also found in predicting math abilities, suggesting stronger associations between task switching and math abilities in AMC versus control group.
Consistent with previous studies [28, 30], AMC group was found to perform better in arithmetical subscale than control group, suggesting the effect of AMC training on basic calculation abilities. Importantly, AMC children were also found to outperform their counterparts in visual-spatial subscale. This finding for the first time suggested that AMC training affects math ability in visual-spatial domain, although this training focused on improving calculation speed and accuracy. It is possible that AMC training enabled children to use some strategies that benefit high-order math ability; one of the strategies proposed by previous studies is visual-based strategy [31, 32]. It is speculated that long-term experience of operating physical and/or imagined abacus might promote the construction and formation of mental images, and then improve mathematical performance in visual-spatial domain.
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