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activation brain differences in children with pure DD compared to typically developing children. The following section will discuss what we know about the neural correlates of DD from functional neuroimaging studies. Studies investigating the integrity of

numerical representations in children with DD compared to typically developing controls have predominantly used the numerical discrimination task (both symbolic and non- symbolic) and have found differences between children with and without DD in the neural distance effect. A neural distance effect in the brain is evident when greater differences in activation are found during the discrimination of close distance pairs compared to far distance pairs (see Figure 1.2). Functional neuroimaging studies with typical adults have found that distance modulates activity in the bilateral intraparietal sulcus (IPS) (e.g. Holloway & Ansari, 2010; Pinel et al., 1999; Pinel, Dehaene, Riviere & LeBihan, 2001). Additionally, studies investigating the neural correlates of numerical magnitude processing in children and adults have found age related changes in the parietal cortex, whereby adults exhibit a greater effect of distance/ratio on IPS activation in comparison to children, suggesting an age related specialization of processing

numerical magnitude (Ansari, Garcia, Lucas, Hamon, & Dhital, 2005; Ansari & Dhital, 2006). Furthermore, a larger ratio effect in the left IPS has been associated with higher arithmetic abilities (Bugden et al., 2012). Taken together, these findings suggest that a large neural distance effect in the parietal cortex is indicative of more precise neural representation of numerical magnitude.

Using a non-symbolic discrimination task (children select the numerically larger dot array from two sets of dots), researchers have found that children with DD did not show typical distance-related modulation of activation in the right intraparietal sulcus (IPS) (Price et al., 2007) (see Figure 1.4 for a map of brain locations). Children with DD showed atypical activation in the right IPS compared to typical controls. More

specifically, children with DD demonstrated similar activation in the right IPS during both far and close distance trials, suggesting that their representation of quantity in this brain region may be less refined, whereas, a typical neural distance effect was found in age matched controls. In addition, the right IPS was recruited to a lesser extent in children with DD. Taken together; these findings demonstrated a parietal dysfunction may underlie reduced capability to process non-symbolic numerical magnitudes in children with DD. Atypical activation in the right IPS has also been implicated in processing symbolic numerical magnitudes. Mussolin and colleagues (2009) found that children with DD demonstrated weak modulation of the right IPS and the left superior

parietal lobule during a symbolic numerical discrimination task (e.g. the discrimination of Arabic numerals, such as 3 and 5). Additionally, Kaufmann et al., (2009) found atypical activation in bilateral regions of the IPS during non-symbolic numerical processing in nine-year-old children with DD. However, in contrast to previous findings, differences were driven by stronger activation in the left IPS and less pronounced deactivation in the right IPS. The majority of studies use arrays of dots or objects in a non-symbolic

discrimination task; in the Kaufmann et al.‟s study, children were instead asked to compare finger patterns (e.g. images of fingers that indicate a specific quantity). Therefore, it is difficult to interpret these conflicting findings.

In an attempt to ascertain whether these findings (and others) yield a consistent pattern of data, Kaufmann et al. (2011) conducted a meta-analysis synthesizing the functional neuroimaging data that have investigated the neuronal correlates of both symbolic and non-symbolic numerical magnitude processing in children with DD. They found that, when considering all available evidence and using meta-analytic tools, children with DD have distinct differences in activation patterns compared to typically developing controls. For example, control children demonstrated greater activation than children with DD in the left posterior IPS, right inferior parietal lobe, left paracentral frontal lobe, the superior frontal gyrus, the right middle frontal gyrus and the left fusiform gyrus. In contrast, DD participants showed greater activation in the left postcentral gyrus, superior frontal lobe, as well as the bilateral inferior parietal regions, more specifically in the right supramarginal gyrus and the left lateral IPS. The researchers interpreted these findings to indicate that children with DD have reduced specialization for processing numerical information in contrast to typically developing controls (Kaufmann et al., 2011). It is important to note that the meta-analysis only included three studies that investigated numerical processing abilities merging data from both symbolic and non- symbolic numerical discrimination in children with DD compared to typical controls. Thus any direct comparisons between the formats are difficult to make in view of the presently published neuroimaging data investigating differences between children with and without DD.

Figure 1.4: An illustration of the approximate locations of brain regions that have been associated with atypical activation during numerical magnitude processing tasks in children with DD. Note. SFG = superior frontal gyrus, PCG = precentral gyrus, PreC = Precuneus, IPS = intraparietal sulcus, SMG = supramarginal gyrus, MFG = middle frontal gyrus.

Taken together, these findings demonstrate atypical recruitment/organization of the intraparietal sulcus, a region known to process semantic representation of numerical magnitude (Butterworth, 1999; 2005; Dehaene, 1992; Dehane et al., 2003). To date, no study has investigated both symbolic and non-symbolic numerical processing abilities in the same sample of DD children, and as a result, there is presently no cognitive

neuroscience evidence to support or refute the representational (i.e. ANS and defective number module) or access deficits hypotheses as the root mechanism underlying DD.

Very few neuroimaging studies have investigated the cognitive mechanisms that contribute to DD deficits and the current state of findings has yielded an inconsistent and difficult to interpret pattern of data (for a review see: Bugden & Ansari, 2014). Given the early stages of functional MRI research, it is nearly impossible to glean from the current set of data what neurobiology underlies cognitive deficits in children with DD. Future studies are required to understand the origins of numerical deficits in the brain, more

specifically, developmental cognitive neuroscience methods are necessary to pinpoint neural correlates of symbolic and non-symbolic processing difficulties. These difficulties cannot be fully explained by behavioural evidence – given that it is unclear whether symbolic processing deficits are caused by an underlying deficit in the ANS or in the decision level processes that involve accessing the semantic representation of numerical symbols leaving the actual representation intact. Therefore at the behavioural level, reaction time and accuracy measures are not informative for disentangling whether different mechanisms are contributing to the output of choosing the numerically larger number or dot array. However, functional imaging analysis can shed light on whether different brain regions that subserve different cognitive processes are recruited differently for format specific responses.