Functional neuroanatomy of arithmetic and word reading and its relationship to age
Introduction
Mastery of reading and arithmetic is crucial for academic achievement. As such, there is an urgent need to understand how both skills become successfully established in the brains of children and adults who master them well. Reading and arithmetic are distinctive in our repertoire of cognitive skills because they are relatively recent cultural inventions that are uniquely human and are explicitly taught over a protracted period of time via formal schooling. It has been proposed that reading and arithmetic rely on brain mechanisms that have an evolutionary history (e.g., language), combined with those that become redirected de novo through learning to accommodate these tasks in a framework described as “neuronal recycling” (Dehaene and Cohen, 2007).
Reading relies on the left temporo-parietal and inferior frontal cortices for aspects that it shares with spoken language, such as phonological processing (Price, 2012), while the left occipito-temporal cortex in the ventral visual stream, which subserves object processing, demonstrates specialization for visual word form recognition in skilled readers (Cohen and Dehaene, 2004, Dehaene and Cohen, 2011, Glezer et al., 2009, McCandliss et al., 2003). Arithmetic is supported by a bilateral fronto-parietal network (Arsalidou and Taylor, 2011, Kaufmann et al., 2011, Menon, 2010, Nieder and Dehaene, 2009), which is modulated based on task demands. As posited by the “triple-code model” of number processing (Dehaene, 1992, Dehaene and Cohen, 1995, Dehaene et al., 2003), particular brain regions are assigned to specific systems of representations of numerical information (quantitative, verbal, and visual). Of these, the quantitative system is unique to numerical processing, whereas the verbal and visual systems share aspects with language processing. Within the domain of arithmetic, the extent to which each operation calls on these systems varies. For example, arithmetic problems with greater quantitative demands (e.g., subtraction) demonstrate increased reliance on bilateral fronto-parietal regions (Rosenberg-Lee et al., 2011a, De Smedt et al., 2011), while arithmetic problems that are solved via more efficient verbal retrieval strategies (such as small-digit addition and multiplication) engage left angular gyrus (AG), and middle temporal and inferior frontal cortices (Dehaene et al., 2003, Grabner et al., 2009, Lee, 2000, Prado et al., 2011). As such, the verbal aspect of arithmetic retrieval shares some neural mechanisms with language.
Associations between some aspects of language and arithmetic have long been supported by behavioral, brain lesion, and more recently, functional brain imaging studies. In behavioral research, a dual-task experiment showed a double dissociation for the interference of a verbal task (phonological suppression) and a visuospatial task (visuospatial suppression) with two types of arithmetic problems (multiplication and subtraction), respectively, suggesting that these two operations are mediated by verbal codes rather than visuospatial codes (Lee and Kang, 2002). Further, verbally mediated retrieval of arithmetic facts is correlated with phonological awareness (Barnes et al., 2014, De Smedt et al., 2010, Hecht et al., 2001, Simmons and Singleton, 2008), a skill that is integral to reading (Melby-Lervåg et al., 2012). Double dissociations reported in patients with brain lesions leading to acalculia (Anderson et al., 1990, Lee, 2000) support the notion of differential involvement of brain systems that are task dependent. For example, lesions to left perisylvian cortex (associated with language processing) are associated with degraded multiplication but spared subtraction. On the other hand, intraparietal cortical lesions interfere with subtraction but not multiplication (Cohen et al., 2000, Dehaene and Cohen, 1997, van Harskamp and Cipolotti, 2001, van Harskamp et al., 2002, Mihulowicz et al., 2014). Brain imaging studies have confirmed these functional specializations for arithmetic tasks and the unique relationships that exist between some specific aspects of arithmetic and left hemisphere language areas. For example, left middle temporal and inferior frontal gyri (IFG), regions that respond during phonological processing (using a phonological localizer task), demonstrate greater activity during multiplication relative to subtraction (Prado et al., 2011). Other research has shown a positive relationship between mathematical competence and activity in the left AG during multiplication tasks (Grabner et al., 2007). These same investigators also report stronger activation of the left AG during arithmetic problem solving for which participants reported using retrieval rather than quantitative strategies (Grabner et al., 2009).
Neuroanatomical investigations of white matter tracts also support the idea that there is specialization for specific arithmetic operations in various brain regions and that amongst these, some, but not all, have a relationship with regions involved in language processing. In a study of unilateral stroke patients, lesion density in the left arcuate fasciculus was shown to correspond with addition and multiplication impairments, but patients had preserved subtraction skills (Mihulowicz et al., 2014). In typically reading children, a relationship has been demonstrated between white matter integrity of left fronto-parietal aspects of the arcuate fasciculus and arithmetic competence in addition and multiplication, but not subtraction and division (Van Beek et al., 2014). Interestingly, integrity of this tract is known to relate to reading ability (Odegard et al., 2009, Rauschecker et al., 2009, Thiebaut de Schotten et al., 2012, Yeatman et al., 2011), and is compromised in the reading disability dyslexia (Vandermosten et al., 2012). As such, it is notable that the relationship between arithmetic supported by verbal retrieval and white matter integrity shown by Van Beek and colleagues disappears when non-word reading skills are controlled for, again suggesting that phonological processing skills (used for decoding of non-words) play a mediating role in addition and multiplication abilities. Together, these behavioral, clinical, and neuroimaging studies support the notion of task-specific brain regions underlying different arithmetic tasks and reading, yet at the same time speak to some shared brain circuitry for specific language tasks and specific arithmetic operations. A more detailed characterization is important for advancing our understanding of brain-based models of learning disabilities in these domains (i.e., dyslexia and dyscalculia) as well as the broader versus more specific impact of instruction.
Naturally, inquiries into the neural bases of reading and arithmetic are highly dependent on the age of the participants, which in turn is associated with expertise of these skills. The brain undergoes profound changes during the course of development. With age, the systems supporting executive function, language and other cognitive tasks mature, and these domain general constructs allow for the mastery of more complex cognitive skills (Shaw et al., 2006). For example, gray matter has been shown to decrease with increasing age in prefrontal and parietal cortices (Sowell et al., 2003). At the same time, experience-dependent learning has an effect on this developmental trajectory, as illustrated by the relationship between increased phonological awareness skills and increases in gray matter in the left IFG (Lu et al., 2007). Reading and arithmetic are learned skills, and their unique and shared neural circuits are therefore likely to change over time. Further, brain areas that constitute, for example, the reading network are brought together as a function of learning to read and not due to any other pre-existing privileged relationship (Vogel et al., 2013). In developmental studies, independent lines of investigation have examined age-related changes during reading (Schlaggar et al., 2002, Turkeltaub et al., 2003; for review see Church et al., 2008; Pugh et al., 2001; Schlaggar and McCandliss, 2007) or arithmetic (Kawashima et al., 2004, Kucian et al., 2008, Qin et al., 2014, Rivera et al., 2005). While no studies to date have looked into the developmental patterns of both in the same subjects, parallel meta-analyses of reading and numerical processing in children show that children are likely to engage a left-lateralized frontal, temporo-parietal, and occipito-temporal network during reading while engaging frontal cortex during numerical comparison, a range of arithmetic tasks, and algebraic problem solving (Houdé et al., 2010). The authors suggest from these analyses in children that, while similar patterns are seen in adults during reading, children appear to rely more heavily than adults on frontal regions during numerical processing (studies of specific arithmetic tasks were not included in the meta-analysis). Another meta-analysis that focused on numerical processing studies in children identified brain regions that include bilateral fronto-parietal cortices during arithmetic problem solving (Kaufmann et al., 2011), but again, did not compare these regions to adult brains. Empirical studies comparing children with adults are mixed, with some showing increased reliance on left posterior parietal cortex with age (Rivera et al., 2005), while others demonstrating greater engagement of bilateral posterior parietal and frontal cortices in adults relative to children for arithmetic (Kawashima et al., 2004, Kucian et al., 2008, Qin et al., 2014). For reading, some developmental work has indicated a posterior-to-anterior shift with age within the left hemisphere (Turkeltaub et al., 2003). It has also been suggested that there is increased specialization of occipito-temporal cortex over development (Pugh et al., 2001), which is consistent with less activity in adults relative to children in left angular and supramarginal gyri (Church et al., 2008). A recent meta-analysis also revealed greater reliance on left superior temporal cortex by children and greater reliance on posterior occipito-temporal/cerebellar regions by adults (Martin et al., 2015). However, longitudinal studies have yet to be conducted to directly test for these developmental patterns. As such, there are some inconsistencies in the few studies aimed at identifying the developmental trajectories of arithmetic or reading.
Nevertheless, the results from these disparate studies suggest two things: First, while reading and arithmetic largely engage different brain regions, they do overlap in the left middle temporal, inferior parietal, and inferior frontal cortices, especially when the arithmetic tasks involve verbally mediated retrieval strategies. Second, neuroplastic changes accompany the acquisition of expertise in each of these skills. These are constrained by the underlying anatomical developmental stages (Giedd et al., 1999) and modulated by the task-specific demands. Here, we directly address the modulation that occurs in brain activity due to task- and age-specific aspects of math processing and reading. We examined brain activity in a sample of typically developing children, adolescents, and adults carefully evaluated for their typical reading and arithmetic abilities.
We employed similarly designed tasks to examine arithmetic and single-word processing, suitable for both children and adults. Naturally, reading and arithmetic differ in the way in which they are executed and in this study we tried to strike a balance to respect these differences whilst at the same time reaching similarity in task design and execution. In a classroom or educational testing setting, arithmetic is typically conducted during silent pencil and paper tasks, while reading can be performed silently or aloud, on single words and on connected text. The constraints of MRI and other aspects of experimental design have led to covert single word processing becoming the favored task, as is reflected in the corpus of functional MRI studies of reading as exemplified in a recent meta-analysis of reading in children and adults (Martin et al., 2015a). As such our goal was to employ a task that elicits activity consistent with this published literature, including areas thought to be involved in visual word form recognition as well as phonological processing. The implicit reading task employed by us (Krafnick et al., 2016, Olulade et al., 2013a, Olulade et al., 2015, Turkeltaub et al., 2003, Turkeltaub et al., 2004) and others (Paulesu et al., 2001, Price et al., 1996) meets this need. For example, group maps of children performing this task (Olulade et al., 2013a) is highly consistent with those published for a meta-analysis of reading based on 20 pediatric studies (Martin et al., 2015a).
Single-digit arithmetic was separated into the operations of addition (more likely to invoke verbal retrieval subserved by areas involved in language processing) and subtraction (more likely to involve quantitative procedures subserved by intraparietal cortex). We first performed analyses for each of these three tasks in a group of subjects ranging in age from 7 to 29 years, for ease of comparison with prior studies. To test our predictions, we then combined the data from all three tasks and examined the effect of Task (subtraction, addition, and reading) via an analysis of covariance (ANCOVA), which also served to reveal the effect of Age (as a continuous variable). Depending on task and processing demands, neural activity in relevant brain structures can either increase (Lewandowska et al., 2010, Vogan et al., 2016) or decrease (Church et al., 2008, Dunst et al., 2014) as expertise develops with age. Here our predictions align with increased activity associated with increased engagement and experience, though we acknowledge that decreases in activity could be attributed to increased neural efficiency or change in strategy (e.g., as in reading where development might be associated with disengagement of superior temporal lobe structures for phonological processing and greater engagement of occipito-temporal cortex for more automatic word form recognition). We predicted that main effects for Task would involve greater activity in bilateral frontal and parietal cortices during subtraction, reflecting reliance on quantitative circuitry. We also predicted co-activation during addition and word processing in left inferior parietal, middle/superior temporal, and inferior frontal cortices, due to mutual involvement of verbal systems, consistent with the behavioral, patient, and neuroimaging work described above. Further, we expected the engagement of these to be generally more pronounced with increasing age due to maturation and greater expertise with these skills. The Task by Age interaction would reveal those areas where any of these tasks are uniquely modulated by age. We predicted increased activity with increasing age in left inferior frontal cortex during reading and addition, and increased activity with increasing age in parietal cortices during subtraction.
Section snippets
Subjects
Thirty subjects participated in this study. The participants ranged in age from 7 to 29 years old. The Georgetown University Institutional Review Board approved all experimental procedures, and written informed consent was obtained from each individual and from the legal guardian for subjects less than 18 years of age. All participants were monolingual English speakers and in good physical health and constituted 12 females and 18 males.
Neuropsychological battery
All subjects were evaluated using standardized measures and
In-scanner behavioral performance
Table 1 provides accuracy and reaction time data for the three tasks and their respective active control tasks from the scans that were used to generate the fMRI group maps for subtraction, addition, and reading. Next, the in-scanner behavioral data were analyzed in ways mirroring the fMRI factorial analyses, that is, subjected to an ANCOVA with Task (subtraction, addition, reading) as a within-subjects factor and Age as a continuous variable. For accuracy, there was no significant main effect
Discussion
In this study, we investigated the functional neuroanatomy of arithmetic, specifically for addition and subtraction of small numbers, as well as single-word reading, using closely matched tasks in children, adolescents, and adults. The purpose was to characterize the neural substrates that mediate these foundational classroom skills in typical subjects in the context of age/experience. We hypothesized subtraction to be subserved by bilateral frontal and parietal cortices, and addition and
Acknowledgments
This work was supported by the National Institute of Child Health and Human Development (P50HD40095 and R01HD056107) and the National Science Foundation (SBE0541953 Science of Learning Center). We are grateful to the staff at the Center for Functional and Molecular Imaging, and for the support of the Intellectual and Development Disorders Research Center (IDDRC5P30HD040677). Thanks to the following for aiding in the acquisition of behavioral and MRI data: Erin Ingala, Emma Cole, Iain DeWitt,
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