Domain-General Cognitive Skills in Children with Mathematical Difficulties and Dyscalculia: A Systematic Review of the Literature

Mathematical performance implies a series of numerical and mathematical skills (both innate and derived from formal training) as well as certain general cognitive abilities that, if inadequate, can have a cascading effect on mathematics learning. These latter skills were the focus of the present systematic review. Method: The reviewing process was conducted according to the PRISMA statement. We included 46 studies comparing school-aged children’s performance with and without math difficulties in the following cognitive domains: processing speed, phonological awareness, short- and long-term memory, executive functions, and attention. Results: The results showed that some general cognitive domains were compromised in children with mathematical difficulties (i.e., executive functions, attention, and processing speed). Conclusions: These cognitive functions should be evaluated during the diagnostic process in order to better understand the child’s profile and propose individually tailored interventions. However, further studies should investigate the role of skills that have been poorly investigated to date (e.g., long-term memory and phonological awareness).


Introduction
Many studies have highlighted the important role of arithmetic and mathematical skills in everyday life [1][2][3][4], job opportunities and professional success [5][6][7]. However, many school-age children have difficulties learning mathematics, a problem with an incidence ranging between 5% and 7% [8][9][10][11]. Given the clinical relevance of this phenomenon, it is important to understand which factors cause or contribute to mathematical difficulties (MD) in order to intervene more effectively.
Mathematics is a composite discipline, including various domains such as arithmetic, algebra, geometry, and statistics. Individual performance in each of these domains implies developing different skills, such as the sense of numbers, and understanding mathematical concepts and procedures [7,12,13]. Thus, mathematical performance depends on a series of specific domain skills that also require the simultaneous development of general cognitivedomain abilities. The impairment of any of these domains could determine a cascade effect on mathematics learning.
Several studies support the existence of a domain-specific deficit in children with MD [14][15][16] or dyscalculia [17,18]. Butterworth [19,20] proposed that mathematical difficulties in children with Developmental Dyscalculia (DD) are due to a deficit in understanding the basic numerical concepts, such as counting or magnitude comparison (i.e., the number processing system). By contrast, Geary [21] highlighted that competencies in each mathematic domain are based on different conceptual and procedural processes supported by Overall, there has been considerable interest in the relationship between mathematical difficulties and cognitive functions over the last years. An analysis of the number of records on these themes carried out on Google Scholar confirmed this impression (see Figure 1) and indicated a progressively increasing number of papers in this area of research in the last years. Given all of the above considerations, we set out to carry out a systematic review of this growing body of literature with the aim to: • Identify the cognitive abilities most impaired in school-age children with MD, independent of the degree of severity and the instruments used for assessment; • Define which cognitive areas might be helpful to assess to support the potential diagnosis of DD; • Pinpoint future research areas to enable a more accurate identification of children with mathematical difficulties at risk of DD.
Analyzing the cognitive abilities most impaired in children with mathematical difficulties would allow clinicians to better evaluate the domain-general cognitive skills that influence mathematical abilities, obtaining a more comprehensive profile of their children's expertise. This knowledge may help clinicians to propose more effective and tuned interventions.

Research Strategies
The systematic search of the international literature was conducted until 20 February 2020, on the following electronic databases: PsycArticles; PsycInfo; Scopus, and Web of Science. The results were limited to articles in English and academic publications. The search was conducted using the following script on each database: ((math* disability OR math* difficulty OR dyscalculia) AND (Cognitive Function*)) and produced a total of 2977 records. After eliminating duplicates (N = 273) through the Mendeley software, 2704 records were screened based on title and abstract. Then, 2448 records were excluded, while the remaining 256 were assessed for eligibility based on reading the full texts. Given all of the above considerations, we set out to carry out a systematic review of this growing body of literature with the aim to: • Identify the cognitive abilities most impaired in school-age children with MD, independent of the degree of severity and the instruments used for assessment; • Define which cognitive areas might be helpful to assess to support the potential diagnosis of DD; • Pinpoint future research areas to enable a more accurate identification of children with mathematical difficulties at risk of DD.
Analyzing the cognitive abilities most impaired in children with mathematical difficulties would allow clinicians to better evaluate the domain-general cognitive skills that influence mathematical abilities, obtaining a more comprehensive profile of their children's expertise. This knowledge may help clinicians to propose more effective and tuned interventions.

Research Strategies
The systematic search of the international literature was conducted until 20 February 2020, on the following electronic databases: PsycArticles; PsycInfo; Scopus, and Web of Science. The results were limited to articles in English and academic publications. The search was conducted using the following script on each database: ((math* disability OR math* difficulty OR dyscalculia) AND (Cognitive Function*)) and produced a total of 2977 records. After eliminating duplicates (N = 273) through the Mendeley software, 2704 records were screened based on title and abstract. Then, 2448 records were excluded, while the remaining 256 were assessed for eligibility based on reading the full texts. To update the results, on 8 November 2021, the search was re-run on each database, limiting by publication data range (e.g., 2020-2021). A total of 261 new records was found, and 219 records were screened based on title and abstract after eliminating duplicates (N = 42). Finally, thirteen records were assessed based on full texts.

Eligibility Criteria
Selections were made independently by two researchers, any disagreement between the two judges was dealt with by a supervisor (M.C.). To be included in this systematic review, the studies must meet the following eligibility criteria: (a) school-age participants, i.e., they must be aged between 6 and 12; (b) the study had to evaluate at least one of the following cognitive domains: processing speed, phonological processing; memory (long or short term, verbal and visual, spatial or visuospatial); executive functions such as working memory, inhibition and cognitive flexibility (switching or set-shifting), and attention; (c) the study had to assess the participants' mathematical abilities and intelligence (e.g., fluid intelligence or verbal or non-verbal IQ).
Cross-sectional and longitudinal studies were included. The cross-sectional studies had to report the measures used for mathematical skill assessment in the screening phase and the criteria adopted to define the group with MD. Furthermore, they had to include a control group. In longitudinal studies, children assessed at preschool-age must have had at least one follow-up during primary school, i.e., during the period of formal math learning. Longitudinal studies also had to include children with persistent MD. Sometimes, MD can be temporarily and spontaneously resolved; therefore, longitudinal studies that did not take this feature into account would not allow us to grasp any cognitive difficulties characterizing the population of interest.
Out of the 269 articles assessed for eligibility, three were excluded because they were in a language other than English, 44 studies were excluded because they were not experimental studies (e.g., book chapters; reviews, metanalyses, theoretical issues, commentaries, or editorials), and 42 were excluded because they did not evaluate the functions of our interest. Furthermore, 10 studies were excluded because they were correlational and, evaluating mathematical skills along a continuum, did not distinguish between children with and without MD. Another ten studies were excluded because they evaluated the neural networks involved in mathematical skills, while five were excluded as they assessed the effectiveness of rehabilitation or enhancement of mathematical skills. Another 65 studies were excluded for methodological reasons (N = 32; absence of validated measures for the screening of mathematical skills, classification of the experimental group based on executive and non-mathematical skills), or because they did not involve primary school participants (N = 35; preschoolers, adolescents, and adults). Finally, 44 studies were excluded as they assessed the comorbidity between MD and other disorders (N = 10), because they did not have a control group without MD (N = 6), or because they did not carry out an intelligence assessment of the participants (N = 27).
Forty-six articles were included in the systematic review, 31 cross-sectional and 15 longitudinal studies. Figure 2 reports the flowchart showing the number of studies identified from the databases and the number of studies examined, assessed for eligibility, and included in the review; the reasons for possible exclusions are also reported.

Data Collection and Quality Assessment
The selection of articles was independently conducted by two researchers; a supervisor resolved any doubt. The data of the 46 articles included in this systematic review were extracted according to the PICOS approach [50]. The following information was extrapolated: author(s) and year of publication; study design; characteristics of participants (gender, mean age); tests used to assess intelligence; instruments, and criteria adopted to define the group with MD, cognitive domains assessed and results. Moreover, the number of measurements carried out over time and the cognitive domains (with related instruments) evaluated in the various follow-ups were considered for the longitudinal studies. Tables A1 and Table A2 in the Appendix reports the extracted data for cross-sectional and longitudinal studies, respectively.
The results are summarized, reporting the performance differences between the MD and control group. The quality of the studies was assessed using the Cochrane Handbook for Systematic Reviews criteria [52], adapted ad hoc according to the objective of this review. For each study, the evaluated domains were: (a) selection of the sample and control of any variables that could play a role in mathematical difficulties (e.g., IQ, socioeconomic status, motivation or performance in reading tests; selection bias); (b) the use of standardized instruments to assess mathematical skills and a clear definition of the MD group (selection bias); (c) the use of appropriate tasks or tests for assessment of the cognitive domains considered (detection bias); (d) incomplete outcome data about cognitive functions (attrition bias); (e) selective outcome reporting in the discussion (reporting bias), and (f) other risks of bias.
The quality of the studies was categorized with an unclear/low/high risk of bias for each item ("0" for a low risk of bias, "1" for a high risk of bias, "Unclear" otherwise). For

Data Collection and Quality Assessment
The selection of articles was independently conducted by two researchers; a supervisor resolved any doubt. The data of the 46 articles included in this systematic review were extracted according to the PICOS approach [50]. The following information was extrapolated: author(s) and year of publication; study design; characteristics of participants (gender, mean age); tests used to assess intelligence; instruments, and criteria adopted to define the group with MD, cognitive domains assessed and results. Moreover, the number of measurements carried out over time and the cognitive domains (with related instruments) evaluated in the various follow-ups were considered for the longitudinal studies. Tables A1 and A2 in the Appendix A reports the extracted data for cross-sectional and longitudinal studies, respectively.
The results are summarized, reporting the performance differences between the MD and control group. The quality of the studies was assessed using the Cochrane Handbook for Systematic Reviews criteria [52], adapted ad hoc according to the objective of this review. For each study, the evaluated domains were: (a) selection of the sample and control of any variables that could play a role in mathematical difficulties (e.g., IQ, socioeconomic status, motivation or performance in reading tests; selection bias); (b) the use of standardized instruments to assess mathematical skills and a clear definition of the MD group (selection bias); (c) the use of appropriate tasks or tests for assessment of the cognitive domains considered (detection bias); (d) incomplete outcome data about cognitive functions (attrition bias); (e) selective outcome reporting in the discussion (reporting bias), and (f) other risks of bias.
The quality of the studies was categorized with an unclear/low/high risk of bias for each item ("0" for a low risk of bias, "1" for a high risk of bias, "Unclear" otherwise). For each study, a mean score was calculated and multiplied by 100. Then, studies were categorized into a low risk of bias (lower than 75%) or a high risk of bias (higher than 75%). Finally, if at least two items were unclear, the study was classified with an unclear risk of bias.

Studies Selection
The systematic search produced a total of 3196 records. After eliminating duplicates (N = 315) and the screening based on title and abstract, 269 articles were evaluated for eligibility, then 46 were included in the qualitative analysis, i.e., 31 cross-sectional and 15 longitudinal studies (see Figure 2).
The studies meeting the inclusion criteria were conducted from 1980 to 2021 and involved 8506 children. Participants were aged between 7 [53,54] and 11 years [44,[55][56][57][58]. The percentage of females in the studies ranged from 31.8% [38] to 83.3% [59]. In five studies, information on the participants' gender was not reported [55,[60][61][62][63]. Figure 3 shows the percentage of articles fulfilling each quality criterion assessed. All but three studies had a generally good quality, with an average risk of bias lower than 75%. The high percentage of studies with low (37.8%) or no risk (55.5%) of bias highlights the validity of this systematic review. No study reports a high risk of bias, while three studies (6.7%) showed an unclear risk of bias. All studies clearly defined the criteria for the MD group and used appropriate statistical analyses. The highest risk of bias was in the detection bias domain (27%), and was due to the assessment of cognitive functions with non-standardized tools that produced some concern of risk of bias.

Quality Assessment
Brain Sci. 2022, 12, x FOR PEER REVIEW 6 of 37 each study, a mean score was calculated and multiplied by 100. Then, studies were categorized into a low risk of bias (lower than 75%) or a high risk of bias (higher than 75%). Finally, if at least two items were unclear, the study was classified with an unclear risk of bias.

Studies Selection
The systematic search produced a total of 3196 records. After eliminating duplicates (N = 315) and the screening based on title and abstract, 269 articles were evaluated for eligibility, then 46 were included in the qualitative analysis, i.e., 31 cross-sectional and 15 longitudinal studies (see Figure 2).
The studies meeting the inclusion criteria were conducted from 1980 to 2021 and involved 8506 children. Participants were aged between 7 [53,54] and 11 years [44,[55][56][57][58]. The percentage of females in the studies ranged from 31.8% [38] to 83.3% [59]. In five studies, information on the participants' gender was not reported [55,[60][61][62][63]. Figure 3 shows the percentage of articles fulfilling each quality criterion assessed. All but three studies had a generally good quality, with an average risk of bias lower than 75%. The high percentage of studies with low (37.8%) or no risk (55.5%) of bias highlights the validity of this systematic review. No study reports a high risk of bias, while three studies (6.7%) showed an unclear risk of bias. All studies clearly defined the criteria for the MD group and used appropriate statistical analyses. The highest risk of bias was in the detection bias domain (27%), and was due to the assessment of cognitive functions with non-standardized tools that produced some concern of risk of bias.

Characteristics of Selected Studies
The characteristics of selected studies are organized into two subsections: characteristics of cross-sectional and longitudinal studies. The mean age of children with MD ranged from 7 to 11 years. The most represented age group was 9 years, considered in 12 out of 31 studies (38.7%) [59,[64][65][66][67][68][69][70][71][72][73][74]. Two studies did not report the mean age of the sample, but the participants were recruited in primary school classes; therefore, they fall within the age range of our interest [31,75].

Characteristics of Selected Studies
The characteristics of selected studies are organized into two subsections: characteristics of cross-sectional and longitudinal studies. The mean age of children with MD ranged from 7 to 11 years. The most represented age group was 9 years, considered in 12 out of 31 studies (38.7%) [59,[64][65][66][67][68][69][70][71][72][73][74]. Two studies did not report the mean age of the sample, but the participants were recruited in primary school classes; therefore, they fall within the age range of our interest [31,75].
The instruments used for the initial assessment of mathematical skills, i.e., for defining groups with MD, are reported in the Supplementary Materials (Table S1). Table S1 also includes the mathematical domains assessed and the cut-offs applied to define children with MD.

Characteristics of Longitudinal Studies (N = 15)
Each longitudinal study included at least one assessment in the first-grade primary school and the definition of MD according to at least two assessments of math achievement.
The studies assessed intelligence using either the Raven's Colored Progressive Matrices (CPM) [63,81,82], Raven's Standard Progressive Matrices (RSPM) [83], Vocabulary and Matrix Reasoning subtests of the Weschler Intelligence Scale for Children (WISC-III) [84,85], the Weschler Abbreviated Scale for Intelligence (WASI) [38,86], the Receptive Vocabulary subtests and the Drawing with Cubes of the WPPSI-III [62]. Other studies used two intelligence measurements, i.e., CPM and some subtests of WISC-III [87] or WASI [88][89][90], at two different points in the study. Finally, a study evaluated verbal IQ through the PMA battery [91], while in the Mazzocco and Grimm study [92], the test used is not specified, but an IQ higher than 80 is reported in the participants.
The instruments and criteria used to assess mathematical skills and their persistence, i.e., for defining groups with MD, are reported in the Supplementary Materials (Table S1).

Results on Cognitive Functioning (N = 46)
The studies included in this systematic review refer to developmental dyscalculia (N = 5), mathematic learning disabilities (N = 13), MD (N = 19), or mathematical disability (N = 9) to consider conditions that appear similar. Notably, the use of these terms was not clearly influenced by the cut-off criteria used to define the severity of mathematical deficit. To report the results of the studies, we chose to refer more generally to mathematical difficulties. In such a way, we included both children who performed well below average (e.g., 10 • percentile) and those performing at or below the 35th percentile (e.g., less restrictive criteria).
The studies that evaluated the difference between groups with and without MD considered the following cognitive domains: processing speed (N = 22), short-term (N = 13) and long-term memory (N = 2), attention (N = 9), executive functions such as working memory (N = 32), cognitive flexibility (N = 7), inhibition (N = 8), and phonological awareness (N = 4). The results will be separately presented and summarized for each cognitive domain. Table 1 summarizes the number of studies reporting worse performance in the MD group than in the control group (CG) for each cognitive domain. Table 1. Number of studies finding worse performance in the MD group than in the CG for each cognitive domain.
Thirteen studies evaluated the ability to process visual stimuli, and most of them adopted barrage tasks, i.e., visual search tasks [31,54,60,67]. Lafay and St-Pierre [59] used a coding task, while composite scores derived from barrage and coding tests were used in two other studies [58,81]. A lower accuracy in performing these pencil and paper tasks within a time limit was observed in all studies [31,54,59,67] except in Chan and Ho's study [60]. A worse performance of children with MD was also observed in a task demanding the identification of the number of dots on certain cards [72].
By contrast, no difference emerged in studies using simple reaction time (RTs) tasks [44,93] or choice RT tasks [79] to assess processing speed.
Longitudinal studies using a RAN task with color naming identified an MD group's persistent slowness even at follow-up [38,92]. Specifically, this difficulty persisted only in children classified according to the 10th percentile [38,92], while children classified with the 25th percentile were slower than the control group only until 6 years of age. One study [85] did not find a worse performance in the MD group than in the typical achievement group.
Three cross-sectional studies [54,60,61] and six longitudinal studies [81,[87][88][89][90]92] used alphanumeric stimuli and found worse performance in children with MD than in the control group. Only Donker and colleagues [47] did not observe any difference between groups in the speed of naming alphanumeric stimuli.
Furthermore, two studies [60,92] found worse performance in naming digits only in the group of younger children with MD (mean age = 8.3), but not in older ones (10 years; [60]) and at the follow-up (14 years; [92]). Murphy and colleagues [38] reported a persistent slowness in naming digits at all follow-ups (up to the third grade, 8 years) only in children with MD classified in the 10th percentile; conversely, the children classified according to the 25th percentile at the last follow-up (third grade) presented a performance equivalent to that of the control group. The slowness of naming letters and colors found in preschoolers persisted even at the follow-up when the children were ranked in the 10th percentile (in 8th grade [92]).

Synthesis of Results and Comments
Processing speed could be assessed with several tasks requiring abilities involved in relatively simple cognitive tasks [94].
This systematic review highlights low processing speed for visual and verbal stimuli in children with MD in most studies (Table 1). Specifically, in visual processing, these difficulties were manifest in the execution of visual search tasks that required the participant to identify the target stimulus among other distractors as quickly as possible [31,54,67] or when the task consisted in reproducing symbols associated with single numbers or letters [81]. The only study that used a composite score (barrage and coding tasks) identified a worse performance in children with MD than in the control group [58]. The same difficulty occurred in the numerosity processing task [72], demanding that participants process the numerosity of the elements represented on a map and quickly calculate the solution. It seems interesting to note how these pencil-and-paper tasks were more sensitive to identifying any difficulties in children with MD (with respect to the control group) than studies using simple RTs as an indicator of processing speed. RTs did not identify differences between children with and without MD [44,79,93], regardless of the cut-off scores and the screening measures used to define the experimental group.
In the Rapid Automatized Naming tasks, children with MD have greater difficulty, mainly linked to a slow execution compared to the control group, regardless of the type of stimulus presented [38,47,54,61,81,87,89,90,92]. However, in Chan and Ho's study [60], only younger children with MD were slower in naming a series of pictures, while this difference disappeared when the older group was considered.
In the longitudinal studies, in which the group of participants with MD was classified according to the persistence of the difficulties, a slower performance in processing-speed tasks persisted only in children classified using a cut-off at the 10th percentile [38,92].

Short-and Long-Term Memory (N = 12)
Among the 12 studies that evaluated verbal short-term memory, most of them did not report worse performance in the MD group compared to the control group [57,59,67,69,71,76,80,84,91,93,95]. These studies used stimuli words [57,69,71,90], non-words [95], or numbers [57,59,67,69,71,76,80,84,91,93]. In order to verify whether the type of stimulus can influence the performance of children with MD, some studies compared their performance in digit and letter [80] or word span tasks [57,67,69,71,91]. The results did not highlight differences based on the type of stimulus proposed [67,71,80,91]. Other authors [57,69] found a worse performance in children with MD exclusively in digit span tasks and not in word span tasks. Webster [55] confirmed this finding regardless of the nature (visual or verbal) of the stimulus and the type of response (written or verbal).
Visuospatial short-term memory was evaluated in four studies. Three studies found no difference between the groups with and without MD using the Corsi Block test Forward [59,69,93], while Szucs and colleagues [71] observed worse performance in children with MD using a Dot Matrix task.
Long-term memory was analyzed in its verbal component only in two studies. Reimann and colleagues [80] found no difference in the ability to recall a story among children with and without MD, while children with MD performed worse on a semantic fluency task [31].

Synthesis of Results and Comments
Nine out of twelve studies evaluating short-term verbal memory found worse performance in children with MD than the control group in tasks that used numbers, letters, words, or non-words as stimuli (Table 1). Only three studies using the Digit Span Forward did not identify differences between the two groups.
All of the studies that analyzed verbal memory have presented the stimuli requiring a verbal response. Webster's study [55] assessed whether the performance of children with MD could depend on the modality of presentation and recall of the stimuli, and found that children with MD recalled more elements when they had to reproduce them verbally than in a graphic-symbolic way; the opposite trend occurred in children with adequate mathematical skills [55].
Concerning the short-term visuospatial memory, the Corsi Block task did not highlight differences between children with and without MD [59,69,93].
Long-term memory has been evaluated only in its verbal component. Using a semantic fluency task, the performance was worse in children aged 8 years with MD; this finding did not occur in children of 10 years or older [31]. However, Reimann and colleagues [80] did not find differences between groups requiring children to recall a story after a latency period.

Attention (N = 9)
Attention was assessed in nine studies. One of them observed the worst performance in children with MD than the control group in divided attention tasks (e.g., dual-task) that required participants to read a sentence or an operation on the computer screen and remember the last word or the result [57].
Children with MD also seem to show greater difficulty in selective attention tasks, in which they were asked to identify elements with a given characteristic, ignoring irrelevant information [80]; this task also implies processing speed. Willcutt and colleagues [58] observed a greater number of omissions in children with MD than in the control group in an 18-minute task in which they were required to press a button when the number "9" appeared immediately after the number "1". With a similar task using images rather than numbers, Kuhn and colleagues [79] observed only a greater number of false alarms in children with MD than in the control group. Worse performance in attentional tasks also emerged in the Cai and colleagues' study [44], who assessed this ability through expressive attention (e.g., Stroop task), number detection (e.g., visual search), and receptive attention (e.g., determining whether the letters presented were physically the same or if they have the same name). Finally, four studies evaluated attention through the Strengths and Weaknesses of ADHD and Normal Behavior (SWAN) administration and reported higher scores in the inattention subscale [31,54,65,89] and hyperactivity/impulsivity scale [64] in children with MD, compared to the control group.

Synthesis of Results and Comments
Most of the included studies observed a worse performance in attentional tasks (Table 1); children with MD presented difficulties in both vigilance/sustained attention tasks [58,79] and those evaluating selective attention in a limited time [80]. Moreover, higher inattention ratings were detected through SWAN in the MD group.

Executive Functions Working Memory (N = 32)
Twenty-one studies assessed verbal working memory and fourteen assessed visuospatial working memory. Five studies evaluated working memory according to the Baddeley model [96].
Concerning verbal working memory, fourteen studies found significantly lower scores in children with MD, compared to the control group, both in Digit Span Backward tasks [31,44,54,[58][59][60]69,70,76,83,84,91,95], and in Word Span Backward tasks [69,79,91]. A significant difference also emerged in the Listening Span task [67] and Sentence Digit task [56] in which the participant was required, respectively, to recall the last word of a sentence pronounced by the experimenter after having given a judgment of its truthfulness, and to recall the number of the street/address pronounced by the investigator. However, controlling for the number of intrusions, any difference in performance disappeared in the Listening Span task [91]. However, the difference persisted in the Listening Span completion task, which required the participant to recall the words he/she used to complete some incomplete sentences. Five studies did not observe a different performance between the two groups using the Listening Span test [71], the Digit Span Backward [82,93], the Word Span Backward [90], or a composite score derived from the number of correct responses in an Auditory Digit Sequence and a Semantic Categorization test. In this task, the participant recalled an address and placed a series of words in the correct semantic category [74].
Out of eight longitudinal studies evaluating working memory, five referred to the Baddeley model [81,[87][88][89][90] and identified a worse performance of children with MD compared to the control groups both in the tasks evaluating the phonological loop and in those assessing the central executive. Even in Cai and colleagues' study [44], in which the central executive was assessed through the Stop-Signal and the Flanker tasks, children with MD performed worse than the control group. Only one study [85] did not find a difference between groups using a task that requires participants to recall, in the correct serial order, a sequence of words while managing an interferential task (e.g., deciding whether each presented word was an animal or not).
Concerning the results in tasks measuring the visuospatial sketchpad, two studies reported a worse performance in children with MD [88,89], while three did not detect any difference [81,87,90] although they used the same tool (WMBT-C).
Out of the 14 cross-sectional studies evaluating visuospatial working memory, nine identified a significant difference between groups with and without MD in visuospatial working memory [44,56,60,69,71,73,74,78,79]. The visuospatial memory tasks proposed to the participants were different. Some used the Mapping and Direction task [56,74], requiring the participant to memorize the symbols found on a path and then recall them. In other studies, different versions of the Visual Matrix task [74,79] or the Spatial Span [69,78] were used, in which the participants were required to recognize in which spaces of a grid (Visual Matrix span, Dot Matrix, Nine-grid task) or a figure (Spatial Span and Odd One Out) the dots were previously shown. In other cases [60,73], the child had to recognize the figures previously shown among distractors, while in the Cai and colleagues' study [44], the 2-back task was proposed, in which the child must press a button if the figure appearing on the screen was the same as that shown one or two times before.
On the other hand, five studies, using the Corsi Block Recall Backward test [59,69,70,84,93]. Furthermore, one study [80], using a subtest of IDS (recognition of tridimensional figures), did not confirm any difference between children with and without MD.

Inhibition and Interference Control (N = 8)
Four studies used the Color-Word Stroop task [4,57,58,77], and only one of them [58] observed a worse performance in children with MD than in the control group.
Worse performance in children with MD emerged using the Number Inhibition task [57,74], while no differences were observed employing the Numerical Stroop task [53].
Poorer performance in children with MD than in the control group was reported with the Stop-Signal task [58,71], which requires participants to inhibit an automatic response (press a button when targets appeared) in the presence of a given stimulus (alert sound). Children with MD also had a higher number of false alarms in the Visual Continuous Performance (CPT) task in which they were required to press a button when a "9" appeared immediately after a "1" [58]. The difficulty of children with MD in cognitive control tasks was also confirmed by Cai and colleagues [44].
The only study using the Go/No-Go task [68] did not find more impaired inhibition in children with MD than the control group. Equally, Censabella and Noël [77] did not find a different performance in children with MD and in the control group in a task requiring suppression of irrelevant information from working memory or performing a Flanker task.

Cognitive Flexibility (N = 7)
Within the four cross-sectional studies evaluating cognitive flexibility, two [71,74] observed a worse performance in children with MD than the control group in a Trail Making test (TMT).
Willcutt and colleagues [58] found that children with MD made more perseverative errors in the Wisconsin Card-Sorting test (WCST). However, Kuhn and colleagues [79] did not observe any difference between children with and without MD using a PC-based flexibility task.
Three longitudinal studies [38,62,86] adopted composite tasks involving different executive functions (e.g., working memory, inhibition, cognitive flexibility). Specifically, two studies [38,86] used the Contingency Naming test (CNT) that required children to name the stimulus according to one attribute (e.g., color or form, based on the stimulus congruence) or two-attribute (color or form based on the stimulus congruence and the presence/absence of an arrow) rules. In the first assessment (e.g., 1st grade), the MD group defined by a 10 • cut-off showed less efficient performance than the control group on the one-attribute subtest [38,86], while the MD group defined by a 25 • cut-off did not [38]. Regarding the two-attribute subtest, Murphy and colleagues [38] assessed MD performance only in 4th grade, showing the worst performance in both MD groups (defined by the 10 • or 25 • percentile), while Mazzocco and Kover [86] did not analyze this subtest, because only one child with MD completed the subtest on the first assessment.
The worst performance in children with MD was also observed in the Chu and colleagues' study [62], adopting the Conflict Executive Function Scale, which required participants to place cards inside two boxes based on different rules (congruence or incon-gruence of the stimuli; color or shape; color or shape based on the presence/absence of the border on the card).

Synthesis of Results and Comments
The number of studies finding a different performance between MD and CG groups on each executive function are summarized in Table 1. In general, children with MD presented a critical performance in visuospatial working memory tasks [44,56,60,69,71,73,74,78,79]. Nevertheless, it is interesting that such difficulties emerged in many tasks, but not when the Corsi Block task was used [59,69,70,93]. This finding suggests that this task may not be sensitive in identifying specific difficulties in visuospatial working memory in children with MD. Concerning other executive functions, children with MD were generally impaired in tasks evaluating cognitive flexibility [58,71,74], inhibition of automatic responses, interference control (i.e., the Stroop Task or its "numerical" variants), and attentional control (i.e., the dual-tasks independently from the numerical nature of the stimuli; [57]). Only Kuhn and colleagues [79] did not identify any difference using a Choice Reaction Times task.
One study observed worse performance in phonological awareness assessed through a composite score, including both deletion (phoneme deletion from a word or a non-word) and manipulation of phonemes (move the first phoneme of a word to the end and then add a sound [58]). The study of Slot and colleagues [61] found a worse performance of the MD group than the control group when the task required participants to delete the onset, middle, or last sound from a word (e.g., phonemic deletion task). No differences between the groups with and without MD were found in tasks that required switching the first sound of two given words [61], removing a sound (syllables or phonemes) varying in position [54], or identifying the initial phoneme [63].

Synthesis of Results and Comments
These few studies, including phonological processing and awareness assessment, indicate mixed results ( Table 1). The lack of homogeneity between the tasks proposed does not allow inferences.

Discussion
The purpose of this review was to identify the cognitive skills involved in MD. Finding general skill deficits in children with MD would be advantageous in clinical assessment because it could help recognize children with specific mathematic learning disabilities. During the diagnostic process, an assessment of cognitive skills is already recommended [97,98], but there is no agreement on which skills should be of greatest interest.
This review highlights that children with MD have greater difficulties than matched controls in several measures of processing speed, working memory, inhibition, and cognitive flexibility.
In particular, the difficulties related to the processing of visual stimuli are more manifest in tasks requiring visual and perceptual discrimination, such as in visual search tasks [31,44,54,67,72] or coding tasks [44,59]. By contrast, children with MD are no slower than children without MD in responding to visual stimuli, as shown by studies using simple reaction time tasks to assess processing speed [44,79,93]. Therefore, their impairment would not depend on the ability to respond promptly to a stimulus, but rather on the request to process this stimulus and recognize its relevant characteristics quickly. This cognitive aspect would also imply the ability to discriminate stimuli correctly. From this point of view, a deficit in visual processing would entail difficulty discriminating between numbers and arithmetic signs [99,100]. These difficulties would affect formal mathematic learning [101,102].
Conversely, children with MD do not appear to have verbal and visuospatial shortterm memory difficulties. However, the results concerning verbal short-term memory seem to contrast with the findings of some recent reviews, in which a worse performance of children with MD has been identified by using these tasks [29,103]. Moreover, according to some authors, children with MD would especially have difficulty in memorizing numerical information. In the studies included in this review, only two out of the eleven studies evaluating performance in verbal and numerical span tasks identify this trend in children with MD [57,69].
The limited working memory capacity of children with MD, linked to normal shortterm memory, could indicate a specific difficulty in retaining information and simultaneously performing manipulations or operations [76]. This difficulty would not emerge in tasks in which the cognitive load is lower, as in the direct memory span task, which requires passive repetition of elements [103].
Another interesting finding is the impairment in attentional control [57] and sustained attention over time [58,79] in children with MD. The difficulties in tasks requiring both verbal and visual manipulation and involving attentional processes could explain the high comorbidity between attention deficit hyperactivity disorder (ADHD) and MD [105][106][107].
Deficits in working memory and attentional control could affect mathematical performance, especially in those tasks that require multistep planning and processing of information, as occurs in the case of MD [29,108].
Children with MD present normal inhibition abilities when assessed through the classic Stroop task [57,71,74,77] or the Stroop task using numbers [53]. However, they show greater difficulties in solving the Number Inhibition tasks [57,74]; in fact, they ignore the presented number, indicating only the quantity of digits (e.g., in the presence of the stimulus "444", they may say: three, referring to the number of digits rather to the quantity indicated by the number). An inhibition difficulty also emerged in the Stop-Signal task that requires participants to inhibit a response (press a button) previously made automatically [44,58,71]. This impairment appears evident in some typical errors that children with MD commit in retrieving arithmetic tables [109,110]. However, the inhibition could also be linked to suppressing ineffective strategies in favor of new, more efficient strategies, revealing high cognitive flexibility [111]. In fact, children with MD have more difficulty changing their response based on the demands of the context [38,58,62,71,74], and this difficulty could affect children's ability to perform complex mathematical calculations in which it is necessary to go from one procedure (e.g., subtraction) to another (e.g., multiplication).
Furthermore, slowness in Rapid-Naming tasks appears to be a common feature in children with MD [47,54,58,60], as it shares with arithmetic some basic processes, such as the rapid retrieval of phonological representations from long-term memory [112]. However, when compared to alphanumeric RAN, the results appear to be mixed. According to Donker and colleagues [47], alphanumeric RAN would mainly involve phonological processing ability, but this skill was not examined in depth in their study. The only study that evaluated phonological processing and Rapid Naming [58] observed worse performance of children with MD in both tasks, supporting Donker's hypothesis.
In non-alphanumeric RAN, children with MD showed worse performance, presumably because it involves elements related to the conceptual and perceptual processing of objects and the ability to use the verbal and visual code interactively [47,113]. Furthermore, it involves the retrieval of semantic information [114]. Therefore, non-alphanumeric RAN requires additional processes compared to alphanumeric RAN, in which children with MD could be specifically and uniquely compromised [47]. On the other hand, other authors [115] found that visual processes, such as visual discrimination, visual problem-solving (e.g., reasoning tasks with matrices), and attention are central in non-alphanumeric RAN tasks.
Words have both a semantic and a phonological representation in the mental lexicon. Letters have phonological representations, but they do not have a meaning [116]. Therefore, the naming of letters activates mainly phonological access; conversely, naming an image requires semantic access. Phonological and semantic accesses are two separate mechanisms that could independently contribute to mathematical skills. Specifically, the difficulty in non-alphanumeric RAN tasks could reflect difficulty integrating the visual-perceptive information (the image of the stimulus) with its semantic representation. It could also be interesting to verify whether children with MD have a specific difficulty in the RAN of numbers, reflecting the same difficulty of symbolization present in the RAN of pictures.
Consequently, the core deficit in children with MD could be linked to visual-perceptual discrimination and rapid scanning of visual information; this impairment would undoubtedly explain the difficulties in visuospatial working memory and perhaps those in verbal working memory.
This finding, combined with those concerning visuospatial skills, would support the hypothesis of a "visual system" [21] necessary to organize and manipulate the information involved in the procedural knowledge that allows good math performance.

Limitations
Some cautions must be considered when interpreting the results of the present review. First, some limitations concern the definition of the mathematical deficit itself. On the one hand, there is no agreement on which term better describes this condition [117,118]. On the other hand, the standardized measures to assess math achievement do not evaluate all the numerical, mathematical, and arithmetic domains that could be compromised in specific learning disabilities in mathematics. Moreover, there is no full consensus about the cut-off criteria for MD or DD diagnoses. Consequently, different cut-off points and various standardized tests are used across studies. These different methodological approaches might determine the presence of heterogeneous samples. By including only studies that assess intelligence we aimed to control for the potential effect of low intellectual ability on mathematical skills. This precaution made it possible to exclude that the poor performances in mathematics could depend on a general intellectual deficit.
Another aspect that must be considered concerns the potential role of factors, such as language, that appears to be predictive of mathematical learning [119,120]. Most of the studies analyzed in this work did not evaluate linguistic skills and did not define the MD group based on both linguistic and mathematical performance. For this reason, we could not analyze the potential role of linguistic skills on MD, and this remains to be carried out in future research.
Another important aspect to consider is the high variability of the tests used to evaluate the different cognitive domains, which prevented a meta-analysis of the results. Consequently, a limitation of this review is the lack of a quantitative analysis that would have given greater force to the inferences through effect-size analyses. In fact, the qualitative analysis does not consider the power of rejection of the null hypothesis; therefore, it is impossible to distinguish studies with different rejection power. The tests used to evaluate cognitive functions certainly represent a crucial problem because they include a pool of many different aspects. For example, if we consider attention, it refers to a multi-component system (see Petersen and Posner's model; [121]), including qualitatively differentiated aspects of attention, such as social attention (e.g., [122]) that presents a critical performance in other developmental disorders (e.g., [123]). Furthermore, mathematical difficulties could be associated with critical interactions between attentional systems rather than with an impairment of a single attentional system (e.g., vigilance, selective attention, etc.). Therefore, it would be useful to use tasks such as the Attentional Network test (ANT; in the versions suitable for children, e.g., [124][125][126]), which can simultaneously assess the efficiency of attentional systems and their interactions. This suggestion is supported by the fact that the ANT is also sensitive to highlighting attentional deficits in other neuropsychological disorders (e.g., [127]).
One additional limit could be publication bias. Some methodological choices allowed the definition of rigorous inclusion criteria for the studies, which lead to not analyzing any grey literature. The choice to include only academic articles published in peer-review journals may have limited the selection only of those studies that have obtained results in line with the literature.

Conclusions
Mathematical performance implies a series of numerical and mathematical skills that are strictly linked to some general cognitive abilities that, if impaired, may have a cascading effect on math learning. This systematic review aimed to identify the most impaired cognitive functions in school-age children with MD. Despite some variability in the tests used to evaluate the various cognitive domains, the main findings revealed poor executive function performance, such as inhibition, flexibility, working memory, and processing speed. These domains should be assessed when a disorder is suspected, in order to support the potential diagnosis and provide an ad hoc treatment.
Furthermore, this review highlights the need to develop a standardized protocol to assess this specific mathematical learning disability. This protocol should consider many mathematical skills representing this complex domain, including formal and informal competencies and general domain abilities such as working memory, processing speed, and executive functions. Mathematical difficulties can be specific to a mathematical domain or represent the outcome of difficulties in other cognitive domains. Defining these domains can make it possible to verify whether mathematical difficulties result from a specific cognitive deficit (e.g., working memory, attention, etc.). In this case, it would be possible to distinguish children with specific deficits in the mathematical area and children for whom mathematical difficulties depend on deficits in other cognitive domains. In the first case, rehabilitation interventions could directly address mathematical skills; in the second case, they might at least initially address the cognitive domain impaired.

Open Challenges and Research Directions
The present work has shed some light on the cognitive abilities that are most impaired in children with mathematical difficulties. Still, some critical issues remain open. First, some cognitive domains, such as long-term memory and phonological awareness, have received scant attention; further studies are needed to understand their role in mathematical learning and difficulties. Second, a future systematic review could investigate the role of language on different mathematical domains, to better understand how linguistic skills support each mathematical domain. Finally, some cognitive abilities appear to be compromised independently of the severity of the mathematical difficulties, suggesting that these competencies could support mathematical learning. However, it might be interesting to focus on each cognitive ability to understand whether their impairment affects all mathematical skills or just a specific one.

Supplementary Materials:
The following are available online at https://www.mdpi.com/article/10 .3390/brainsci12020239/s1, Table S1: Tools, domains, and criteria used to define the group with MD in included studies.