Children with developmental dyscalculia fail in a wide range of numerical tasks. For example, they present difficulties in retrieval of arithmetical facts 45678, 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 1011 magnitude comparisons 512 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 45678]. 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.

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 1011 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., 2930]. 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., 3637] or in working memory [e.g., 132138]. 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., 1328363840], 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., 1011]. The present study explores attentional deficits in developmental dyscalculia by studying developmental dyscalculia participants not suffering from ADHD.

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 4243444546 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 4748.

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 5051]. 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 3054 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 5556.

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.

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., 151617], 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.

Twenty-eight students from Ben-Gurion University of the Negev and Achva Academic College participated in the experiment. Fourteen of them were diagnosed as suffering from developmental dyscalculia and the other fourteen were age and sex matched controls. The controls did not have any learning or other disabilities. All students were paid 20 NIS ($5) for participation in the experiment or were given a course credit.

The mathematical ability test was administered individually. Time was measured for every sub-test and was divided by the number of trials in the sub-test (when applicable) to give an average RT. The test was divided into two parts, the first part dealing with number comprehension and production, and the second part dealing with calculation.

The results of the developmental dyscalculia and control participants in the mathematical ability test are presented in Tables 1 and 2. The RTs in the tables are for the various sub-tests. In most subtests it took developmental dyscalculia participants longer to respond than the control participants, both in number comprehension and production (particularly in comparing digits, counting, series, and fraction comparison), and in calculation (particularly in simple operations, horizontal operations and fractions). In contrast to the wide-scale differences that were found between the groups in the RTs measurements, a higher error rate for the developmental dyscalculia group compared to controls was observed in the following sub-tests: number comprehension and production (particularly in counting and series), and in calculations (particularly in horizontal operations--division; vertical operations--adding, subtraction; decimals--subtraction, multiplication; fractions--subtraction).

For reading assessment, we used a reading test that was composed and published by Shalev and colleagues 2 and standardized in a separate study 8. Our sample of developmental dyscalculia students did not have any reading difficulties and there were no differences in the scores of any reading tests compared with the control group (for more details see Table 3). We converted participants' scores on the Raven's Progressive Matrices to IQ scores. All the participants achieved an average or above average IQ score.

For attention deficits examination, we used the Conners' Continuous Performance Test II (CPT II V.5). In this test, a single letter is presented at the center of the screen. The participants are asked to press the right mouse key when they spot a letter in the alphabet (e.g., A, B, C), except for the letter 'X'. If the letter 'X' is presented, they have to withhold their response until the letter disappears. In addition, in a questionnaire we asked our participants if they thought they had a possible deficit in attention. We excluded two participants from the developmental dyscalculia group due to deficits in attention in the CPT and in the questionnaire. There were no significant differences in attention abilities between the developmental dyscalculia and the control group. Mean chance for ADHD was 27% in the developmental dyscalculia group and 28% in the control group [F < 1]. In addition, there was no significant difference between the control and the developmental dyscalculia group in the omission [F < 1] or commission rates [ns] (for more details see Table 3).

In each trial, participants were presented with a fixation point of a variable duration ranging from 400 to 1,600 ms. In half of the trials, fixation was followed by a 2,000 Hz 50 ms tone. After a stimulus onset asynchrony (SOA) of 400 ms, a cue was presented for 50 ms in 2/3 of the trials. Half of the time the cue was presented at the location of the target (valid trials) and the other half, at the location opposite to that of the target (invalid trials). Fifty ms after this, the target was presented until a response.

Discussion in the literature suggests that the executive function network is needed when an individual is requested to make a decision, for conflict resolution, error monitoring, planning an action, and inhibiting a response. The present study reveals a deficit in the ability to inhibit responding among developmental dyscalculia participants or a deficit in conflict resolution.

The connection between mathematical abilities and inhibition of response or executive functions was previously discussed 21. Bull and Scerift examined executive functions in 3^rd graders and found a strong correlation between their mathematical abilities and their executive functions. It has been reported that children of lower mathematical ability do indeed show difficulties on tasks that measure the ability to inhibit both prepotent information (Stroop interference) and learned strategies (Wisconsin card sorting task, preservative responses). In relation to developmental dyscalculia, difficulties in executive functions were reported earlier [e.g., 3637]. A recent neuro-anatomical study by Rotzer and colleagues 61 adds to the behavioral results. They discovered abnormalities in gray matter volume of their developmental dyscalculia participants compared to controls in frontal sites that are believed to be a part of the executive network. The gray matter volume of developmental dyscalculia participants was smaller in the bilateral middle frontal gyrus, the left inferior frontal gyrus, the bilateral anterior cingulum and the right intraparietal sulcus.

How can the deficit in the executive function network be related to the arithmetic difficulties in developmental dyscalculia? First, it is well known that developmental dyscalculia participants present deficits in retrieval of arithmetical facts 45678. The deficit in retrieval of arithmetical facts is related to difficulty in conflict resolution 45678. When children acquire knowledge of arithmetical expressions (e.g., 3 + 5), they have to reject various alternative solutions and to associate the expression with the correct solution (e.g., 8) 62. This could be especially true when children learn the various operations, so that solutions associated with various operations might pop-out automatically [i.e., the associative confusion effect, 63]. Difficulty in conflict resolution could produce deficits in retrieval of the correct solution. It was reported that the executive function network was activated more during passive viewing of incorrect solutions (e.g., 2 + 2 = 5) compared to correct solutions (e.g., 2 + 2 = 4) 64. Moreover, Thompson-Schill, and co-workers 65 suggested that the left inferior frontal gyrus is involved in the retrieval of facts from semantic memory and the differentiation between correct and incorrect facts. Abnormalities of these frontal structures in those with developmental dyscalculia might be responsible for this deficit 62. In addition, this same frontal structure and also the anterior cingulate gyrus may also be responsible for the size congruity deficit reported in developmental dyscalculia 1011.

In contrast to previous results and the current results, a recent study by Censabella and Noël 39 suggested that children with MD and controls have comparable executive functions. As in the present study, Censabella and Noël used the flanker task to examine the executive network. However, there were some differences between their investigation and the current study. First, the present study did not examine the flanker task only; the influence of cueing and alertness conditions was also monitored. It is possible that manipulation of several variables at the same time, and possibly other characteristics of our study, created a situation with more cognitive load, which was harder for the developmental dyscalculia participants to cope with. Second, it is also possible that age had a major effect. The executive function network develops until the age of 19 years old 66. Huiziga and colleagues found that in a flanker task there was a larger congruity effect for a group of 7 year olds compared to 11 year olds and a larger congruity effect for a group of 11 year olds compared to 15 year olds. It is possible that a not-fully-developed executive network prevented the appearance of group differences in the Censabella and Noël study.

The present work found developmental dyscalculia participants to have a deficient executive network, whereas a former study that used a similar test (ANT) found no such deficit in children with ADHD 59. However, other studies of people with ADHD showed they presented difficulties in the executive network 67686970. One of these reports employed the go-no-go task. In this task, participants are instructed to respond to the 'go' signal (e.g., as in the CPT II task, all the alphabet letters except the letter 'X', see Method for more details regarding the Connors' attention examination) and to ignore the 'no-go' signal (e.g., as in the CPT II task, the letter 'X'). The flanker task and the go-no-go task share the same requirement to inhibit a response, and the current study suggests that this ability was deficient in the developmental dyscalculia group. The flanker task is also used to study conflict situations and it was found to activate the anterior cingulate cortex. Hence, it is possible that those with developmental dyscalculia have difficulty in either inhibition of irrelevant responses or in monitoring conflict situations or both.

As mention earlier, developmental dyscalculia participants presented abnormalities in the gray matter volume of frontal areas 61. Abnormalities in the gray matter volume were found in those with ADHD in the right putamen/globus pallidus regions 71. Due to connections between these areas and the frontal lobe, such a deficiency may modulate activity of the frontal cortex.

To sum up, the neuroimaging studies of those with developmental dyscalculia and ADHD demonstrated abnormalities in areas of the frontal lobe or areas connected to the frontal lobes. In line with this finding, both the ADHD and developmental dyscalculia groups seem to suffer from a deficit in the executive network.

The larger alerting effect in the developmental dyscalculia group found in the current study is similar to the results that were previously found in populations that have deficits in attention. For example, this was found in ADHD children of the inattentive subtype, but not in those of the combined subtype 59. In addition, senior and Alzheimer's disease patients presented a larger alerting effect compared to younger controls 72. Deficiencies in alertness were found in brain injuries of the posterior cortex 73. This fits in with the suggestion that alerting involves the intraparietal sulcus 74. As discussed in the introduction, the intraparietal sulcus is involved in numerical processing and in particular, in the size congruity task [e.g., 18]. It is possible that an intraparietal sulcus abnormality in students suffering from developmental dyscalculia is responsible for their alerting deficit.

Posner and Raichle 75 suggested that the alerting network is dependent on the other two networks and cannot operate independently. Increased alertness modulates performances of the other attentional networks and facilitates their operation. A high alerting state improves RT in orienting and executive function tasks, and as a trade-off, results in an increase in error rates. In a state of high alertness, the selection of a response occurs more quickly, based upon a lower quality of information. This effect has a major influence on the executive function network in conflict situations. In the developmental dyscalculia group, we found that a high alerting state increased the congruity effect, more than in the controls. As mentioned earlier, alertness generally speeds up responding. However, because it increased the flanker effect in the developmental dyscalculia group much more than in the control group, the expected decrease in RT was not evident in incongruent trials.

We hypothesized that the developmental dyscalculia group would present deficits in the performance of the orienting network. The malfunction of the intraparietal sulcus in developmental dyscalculia participants was the basis of this prediction 161718. However, contrary to our hypothesis, no group difference was found in the orienting between the developmental dyscalculia participants and controls. Corbetta and Shulman 76 suggested that the intraparietal sulcus is more involved in endogenous orienting compared to exogenous orienting (but see appendix 2). The ANT-I paradigm examines the ability of the orienting network using exogenous attention. Hence, the present study revealed comparable exogenous orienting ability in developmental dyscalculia participants and controls. The possibility of difficulties in the endogenous orienting system in the developmental dyscalculia group remains open.

In relation to the interaction between executive function and orienting, developmental dyscalculia participants had a larger congruity effect in the non-cued condition. However, in the valid condition (i.e., line of arrows appeared in the cued location), they could filter irrelevant distractors or operate more control, similar to the control group. In the invalid trials, the two groups presented a larger congruity effect than in the valid trials. It seems that when stimuli appear in uncued locations, the two groups have less ability to operate control. In this case, the performance of the two groups appeared similar, and the advantage of the control group over the developmental dyscalculia group disappeared.

This pattern of results suggest that, similar to controls, a preparatory cue may improve the performance of the developmental dyscalculia group (i.e., reduce the congruity effect) in executive tasks. Moreover, this result reiterates the suggestion that those with developmental dyscalculia have a lower ability to monitor conflict, which can be reduced by focussing their attention on the spatial location of the stimuli.

Is developmental dyscalculia a unique pathophysiology that involves abnormalities restricted to the intraparietal sulcus or is it due to multiple brain dysfunctions with multiple cognitive deficits 24? The present study hints that those with developmental dyscalculia present multiple cognitive deficits. As mentioned earlier, Rotzer et al. 61 discovered abnormalities in the gray matter volume of developmental dyscalculia participants compared to controls, in frontal sites that are considered to be part of the executive functions network. In addition, neuroimaging studies discovered functional and structural abnormalities of the right intraparietal sulcus among those with developmental dyscalculia [e.g., 161761]. Hence, the cognitive deficits that might underlie developmental dyscalculia may be due to multiple brain abnormalities. It seems that the "pure" developmental dyscalculia we studied is characterized by multiple deficits that involve the executive function and alertness networks.

Finally, we do not claim that the deficit in attention is the only deficit observed in developmental dyscalculia or that the numerical deficiencies in developmental dyscalculia are due to attention deficits (as the domain-general hypothesis would suggest). We suggest that in developmental dyscalculia, numerical deficits are the crucial factor, but similar to other developmental disorder [e.g., attention deficits in dyslexia, see 78], additional domains are also damaged but to a lower degree 25.

There are several differences between the two tasks. 1) The ANT and the ANT-I both examine the executive function network using flankers with congruent and incongruent conditions. The ANT uses neutral trials whereas the ANT-I does not. 2) The orienting system is tested using an asterisk above or below the fixation point. The ANT uses only a valid/predictive (endogenous) cue. Namely, there are two conditions: cued, where the target appears at the cued location (100% predictive), or uncued, where the target follows a central cue. The ANT-I uses a nonpredictive cue (exogenous) with valid (target at cued location), non-cued (no spatial cue is presented), and invalid (target appears opposite to the cued location) conditions. 3) The alertness of attention is manipulated differently in the two tasks. In the ANT it is examined using two asterisks (double cue), while in the ANT-I a high pitched tone is used.

Note however, that others have distinguished between a posterior and an anterior system of attention; (a) an automatic posterior attention system involves the superior parietal cortex (intraparietal sulcus); and (b) a voluntary anterior attention system involves frontal sites. According to this view, the intraparietal sulcus is more related to exogenous attention [e.g., 77]. This would lead one to expect a difference in exogenous attention between those with developmental dyscalculia and controls, which was not found.