Developmental dyscalculia is generally defined as a disorder in mathematical abilities presumed to be due to a specific impairment in brain function [1, 2]. Developmental dyscalculia is supposed to be a unique deficit that is not caused by a reading disorder (dyslexia), attentional disorder (ADHD/ADD- attention-deficit disorder) or general intelligence (IQ) problems. The present study aims to examine attention in developmental dyscalculia by employing a recently designed test of three attentional networks and their interactions [3].

Characteristics of developmental dyscalculia: Does developmental dyscalculia involve domain-general or domain-specific deficits?

Children with developmental dyscalculia fail in a wide range of numerical tasks. For example, they present difficulties in retrieval of arithmetical facts [4–8], in using arithmetical procedures [e.g., [7]], and in solving arithmetical operations in general [9]. Recently, studies on developmental dyscalculia concentrated on basic numerical processing and found those with developmental dyscalculia exhibited an atypical effect; size congruency [10, 11] magnitude comparisons [5, 12] and subitizing [13].

Neuro-functional studies indicate that mathematical difficulties involve abnormalities in the structure or the activity of the parietal lobes, mostly the intraparietal sulcus. A focused infarct to the left intraparietal sulcus could produce primary acalculia [14]. Isaacs and co-workers [15] found reduction in gray matter in the left intraparietal sulcus in children born preterm who suffered from calculation deficits. A structural and functional abnormality in the right intraparietal sulcus was found in women with Turner syndrome who had dyscalculia [16]. Recent work by Price and co-workers [17] examined the activity in the brains of those with developmental dyscalculia and discovered reduced activity in the right intraparietal sulcus during non-symbolic magnitude processing. Finally, Cohen Kadosh and co-workers [18] showed that TMS (transcranial magnetic stimulation) to the right intraparietal sulcus in normal control participants induced a dyscalculia-like pattern. Accordingly, one line of thinking is that developmental dyscalculia is a domain-specific (pure) disorder that involves only deficits in basic numerical processing and is related to one biological marker (i.e., a deficit in the intraparietal sulcus) [e.g., see [19]].

Alternatively, some refer to deficits in arithmetic as a domain-general phenomenon. One of the main deficits in developmental dyscalculia is a difficulty in retrieval of arithmetical facts [e.g., see [4–8]]. It has been suggested that this difficulty is more related to deficits in attention, working memory or long-term memory than to deficits in conceptual knowledge of arithmetic [e.g., see [20]]. In addition, there are indications that mathematical abilities are directly related to general abilities such as executive functions [e.g., [21]] and verbal or visuo-spatial working memory [e.g., [22]]. Finally, there are indications that the developmental course of the numerical distance effect is domain-general rather than domain-specific [see [23]]. Moreover, it has been suggested that mathematical learning difficulties are characterized by heterogeneity in symptoms and possibly in deficient mechanisms [24].

Karmiloff-Smith [25] suggested that developmental disorders characterized by a domain-specific end state can stem from a domain-general starting point. In addition, she suggested that neuropsychological dissociation studies of brain injuries and stroke patients that have dramatically influenced cognitive research may not apply to developmental disorders such as developmental dyscalculia. First, the basis of developmental disorders is believed to be genetic and one could not expect a one-to-one correlation between genes and specific cognitive functions (such as a deficit in processing of quantities in developmental dyscalculia). Second, there are compensation mechanisms that operate throughout development and change the observed deficits during adolescence. Third, some of the tests employed in the screening process of research participants (e.g., screening for attentional deficits in developmental dyscalculia) are not sensitive enough to reveal deficits in the "preserved" domain. Hence, it is possible that an abnormal expression of genes affects multiple aspects of development with the strongest effect being on one specific aspect. In the case of developmental dyscalculia, this could be core numerical processing.

The present study investigates attention, in a group of those with "pure" developmental dyscalculia. Namely, the participants have no indication of deficits in commonly used tests of attention and reading, and have a normal level of intelligence. We focus on attention because the intraparietal sulcus, involved in number processing and possibly which is abnormal in those with developmental dyscalculia, has a critical role in orienting of attention [see [26]]. Moreover, several researchers have suggested that some of the difficulties in developmental dyscalculia may be related to attention [e.g., see [20]]. The next section discusses possible abnormalities in attention in the developmental dyscalculia population.

Attention and developmental dyscalculia

Shalev and co-workers [27] found that children diagnosed as having developmental dyscalculia had a higher mean score on an attentional problem subscale than matched controls. A similar pattern of results was found in Lindsay et al.'s [28] study--the developmental dyscalculia group in their study presented more commission and omission errors compared to the controls in the Conners' Computerized Continuous Performance Test (CPT). In addition, many deficits that characterize developmental dyscalculia can be connected to deficits in recruiting attention.

Rubinsten and Henik [10, 11] examined developmental dyscalculia participants using the numerical Stroop task and discovered a lack of facilitation. They concluded that the ability to connect Arabic numerals to internal magnitudes is damaged in those with developmental dyscalculia. However, deficits in the executive functions network in the developmental dyscalculia population can also influence performance in the numerical Stroop task. In Stroop and Stroop-like tasks, a multi-dimensional object is presented and participants have to attend to one dimension while ignoring other dimensions. Performance in these tasks is considered to be based, among other things, on selective attention abilities and on executive functions, examined frequently in conflict situations [e.g., [29, 30]]. Moreover, the anterior cingulate cortex is considered to be involved in conflict monitoring [e.g., [31]]. In a study by Kaufmann et al. [32], activity in the anterior cingulate cortex was discovered during the numerical Stroop task. In addition, we recently found that normal participants presented a developmental dyscalculia-like pattern in the numerical Stroop task under a condition of attentional load, namely, they showed a lack of facilitation [33].

Those with developmental dyscalculia have a smaller subitizing range [13]. Subitizing is a fast and accurate evaluation of a small set of objects [13]. However, it was recently suggested that subitizing may be modulated by attention. A recent study by Railo and co-workers [34] examined the role of attention in the subitizing process and discovered that when attention is limited, the subitizing range decreases to 2 dots. In addition, attentional training increases the subitizing range [35].

Several studies directly proposed that those with developmental dyscalculia suffer from deficits in executive functions [e.g., [36, 37]] or in working memory [e.g., [13, 21, 38]]. In contrast, Censabella and Noël [39] found no evidence for deficient executive functioning in mathematically disabled (MD) children. They used the Stroop and the flanker tasks to examine the inhibition ability in MD children and matched controls. The ability to inhibit irrelevant information is considered to be part of the executive function network. Their results indicated that MD children showed normal performance on these tasks. No group differences were found in their study.

Some of the studies that were described above did not differentiate between pure developmental dyscalculia and the co-morbidity between developmental dyscalculia and ADHD [e.g., [13, 28, 36, 38, 40]], thus it is not clear whether the attentional difficulties in those with developmental dyscalculia are part and parcel of their dyscalculia or of the co-morbid deficit (i.e., ADHD). To this end, it is important to exclude participants with co-morbidity between ADHD and developmental dyscalculia [e.g., [10, 11]]. The present study explores attentional deficits in developmental dyscalculia by studying developmental dyscalculia participants not suffering from ADHD.

Three brain networks of attention

Early discussions defined attention as a cognitive process that selectively concentrates on one aspect of the environment while ignoring other aspects. This early definition viewed attention as one system. More recent works differentiated between several networks of attention. For example, Posner and Petersen [41] and later Posner and others [42–46] defined three separate networks of attention in the brain, which differ from one another in brain locations and functions. These networks carry out the functions of alerting, orienting, and executive control.

The alerting network is related to the awakeness state. Its role is to activate and preserve attention. Brain tissue involved in this network includes frontal and parietal regions of the right hemisphere. The alerting network is based on the distribution of the brain norepinephrine system [47, 48].

The orienting network is involved in moving attention to a specific location in space. Attention can be shifted by moving the eyes, head or body position or without changing position [49]. The function of the orienting network can be stimulus-driven (exogenous, automatic, or bottom-up) and goal-directed (endogenous, voluntary, or top-down). The orienting network involves the superior parietal lobes, in particular, the intraparietal sulcus [26]. The parietal lobes are involved in suppression of old attended locations and in voluntary movement of attention to new locations [e.g., see [50, 51]]. In addition, other brain areas are considered to be involved in the orienting system, that is, the superior colliculus [52] and the thalamus [53].

The executive control of attention is the third system and is involved in conflict situations. Commonly, the Stroop and the flanker tasks are employed to study this system. The frontal lobe, mostly the midline frontal areas (anterior cingulate cortex) and the lateral prefrontal cortex [30, 54] subserve the executive system. It has been suggested that the midline areas (i.e., anterior cingulate cortex) are responsible for conflict monitoring and the lateral areas (i.e., lateral prefrontal cortex) are responsible for inhibition of irrelevant responses and maintaining task requirements [55, 56].

In 2002, Fan et al. created a general test for the three attention systems--the Attention Network Test (ANT). The basic assumption of the ANT is that the three attentional networks are isolable. In contrast with this claim, Callejas et al. [3] reported an interaction between the three attentional networks and created a new test, the ANT-I, which examines the three systems and their interactions (see appendix 1). Several populations have already been tested with the ANT (e.g., children [57], borderline disorder [58]; ADHD [59]).

Rueda et al. [57] examined children aged 6 to 10 years old and compared their performance in the 3 attentional networks. Alertness was fully developed by the age of 10, the executive functions network was fully developed by the age of 7, and the orienting network was found not to be modulated by age.

Booth et al. [59] examined participants with ADHD using the ANT test. They reported that only the alertness network of ADHD participants presented an abnormal pattern of performance. In addition, they revealed that subtypes of ADHD presented different patterns of abnormal performances: the ADHD of the combined subtype (ADHD/C) showed a smaller alerting effect compared to typically developing children, whereas the inattentive subtype (ADHD/IA) showed a larger alerting effect compared to typically developing children, that is, a greater benefit from the high alerting state compared to controls.

The present study

Very little is known about attention deficits in developmental dyscalculia, hence, this study was designed to provide the missing information. Most of the studies see developmental dyscalculia as a pure disorder that does not involve deficits in attention. In the present study we would like to suggest that even in "pure" developmental dyscalculia one can observe abnormalities in attention. We examined attention abilities of participants suffering from developmental dyscalculia using the ANT-I test [3].

The ANT-I test examines executive function by using a variation of the flanker task [60]. In the flanker task the participants have to attend to one object while ignoring other objects. In the version that was used in the present study, participants were asked to respond to a central target and ignore flanking distractors. It is hard to determine whether this network would be damaged in developmental dyscalculia participants because the evidence provided by the literature is inconsistent. Orienting of attention is tested by using spatial cueing. Based on earlier findings [e.g., [15–17]], we hypothesized that developmental dyscalculia participants would present an abnormal pattern of attentional orienting. Alertness was tested by the presentation of a tone at the beginning of a trial. The intraparietal sulcus is considered to be involved both in the orienting network and in the alertness network. Due to the anatomical proximity of the alertness network and the orienting network, similar to our prediction about the orienting system, we hypothesized that developmental dyscalculia participants would present abnormal alerting as well.