Forecasting Longitudinal Growth in Children's Numerical Abilities

Modern society requires individuals to possess solid numerical skills to succeed in everyday life (Gerardi et al., 2013). Understanding the cognitive and neural markers of early numerical skills could provide much needed information about the development of long-term mathematical capabilities, and inform early intervention for those at risk of mathematical learning disability. In this regard, a longitudinal approach can disentangle whether specific brain networks and cognitive processes are predictive, rather than the consequential effect, of mathematical achievement.

In a recent study published in The Journal of Neuroscience, Evans et al. (2015) investigated whether morphometric and functional brain indices acquired from children aged 8 years could predict their respective longitudinal gains in numerical skills. After assessing participants' mathematical skills, IQ, and reading comprehension, the authors acquired structural and resting-state functional MRI data. Assessments were repeated two or more subsequent times during the children's development, acquiring data up to age 14 years in some instances. Rather than using children's scores in mathematical ability, the authors calculated a measure of performance change as the main outcome variable in their study. To compute this change measure, for each child, the authors fit a linear regression to the standardized scores of the Numerical Operations subscale of the Wechsler Individual Achievement Test-II (WIAT-II; Wechsler, 2001) as a function of age. This approach provided a measure that captured each child's change in performance between testing sessions, which was used as an explanatory variable within the neuroimaging analyses. This enabled the authors to identify the neural correlates of a change in performance, rather than those responsible for an absolute level of achievement.

Evans et al. (2015) sought specificity to identify brain regions involved in longitudinal growth for numerical operation skills, rather than other academic skills or cognitive processes. This was achieved by using two different scales to evaluate specific aspects of mathematical ability. One scale featured mathematical problems that were embedded in short stories. In this instance, additional reasoning skills, beyond pure calculation, are required to solve each mathematical problem (Lucangeli et al., 1998). Conversely, the second scale evaluated knowledge of calculation algorithms and numerical symbols (e.g., x⁹/x³) and can be considered a purer measure of numerical skill. By controlling for the first scale, the authors obtained a neurocognitive measure of performance change on the basis of numerical skill acquisition, rather than improvements in fluency with the language of mathematics per se.

Informed by the results of a whole-brain analysis, structural and functional connectivity measures extracted from the left ventrotemporal occipital (VTOC; particularly the fusiform gyrus), posterior parietal (PPC) and prefrontal (PFC) cortices were shown to be correlated with longitudinal gains in numerical abilities. Gray matter volume in these regions was associated with longitudinal growth of numerical skills and not with mathematical achievement, reading, working memory, or IQ measures acquired at baseline. Importantly, the association between gray matter in this network and the growth in numerical skills remained significant even when measures of mathematical reasoning, word reading, and working memory were statistically controlled. Similarly, functional connectivity among these regions was correlated with longitudinal gains in numerical abilities, but not with mathematical reasoning or reading. These results were validated using machine learning, wherein it was possible to define functions that were predictive of the change measure, based on gray matter volume in the VTOC, PPC, PFC, and, separately, connectivity metrics.

The left lateralised network described by Evans et al. (2015) is consistent with previous reports of typical cortical development, where left PFC and PPC mature earlier than the corresponding regions in the contralateral hemisphere (Gogtay et al., 2004). Moreover, the involvement of a predominantly left lateralized fronto-parietal network in number cognition is relatively well established (Moeller et al., 2015; for review, see Matejko and Ansari, 2015). The balance of frontal to parietal recruitment shifts as greater mathematical proficiency is achieved during childhood or, analogously, in adults following mathematical training. Reduced activation in the frontal cortices is accompanied by increased recruitment of parietal regions, which may reflect less reliance on resource-heavy computations requiring, for example, working memory and attention, toward specialized numerical processes computed within PPC (Matejko and Ansari, 2015). Relatedly, fractional anisotropy (FA) in the superior longitudinal fasciculus (SLF), an association tract that connects temporal and lateral PFC through PPC, is correlated with greater arithmetic skill in children (Tsang et al., 2009), and changes in FA in the left SLF following math tutoring parallel performance gains in mathematical learning (Jolles et al., 2015). FA in the inferior longitudinal fasciculus (ILF), an occipito-temporal tract that is thought to support consolidation of visual memories (Catani et al., 2003), correlates with performance in calculation, but not in mathematical problem solving (van Eimeren et al., 2008). Together, these data highlight that brain indices consistent with the network outlined by Evans et al. (2015) relate to current mathematical ability and changes in mathematical performance. Evans et al. (2015) add to this literature by highlighting that features of this network might also be prognostic in this domain.

There is growing evidence for the utility of baseline brain metrics to predict learning outcomes. For example, Gryga et al. (2012) demonstrated that initial cerebellar gray matter volume could predict relevant motor performance outcomes, as well as the amount of gray matter change in other cortical regions, including M1, after motor skill learning. Initial hippocampal gray matter volume was correlated with behavioral improvements after short-term math tutoring (Supekar et al., 2013). Likewise, midline occipito-parietal gray matter volume was predictive of learning rate when learning to juggle (Sampaio-Baptista et al., 2014). While these studies reflect relatively short-term learning interventions, Qin et al. (2014) demonstrated that fine-tuning of hippocampal-neocortical circuits around adolescence accompanies the transition to mature strategies in arithmetic problem solving. Such circuits were relatively unstable in participants aged 7–9 years, during which time counting strategies, rather than arithmetic facts, tended to be used. The absence of any predictive role for the hippocampi in Evans et al. (2015) may be explained by heterogeneity in problem-solving strategies adopted for the Numerical Operations subtest, and related variability in hippocampal–neocortical architecture at the initial time point. It could also be that the protracted analyses within their work preclude the relevance of the hippocampi, where hippocampal indices would be relevant for a more transient period.

Evans et al. (2015) demonstrate an enduring role for neural features in future learning outcomes, indicating that numerical ability may reflect considerable genetic predisposition. Indeed, in adolescence, genetic factors explain over two-thirds of the variance in FA in the parietal and frontal lobes (Chiang et al., 2009). Over half of the phenotypic variability in children's mathematical ability can be explained by genetic effects, where the degree to which structural and functional connectivity can be modified is likely to be largely determined by genetics (de Zeeuw et al., 2015). Nevertheless, recent data suggest that brain stimulation, teamed with mathematical training, may facilitate plasticity over and above training alone, allowing the possibility to enhance each individual's capacity to learn (Snowball et al., 2013; Grabner et al., 2015). In addition to acting as early biomarkers for learning disability as Evans et al. (2015) suggest, the potential for their approach to inform neuroenhancement-based interventions, and to measure the efficacy of such interventions (for example, by highlighting achievement beyond an individual's neural predicted level) is also worthy of note.

Evans et al. (2015) present a fronto-parietal network comprising VTOC, PFC, and PPC where brain indices extracted at around 8 years of age were predictive of longitudinal change in numerical skills. Recent evidence suggests that this network is likely to be supported by the SLF, connecting PPC and PFC to support domain-general and specialized numerical processes, and the ILF, an occipito-temporal pathway responsible for visual memory consolidation, which will be accomplished in part by the fusiform gyrus. These data suggest what may be a somewhat unexpected fixedness in mathematical ability, which is supported by behavioral genetics. However, in addition to directing early detection of learning disabilities, their work is informative to future research examining plasticity following cognitive training, neuroenhancement, and educational interventions.