Reduction but no shift in brain activation after arithmetic learning in children: A simultaneous fNIRS-EEG study

Neurocognitive studies of arithmetic learning in adults have revealed decreasing brain activation in the fronto-parietal network, along with increasing activation of specific cortical and subcortical areas during learning. Both changes are associated with a shift from procedural to retrieval strategies for problem-solving. Here we address the critical, open question of whether similar neurocognitive changes are also evident in children. In this study, 20 typically developing children were trained to solve simple and complex multiplication problems. The one-session and two-week training effects were monitored using simultaneous functional near-infrared spectroscopy (fNIRS) and electroencephalography (EEG). FNIRS measurement after one session of training on complex multiplication problems revealed decreased activation at the left angular gyrus (AG), right superior parietal lobule, and right intraparietal sulcus. Two weeks of training led to decreased activation at the left AG and right middle frontal gyrus. For both simple and complex problems, we observed increased alpha power in EEG measurements as children worked on trained versus untrained problems. In line with previous multiplication training studies in adults, reduced activation within the fronto-parietal network was observed after training. Contrary to adults, we found that strategy shifts via arithmetic learning were not contingent on the activation of the left AG in children.

It should be noted that because the online training platform was used at home, it was not possible to fully control the training procedure. As we discussed in the paper, there were some incomplete sessions, which might influence the training effect. Therefore, based on the interval between the incomplete session and the nearest complete session preceding or following it, we considered the incomplete session part of one of these neighboring sessions. Moreover, because of some very rare technical problems in the online platform, in some sessions, the problems were presented 7 times instead of 6 times (cf . Table S2). For each problem, one correct solution and 11 distractors were presented. Each distractor was made based on one of the following rules: adding 1 to or subtracting 1 from the first or second operand, adding or subtracting 1, 2, 10 from the correct solution, or inversing the unit and decade of the correct solution.

Neuropsychological tests
Children's performance on IQ subtests of similarity and matrix reasoning, along with memory components (verbal STM, verbal WM, visuospatial STM, visuospatial WM), are presented in Table S3. To investigate the transfer effect of multiplication training to other operations (addition, subtraction, multiplication, division), we used two closely matched sets of all four basic arithmetic operations before and after the training. The test was a modified version of an arithmetic test 1 with two levels of complexity resulting in eight lists of problems. Children had 45s for each simple list and 60s for each complex list, and they were required to answer as many problems as possible while avoiding errors.

FNIRS
As shown in Fig. S1 and Table S4, 4 ROIs were defined for fNIRS analysis and 6 ROIs were defined for EEG analysis.  Additionally, in order to investigate the difference between trained and untrained conditions within each measurement time (pre-training, first post-training, and second post-training), multiple paired t-tests were applied: trained simple versus untrained simple; trained complex versus untrained complex. The significance level was 0.05 and corrected using the Dubey/Armitage-Parmar (D/AP) method for multiple comparisons 2 . Note that the contrast of trained versus untrained in the second post-training measurement is the typical analysis that has been conducted in previous studies in adults 3 .

EEG
Again similar to the fNIRS data, the contrast of trained versus untrained conditions was calculated with paired t-tests within each measurement time. The significant level was 0.05 uncorrected.

RT
The analysis of median RT after one session of training revealed a significant main effect of complexity, showing that children responded faster to simple than to complex problems [F(1,19) = 188.82, p < 0.001, η 2 = 0.91]. No other significant main effect or interaction was found in the analysis of median RTs with respect to one-session training (cf. Fig. S2a).   Fig. S2b).

Error rate
Regarding the error rate after one session of training, a significant main effect of complexity demonstrated that children responded more accurately to simple compared to complex problems [F(1,19) = 105.23, p < 0.001, η 2 = 0.85]. Moreover, a significant interaction of training × complexity was observed [F(1,19) = 7.89, p = 0.011, η 2 = 0.29]. No other significant effect was found in analysis of error rate after one session of training (see Fig. S3a). In order to explore training effects for simple and complex problems, two separate rmANOVAs were conducted for simple and complex multiplication. With respect to simple multiplication, no significant effect was found (cf. Fig.  S3b). Regarding complex multiplication, a significant main effect of training [F(1,19) = 17.09, p = 0.001, η 2 = 0.47] was observed. A significant interaction effect of measurement time × training revealed that after training, children provided fewer errors in trained complex compared to untrained complex problems [F(1,19) = 5.57, p = 0.029, η 2 = 0.23]. Furthermore, a significant interaction of training × complexity was observed [F(1,19) = 12.74, p = 0.002, η 2 = 0.40].

Results from the whole measurement area for each measurement time
Furthermore, differences between trained and untrained conditions within each measurement time were investigated for fNIRS data. In the pre-training measurement, there was no significant difference in the contrast of trained simple versus untrained simple multiplication, or in the contrast of trained complex versus untrained complex (cf. Fig. S4a).
In the first post-training measurement, in the contrast of trained complex versus untrained complex multiplication, right SPL and IPS (channel 44) displayed significantly decreased activation [t(19) = -2.52, D/AP corrected p < 0.05, d = 0.56] (see Fig. S4b). Although reduced activation of the left AG (channel 14) and surrounding areas was observed, it did not survive correction for multiple statistical comparisons. No significant difference was found in the contrast of trained simple versus untrained simple multiplication.
In the two-week post-training measurement, in the contrast of trained complex versus untrained complex multiplication, the left MFG (channel 18) showed significantly decreased activation [t(19) = -2.94, D/AP corrected p < 0.05, d = 0.66] (cf. Fig. S4c). Although reduced activation of the left AG and STG (channel 5) was observed, this effect did not survive correction for multiple statistical comparisons. In the two-week post-training measurement, no significant difference between trained simple and untrained simple conditions was observed. Fig. S4: a) FNIRS data showed no difference between trained and untrained conditions before the training. b) Although no effect of one-session training was observed in simple conditions, decreased activation of right SPL and IPS was found in trained complex compared to untrained complex multiplication. In the contrast of complex conditions, the huge deactivated area in the left parietal region did not survive correction for multiple comparisons. c) FNIRS data showed no two-week training effect in simple condition. The lower panel shows reduced activation of the left MFG for trained complex condition in the second post-training session after two weeks. In the contrast of complex conditions, the deactivated area in the left AG did not survive correction for multiple comparisons. The blue represents reduced activation, and the green represents non-significantly reduced activation.

Results from the whole measurement area for each measurement time
Regarding EEG, differences between trained and untrained conditions within each measurement time were investigated, the same as for fNIRS data. In the contrast of trained simple versus untrained simple multiplication in pre-training, greater theta ERS in the left temporal site (T7) [t(19) = 2.29, p < 0.05, d = 0.51], and lower theta ERS on the right frontal site (AFF4) [t(19) = -2.30, p < 0.05, d = 0.51], were observed (cf. Fig. S5a). No difference in alpha band in this contrast was demonstrated. In the contrast of trained complex versus untrained complex multiplication, no significant difference was found in the theta or alpha band (see Fig. S5a).
In the first post-training measurement, in the contrast of trained complex versus untrained complex multiplication, no significant difference was observed in the theta band, while in alpha band, greater alpha ERD on the occipito-parietal site (Pz, O2) was observed [ts(19) < -2.10, ps < 0.05, ds > 0.47] (cf. Fig.  S5b). No significant difference was found in the contrast of trained simple versus untrained simple multiplication in the theta or alpha band (cf. Fig. S5b).
In the second post-training measurement, in the contrast of trained complex versus untrained complex multiplication, significantly decreased alpha ERD at the left occipital site (O1) was found [t(19) = 2.85, p < 0.05, d = 0.64]. In the contrast of trained simple versus untrained simple multiplication, an increased alpha ERD on the right temporal site (T8) [t(19) = -2.17, p < 0.05, d = 0.49], and a decreased alpha ERD on the right occipital site were observed (O2) [t(19) = 2.20, p < 0.05, d = 0.49]. No significant difference was found in the theta band in any of the contrasts (cf. Fig. S5c). Fig. S5: a) Pre-training measurement showed no difference between trained and untrained conditions, except on theta band in the simple multiplication contrast. b) First post-training measurement shows no training effects in the simple condition, but increased alpha ERD in the trained complex compared to untrained complex multiplication. c) Alpha ERD changes were observed in both trained simple and complex conditions in the two-week post-training session. While no training change was observed in theta ERS, training led to changes in alpha ERD in both simple and complex multiplication. Red represents increased theta ERS/decreased alpha ERD, and blue represents decreased theta ERS/increased alpha ERD.

Correlation between behavioral performance and neuropsychological tests
In each measurement time, there were some significant correlations between performance factors including error rates, RTs, and inverse efficiency score with neuropsychological tests, especially verbal working memory in two-week measurement time (cf . Table S5).