Behavioral and Gray Matter
Differences in Children Training
Mathematics and Working
Memory
Nicholas Judd 11118032 Klingberg LabMSc in Brain and Cognitive Sciences (Cognitive Neuroscience) University of Amsterdam
Karolinska Institutet
Abstract
Neuroimaging research has started to identify the neural mechanisms underpinning working memory (WM) training and development. The first phase of our study examined post-training WM scores following a 30 day WM intervention in 6-year old children (n = 266). Our behavioral results add to the existing body of research by showing a positive association of WM improvement with WM training in children. In the second phase of the study we used voxel-based morphometry (VBM) in an attempt to associate gray matter volume changes with 1) WM and mathematical behavioral improvement and 2) training group assignment. Using a permutation test no significant gray matter volume clusters were identified within WM or mathematical related cerebral networks. We hypothesize our null result is due to a combination of factors such as small sample size, limited time between scans and the use of subtraction images. Further research is needed to clarify these null results.
Introduction
Working memory (WM), the ability to maintain and manipulate information for a short period of time is a necessary prerequisite for mathematical processing. This is evident in tasks such as complex arithmetic which require WM resources or calculation problems that demand the ability to manipulate information (Fehr, Code, & Herrmann, 2007; Kong et al., 2005). Research using dual-task and correlational methods have confirmed the link between working memory and mathematical skill (Raghubar, Barnes, & Hecht, 2010).
Recently, neuroimaging studies have outlined the brain regions associated with mathematics and working memory (WM). For example, the middle frontal gyrus and the posterior part of the superior frontal gyrus along with the intraparietal and superior parietal cortex are the most commonly activated areas for visuospatial WM (Constantinidis & Klingberg, 2016). While a large number of brain areas have been implicated in mathematics, varying depending on the type of mathematical operation studied, a key area involved for all operations is the intraparietal sulcus (Arsalidou & Taylor, 2011). Interestingly, some studies have reported that arithmetic tasks elicit activity in the prefrontal cortex, thought to be linked to the WM aspect of these mathematical operations (Fehr et al., 2007; Kong et al., 2005).
Since WM and mathematical abilities are correlated and share a partially overlapping neural substrate, it would be interesting to examine the behavioral and neural effect of training WM and training mathematics in children (Geary, 2011). Previous research has shown the efficacy of WM training (Klingberg et al., 2005; Schwaighofer, Fischer, & Bühner, 2015; Spencer-Smith, Klingberg, McGuffin, Kuntsi, & Chimiklis, 2015). WM training studies have gone a step further to identify the neural mechanisms involved (for a recent review see Constantinidis & Klingberg, 2016).
Research examining the neural mechanisms underpinning mathematical training is less prevalent. Supekar and colleagues (2013) present a study in which they outline the neural predictors of mathematical improvement following one-to-one tutoring in primary school children (n = 24). Yet this tutoring technique emphasized declarative learning techniques which may explain the authors’ emphasis of the critical role of the hippocampus in mathematical training. Recently, a paper by Nemmi and colleagues (2016) examined the impact of dual WM and mathematic training on mathematical improvement, yet did not find a significant interaction. The study also used behavior and imaging data at baseline to predict improvement in children. Interestingly, the mathematical training in this study used number line based techniques to help children grasp the conceptual property of numbers, rather than the declarative techniques used by Supekar and colleagues (2013).
The current study examined the behavioral WM improvement of preschool children in relation to different training regime placement. The focus of the behavioral analysis of this report is WM training orientated since Nemmi and colleagues (2016) have already reported on the mathematical training results of this sample. We hypothesize that WM training will lead to an
improvement in the WM related behavioral measures. To test this, we constructed a linear model to examine WM improvement.
A major part of this study was to examine neural changes related to the different training regimes. This was accomplished by using voxel-based morphometry (VBM). VBM is a whole brain analysis technique that allows for the quantification of regional volume and tissue concentration differences from structural MRI scans (Mechelli, Price, Friston, & Ashburner, 2005). This technique has been used extensively to correlate behavioral measures to structural changes in the brain (Kanai & Rees, 2011). Since it is still an open question whether WM training or mathematics training relies on different or similar mechanisms we utilized VBM in two ways, 1) to correlate structural changes to behavioral changes in mathematics/WM and 2) to examine structural changes due to differing training regime placement. To accomplish the first goal, we derived a subtracted improvement score from independent behavioral measures. Any observed regional gray matter volume change is hypothesized to be found in a domain relevant area (i.e. mathematical or working memory related region).
Materials and Methods
Subjects
The larger behavioral study consisted of 266 children (mean age = 80.3 months, sd = 3.5), which had trained for at least 30 days. Within this population 51 children were selected
specifically for having low working memory (lowest 20th percentile working memory task
performance). The recruitment phase spanned two academic years and only included subjects without neurological or psychiatric disorders. For more information, see Nemmi and colleagues’ (2016).
Training and Testing Procedure
Two schools were contacted for the study, both of which agreed to participate. For all children included in the study written consent was obtained. Participants were randomly assigned to one of four training groups: Mathematics and Working Memory training (Ma/WM), Mathematics and Reading training (Ma/R), Working memory and Reading training (WM/R) or only Reading training (R/R). The reading training group was designed to act as an active comparison group. Cognitive tests assessing working memory, mathematical and reading abilities were performed before and after the training period. The visuospatial WM tasks administered were a grid task and block repetition forward and backward (Alloway, 2007). Three cognitive tests were used to assess mathematical abilities: verbal arithmetic (WISC-IV) along with addition and subtraction tasks administered via an iPad. Training always took place in the classroom on IPad’s at the same time each day. Each training group completed 30 minutes of cognitive training in their respective domain (e.g. the reading only group completed 30 minutes of reading training while the math and reading group completed 15 minutes of math training and
15 minutes of reading training). Teachers monitored the children and were responsible for ensuring compliance. For our analysis we included all children that trained for at least 30 days. The training program was developed in house. An updated version is now available for free on the AppStore and GooglePlay (‘Vektor’). The program was designed to be intuitive for 6-year-old children without previous knowledge of math, reading or tablets. Compliance to the prescribed training regime was done automatically by the program. For example, in the training regimes with two cognitive modalities (e.g. Math/WM) the app automatically switched modality after 15 minutes.
Within the training application progress was clearly marked with rewards following task completion. For example, each task was constructed as a race against a foe. Therefore, each successful trial advanced the child’s avatar, while each unsuccessful trial advanced the opponent. The child would win or lose races based on their performance. More explicit motivational factors were also included, such as small gifts (pencils, erasers, stickers or rulers)
each 6th training day. Lastly, the teachers received feedback on the children’s training progress.
This class overview automatically highlighted children that might be stuck on a particular exercise, allowing the teacher to offer extra instruction or motivation.
Overview of Training Tasks
All of the training tasks adapted to individual performance by varying the level of difficultly so that performance stayed around 75% task accuracy.
Working memory tasks were visuospatial in nature and followed a general scheme in which the subject had to remember and repeat a sequence of spatial position. Difficulty was adaptive based on the child’s memory span (i.e. the amount of remembered sequences).
Mathematical training mainly focused on number line training, in which the child had to drag their finger along a number line to respond. The number line was intentionally designed to connect different representations of a number: spatial position, length and number of objects and the Arabic numeral. Number line tasks included addition and subtraction problems; addition was completed by dragging to the right while subtraction was achieved by dragging to the left. Difficulty was increased through a variety of ways, such as reducing the number of Arabic markings (e.g. 1,2,3…) on the number line, expanding the length or combined addition and subtraction (e.g. 1+7-2). For more information on number line tasks, see Nemmi et al. (2016).
The reading tasks intrinsically varied in difficulty (i.e. some tasks were more difficult than others), therefore some tasks such as a crossword or matching rhyming words would only be presented later in training. Earlier tasks can be seen as prerequisites to the harder reading tasks. Examples of these earlier tasks include matching sounds to letters or spelling words.
Behavioral Pre & Post Measure
A behavioral pre-training WM score was constructed from the WM tests preceding cognitive training. Each test was normalized and then the tests were averaged. In contrast, the behavioral WM post-training (i.e. improvement) score was constructed by a normalization method that used the average and standard deviation of the respective pre-training test. Following this ‘pre-training normalization’ procedure, the post-‘pre-training WM indices were averaged together to result in the post-training WM score. Children were only included if they had completed all of the WM behavioral tests.
Behavioral Analysis Methods
To test WM improvement, we used the following general linear model:
Post training WM = β0 + β1WM group + β2Math group + β3WM group x Math group + β4Pre
training WM + β5WM group x Pre training WM + β6Cohort + β7Age + β8Gender +
β9Population + e
The model was constructed to test the effect of working memory training (WM group), math training (Math Group) and their interaction (WM group x Math group) on behavioral post-training WM scores, while controlling for baseline WM levels (Pre-post-training WM). WM group and Math group affiliation was coded using two logical vectors were 1 corresponded to having trained while 0 corresponded to not having trained that modality. The benefit of this approach is that it allows the inclusion of the entire sample, even children that had only trained reading. The model is similar to the one reported in Nemmi and colleagues (2016) testing for improvement in mathematics.
Neuroimaging Acquisition
Of the larger behavioral sample 44 children had pre and post training structural T1 scans, one subject had to be excluded for excessive movement. Within the imaging sample the distribution of training groups was: Math/Read = 11, Read/Read = 11, WM/Math = 8 and WM/Read = 13. MRI data was acquired on a 3 Tesla MRI scanner (Discovery General Electric) with an 8-channel phased array receiving coil at the Karolinska Hospital (Solna Campus). T1-weighted
images were acquired at a 1-mm3 isotropic resolution (TE = 3.06 ms, TR = 7.9 ms, TI = 450
ms, FoV = 24 cm, 176 axial slices, flip angle of 12◦). Gray matter volume
We used the CAT12 toolbox (C. Gaser, Structural Brain Mapping group, Jena University Hospital, Jena, Germany) implemented in SPM12 (Statistical Parametric Mapping, Institute of Neurology, London, UK) on Matlab 2014a. CAT12 has a preprocessing pipeline and analysis tools for VBM. Special considerations were taken since our data was longitudinal in nature and involved children: we created custom tissue probability maps using the average approach (baseline image age = 6.8) on the SPM toolbox TOM8 (Wilke, Holland, Altaye, & Gaser,
2008). This tissue probability map was then used in the CAT12 pipeline for affine registration. We used the CAT12 longitudinal batch, which is specifically designed for detecting small changes over time as a response to short-term plasticity effects. This is done by estimating spatial normalization parameters using a mean image of all time points. Quality control was assessed through displaying one slice at a time and via an automated report card outputted by CAT12. These methods led to the discovery of a follow-up scan from one child with excessive movement, resulting in the exclusion of this subject. Modulated normalized segmentations were spatially smoothed with a Gaussian kernel of 8 mm full-width at half-maximum (Ashburner & Friston, 2005; Mechelli et al., 2005). To exclude artifacts, we applied a threshold of 0.1 on the gray matter segmentations. Lastly, gray matter difference images were calculated using SPM12 by subtracting a subjects post-training GM segmentation by the segmentation preceding training.
Behavioral Improvement Measure
With behavioral improvement we refer to the subtraction measures from the pre and post training cognitive tests. To derive this index, we first simply subtracted the post-training tests by the pre-training tests. This resulted in a delta score for each behavioral test, which was then normalized. These normalized delta scores where then grouped into a domain and averaged (i.e. Working memory, Mathematics or Reading). The end result was three improvement scores per domain for each child.
Neuroimaging analysis methods 1) Behavioral improvement
Using a mass univariate approach, a linear model was constructed in which change in regional gray matter volume was the dependent variable and WM behavioral improvement was the independent variable. To test the effect of mathematics on gray matter volume another linear model was constructed yet with mathematical behavioral improvement as the independent variable. Structural differences were considered significant if p < .001, in combination with a FWE-corrected cluster probability of p < .05 (Woo, Krishnan, & Wager, 2014).
To confirm any significant results, we completed a post hoc analysis using statistical non-parametric mapping (SnPM). This approach is warranted in studies involving small sample sizes in which the data may not be normally distributed (Nichols & Holmes, 2001; Scarpazza, Sartori, De Simone, & Mechelli, 2016). We used the SnPM toolbox (8b) implemented in
SPM12 (available at:
https://www2.warwick.ac.uk/fac/sci/statistics/staff/academic-research/nichols/software/snpm8/). Specifically, we permuted the data 5000 times with a cluster forming threshold of p < .001.
We used the following general linear model for each voxel to test the effect of training group on gray matter volume differences:
Delta GM = β0 + β1Working Memory group + β2Math group + β3WM group x Math group + e
The model was constructed to test the effect of working memory training (Working memory group), math training (Math group) and their interaction (WM group x Math group) on gray matter volume differences. Similar to the behavioral analysis, WM training and Math training was coded using two logical vectors were 1 corresponded to having trained while 0 corresponded to not having trained that modality. Similar to the behavioral analysis methods, SnPM was used in a confirmatory manor.
Results Section
Behavioral ResultsWithin typically developing children (n=195), there was a significant effect for WMT (F(1,185) = 75.46, p < .001, β = .46) yet no effect was found for MT (F(1,185) = .00, p = .96, β = .00) or the interaction of both (F(1,185) = 1.11, p = .29, β = .06) on post-training WM scores. Interestingly, there was a significant positive association (F(1,185) = 87.19, p < .001, β = .51) of baseline WM scores with post training WM scores, yet no effect was found for the interaction of training WM and pre-training WM scores (F(1,285) = .30, p = .59, β = .03). None of the control variables (sex, age and cohort) were significant (respectively p = 0.30, p = 0.18, p = 0.12). The inclusion of the children selected for having low working memory (n = 46) did not change the results. Yet the added control variable of population in the model showed significance (F(1,230) = 5.07, p < .05, β = -.12), this result is hardly surprising in light of the association of baseline WM scores with post-training WM scores.
Neuroimaging Results 1) Behavioral improvement
Table 1
Overview of VMB-‐results of mathematical improvement or working memory improvement
Co-‐ordinates of maximum voxel, Anatomical region, k (num voxels), T, p at peak-‐level (FWE-‐corr.), SnPM FWE
Working memory improvement – positive association no significant effects found
Working memory improvement – negative association no significant effects found
Mathematical improvement – positive association
63; -‐18; 6 Planum Temporale 228 5.14 <.000 .0856 Mathematics improvement – negative association
-‐48; -‐54; -‐18 Inferior Temporal Gyrus 110 4.86 .028 .2598
4; -‐58; 0 Lingual Gyrus 137 4.75 .008 .1848
As seen on the table 1 significant clusters were found in positive and negative associations to mathematical improvement using parametric methods. Yet using non-parametric methods (SnPM) these results lost significance.
2) Training group
Table 2
Overview of VMB-‐results due to the specific variance associated to training mathematics or working memory Co-‐ordinates of maximum voxel, Anatomical region, k (num voxels), T, p at peak-‐level (FWE-‐corr.), SnPM FWE
Working memory – positive association no significant effects found
Working memory – negative association no significant effects found
Mathematics – positive association
-‐18; -‐15; 6 Left Thalamus 151 4.59 .004 .124
-‐14; -‐87; -‐20 Occipital Fusiform Gyrus 189 4.41 .001 .079 Mathematics – negative association
no significant effects found Interaction – positive association
68; -‐36; -‐2 Middle Temporal Gyrus 269 5.75 .005 .048 Interaction – negative association
no significant effects found
Figure 1 The cluster above (Middle Temporal Gyrus) was shown to be positively associated with the interaction of training
WM and training Mathematics.
The effect of different training regime differences on gray matter volume showed a positive association for gray matter volume in the left Thalamus and Occipital Fusiform Gryus for the mathematical training group when correcting for FWE. Yet these clusters lost significance when using non-parametric methods (see Table 2). A positive association for the interaction of training WM and mathematics on gray matter volume in the Middle Temporal Gyrus was observed (Figure 1). This cluster retained significance (p = .048) using non-parametric methods, yet does not survive Bonferroni correction (p = .288).
Discussion
Behavioral intervention
The main goal for the behavioral analysis was to determine if a WM training effect was present in our larger sample, before proceeding to image analysis on a smaller sub-sample. This hypothesis was confirmed by a significant effect of the WM training variable on post-training WM scores. This result confirms once again the well-known effect of adaptive working memory training on WM span in children. Notably, the combination of both types of training (i.e. Mathematics & WM) did not produce a significant interaction. This result should be considered in light of Nemmi and colleagues (2016) mathematics finding. The researchers found no significant interaction between WM and mathematical training, using a similar statistical model. Interestingly, the combined training group showed the largest absolute change in post-training mathematical scores and was reported to be the only group to have improved significantly more than the reading only training group. In contrast to Nemmi and colleagues (2016) results, the combined training group did not show the largest absolute change in post-training WM scores.
The results of the behavioral portion of this study, in combination with the behavioral results from Nemmi et al. (2016), can lead to the conclusion that while both WM and Math training are effective on their own merit, the combination does not necessarily lead to an increased effect for either mathematics or working memory. This result should not discourage the use of combined WM and mathematical training since they both show significant improvement for their respective domains. Future research should attempt to alter the proportion of WM and mathematical training on an individualized basis as this may enhance the effect of combined training.
Another interesting finding is the positive association of pre-training WM to post-training WM, entirely independent of type of training. This demonstrates that children with higher WM at baseline still have higher WM scores after 3 month of training than those with lower WM. This phenomenon, coined Matthew’s effect, was initially proposed by Merton (1968) to describe scientific productivity (e.g. working with prominent scientists in prestigious universities leads to a higher impact factor). Interestingly, this effect is well documented in reading achievement and IQ (Shaywitz et al., 1995; Stanovich, 1986). Nemmi and colleagues (2016) also found this effect, yet within training group (i.e. Children with higher baseline WM improved more from WM training and children with higher mathematics improved more from mathematical training). The authors postulate that the mechanisms causing lower plasticity could be the same mechanisms contributing to below average development. Alternatively, Shaywitz and colleagues (1995) emphasize environmental influences as playing a factor in the Matthew’s effect, specifically its recursive nature (e.g. low WM leads to lower expectations/class placement, leading in turn to lower WM). While in our sample this effect was not observed within the WM training group, this effect presents a unique issue: the children most in need of the intervention benefit the least. Future cognitive interventions should focus specifically on
mitigating the Matthew’s effect for underperforming children. It is important that any future cognitive intervention makes sure to bring up the underperforming children without restricting the higher performers.
Neuroimaging
We ran two analyses on subtracted gray matter volume images: the first examined WM and mathematical behavioral change irrespective of training group, while the later analysis examined the effect of training group. The only cluster which retained significance via non-parametric methods, Middle Temporal Gyrus, was positively associated with the interaction of WM and Mathematical training. Yet this result can be disregarded for two reasons, 1) it does not survive Bonferroni correction and 2) it does not fall in WM or math related cerebral networks (Glasser & Rilling, 2008; Vigneau et al., 2006).
The inconclusive nature of the neuroimaging results is due to a discrepancy of statistical significance between the parametric and non-parametric image analysis methods (i.e. SPM and SnPM respectively). This discrepancy highlights a broader issue: how to appropriately deal with multiple comparisons? One of the most notable examples for the need of multiple comparison correction in neuroimaging was presented by Bennet and colleagues (2010), in which they report on significant fMRI activation in a dead salmon undergoing a social cognition task. Yet these issues still plague the field of neuroimaging, as recently demonstrated by Eklund and colleagues (2016) in a study that compared the empirical false-positive rate of a variety of parametric analyses to that of a permutation test. This resulted in the finding that the permutation test produced the lowest empirical false-positive rate for cluster wise inference. Taking these results into consideration we took an approach of using parametric methods as a preliminary analysis. Cluster-extent based thresholding was used with a voxel-level primary threshold of p < .001 and a FWE-corrected cluster-level extent threshold of p < .05 (Woo et al., 2014). The clusters retaining significance would then be confirmed via permutation methods with the same thresholds. The key difference between the two theoretical methods is how they estimate the sampling distribution of the largest null cluster size under the global null hypotheses. Gaussian random field theory relies on the assumption of normality, while permutation methods do not assume a certain distribution of the data (Hayasaka & Nichols, 2003; Worsley, Evans, Marrett, & Neelin, 1992). Two key factors can lead us to the conclusion that the clusters observed via parametric methods are false-positives, 1) a lack of localization in domain relevant areas and 2) the loss of significance via permutation methods.
The lack of significant gray matter volume changes in mathematical or WM related cerebral networks could be due a variety of complementary factors such as, limited sample size, insufficient time elapse between scans or the use of delta images. Sample size considerations are more pertinent in the second analysis since each training group consisted of around 10 participants, yet this explanation holds less weight for the behavioral improvement analysis (n = 43).
Another contributing factor for the lack of observed gray matter volume changes could be the amount of time between scans, which in our study was around 4 months. Yet this time frame has been shown to be adequate in previous studies. Specifically, a study by Driemeyer and colleagues (2008) puts forward the claim that adults learning to juggle can alter gray matter from as early as 7 days. The results of this study (n = 20) should be interpreted with caution since a whole-brain uncorrected threshold of p < .001 was applied. Taking into consideration that our intervention period lasted 3 months and included children, insufficient time between scans should be viewed as a possible contributing factor, yet not a primary one.
One of the more convincing reasons behind our non-significant results is our methodological choice to use subtraction images. Our choice of using subtraction images, rather than using post-training GM volume and controlling for pre-training GM volume, was due to the inability to use a voxel-wise variable in SPM. Due to the non-normal distribution of noise in imaging data, adding or subtracting images will inevitably increase the noise and thus decrease the signal to noise ratio. Therefore, without ample sample size and underlying power any true signal present could be masked by noise. Of course it is also important to acknowledge the most likely reason for our non-significant results: a lack of effect.
Conclusion
Our behavioral results are in line with previous research by showing an improvement in WM measures following a 30-day WM training intervention in children. Yet our results are not indicative of an enhanced effect, in terms of higher WM scores post-training, with combined WM and mathematics training. The second phase of the study examined gray matter volume in relation to training group assignment and behavioral improvement. Both analyses failed to find statistically significant clusters when using non-parametric methods. We hypothesize this may have been due to a combination of factors such as sample size, insufficient time elapse between scans and the use of subtraction images. More research is needed to distinguish if the null result holds or is due to the aforementioned limitations.
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