Introduction

Understanding what causes numerical difficulties/disorders (henceforth, NDD) is crucial for the prevention of NDD at earlier stages and for a reliable diagnosis of groups with a high risk factor. Such an understanding requires the integration of scientific findings from different fields investigating at the molecular level (genetics, receptors) or the behaviour-brain relations level. Currently knowledge from most of these fields is rather limited or absent. The main focus of this Encyclopedia entry will therefore be the level of the neurocognitive mechanism(s) that subserve NDD.

Key Research Questions

NDD can occur in isolation, but also in conjunction with other developmental disorders such as dyslexia, Williams syndrome, Turner syndrome, or attention deficit hyperactivity disorder (Ansari, Donlan, & Karmiloff-Smith, 2007; Braundet, Molko, Cohen, & Dehaene, 2004; Kaufmann & Nuerk, 2008; Molko et al., 2003; Rubinsten & Henik, 2009; van Herwegen, Ansari, Xu, & Karmiloff-Smith, 2008). In such cases, when other developmental disorders are diagnosed, NDD is attributed to non-numerical factors, rather than being specific to only numerical abilities. Therefore, if other factors such as education, intelligence, motivation, anxiety, or other disorders (e.g., dyslexia, attentional problems) can explain the substantial underachievement on a standardized numerical/mathematical test relative to the peers' scores, then NDD is considered a secondary problem, and the person's NDD is not attributed to a dyscalculic origin (Rourke, 1993; Shalev, 2004). For example, as much as 4% of the students can experience anxiety in dealing with mathematical material, and this in turn can impact their performance (Chinn, 2009). Reducing their anxiety can lead to an improved numerical performance (Hardiman, 2003).

This entry focuses mainly on the possible primary causes, rather than on secondary factors, leading to NDD. Namely, the two questions discussed in this entry are:

1. Which brain areas are associated with NDD? and
2. What can lead to atypical development in these brain areas?

Parents and teachers, however, should be aware that secondary factors, which will be discussed briefly below, can lead to NDD.

Recent Research Results

The following factors have been shown to be relevant for NDD: environmental deprivation, poor teaching, classroom diversity, untested curricula, and mathematical anxiety (Shalev, 2004). In addition to these environmental factors, there is also a strong evidence for a genetic basis. For example, if a monozygotic (identical) twin is diagnosed with NDD there is a greater chance that the other twin will also have NDD, as compared with dizygotic (fraternal) twins, who share roughly half of their DNA (Alarcon, DeFries, Gillis Light, & Pennington, 1997). The same is also true for siblings; compared to the general population, if one sibling has NDD there is an up to 10 times increased chance that the other sibling might have NDD too (Shalev et al., 2001). However, it seems that in contrast to some suggestions for a disproportional gender distribution among NDD, there is almost identical prevalence among the genders (male-female 1:1.1), a surprising finding given that learning disabilities are generally more frequent in boys. However, at the moment the genes that are involved in NDD are not yet discovered.

How can these molecular effects for NDD be observed on the neuroanatomical level? Before moving on to describe the brain mechanism(s) that are involved in atypical numerical processing, I will focus briefly on the typical brain areas that are involved in numerical processing.

To process numbers fluently, several processes need to occur including digit recognition (e.g., 7), which is the most commonly used symbol for numerical magnitudes and calculation. Digit recognition is mainly done by the occipito-temporal areas in the ventral stream of the brain (e.g., fusiform gyrus) (Pesenti, Thioux, Seron, & De Volder, 2000). Extraction of the numerical magnitude (e.g., 7 is larger than 6 and smaller than 8) was found in many studies to be based on the parietal lobes, and especially the intraparietal sulcus (IPS). The IPS is the sulcus (a long groove on the surface of the brain) that differentiates the upper parietal lobe and the lower portion of the parietal lobe in both hemispheres (both sides of the brain), and that plays a dominant and crucial role in quantity representation (Cohen Kadosh, Lammertyn, & Izard, 2008). In children it has been found that the prefrontal cortex is also involved during numerical processing, and that the involvement of this area is reduced as age and numerical proficiency increases (Ansari & Dhital, 2006; Cantlon, Brannon, Carter, & Pelphrey, 2006; Cantlon, Libertus, Brannon, & Pelphrey, 2009; Rivera, Reiss, Eckert, & Menon, 2005).

While there is abundant knowledge on numerical processing in normal participants (Ansari, 2008; Brannon, 2006; Cohen Kadosh et al., 2008; Dehaene, Piazza, Pinel, & Cohen, 2003) and acalculic people, i.e. those with deficits in numerical abilities following brain damage (Willmes, 2008), little is known about the specific brain mechanism(s) that underlie NDD. A handful of recent studies yielded somewhat contradictory results. A study that compared preterm children with and without NDD found in the former group reduced grey matter volume (a measure of the density of brain cells) in the left but not the right IPS (Isaacs, Edmonds, Lucas, & Gadian, 2001). Later studies, however, suggested that a functional deficit in the right IPS, rather than the left, is associated with NDD. A neuroimaging study has found that adults who suffer from NDD and also have visuospatial impairments (the inability to understand visual representations and their spatial relationships) have reduced grey matter volume in the right IPS, and also show reduced brain activation during arithmetic, especially in the right, but also the left IPS, as compared to the control group (Molko et al., 2003). Another study examined the differences in grey matter between children with and without NDD. It was found that children with NDD have reduced grey matter volume in the right IPS but also in other brain areas such as the left and right prefrontal cortex, and the anterior cingulum, which are involved among other functions in working memory and attention (Rotzer et al., 2008). A different study examined the brain activation of children with NDD. The researchers revealed that in comparison to children without NDD, children with NDD showed a reduction in the right IPS activity when they compared numerical quantity. Notably, differences were also observed in brain areas outside the IPS, such as the prefrontal cortex, and the fusiform gyrus (Price, Holloway, Rasanen, Vesterinen, & Ansari, 2007). Another study used transcranial magnetic stimulation (TMS), a technique that causes a temporary neuronal disruption, and thus creates a transient virtual lesion in the healthy brain. This study showed that subjects without NDD after a temporary disruption to the right IPS show similar numerical processing performance to subjects with NDD (Cohen Kadosh et al., 2007). Crucially, the behavioural performance following TMS to the left IPS was intact, suggesting a causal relationship between right IPS function and NDD.

These findings are somewhat confusing and contradictory. Why is it that in some studies the left IPS seems to be correlated with NDD, while in others the right IPS seems to be crucial for NDD? How come that aside from a consistent finding of abnormal activity/morphology of the IPS (independent of laterality), different studies found different brain areas to be correlated with NDD? Some of these differences might be attributed to the use of different testing batteries and standards for diagnosing and recruiting dyscalculic participants, therefore leading to different types of NDD in each study. Other possible factors might be the inclusion of different age groups, and maybe even different educational methods for mathematics.

Now that we know which areas are involved in NDD, how does NDD occur? Some researchers have suggested that NDD is due to a number of core deficits and that it is associated with IPS impairment from infancy (Butterworth, 2004; Wilson & Dehaene, 2007). This view is based on the idea that humans are equipped with numerical abilities from the beginning (de novo), what some researchers termed the "number sense" (Dehaene, 1997). Another view is that during infancy numbers do not have their own representation (Rips, Bloomfield, & Asmuth, 2008), and other non-numerical dimensions, separately or jointly, can serve as cues in order to detect changes in quantity/magnitude. A likely reason for this might be a shared magnitude mechanism for non-numerical dimensions such as size, density, time, that precedes neurons that are specialized for numerical magnitude. In this scenario, different magnitudes, possibly also numbers, are jointly represented from infancy (Cohen Kadosh et al., 2008; Feigenson, 2007). Later, in development, there is an increase in the specialization for numbers, and this leads to the emergence of a dedicated neuronal circuits for numerical magnitude (Cohen Kadosh & Walsh, 2008). This idea of development of intact numerical magnitude understanding is in line with evidence from other fields of research that have examined neuronal specialization, such as face perception (Cohen Kadosh & Johnson, 2007; Johnson, 2001). This idea is supported by the finding that people with NDD have problems not only with automatic processing of numerical quantity (Cohen Kadosh et al., 2007; Koontz & Berch, 1996; Rubinsten & Henik, 2005, 2006), but also with other magnitudes (Cappelletti, Freeman, & Butterworth, 2009; Cohen Kadosh et al., 2007). However, whether we are indeed born with a number sense or not, is still highly debated.

Future Directions

In contrast to reading difficulties/disorders, where the neurobiological basis has been convincingly demonstrated and some effective treatment possibilities have been introduced, remediation for NDD is still in its infancy. This is mainly due to the fact that compared to other difficulties/disorders NDD was beyond the interest of many scientists, educators, and policy makers. This is unfortunate as recent studies showed that poor numeracy has a greater impact on one's life compared to poor literacy (Parsons & Bynner, 2005).

Finding the different developmental stages at which NDD occurs will promise more efficient rehabilitation and a proper educational environment, and might shed light on the question of whether NDD includes a single or several subtypes (Butterworth, 1999; Rubinsten & Henik, 2009; Wilson & Dehaene, 2007).

Another open question is whether the finding that NDD is correlated with impairment at multiple brain areas implies that the underlying neural basis of NDD is distributed over multiple brain regions. This is a possible explanation, and in this vein future studies should also pay attention to the function of other brain areas outside the IPS (e.g., prefrontal cortex, fusiform gyrus). However, it is likely that atypical development of cognitive function in a given brain area, in this case the IPS, can result in a change in other connected brain areas during development (Knudsen, 2004). In this vein, it is quite possible that NDD will never appear in isolation, that is, pure NDD might never be found to exist. Rather, NDD will be accompanied by more subtle impairments in other areas of cognitive functioning (e.g., attention, working memory, language), some of which might have nothing to do with numerical abilities per se, aside from being subserved by a similar brain structure (e.g., the parietal lobe) (Karmiloff-Smith, 1998).

The future success of remediation programs rests, of course, not only on a better understanding of NDD at the cognitive and anatomical levels. Together with an increased focus on the genetic and molecular basis of NDD, we will be able to provide effective solutions and consequently a better future for people suffering from dyscalculia. Such understanding will enable accurate and early diagnosis of the different subtypes of NDD, and referring the person for appropriate intervention.

Conclusions

This entry's aim was to define the causes of NDD. It seems that NDD occurs as a result of the interaction between environmental and genetic factors. At the brain level, NDD is associated with functional and structural abnormalities in the IPS, while the involvement of other brain areas is still ambiguous and requires further examination. Further knowledge on the causes of NDD will enable early and accurate diagnosis, and will allow for more effective intervention, thus improving the quality of life at the micro level and providing a gain for the economy and society at the macro level.