Exact (EX) and approximate (AP) calculations rely on distinct neural circuits. However, the training effect on the neural correlates of EX and AP calculations is largely unknown, especially for the AP calculation. Abacus-based mental calculation (AMC) is a particular arithmetic skill that can be acquired by long-term abacus training. The present study investigated whether and how the abacus training modulates the neural correlates of EX and AP calculations by functional magnetic resonance imaging (fMRI). Neural activations were measured in 20 abacus-trained and 19 nontrained Chinese children during AP and EX calculation tasks. Our results demonstrated that: (1) in nontrained children, similar neural regions were activated in both tasks, while the size of activated regions was larger in AP than those in the EX; (2) in abacus-trained children, no significant difference was found between these two tasks; (3) more visuospatial areas were activated in abacus-trained children under the EX task compared to the nontrained. These results suggested that more visuospatial strategies were used by the nontrained children in the AP task compared to the EX; abacus-trained children adopted a similar strategy in both tasks; after long-term abacus training, children were more inclined to apply a visuospatial strategy during processing EX calculations.
Arithmetical calculation is executed everywhere in our daily life, for example, statistics of population in the government, management of financial affairs in a company, and calculation of the sum of price at a grocery store. These calculations are mainly performed by physical tools or devices (pencil with paper, calculators, and computers). With these tools, complex calculations can be done more precisely and efficiently. However, it is discommodious for everyone to carry a physical device everywhere. Therefore, it is more convenient to calculate by mental calculation.
Several studies have investigated the cognitive mechanism of exact (EX) and approximate (AP) calculations [
The other studies found that practice and experience of high-level cognitive skills can change the structure of the cerebral cortex [
Abacus addition procedure and design of the experimental tasks. (a) An addition example on the abacus (
Positive emission tomography (PET) and functional magnetic resonance imaging (fMRI) studies have attempted to explore the neural correlates of the AMC mechanism in EX calculations [
However, all those studies only focused on the abacus training effect on EX (simple, complex, or both) calculations. To the best of our knowledge, no study has been done to explore the training effects on the AP calculation or the difference between EX and AP calculations. Since the strategy adopted in the EX calculation was changed by long-term abacus training, the difference of the underlying neural correlates between EX and AP calculations might be altered, too. Thus, we hypothesize that: (1) the neural difference between the simple EX and AP calculations should disappear or decline after the abacus training; (2) for simple EX calculations, the mechanism should be changed and more visuospatial representations should be involved after the abacus training.
Since the combined abacus operation and AMC course was instructed only in a few experimental classes at certain elementary schools, starting from Grade 1 to 4, only children were recruited in this study. Thus, our present fMRI study aimed to explore whether and how the abacus training modulates neural correlates of EX and AP calculations in Chinese children.
Two groups of children participated in the present study, including an abacus-trained group (10 boys and 10 girls, mean age =
The intelligence quotient (IQ) of each child was assessed by the Wechsler Intelligence Scale for Chinese Children-Revised (WISCC-R) in the same week of MRI study [
All participants were right-handed urban Chinese children with normal or corrected-to-normal vision and reported no history of neurological or psychiatric disorders. Written informed consent was obtained from each subject and his/her guardian. This study was approved by the Institutional Ethic Committee and the Institutional Review Boards (IRBs) of the Affiliated Hospital of Medical College of Qingdao University.
EX and AP addition tasks were applied in this study. The addend ranged from 1 to 9, and the sum ranged from 3 to 17. In the EX addition task, one of the two alternative answers was correct, another was wrong (off by two units at most). In the AP addition task, one of the two alternative answers was a number off by one unit which was the one to be chosen, and another was a number off by at least four units.
Subjects were instructed to press the left or right button corresponding to the answer they chose. The buttons of correct answers were counterbalanced: half of them were on the left side and another half on the right. Once the answer-choosing screen appeared, subjects were required to push the correct button by their forefingers as fast as possible.
All subjects received 4 blocks of tasks (2 blocks for each). The blocks were separated by a resting period of 16 s. Each block started with a cue of 4 s to remind the subjects of the type of tasks and followed by 12 continuous addition problems. The sequence of blocks was shown in Figure
The experimental task was carried out on a computer using E-prime 1.2 [
Data acquisition was performed on a 3.0 T Philips MRI scanner using a standard circularly polarized head coil. For fMRI, a whole brain single-shot gradient-echo echo-planer imaging (EPI) sequence was used, which is sensitive to the blood-oxygen-level dependent (BOLD) contrast. Images were acquired in an interleaved order and approximately parallel to the AC-PC line. Acquisition parameters were as follows: TR = 2000 ms, TE = 30 ms, slice thickness = 4 mm, gap between slices = 0.8 mm, flip angle = 90°, field of view = 230 mm, matrix size
Three participants (2 from abacus-trained group, 1 from nontrained group) were excluded due to high error rate (>30%) of the addition tasks. Thus, we got 18 participants for each group.
Trials with RT < 300 ms were discarded from the analysis. Only correct trials were used to calculate the median RTs for each participant under each task condition. These median correct RTs were subjected to a repeated measures of analysis of variance (ANOVA) with task type (the EX and AP task) as a within-subjects factor and group (the abacus-trained and nontrained group) as a between-subjects factor. The same ANOVA was also applied to accuracies in each condition for all participants.
Image preprocessing and statistical analysis were carried out with SPM8 (FIL, London,
After preprocessing, statistical analyses based on general linear model (GLM) and the theory of Gaussian fields [
In order to determine brain activations for different addition tasks, paired
To reveal the differences of brain activity between the abacus-trained and nontrained groups, two-sample
The accuracies and median correct RTs for each task in both groups were summarized in Table
The RTs and accuracies for each task of each group.
Group | Task type | Reaction time (ms) | Accuracy |
---|---|---|---|
Abacus-trained | EX addition | 526 (101) | 0.95 (0.05) |
AP addition | 661 (144) | 0.89 (0.08) | |
Non-trained | EX addition | 538 (71) | 0.89 (0.04) |
AP addition | 690 (102) | 0.86 (0.05) |
Numbers in the parenthesis are standard deviations.
A significant difference was detected in accuracies between two tasks:
Brain regions activated by the AP and EX addition task in the abacus-trained and nontrained groups were investigated separately. A preview of the brain activity was shown in Figure
Brain regions activated by the AP and EX addition task in the abacus-trained and nontrained group. (a) The activity pattern revealed by the AP addition task in the abacus-trained group. (b) The activity pattern revealed by the EX addition task in the abacus-trained group. (c) The activity pattern revealed by the AP addition task in the nontrained group. (d) The activity pattern revealed by the EX addition task in the nontrained group. The left column showed the right hemisphere; the middle showed the left hemisphere, and the right showed the vertical view of the brain. (
In the abacus-trained group, activations elicited by the AP addition task were detected in the supplementary areas (SMA), bilateral precentral sulcus, inferior frontal cortex, bilateral inferior parietal cortices, and bilateral middle temporal and occipital cortices and bilateral insula and thalamus (Figure
In the nontrained group, activations elicited by the AP addition task were detected in the SMA, bilateral inferior and superior parietal cortices, insula, precentral sulcus in the middle frontal cortex, inferior and middle frontal cortices, inferior temporal cortex, thalamus, inferior occipital cortex, and cerebellum (Figure
In the nontrained group, no significant areas were activated in favor of the EX addition task when compared to the AP addition task (
Brain regions activated by the AP addition task (contrasted to the EX addition task) in the non-trained group.
Regions | Voxel size | BA | Hemisphere |
|
MNI coordinate | ||
---|---|---|---|---|---|---|---|
|
|
| |||||
(1) SMA, left precentral sulcus, left superior frontal cortex | 696 | 6/32 | L/R | 10.72 | 9 | 15 | 48 |
8.51 | −6 | 0 | 57 | ||||
8.38 | −6 | 9 | 51 | ||||
| |||||||
(2) Thalamus, striatum, insula | 953 | — | L/R | 10.19 | −12 | −15 | 3 |
7.99 | −15 | 6 | 9 | ||||
7.77 | 15 | 12 | 12 | ||||
| |||||||
(3) Middle occipital cortex, inferior parietal cortex, superior parietal cortex | 454 | 7/40 | L | 9.24 | −24 | −75 | 30 |
8.62 | −51 | −45 | 54 | ||||
8.48 | −30 | −63 | 48 | ||||
| |||||||
(4) Precentral sulcus | 30 | 9 | R | 7.96 | 57 | 15 | 36 |
5.81 | 54 | 6 | 39 | ||||
| |||||||
(5) Middle occipital cortex, angular | 185 | 7/40 | R | 7.40 | 33 | −63 | 33 |
6.85 | 39 | −54 | 54 | ||||
6.62 | 33 | −66 | 45 | ||||
| |||||||
(6) Cerebellum | 72 | — | L | 6.62 | −33 | −81 | −21 |
6.47 | −42 | −60 | −27 | ||||
6.21 | −27 | −87 | −18 | ||||
| |||||||
(7) Precuneus | 43 | 7 | L | 6.32 | −6 | −75 | 45 |
BA: Brodmann area.
(a) Brain regions activated by the AP addition task (contrasted to the EX addition task) in the nontrained group. (b) Comparison of the mean beta values of these brain regions between two tasks. Uppercase letters in the parenthesis represent these brain regions. (A): cerebellum; (B): left insula; (C): right insula; (D): left thalamus; (E): right thalamus; (F): right striatum; (G): left striatum; (H): left precentral sulcus; (I): right precentral sulcus; (J): left middle occipital lobule; (K): right middle occipital lobule; (L): left inferior parietal lobule; (M): left superior parietal lobule; (N): right angular; (O): left precuneus; (P): SMA; (Q): left superior frontal lobule. (
In the abacus-trained group, no significant differences were found in favor of the AP addition task when compared to the EX addition task (
In the AP addition task, more activations were elicited in abacus-trained children, including the bilateral middle temporal cortices (
In the EX addition task, more activations were elicited in abacus-trained children, including the medial prefrontal cortex (MPFC), right caudate, right thalamus, right superior temporal cortex, and the right angular gyrus (see Table
Brain regions activated by the EX addition task in the abacus-trained group (contrast to the non-trained group).
Regions | Voxel size | BA | Hemisphere |
|
MNI coordinate | ||
---|---|---|---|---|---|---|---|
|
|
| |||||
(1) Medial prefrontal cortex | 115 | 8/9 |
|
5.56 | 18 | 42 | 18 |
5.29 | 27 | 36 | 15 | ||||
5.05 | 12 | 39 | 36 | ||||
| |||||||
(2) Superior temporal cortex | 31 | 22 |
|
5.13 | 66 | −33 | 9 |
4.80 | 66 | −24 | 3 | ||||
4.77 | 63 | −42 | 0 | ||||
| |||||||
(3) Caudate | 48 | — |
|
5.00 | 15 | 18 | 15 |
4.43 | 18 | 21 | −3 | ||||
| |||||||
(4) Angular | 46 | 39 |
|
4.90 | 57 | −63 | 27 |
4.80 | 48 | −57 | 27 | ||||
| |||||||
(5) Thalamus | 51 | — |
|
4.84 | 12 | −3 | 3 |
4.67 | 18 | −12 | 6 |
BA: Brodmann area.
(a) Brain regions activated by the EX addition task in the abacus-trained group (contrasted to the nontrained group). (b) Comparison of the mean beta values of these brain regions between groups. Uppercase letters in the parenthesis represent these brain regions. (A): thalamus; (B): superior temporal lobule; (C): caudate; (D): MPFC; (E): right angular. (
The present study aimed to explore whether and how the long-term abacus training modulates the neural correlates of EX and AP calculations in Chinese children. To address this issue, we compared functional activations between the AP and EX addition task for each group (the abacus-trained and nontrained groups), and we also compared the brain activity patterns between the abacus-trained and nontrained group for each addition task. To the best of our knowledge, this is the first report revealing the specific effect of abacus training on the neural correlates of EX and AP calculations.
The findings confirm our hypothesis. Firstly, the difference between AP and EX addition tasks for abacus-trained children existed only in the FDR-corrected result, demonstrating that the neural correlates underlying the two addition tasks were similar after the abacus training, and the pattern of brain activity during the two addition tasks in the nontrained group was consistent with previous neuroimaging studies [
Secondly, no differences were detected between the two groups in the AP addition task; while, in the EX addition task, hyperactivity was detected for the abacus-trained children in the right MPFC, right caudate, right thalamus, right superior temporal cortex, and the right angular. These results illustrated that the processing of AP addition task for abacus-trained children was similar to that for nontrained children, but the long-term training changed the neural correlates of the EX addition task; a frontal-temporal circuit was observed, which was also found in a previous study by our group [
Furthermore, no differences were detected between the IQs of the two groups, indicating that both groups had comparative intelligence. This supported the argument that the observed differences were likely to correspond to specific neuronal differences.
Both of the RT and accuracy analysis showed differences between EX and AP addition tasks. However, the difference between the two groups was only detected for the accuracy of EX addition problems, revealing that abacus-trained children were more accurate than nontrained children in the EX addition task. This was in accordance with previous studies that the abacus experts performed computation tasks with a higher accuracy than control [
From the general pattern of brain activities in two addition tasks for both groups, we found that the AP addition task that related brain activations for both groups were distributed bilaterally, while the EX addition that related brain activations were lateralized to the left hemisphere, especially for nontrained children. Moreover, common regions were induced among different addition tasks for both groups, including the SMA, left precentral sulcus (BA 6), insula, IPS, and adjacent parietal areas. Interestingly, the inferior frontal cortex was also activated except in the EX addition task for the abacus-trained group. Basically, these frontal-premotor-parietal areas were specified in numerical representation and calculation, and were consistent with the regions that are engaged in mental calculation tasks in human imaging studies [
In the nontrained group, common activations across addition tasks covered a cortical network comprised mostly of left-sided superior parietal cortex, SMA, and left precentral sulcus, and these regions were mainly involved in the number of representation and operation tasks [
A significant difference was detected between the activity patterns of two addition tasks. More activities were induced by the AP addition task, especially in the bilateral parietal areas around the IPS, the precuneus and the superior frontal cortex, indicating that the language-independent visuospatial strategy, were adopted in the AP addition task. This was consistent to the result of previous adult studies [
Taken together, these findings provided evidence for the greater involvement of and greater reliance on language-independent strategy and visuospatial working memory in AP addition tasks for nontrained children.
On the other hand, no hyperactivity was detected in favor of the EX addition task. This was dissimilar from previous adults studies in which they found significant activations for EX calculation in the language-dependent areas located in the left hemisphere [
In the abacus-trained group, common activations across addition tasks covered a distributed cortical network that was comprised of bilateral superior parietal cortices, bilateral middle occipital cortices, bilateral inferior temporal cortices, bilateral precentral gyrus, bilateral insula, the SMA, left inferior parietal cortex, and cerebellum. These regions were also found in previous abacus studies [
In the AP addition task, no significant differences were found between the two groups in the corrected result, indicating that a similar strategy was adopted in the AP addition task for both groups, whereas, slight differences were detected in the uncorrected result; the spatial related area (left precuneus) and the bilateral middle temporal cortices were more activated in abacus-trained children, while premotor regions (SMA and precentral sulcus) were more activated in nontrained children. Additionally, from the general pattern of the brain activity, we knew that bilateral inferior parietal cortices were activated in both groups during the AP addition task, suggesting the engagement of a visuospatial strategy. These results indicated that a similar but slightly different visuospatial strategy was adopted during the AP addition task in both groups.
In the EX addition task, the abacus-trained group revealed more activations than the nontrained group, including the right MPFC, right caudate, right superior temporal cortex, and the right angular. This activity pattern was specifically lateralized to the right hemisphere, which is consistent to previous abacus studies [
More interestingly, the MPFC were mainly included in the default mode network (DMN) which contained a group of areas that exhibit higher metabolic activity at rest than during tasks [
All these areas may constitute a circuit involved in the visuospatial-specific retrieval and the processing of imaginary abacus.
With two matched groups of Chinese children aged about 10 years, the present study investigated the abacus training effect on children’s behavioral performance and brain activity pattern during AP and EX addition tasks. Our findings showed that: (1) nontrained children engaged more visuospatial representations in the AP calculation task with contrast to the EX; (2) abacus-trained children adopted a similar strategy for both tasks; (3) after the abacus training, children were more inclined to apply a visuospatial strategy when processing EX problems. For the first time, this study provided evidence for the specific effects of abacus training on EX and AP number processing in children.
However, there were limitations in our study. The lacking of adult contrast made our comparative result between children and adults less persuasive. Furthermore, only one group of abacus-trained children participated in our study; children with different training intensities should be involved in future studies.
Nonetheless, our results still demonstrated an obvious effect of the long-term abacus training on both of the behavior performance and neural correlates of addition tasks. The present study might be helpful for understanding the neural mechanism of abacus training and also have some positive significance for children’s early educations.
The authors declare that they have no conflict of interests.
The authors thank the contribution of the Chinese Abacus and Mental Arithmetic Association, Finance Departments and Abacus and Mental Arithmetic Association of Weifang for their kind supports. The authors thank also to the children from Beiguan Primary School of Weifang for their kind supports in data collection. The Project was partially supported by NSFC (no. 81271601, no. 30900389, no. 31270026).