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10.1371/journal.pone.0310525
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Cognitive correlates of math abilities in autism spectrum disorder
Cognitive correlates of math abilities in autism
https://orcid.org/0000-0002-1690-0105
Tonizzi Irene Conceptualization Data curation Visualization Writing – original draft Writing – review & editing *
Usai M. Carmen Conceptualization Project administration Supervision Writing – review & editing
Department of Educational Sciences, University of Genoa, Genoa, Italy
Mandolesi Laura Editor
University of Naples Federico II: Universita degli Studi di Napoli Federico II, ITALY
Competing Interests: The authors have declared that no competing interests exist.

* E-mail: irene.tonizzi@edu.unige.it
16 9 2024
2024
19 9 e031052515 3 2024
27 8 2024
© 2024 Tonizzi, Usai
2024
Tonizzi, Usai
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

The purpose of the current study was to investigate the contribution of different cognitive processes to specific math abilities in students with autism spectrum disorder (ASD) and typically developing (TD) students. The study involved a group of students with ASD without intellectual disabilities (n = 26) and a group with TD students (n = 52). The two groups aged from six to 20 years old and were matched for age, sex ratio and visuospatial reasoning. To assess math abilities, four math tasks were administered: arithmetic facts, mental calculation, mathematical inferences and math problem solving. Concerning cognitive processes, participants were tested on vocabulary, verbal working memory, visuospatial working memory, response inhibition and interference control. The group with ASD showed lower scores on all specific math measures than the TD group; cognitive processes differently contributed to diverse math abilities, and vocabulary and verbal working memory were stronger associated to specific math abilities in the group with ASD than in the TD group. The current results suggest that students with ASD had lower math abilities that are generalized to different math tasks. Implications for research and clinical assessment and intervention were discussed.

The author(s) received no specific funding for this work. Data AvailabilityAll relevant data are within the manuscript and its Supporting Information files.
Data Availability

All relevant data are within the manuscript and its Supporting Information files.
==== Body
pmcIntroduction

Previous literature suggested that children with ASD without intellectual impairment may show relative weaknesses in certain subdomains of mathematics [1, 2]. Deficits in inhibitory control (IC) and working memory (WM), found in previous studies and meta-analyses [3–5] may account for the discrepancy among students with ASD that show average or above-average level of intellectual functioning but difficulties in some mathematics areas. In the literature on typical developing, recent studies suggested that the contribution of IC and WM may differ across different components of mathematical learning [6–8]. However, the relationship between IC, WM and specific math competencies remained quite unexplored in children with ASD [9].

Understanding the relative points of strength and weakness in mathematical learning in children with ASD and investigating to what extent IC and WM contributed to these abilities may be of fundamental importance to deepen our knowledge of learning processes in ASD and improve educational strategies for these children.

Math abilities in autism spectrum disorder

Autism spectrum disorder (ASD) is a neurodevelopmental condition characterized by challenges in social communication and the presence of restricted or repetitive behaviors, interests, or activities. These characteristics are seen across diverse cultural, racial, ethnic, and socioeconomic backgrounds status [10]. The last edition of both diagnostic manuals, DSM-5 and ICD-11, highlighted the high heterogeneity of ASD, which arises from different levels of symptoms, intellectual and linguistic abilities, and the presence of comorbidities [11]. They also distinguished between ASD with or without intellectual disabilities and functional language impairment, with ICD-11 that even provided different diagnostic codes. In addition, in ICD-11, it is acknowledged that some individuals with ASD may not show evident social challenges and distress in childhood, as their ability to adapt to various contexts requires exceptional effort; thus, the core features of ASD may only become fully apparent in adolescence or adulthood when social demands surpass their capacities. The new approach proposed by ICD-11 highlighted the importance of better understanding the features associated with autism, even in children, adolescents, and adults who do not have cognitive disabilities, but whose difficulties imply a significant effort to adapt to social contexts [12]. Concerning academic achievement, it is worth to note that a significant group of students with ASD without concurrent intellectual disability still struggle to achieve their full potential in educational settings without proper support [1].

Understanding their academic strengths and weaknesses is vital, especially since many are in regular education settings, and this is even true for STEM disciplines that have a high impact on academic and professional career [13, 14]. However, research on math achievement in individuals with autism is limited; this gap may be due to the idea supported by the "male brain theory" that people with autism have a preference for rule-based fields and have exceptional math abilities; however, evidence for this is mostly anecdotal [15, 16].

In fact, only a small proportion of individuals with ASD display exceptional mathematical talents and mathematical challenges appear to be more prevalent among students with ASD compared to their typically developing (TD) peers [17, 18]. However, research on math achievement in ASD is limited and often yields inconsistent results [1]. Some studies suggest better math abilities in students with ASD than in their TD peers [19, 20], while others show the opposite outcomes [21, 22]. A previous meta-analysis showed a significant small-to-medium difference between the two groups in the performance of math tasks [23], in contrast with the stereotype of increased mathematical proficiency among individuals with ASD, which has been supported by some descriptive studies [15, 16].

In terms of strengths and weaknesses within the specific domain of mathematics, a part of literature suggested that children with ASD tend to excel in fact-based math, such as recalling arithmetic facts, but struggle with more complex math tasks, including solving word problems and equations [1, 2, 24, 25]. Recent studies also indicate that students with ASD perform worse in problem-solving tasks compared to computation tasks, which is not seen in typically developing or ADHD groups [22, 26]. However, a previous meta-analysis found that the difference between participants with ASD and TD did not vary with the type of math task, suggesting that students with ASD show similar performance on different math tasks [23]. However, it’s important to note that this result was based on an analysis of the two most commonly used tasks, which are numerical operations and problem solving, and did not allow for an exploration of other math domains that may involve different processes and knowledge; for example, a still underexplored domain is represented by arithmetic facts, that require a factual mathematical knowledge that can be more easily automatized, compared to mathematical conceptual knowledge implied, for example, in mathematical reasoning tasks [6].

Also, domain-general cognitive processes play a significant role in explaining differences in math performance between students with ASD and TD peers. While intellectual functioning has consistently been linked to math achievement in TD students [e.g., 27] the relationship between intelligence and math performance in students with ASD is less clear. The aforementioned meta-analysis suggested that Verbal IQ plays a significant moderating role in the relationship between IQ and math performance in participants with ASD [23]. This finding aligns with earlier research indicating that verbal subtests on tests like the WISC-III and WISC-IV have stronger associations with academic achievement than performance subtests [28]. Additionally, research has suggested that early atypical language development in ASD may lead to the use of less efficient strategies in verbal problem-solving tasks [22, 29].

Notably, recent studies and reviews have also proposed that, in addition to intellectual functioning, impairments in working memory (WM) and inhibitory control (IC) may affect mathematics achievement in students with ASD.

Working memory, inhibitory control and math abilities in autism spectrum disorder

According to recent meta-analyses, children with ASD may show significant impairments in both WM [5, 30] and IC [4, 31]. Working memory is the ability to actively elaborate the material in mind by adding new information and, for example, allows children to keep in mind and update data in mental calculations [6]. IC is the ability to suppress automatic responses and ignore distracting stimuli to perform alternative behaviors; it is necessary, for example, in the selection of data when irrelevant information is present in the text of a problem or in suppressing an overlearned strategy in favor of a less dominant response [32]. The relative strengths and weaknesses in certain mathematics skills, in conjunction with their difficulties in WM and IC suggested specific connections between these cognitive processes and mathematics in children with ASD. However, despite the extensive literature on WM and math skills in TD children [6, 33, 34], relatively little is known about this relationship in autism [20, 22, 35–37]. Some studies have suggested that WM impairments, especially in the verbal and central components, plays a fundamental role in predicting mathematics performance in ASD, both in computation and problem-solving tasks [22, 38]. Interestingly, Wang and coauthors [39] suggested that WM impairment in preschool may represent the main cause of later math difficulties in autism, suggesting that strong early WM may help children with ASD catch up with their peers in math. Differently, a measure of response inhibition (i.e., Day/Night Stroop) was not a significant predictor of early math abilities in this sample of preschoolers. Also, in a study conducted by Polo-Blanco and co-authors [40] with older children, inhibition was not a significant predictor of math problem solving when the entire sample of participants with ASD was considered. However, poorer performers (i.e., children who obtained ≤ 25% correct answers) showed lower scores in inhibition, theory of mind and verbal comprehension. Interestingly, the authors also found a connection between the degree of abstraction employed in their strategies during the resolution of math problem and three cognitive factors: inhibition, cognitive flexibility, and theory of mind. Surprisingly, this correlation was found only in the sample of children with ASD and absent among the non-ASD group. Notably, both studies used a response inhibition measure, while to our knowledge, no previous study investigated the effect of interference control on math abilities in participants with ASD, although previous research have suggested that the ability to filter out distractors may be more related to mathematical learning [8, 32]. In addition, studies addressed the role of WM and IC adopted math problem solving [40] and numerical operation [22] without considering other math abilities. Thus, a detailed investigation of the contribution of specific cognitive processes to different math knowledge in students with ASD is needed.

Theoretical framework

Studies focusing on typical development suggested that the contribution of working memory and inhibition may differ across specific components of math ability [6–8]. To investigate in depth the math profile and the cognitive underpinning of math abilities in students with ASD, as compared with TD participants, it is necessary to consider both the multidimensionality of math abilities and the specific contribution of domain-general processes. In this regard, the model proposed by Cragg et al. [6] for identifying the cognitive correlates of math abilities in typical development could be helpful to better understand these associations also in autism. In fact, the authors [6] considered math abilities as a multidimensional construct that involve three types of math knowledge: factual knowledge (i.e., the ability to retrieve arithmetic facts from long term memory), procedural skills (i.e., the ability to both know which procedure to follow and complete the appropriate steps to arrive at the correct answer, for example in resolving arithmetic word problems or mental calculations) and conceptual knowledge (i.e., ability to understand the mathematical principles or relationships that underlie the targeted concept, for example the understanding of the properties of the operations). The model indicated that WM contributed to all math knowledges, whereas IC was associated with factual knowledge and procedural skill [6]. Based on recent literature [17, 24], it could be hypothesized that students with ASD may encounter more difficulties in procedural and conceptual understanding, than in factual knowledge. In addition, math tasks that require complex procedural skills and the understanding of abstract math concept could be more challenging for students with ASD and they may rely more on IC and WM. According to previous studies, verbal working memory may play an important role in math abilities in both participants with ASD and TD [22, 23]. However, it is also possible that visuospatial WM could explain a portion of the difference between the ASD and TD groups in math achievement; for example, visuospatial WM could play an important role in decomposition strategies in solving numerical operations but also in generating the mental representation of math word problems [6]. For this reason, studies assessing the contribution of visuospatial WM in participants with ASD are needed. The contribution of IC to math abilities was less clear in TD students [6, 41] and rarely addressed in studies with participants with ASD; in addition, these studies adopted only response inhibition tasks and not interference control tasks [39, 40]. In addition to WM and IC, also verbal intellectual abilities may impact on specific math abilities, especially in participants with ASD, in line with the hypothesis that WM and verbal IQ may account for a significant portion of variability in math performance in students with ASD [22, 38, 42].

In summary, there is a need to investigate the mechanisms by which cognitive processes supports math achievement in students with ASD, as compared with TD students, adopting a multidimensional approach that investigate the specific contribution of cognitive processes to different math abilities.

The present study

The first aim of the current study was to investigate whether the group with ASD shows poorer math abilities than the TD group. As reported above, studies on this issue often showed heterogeneous results [1, 17]. with some studies that found poorer math abilities in autism [22, 43] others reporting no differences [44], and still others finding better math abilities in participants with ASD [19, 20]. A previous meta-analysis [23]. showed a statistically significant difference with a small-to-medium effect size between the two groups, with a poorer math performance in students with ASD. However, previous studies generally used one or two math tasks (mainly numerical operations and math problem solving) and, generally did not include other types of math skills, such as arithmetic facts [e.g., 22, 36]. As some studies suggested that students with ASD could encounter more difficulties in more abstract and complex math tasks that mainly required conceptual knowledge [24, 25] we investigated math abilities in group with ASD and in a TD group, using different tasks intended to measure specific types of math knowledge. Therefore, we adopted a battery of math tasks that included arithmetic facts, mental calculation, mathematical inferences and math problem solving tasks. It is conceivable that the participants with ASD showed more difficulties in the last two tasks (mathematical inference and math problem solving) as they are more complex tasks, requiring more conceptual knowledge than the other two tasks; in fact, arithmetic facts mainly measured factual knowledge and mental calculations mainly measured procedural math knowledge, together with factual knowledge [6].

The second aim of the study was to examine the contribution of domain-general cognitive processes to math abilities. Therefore, we investigated which cognitive processes among vocabulary, verbal and visuospatial WM, response inhibition and interference control contributed to specific math abilities, and if this association differed between the two groups. The previous meta-analysis highlighted the role of verbal working memory on explaining group’s differences between the two group, but the role of visuospatial working memory and inhibitory measures remained quite unexplored [20, 40]. In summary, the study aimed to answer to the following research questions:

Are there differences between the group with ASD and the TD group in specific math abilities? Are there relative areas of strength (e.g., arithmetic facts and mental calculations) and areas of weakness (e.g., mathematical inferences and math problem solving)?

Which cognitive processes contributed to specific math abilities, over and above vocabulary? Does this contribution differ between the group with ASD and the TD group?

Method

Participants

The study involved a group of participants with ASD and a comparison group of TD participants, composed of children, adolescents and young adults. Concerning the inclusion criteria, participants of both groups had to be over six years and scored at or above the average (Scaled Score ≥ 8) on the Matrix Reasoning subtest of the WISC-IV or the WAIS-IV. The choice to use a sample with an age older than six years is due the fact that, at this age, the two dimensions of IC should already be distinguished, although still under development [45]. Concerning the group with ASD, all participants had a previous formal diagnosis of ASD according to the criteria of the Diagnostic and Statistical Manual of Mental Disorders, 5th edition or 4th edition, Text Revision or International Classification of Diseases 10th edition or 11th edition. This formal diagnosis was confirmed by a score above the ASD cut-off (T-score > 60) on the Italian version of the Social Responsiveness Scale, Second edition (SRS-2 [46]) and a score above the ASD cut-off on the Childhood Autism Rating Scale, Second Edition (CARS-2 [47], ASD cut-off corresponds to a score above 28 in the CARS-2-High Functioning Version and above 30 in the CARS-2-Standard Version). Concerning the TD group, only participants without any previous diagnosis and with a T-score < 60 in the SRS-2 were included.

As for the ASD group, 33 participants joined the study; however, only 26 participants were included. In fact, seven of them were excluded because they did not meet the inclusion criteria (n = 3 excluded due to the lack of a formal diagnosis of ASD; n = 4 excluded due to a scaled score on the Matrix Reasoning subtest ≤ 8). As for the control group, 62 participants joined the study, but we had to exclude from the statistical analysis 10 participants because five of them did not meet the inclusion criteria (n = 4 had a previous diagnosis of Learning Specific Disorder, n = 1 had a previous diagnosis of Attention-deficit/hyperactivity disorder) and the other five have only completed the first session.

Therefore, the final sample was composed of 78 participants (n = 26 for the group with ASD and n = 52 for the TD group). As shown in Table 1, the two groups were matched for age and visuo-perceptual reasoning measured with the Matrix Reasoning subtest; however, they significantly differed in the Vocabulary subtest (WISC-IV or WAIS-IV), where the TD group obtained higher score than the ASD group. Moreover, concerning other cognitive variables, the two groups significantly differ in visuospatial working memory (Mr. Peanut) but not in verbal working memory (Backward digit span, BDS); a significant difference between the two groups was also found in the response inhibition task (Matching Familiar Figure tasks, MFFT) in both errors and RTs, and in the accuracy in the interference control task (Flanker task).

10.1371/journal.pone.0310525.t001 Table 1 Age and cognitive measures of the group with ASD and the TD group.

	ASD group	TD group			
	N	M	SD	Min	Max	N	M	SD	Min	Max	t test	Cohen’s d	
Age	26	11.99	3.21	6.41	19.12	52	12.41	3.58	7.18	19.53	t(76) = 0.50, p = .618	0.12	
Matrix Reasoning	26	12.35	2.86	8.00	17.00	52	12.25	2.47	8.00	18.00	t(76) = -0.15, p = .878	-0.04	
Vocabulary	26	10.23	3.34	2	15	52	11.85	2.65	6	19	t(76) = 2.32, p = .023	0.56	
BDS	26	6.88	2.14	3	13	52	7.75	1.86	4	12	t(76) = 1.84, p = .069	0.44	
Mr. Peanut	22	6.32	2.88	3.00	13.00	51	8.12	2.70	3.00	16.00	t(71) = 2.56, p = .013	0.65	
MFFT errors	25	8.28	6.93	0	24	50	4.86	3.96	0	18	t(73) = -2.72, p = .008	-0.67	
MFFT RT	25	27.49	12.38	11.82	58.83	50	20.55	10.47	7.47	56.59	t(70) = -2.47, p = .016	-0.62	
Flanker AI	22	0.90	0.10	0.60	1.00	48	0.96	0.05	0.77	1.00	t(68) = 3.34, p = .001	0.86	
Flanker RTI	22	1063.44	394.71	513.97	1813.17	48	943.07	333.03	427.50	1925.35	t(68) = -1.32, p = .190	-0.34	

Procedure

The study began on 1st December 2020, and concluded on 8th January 2023.As the study started during the COVID-19 pandemic, the tasks were adapted to be administered online. This modality was used for the entire duration of the study to avoid possible effects due to administration mode. Each participant was tested individually during online video calls. Specifically, the tasks were administered in three online sessions: the first session included vocabulary, matrix reasoning and backward digit span; the second session included Matching Familiar Figures task, Mr. Peanut and Flanker task and the third session included four math tasks. All the tasks requiring visual materials were administered using screen sharing (Matrix Reasoning, Vocabulary, Matching Familiar Figures task). For Mr. Peanut and Flanker tasks a computerized version was used, administered through Inquisit Web. in these cases, the links were sent to participants, and they were asked to share their screen during the task. For participants with ASD, an additional in-person session was included to administer the CARS-2 that required the direct observation of participants’ behavior. Parents of each participant were asked to complete the SRS-2.

Measures

Vocabulary and visuospatial reasoning measures

Vocabulary subtest and Matrix Reasoning of the WISC-IV [48] were administered to participants between the ages of 6 and 16 years and the same subtests of the WAIS-IV [49] were administered to participants over 16 years. Scaled scores were used.

Vocabulary (VC). It is an important indicator of Verbal Comprehension Index and measures participants’ verbal fluency and concept formation, word knowledge, and word usage. In this subtest, participants are asked to define a given word. Scaled score ranged from 1 to 19. The WISC-IV Vocabulary subtest [48] was administered to participants between the ages of six and 16 years and the WAIS-IV Vocabulary subtest [49] was administered to participants over 16 years. Scaled scores were used (range 1–19).

Matrix Reasoning (MR). It is an untimed core subtest of Perceptual Reasoning Index that measures visual processing and abstract, spatial perception. Participants are shown colored matrices or visual patterns with a missing piece. The participant is asked to select the missing piece from five alternatives. The WISC-IV Matrix Reasoning subtest [48] was administered to participants between the ages of six and 16 years and the WAIS-IV Matrix Reasoning [49] was administered to participants over 16 years. Scaled score were used (range 1–19).

Working memory measures

Backward digit span (BDS; [48, 49]). The Backward digit span task requires the participant to repeat numbers in reverse order. There is no time limit for the participant to respond, but the examiner reads each number out aloud at the rate of one number per second. The task is composed of eight levels with increasing difficulty; each level was composed of two items and the number of digits to remember increases by one every level from two to nine digits. One point was given for each correct trial (Backward digit span, expected range 0–16). The WISC-IV Backward Digit Span [48] was administered to participants between the ages of six and 16 years and the WAIS-IV Backward Digit Span [49] was administered to participants over 16 years. Row scores were used (range 0–16).

Mr. Peanut. This task is considered a measure of visuospatial WM [50, 51]. We used a computerized version of this task. Participants were shown a character, Mr. Peanut, with a number of coloured stickers attached to different parts of his body (e.g., on the right leg, on the nose, etc.) for five seconds. Then, Mr. Peanut disappeared and reappeared without stickers. The participants had to indicate the position and the colour of the stickers as they were presented in the previous figure. There are three items per level (from 1 to 7 stickers). An item is scored as correct if the participants select the correct coloured stickers and locate them in the correct body parts. If a level is successfully mastered (at least one correct attempt per level), participants move up a level. If all 3 attempts per level fail, the test concludes. Test-retest reliability (Pearson’s r) calculated in 75 TD children was .39, p < 0.001) [52]. The total of correct items was registered (Mr. Peanut, expected range 0–21).

Inhibitory control measures

Matching Familiar Figure task (MFFT; adapted from [53]). This task is considered a measure of response inhibition because the participant is required to control the tendency to respond before evaluating which is the correct picture. In this task, a target figure and five alternatives below were shown, and the participant had to select among the five alternatives, which are quite similar to the target, the one that is identical to the target. The task involves five alternatives and is comprised of two practice items and 20 experimental items; for each item, the number of errors (the number of times in which the participant pointed at a wrong picture) was recorded (MFFT errors, expected range 0–100); in addition, the RT for the first response in each trial was recorded (MFFT RT). The test–retest reliability reported for this task in a sample of primary school children was .49 [53].

Flanker task. This task is considered a measure of interference control. We used a computerized version of the task where stimuli and procedures were similar to those used in previous studies [54, 55]. Participants completed a series of items in which they were shown five fish in one horizontal row and are instructed to pay attention to the fish in the middle, which is the target fish. On each trial, they were asked to respond as quickly as possible as to whether the target fish was looking to the left or right, pressing the left or the right bottom respectively. The other four fish flanking the middle fish (the flankers) can either look in the same (compatible) or the opposite direction (incompatible) as the target fish. The target fish was always located in the same location (i.e., the centre of the display) on every trial. For each trial, stimuli were presented until a response was made or until more than 3000 ms elapsed. Each trial was presented after 1500 ms. After an intertrial interval of 1500 ms, a new trial was presented. If a participant responded in less than 200 ms, this was considered an anticipatory error in line with Christ [54]. Children completed two practice blocks of 20 items each (in the first practice block, the target fish was presented alone, while in the second practice block the target fish and the four flanking fish were shown). After these two practice blocks, children completed a total of 120 experimental items (60 compatible and 60 incompatible items) that were randomly intermixed. At intervals of 40 items, children were offered a one-minute break. The proportion of correct responses and the response times in the incongruent and congruent items were recorded. Regarding response times, we only considered RT in the correct items (Flanker accuracy, expected range 0–1; Flanker RT, expected range-200-3000 ms). Split-half reliability ranged from 0.34 to 0.42 was reported in a sample of adolescents [56].

Mathematical measures

To assess specific math abilities, we used four types of tasks (arithmetic facts, mental calculation, inferences and math problem solving) taken from Italian standardized mathematical batteries chosen according to the age of participants. Arithmetic facts and mental calculation can be administered to the entire age range of our sample, whereas inferences and math problem solving were not available for participants of high school and university. As the number of item and the level of difficulty varied with age, z scores were used for all math tasks.

Arithmetic facts (AC-MT 3 [57] for primary and middle school students; MT-3 Advanced Clinical, [58] for high school students; LSC-SUA [59] for participants over 19 years)

This test assesses the ability to memorize and retrieve arithmetic facts (i.e., whether the participant already has the information available in memory and can access it without performing calculation procedures). Participants are orally presented with simple operations, to which they must respond as quickly as possible, within three seconds. Each item can only be repeated once. The number of items and the level of difficulty vary based on the corresponding school grade. Test-retest reliability (Pearson’s r) calculated in 215 TD primary and middle school students was .91. The total score was the number of correct items within time limit, transformed into z scores according to test norms for each school grade.

Mental calculation (AC-MT 3 [57] for primary and middle school students; MT-3 Advanced Clinical [58] for high school students; LSC-SUA [59] for participants over 19 years)

This task assesses the child’s ability to apply mental calculation strategies to arrive at the correct result of an operation. Participants are required to mentally solve operations presented orally, within 30 seconds. Each item can only be repeated once. Test-retest reliability (Pearson’s r) calculated in 211 TD primary and middle school students was .80 The total score was the number of correct items within time limit, transformed into z scores according to the standardized norms for each school grade.

Inferences (AC-MT 3 [57])

This test investigates the partecipant’s ability to perform inferential mathematical reasoning, their understanding of mathematical symbols, and the degree of automation of arithmetic procedures and fundamental principles. The subtest is divided into three different tasks. The first one required to solve calculation with figures (e.g., in the operation “flower + flower = 8”, the participant has to understand that one flower is equivalent to 4). In the second task, the participant had to add the missing mathematical symbol in numerical operations. In the last, the third task, there are two operations: one complete, while in the other the result is missing. Students were required to complete the calculation using the second operation as an aid. The total time available for the subscale was two minutes, one minute for the first type of the task and one minute for the other two tasks. Test-retest reliability (Pearson’s r) calculated in 198 TD primary and middle school students was .69. The total score was the number of correct items within time limit, transformed into z scores according to the standardized norms for each school grade.

Math problem solving (AC-MT 6–11, [60]; AC-MT 11–14 [61])

In this task participants had to solve arithmetic word problems, presented in a written form. During the task, they were able to write the resolution on a paper. Five math problems were administered to primary students (from 3rd to 5th grade) and ten math problems were administered to middle school students; the time limit for this task was 40 minutes for primary school and 30 minutes for middle school. Cronbach’s alphas between .68 to.73 were reported in samples of primary school students. For each solution, one point was given if both the procedure and calculation were correct, and 0.5 point was given if only the procedure was correct. Z scores calculated according to the standardized norms for each school grade were used.

Analytic strategy

All the analyses were performed with Jamovi software, version 2.3.18. Descriptive statistics and zero-order correlations among math measures were computed. To assess groups’ differences in math measures (research question a), a t-test for each math ability was conducted to compare the group with ASD and the TD group. Then, we investigated the effect of group (ASD or TD) and domain-general cognitive processes on specific math abilities and examined if the contribution of cognitive processes varied according to the group (research question b). To this end, we first investigated zero-order correlations (Pearson) between cognitive processes and specific math abilities. Math abilities variables were expressed in z scores, as different items were administered to different school age. To take the participants different ages into account, we calculated residual scores for each cognitive process running a series of regression analysis with age as predictor and raw score of each cognitive process as dependent variable [62, 63]. To determine the contribution of group and each cognitive process to specific math abilities, a series of hierarchical linear regression analyses were conducted; each math ability was used as dependent variable, whereas the independent variables were included in two three blocks: group (ASD or TD) and vocabulary in the first block, residual scores of cognitive processes (included one by one in separate regressions) in the second block, while the interaction between group and the cognitive processes was added in the third block. Before running the analysis, we verified that all the necessary assumptions of regression were met, and then, when evaluating the models, we verified there were no collinearity problems (tolerance values were greater than .50, VIF < 2, and condition indices were less than 4.2; Durbin-Watson values ranged from 1.5 to 2.2).

Results

Group differences on specific math abilities (research question a)

Table 2 showed the descriptive statistics (N, mean, SD, minimum and maximum) of mathematical measures for the group with ASD and the TD group. The numerosity were lower for inferences and math problem solving as these tasks were administered to participants from the second (inferences) or third grade (math problem solving) of primary school to the third grade of middle school. To assess group differences on each math ability, a t-test was conducted to compare the group with ASD and the TD group. As shown in Table 2, the group with ASD showed lower scores on all the math measures, with a large effect size (Cohen’s d).

10.1371/journal.pone.0310525.t002 Table 2 Specific math abilities of the group with ASD and the TD group.

	ASD group	TD group			
Task	N	M	SD	Min	Max	N	M	SD	Min	Max	t test	Cohen’s d	
Arithmetic facts	24	-1.63	1.22	-3.50	1.09	52	0.18	0.71	-1.35	1.36	t (74) = 8.12 ***	2.00	
Mental Calculation	24	-1.33	1.12	-2.71	1.17	52	0.34	0.88	-1.73	1.81	t (74) = 7.05 ***	1.74	
Inferences	21	-1.66	1.22	-2.84	1.71	34	0.17	0.88	-1.91	1.55	t (53) = 6.41***	1.78	
Math problem solving	18	-1.58	0.99	-2.53	1.37	27	-0.17	0.92	-1.46	1.58	t (43) = 4.91 ***	1.49	
Note: ASD = autism spectrum disorder; TD = Typical Development; M = mean; SD = Standard Deviation

*p < .05

**p < .01

***p < .001.

Zero order (Pearson) correlations between math abilities and domain-general cognitive processes

Table 3 showed zero-order (Pearson) correlations between specific math abilities and domain-general processes. High correlations among all math measures were found, with values ranging from 0.58 to 0.85.Most cognitive variables were statistically significant correlated with all considered specific math abilities; in particular, vocabulary, VWM, VSWM, MFFT errors, Flanker AI, were significantly correlated with Arithmetic Facts, Mental Calculation, Mathematical Inferences and Math Problem Solving. No significantly correlations were found between between RT indices of inhibitory measures (MFFT RT, Flanker RTI) and math abilities.

10.1371/journal.pone.0310525.t003 Table 3 Zero-order (Pearson) correlations among specific math abilities and domain-general cognitive processes.

	Arithmetic Facts	Mental Calculation	Mathematical Inferences	Math Problem Solving	
Arithmetic Facts		0.77***	0.85***	0.69***	
Mental Calculation		-	0.66***	0.58***	
Mathematical Inferences			-	0.78***	
Matrix Reasoning	0.22	0.17	0.17	0.29*	
Vocabulary	0.39 ***	0.27*	0.36**	0.54***	
BDS	0.35**	0.44***	0.36**	0.46**	
Mr. Peanut	0.27*	0.39**	0.38**	0.37*	
MFFT errors	-0.25*	-0.33**	-0.28*	-0.41**	
MFFT RT	-0.17	-0.13	-0.12	-0.03	
Flanker AI	0.29*	0.32**	0.49***	0.44**	
Flanker RTI	-0.05	-0.13	-0.08	-0.01	
Note: MR = Matrix Reasoning; VC = Vocabulary; BDS = Backward digit span; MFFT errors = number of errors on Matching Familiar Figures Task; MFFT RT = reaction time on Matching Familiar Figures Task; Flanker AI = Flanker accuracy on incongruent items; Flanker RTI = Flanker reaction time on incongruent items

*p < .05

**p < .01

***p < .001.

Contribution of group and cognitive processes on specific math abilities (research question b)

As shown in Table 4, a series of hierarchical linear regression analyses were conducted with each math ability used as dependent variable. For each dependent variable, the following regression were conducted:

in the first hierarchical linear regression, the contribution of group and vocabulary was investigated, including them as independent variable in the first step and interaction between the two included in the second step;

in the other hierarchical linear regressions, group and vocabulary (here used as a covariate as the two groups significantly differed on this measure) were included as independent variable in the first step; residual scores of cognitive processes (included one by one in separate regressions) were included in the second step; the interaction between group and the cognitive process was added in the third step. In these analyses, we did not include as predictors the cognitive variables that were not significantly correlated with any math ability.

10.1371/journal.pone.0310525.t004 Table 4 Hierarchical linear regression analysis.

		Arithmetic facts	Mental Calculation	Inferences	Math problem solving	
	F(3,72) = 28.75
p < .001, R2 adj = 0.53
R2Δ = 0.03***	F(3,72) = 21.31
p < .001, R2 adj = 0.45
R2Δ = 0.06**	F(3,51) = 14.60
p < .001 R2 adj = 0.43
R2Δ = 0.01	F(3,41) = 11.51
p < .001 R2 adj = 0.42
R2Δ < .001	
	IV	b	SE	β	b	SE	β	B	SE	β	b	SE	B	
Block 1	Group	-1.65	0.22	-1.34 ***	-1.60	0.25	-1.30 ***	-1.69	0.30	-1.24 ***	-1.05	0.30	-0.90**	
	Vocabulary	0.09	0.04	0.21 *	0.04	0.04	0.09	0.06	0.05	0.14	0.12	0.04	0.35**	
Block 1&2	Group	-3.36	0.77	-1.27 ***	-3.92	0.84	-1.21***	-2.58	1.12	-1.23*	-0.87	1.08	-0.91	
	Vocabulary	0.02	0.04	0.05	-0.05	0.05	-0.13	0.02	0.07	0.05	0.13	0.07	0.37	
	Group*Vocabulary	0.16	0.07	0.39 *	0.22	0.07	0.52**	0.08	0.09	0.18	-0.02	0.09	-0.05	
	Arithmetic facts	Mental Calculation	Inferences	Math problem solving	
	F(4,71) = 29.39
p = < .001, R2 adj = 0.60
R2Δ = 0.09***, 0.03*	F(4,71) = 19.51
p = < .001, R2 adj = 0.59
R2Δ = 0.11***, 0.01	F(4,50) = 17.31
p = < .001, R2 adj = 0.55
R2Δ = 0.09**, 0.04*	F(4,40) = 14.10
p = < .001, R2 adj = 0.55
R2Δ = 0.10**, 0.03	
	IV	b	SE	B	b	SE	B	B	SE	B	b	SE	Β	
Block 1	Group	-1.65	0.22	-1.34 ***	-1.60	0.25	-1.30 ***	-1.69	0.30	-1.24 ***	-1.05	0.30	-0.90 **	
	Vocabulary	0.09	0.04	0.21 *	0.04	0.04	0.09	0.06	0.05	0.14	0.12	0.04	0.35 **	
Block 1&2	Group	-1.52	0.21	-1.24 ***	-1.48	0.23	-1.20 ***	-1.55	0.28	-1.15 ***	-0.96	0.28	-0.82 **	
	Vocabulary	0.07	0.03	0.18 *	0.02	0.04	0.06	0.06	0.04	0.13	0.11	0.04	0.30 *	
	VWM	0.21	0.05	0.31 ***	0.22	0.06	0.32 ***	0.24	0.08	0.30**	0.22	0.07	0.32 **	
Block 1&2&3	Group	-1.58	0.20	-1.24 ***	-1.51	0.23	-1.20 ***	-1.72	0.28	-1.16 ***	-1.12	0.28	-0.85 ***	
	Vocabulary	0.06	0.03	0.15	0.02	0.04	0.04	0.03	0.04	0.08	0.09	0.04	0.26 *	
	VWM	0.10	0.07	0.15	0.16	0.08	0.24 *	0.08	0.10	0.11	0.07	0.11	0.10	
	Group*VWM	0.24	0.10	0.36 *	0.13	0.12	0.19	0.32	0.15	0.41 *	0.27	0.14	0.39	
	Arithmetic facts	Mental Calculation	Inferences	Math problem solving	
	F(4,66) = 20.50
p = < .001, R2 adj = 0.54
R2Δ = 0.04*, 0.01	F(4,66) = 15.36
p = < .001, R2 adj = 0.45
R2Δ = 0.05*, 0.02	F(4,46) = 14.08
p = < .001, R2 adj = 0.51
R2Δ = 0.03, 0.01	F(4,36) = 8.98
p = < .001, R2 adj = 0.44
R2Δ = 0.01, 0.04	
	B	SE	Beta	B	SE	Beta	B	SE	Beta	B	SE	Beta	
Block 1	Group	-1.74	0.23	-1.43 ***	-1.69	0.26	-1.37 ***	-1.88	0.29	-1.41 ***	-1.11	0.32	-0.94 **	
	Vocabulary	0.08	0.04	0.18 *	0.03	0.04	0.07	0.06	0.05	0.13	0.14	0.05	0.35 *	
Block 1&2	Group	-1.61	0.23	-1.32 ***	-1.53	0.26	-1.24 ***	-1.69	0.31	-1.27 ***	-1.00	0.34	-0.85 **	
	Vocabulary	0.07	0.04	0.16	0.02	0.04	0.04	0.06	0.05	0.12	0.14	0.05	0.34 *	
	VSWM	0.10	0.04	0.20 *	0.11	0.05	0.23 *	0.11	0.07	0.17	0.06	0.07	0.12	
Block 1&2&3	Group	-1.53	0.23	-1.26 ***	-1.44	0.26	-1.17 ***	-1.65	0.32	-1.24 ***	-0.97	0.33	-0.81 **	
	Vocabulary	0.07	0.04	0.15	0.01	0.04	0.03	0.06	0.05	0.13	0.14	0.05	0.36 *	
	VSWM	0.06	0.05	0.13	0.07	0.05	0.14	0.05	0.10	0.07	-0.06	0.10	-0.11	
	Group*VSWM	0.12	0.09	0.25	0.16	0.10	0.33	0.12	0.13	0.19	0.22	0.13	0.42	
														
		Arithmetic facts	Mental Calculation	Inferences	Math problem solving	
		F(4,68) = 20.43
p = < .001, R2 adj = 0.52
R2Δ = < .001, 0.01	(4,68) = 15.48
p = < .001, R2 adj = 0.45
R2Δ = 0.01, 0.02	F(4,47) = 14.07
p = < .001, R2 adj = 0.50
R2Δ = 0.01, 0.03	F(4,37) = 9.03
p = < .001, R2 adj = 0.44
R2Δ = 0.03, 0.01	
		B	SE	Beta	B	SE	Beta	B	SE	Beta	B	SE	Beta	
Block 1	Group	-1.68	0.23	-1.36 ***	-1.57	0.25	-1.28 ***	-1.79	0.30	-1.31 ***	-1.02	0.31	-0.86 **	
	Vocabulary	0.09	0.04	0.22 *	0.06	0.04	0.15	0.07	0.05	0.16	0.14	0.05	0.37 **	
Block 1&2	Group	-1.64	0.23	-1.32 ***	-1.52	0.25	-1.24 ***	-1.73	0.30	-1.26 ***	-0.90	0.32	-0.76 **	
	Vocabulary	0.09	0.04	0.20 *	0.05	0.04	0.12	0.06	0.05	0.13	0.12	0.05	0.33 *	
	MFFT	-0.02	0.02	-0.07	-0.02	0.02	-0.08	-0.03	0.03	-0.10	-0.05	0.03	-0.20	
Block 1&2&3	Group	-1.66	0.23	-1.30 ***	-1.55	0.25	-1.20 *	-1.84	0.30	-1.26 ***	-1.01	0.34	-0.78 **	
	Vocabulary	0.09	0.04	0.21 *	0.06	0.04	0.14	0.06	0.05	0.14	0.12	0.05	0.33 *	
	MFFT	0.02	0.03	0.08	0.05	0.04	0.19	0.03	0.04	0.14	-0.01	0.05	-0.05	
	Group* MFFT	-0.06	0.04	.0.25	-0.11	0.05	-0.25	-0.10	0.05	0.38	-0.05	0.07	-0.21	
		Arithmetic facts	Mental Calculation	Inferences	Math problem solving	
		F(4,63) = 18.50
p = < .001, R2 adj = 0.52
R2Δ = 0.01, 0.01	F(4,63) = 13.6
p = < .001, R2 adj = 0.43
R2Δ = 0.01, 0.01	F(4,44) = 17.18
p = < .001, R2 adj = 0.57
R2Δ = 0.04*, 0.01	F(4,35) = 10.7
p = < .001, R2 adj = 0.50
R2Δ = 0.04, 0.01	
		B	SE	Beta	B	SE	Beta	B	SE	Beta	B	SE	Beta	
Block 1	Group	-1.74	0.23	-1.42 ***	-1.76	0.26	-1.42 ***	-1.91	0.30	-1.39 ***	-1.13	0.32	-0.94 ***	
	Vocabulary	0.08	0.04	0.18 *	0.02	0.04	0.04	0.07	0.05	0.15	0.14	0.05	0.37 **	
Block 1&2	Group	-1.65	0.24	-1.35 ***	-1.67	0.27	-1.34 ***	-1.61	0.32	-1.17 ***	-0.87	0.34	-0.72 *	
	Vocabulary	0.08	0.04	0.18 *	0.02	0.04	0.03	0.08	0.05	0.17	0.15	0.05	0.39 **	
	Flanker	1.90	1.60	0.11	1.91	1.77	0.10	3.85	1.76	0.23 *	3.26	1.77	0.23	
Block 1&2&3	Group	-1.65	0.24	-1.33 ***	-1.67	0.27	-1.33 ***	-1.65	0.32	-1.20 ***	-0.92	0.34	-0.78 *	
	Vocabulary	0.07	0.04	0.16 *	0.01	0.04	0.02	0.07	0.05	0.15	0.14	0.05	0.37 **	
	Flanker	0.05	2.44	-0.03	0.21	2.72	0.01	0.83	3.41	0.05	0.03	3.95	< ..001	
	Group* Flanker	4.20	3.25	0.23	2.96	3.62	0.16	4.10	3.98	0.25	4.04	4.41	0.29	
Note: VWM = Verbal Working memory (Backward digit span); VSWM = visuospatial working memory (Mr. Peanut), MFFT = number of errors on Matching Familiar Figures Task; Flanker AI = Flanker accuracy on incongruent items

*p < .05

**p < .01

***p < .001

Contribution of group and cognitive processes on arithmetic facts

In the following hierarchical linear regression analyses, arithmetic facts were used as dependent variable.

Contribution of group and vocabulary to arithmetic facts. The first regression model, with group and vocabulary as independent variable in the first step, explained 50% of variance and both the variable were significantly predictors. In the second step, the inclusion of interaction between vocabulary and group significantly improved the amount of explained variance; the final model explained 53% of variance and showed that the association between vocabulary and arithmetic facts was stronger in the group with ASD than in the TD group.

Contribution of group, vocabulary and VWM to arithmetic facts. VWM, entered as independent variable in the second step, was a significant predictor and significantly improved the amount of explained variance compared to the first step in which only group and vocabulary were included. The interaction between group and VWM in the third block was also a significant predictor and improved the amount of explained variance. The final model explained 60% of variance and showed that the association between VWM and arithmetic facts was stronger in the group with ASD than in the TD group.

Contribution of group, vocabulary and VSWM to arithmetic facts. Also VSWM, entered as independent variable in the second step, was a significant predictor and significantly improved the amount of explained variance, compared to the first step in which only group and vocabulary were included. The interaction between group and VSWM in the third block was not a significant predictor and did not improve the amount of explained variance. The final model explained 54% of variance and showed that the association between VSWM and arithmetic facts was similar in the two groups.

Contribution of group, vocabulary and inhibitory measures to arithmetic facts. Either the inhibitory measures, i.e., MFFT errors and Flanker AI, and their interaction with group were not significantly predictors of arithmetic facts and did not significantly improve the amount of explained variance.

Contribution of group and cognitive processes on mental calculation

In the following hierarchical linear regression analyses, mental calculation was used as dependent variable.

Contribution of group and vocabulary to mental calculation. The first regression model, with group and vocabulary as independent variable in the first step, explained 39% of variance and only group, but not vocabulary, was a significant predictors; in the second step, interaction between vocabulary and group was a significant predictor and improved the amount of explained variance. The final model explained 45% of variance and showed that the association between vocabulary and mental calculation was stronger in the group with ASD than in the TD group.

Contribution of group, vocabulary and VWM to mental calculation. VWM, entered as independent variable in the second step, was a significant predictor and significantly improved the amount of explained variance compared to the first step in which only group and vocabulary were included. The interaction between group and VWM in the third block was not a significant predictor and did not improve the amount of explained variance. The final model explained 59% of variance and indicated that the association between VWM and mental calculation was similar in the two groups.

Contribution of group, vocabulary and VSWM to mental calculation. VSWM, entered as independent variable in the second step, was a significant predictor; the model explained 43% of variance and significantly improved the amount of explained variance, compared to the first step in which only group and vocabulary were included. The interaction between group and VSWM in the third block was not a significant predictor and did not improve the amount of explained variance. The final model explained 45% of variance and showed that the association between VSWM and mental calculation was similar in the two groups.

Contribution of group, vocabulary and inhibitory measures to mental calculation. Either the inhibitory measures, i.e., MFFT errors and Flanker AI, and their interaction with group, were not significantly predictors of mental calculation and did not significantly improve the amount of explained variance.

Contribution of group and cognitive processes on inferences

In the following hierarchical linear regression analyses, inferences were used as dependent variable.

Contribution of group and vocabulary to inferences. The first regression model, with group and vocabulary as independent variable in the first step, explained 42% of variance and only group but not vocabulary was a significant predictor. In the second step, interaction between vocabulary and group was not a significant predictor and did not improve the amount of explained variance. The final model explained 43% of variance.

Contribution of group, vocabulary and VWM to inferences. VWM, entered as independent variable in the second step, was a significant and significantly improved the amount of explained variance in addition to the first step in which only group and vocabulary were included. In addition, the interaction between group and VWM in the third block was also a significant predictor and significantly improved the amount of explained variance. The final model explained 55% of variance and showed that the association between VWM and inferences was stronger in the group with ASD than in the TD group.

Contribution of group, vocabulary and VSWM to inferences. VSWM, entered as independent variable in the second step, was not a significant predictor and did not improve the amount of explained variance compared to the first step in which only group and vocabulary were included. The interaction between group and VSWM in the third block was not a significant predictor and did not improve the explained variance. The final model explained 51% of variance.

Contribution of group, vocabulary and inhibitory measures to inferences. Among inhibitory measures, Flanker AI, included in the second step, was a significant predictor and improve the amount of explained variance compared to the first step in which only group and vocabulary were included. The interaction between group and Flanker AI in the third block was not significant and did not improve the explained variance suggesting that the association between Flanker and inferences was similar in the two groups. The final model explained 57% of variance.

The other inhibitory measure (MFFT errors) and its interaction with group was not significant predictor of inferences and did not significantly improve the amount of explained variance.

Contribution of group and cognitive processes on math problem solving

In the following hierarchical linear regression analyses, math problem solving was used as dependent variable.

Contribution of group and vocabulary to math problem solving. The first regression model, with group and vocabulary as independent variable in the first step, explained 41% of variance and both group and vocabulary were significant predictors. In the second step, interaction between vocabulary and group was not a significant predictor and did not improve the amount of explained variance, showing that the association between vocabulary and math problem solving was similar in the two groups. The final model explained 42% of variance.

Contribution of group, vocabulary and VWM to math problem solving. VWM, entered as independent variable in the second step, was a significant predictor and significantly improved the amount of explained variance compared to the first step in which only group and vocabulary were included. The interaction between group and VWM in the third block was not significant and did not improve the amount of explained variance and showed that the association between VWM and math problem solving was similar in the two groups. The final model explained 55% of variance.

Contribution of group, vocabulary and VSWM to math problem solving. VSWM, entered as independent variable in the second step, was not a significant predictor and did not improve the amount of explained variance in addition to the first step in which only group and vocabulary were included. The interaction between group and VSWM in the third block was not a significant predictor and did not improve the explained variance. The final model explained 44% of variance.

Contribution of group, vocabulary and inhibitory measures to math problem solving. Either the two inhibitory measures, i.e., MFFT (errors) and Flanker AI, and their interaction with group were not significantly predictors of math problem solving and did not significantly improve the amount of explained variance.

In summary, vocabulary was significantly associated to arithmetic facts, mental calculation and problem solving, but not to inferences. In both arithmetic facts and mental calculation, this association was stronger in the group with ASD. VWM was significantly associated to all the specific math abilities, and in arithmetic facts and inferences this association was stronger in the group with ASD. VSWM was associated with arithmetic facts and mental calculation and its contribution was similar in the two groups. Among inhibitory measures, Flanker AI was associated with inferences and its contribution was similar in the two groups.

Discussion

The current study aimed to examine specific mathematical abilities (research question a) and how they be influenced by domain-general cognitive processes (research question b) in a group with ASD and a TD group. The results demonstrated that the group with ASD exhibited lower performance across all mathematical tasks considered, with a comparable large effect. This supports the conclusions of a previous meta-analysis, which found no significant differences based on the type of math task [23]. In this study, it’s important to note that the task type includes not just numerical operations and math problem-solving, but also encompasses arithmetic facts and the capacity to draw mathematical inferences.

Beyond uncovering a generalized deficit across various mathematical abilities, our results offer valuable insights into understanding the processes that contribute to these abilities in both typical development and autism. Overall, our findings closely align with the model proposed by Cragg and coauthors [6]. In fact, our study identified a crucial role of verbal working memory, a significant predictor for all specific math tasks. Additionally, we examined vocabulary, which proved to be a significant predictor for all evaluated mathematical abilities, except for inferences.

Consistent with Cragg et al.’s [6] research, our study found that both verbal and visuospatial working memory play roles in arithmetic facts and calculations. Specifically, verbal working memory was linked to factual knowledge, while visuospatial working memory was associated with procedural knowledge. On the other hand, only verbal working memory was associated with tasks requiring more conceptual knowledge, like inferences and mathematical problem-solving. This finding supports the notion that working memory is crucial for accessing information stored in long-term memory, suggesting that conceptual information is predominantly stored in a verbal format [6]. Students with low verbal working memory capacity are less likely to choose a retrieval strategy in math problem solving tasks and are also likely to retrieve them less accurately [64, 65]. Arithmetic facts, though primarily conceptualized in terms of numerical information, may also incorporate a visuospatial component. This connection is likely influenced by factors such as the format of presentation or the utilization of visual aids (e.g., using charts to memorize times tables) during the encoding process [6, 66].

Notably, the current study showed that these relationships may have a different strength in the group with ASD and the TD group. In fact, in arithmetic facts and inferences the effect of verbal working memory was stronger in the group with ASD, whereas in mental calculation and math problem solving the contribution was similar in the two groups. A quite similar result was found considering vocabulary, as its contribution was stronger for the group with ASD in arithmetic fact and mental calculation, whereas was similar in the two groups in math problem solving. The fundamental role of vocabulary and verbal working memory confirmed the results from the previous meta-analysis [23] and previous studies with participants with ASD [20, 22, 35]. It is well known that language and working memory facilitates knowledge retrieval from long-term memory during mathematics performance [67]. However, in typical development, as students cumulatively build their mathematics knowledge, the direct retrieval of arithmetic facts from long-term memory can reduce cognitive load and, therefore, working memory demands [68]. Thus, when the retrieval of arithmetic facts becomes more automatic, verbal ability and working memory become less relevant. However, the current study seemed to suggest a different pattern for students with ASD; their performance on arithmetic facts was predicted by both verbal ability and verbal working memory, with a stronger association than in the TD group [67, 68]. Therefore, for students with ASD, arithmetic facts appeared to pose greater challenges and were less automatized compared to their peers. The retrieval of these facts seemed to depend more on verbal resources. Instead, the contribution of both vocabulary and verbal working memory to math problem solving was similar in the two groups. This result was in line with previous studies suggesting that the direct retrieval of general knowledge stored in long-term memory can enhance the understanding of word problems [69, 70]. The results showed that solving math problems was generally a complex ability that place high demands on working memory for both students with ASD and their TD peers.

We also examined how inhibitory control was related to specific math skills. Differently from Cragg’s model [6], we didn’t find inhibitory control contributing to arithmetic facts or mental calculation. However, it’s worth noting that in Cragg’s study, only a response inhibition task with numerical stimuli was a significant predictor, while the response inhibition task without numerical stimuli wasn’t linked to any math variables. In our study, inhibitory tasks didn’t involve numerical stimuli because it’s known that these are more closely related to math tasks [7, 32]. Additionally, unlike most previous studies, we used not only response inhibition measures but also interference control measures. This allowed us to see how the ability to filter out irrelevant stimuli supports more conceptually based math skills such as mathematical inferences. Thus, it’s possible that interference control, rather than just response inhibition, might play a significant role in certain areas of math learning [32]. Moreover, the results suggest that the association between interference control (in our case, accuracy on incongruent Flanker items) and mathematical inferences is statically significant and similar in both the group with ASD and the TD group.

Limitations and future directions

The study’s findings should be considered in light of some limitations. First, the limited sample size of the group with ASD reduces statistical power and the wide age range prevents control over confounding variables, such as varying treatment types and durations based on participant cohorts. Regarding the procedure, online administration posed challenges due to participants’ lack of appropriate technology. To ensure controlled assessment, all tasks, including computerized ones, were conducted via screen sharing. Lastly, there are limitations related to the tests used. Using only two tasks (Reason Matrix and Vocabulary) to investigate intellectual domains is a limitation due to session length. We selected the most representative tasks from these domains to avoid participants’ overwhelming. Also concerning working memory measures, it’s important to note that verbal working memory task was a digit span task and therefore the use of numerical stimuli could have increased the association with math tasks. In addition, a larger sample size would have also allowed the investigation of the contribution of each domain-general processes, while controlling for the effect of the others.

The findings of the present study also suggested practical implications. To provide effective education that enhances academic achievement in students with ASD, a deeper understanding of factors influencing individual differences in academic performance is required, considering both domain-general and domain-specific processes [26, 38, 71]. Additionally, these students benefit from general education, but they may need multidimensional assessments to pinpoint strengths, weaknesses and additional support to improve academic outcomes of students with ASD [71]. Moreover, it is crucial to translate research findings into intervention strategies. On one hand, it is essential to adopt compensatory strategies such as reducing linguistic working memory demands, facilitating task focus, creating suitable settings with the use of visual aids to support students in remembering procedures and focussing on relevant aspects. On the other hand, it’s important to implement interventions that enhance both domain-general and domain-specific processes and focus on the automatization of procedures and strategies that can reduce the cognitive load, especially for those students with difficulties in WM.

Conclusions

In conclusion, the current study suggested the importance of considering both domain-specific and domain-general aspects from a multidimensional perspective, even in the context of atypical development. Advancing toward integrating domain-general processes and domain-specific abilities is crucial in research involving atypical development to better understand these complex skills and the reasons behind the challenges faced by students with ASD.

Supporting information

S1 Data (XLSX)

10.1371/journal.pone.0310525.r001
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2024
Laura Mandolesi
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Submission Version0
23 Jun 2024

PONE-D-24-09141Cognitive correlates of math abilities in autism spectrum disorderPLOS ONE

Dear Dr. Tonizzi,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

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Laura Mandolesi

Academic Editor

PLOS ONE

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Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

********** 

2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

********** 

3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

********** 

4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

********** 

5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: First of all, I appreciate the opportunity to review the article entitled “Cognitive correlates of math abilities in autism spectrum disorder”. It's a commendable piece of work, demonstrating a meticulous and thorough methodological approach. The study's commitment to ensuring the reliability and validity of its findings is evident. Below are just some suggestions to further enhance its impact.

The introduction provides a comprehensive overview of previous literature on mathematics abilities in children with Autism Spectrum Disorder (ASD), including references to relevant studies and meta-analyses. It clearly outlines the objectives of the study, emphasizing the importance of understanding the strengths and weaknesses in mathematical learning in children with ASD and investigating the contributions of inhibitory control (IC) and working memory (WM) to these abilities. By addressing the gaps in existing research, it underscores the need for further investigation in this area.

On the other hand it presents dense information, potentially overwhelming readers and hindering clarity. Simplifying the language and condensing content could improve readability. For example, repetitive discussions on ASD heterogeneity and research limitations are evident, requiring streamlining to enhance coherence. While effectively summarizing existing knowledge, I suggest that the introduction could be strengthened by further emphasizing the contribution to knowledge of the proposed study. Explicit insights into how to fill existing gaps would strengthen its significance.

Regarding the study description, the author clearly outlines the two main aims of the study, providing context on the current state of research and the challenges encountered in analyzing mathematical abilities in children with Autism Spectrum Disorder (ASD). The methodological approach is well defined, intending to examine differences in mathematical abilities between individuals with ASD and typically developing ones through a series of specific mathematical tasks. The methods employed are robust and reflect a rigorous and accurate scientific approach to research.

However, some limitations should be highlighted, such as the representativeness of the samples and the generalizability of the results to larger populations, especially concerning the implications that these findings can have on the individualized interventions that should derive from them. I suggest delving deeper into this aspect (in the discussion or limitation section), citing some studies that highlight the difficulty of finding the most effective appropriate treatment considering the extreme phenotypic variability of autism, especially with reference to the practical and treatment implications, also in other areas of intervention, for example:

Simeoli, R., Cerasuolo, M., Nappo, R., Gallucci, M., Iovino, L., Frolli, A., & Rega, A. (2022). Examining predictors of different ABA treatments: A systematic review. Behavioral Sciences, 12(2), 267.;

Klinger, L. G., Cook, M. L., & Dudley, K. M. (2021). Predictors and Moderators of Treatment Efficacy in Children and Adolescents with Autism Spectrum Disorder. Journal of clinical child and adolescent psychology : the official journal for the Society of Clinical Child and Adolescent Psychology, American Psychological Association, Division 53, 50(4), 517–524. https://doi.org/10.1080/15374416.2020.1833735

Results and general findings are well-supported by existing literature. The study extends previous literature by highlighting the differential contributions of verbal and visuospatial working memory to various math tasks, suggesting a nuanced relationship between cognitive processes and mathematical abilities.

Overall, the manuscript provides valuable insights into the cognitive correlates of math abilities in ASD, shedding light on potential intervention targets and informing educational practices for individuals with neurodevelopmental disorders. The thorough methodology and robust statistical analyses strengthen the study's contribution to the field of cognitive psychology and autism research. However, further discussion on the implications of these findings for educational interventions and future research directions would enhance the manuscript's impact and relevance.

Reviewer #2: The article addresses the topic of math abilities in autism spectrum disorder (ASD), particularly focusing on the cognitive processes that can contribute to ASD math outcomes. This is an important topic, especially given the ongoing interest in individualized academic programs for students with neurodevelopmental disorders. However, several issues with the methods and analysis need to be addressed. Below are more specific comments by section:

Abstract

I recommend adding a short sentence regarding the theoretical framework that supports the study methods.

Introduction

The research question (a) described from lines 206 to 208 should be more detailed, explaining better what kind of differences between the ASD and TD groups the authors aimed to analyze. Besides research questions, the authors have not presented the hypothesis of the current study. It is difficult for the reader to understand the scope of the study.

Method

Regarding the method section, first, I point out that ASD participants’ diagnosis is based on DSM, ICD, SRS, and CARS, which are not gold standard measures for the diagnosis of ASD. This should be a limitation underlined in “Limitations” section.

Additionally, I recommend adding a power analysis to explain how the authors determined the sample size needed for analysis.

Third, from lines 238-242, I suggest briefly describe in narrative form (in the text) how the groups differ on the cognitive tasks mentioned.

Lastly, the method section is missing a crucial procedure: a description of how informed consent was obtained from participants and their parents, information on the ethics committee that approved the study, and a reference to the Declaration of Helsinki. I highly recommend including these details.

Analytic Strategy

From lines 377 to 380, it is reported: “To take the participants' different ages into account, we calculated residual scores for each cognitive process by running a series of regression analyses with age as the predictor and the raw score of each cognitive process as the dependent variable [62, 63].” However, it seems that these analyses are not reported in the results section.

Results

Regarding the “Zero Order (Pearson) correlations between math abilities and domain-general cognitive processes,” I recommend adding multiple corrections (e.g., Bonferroni or Holm-Bonferroni correction).

Discussions

Discussions of the study results seem complete and adequate.

General suggestions

I advise the authors to review the writing to correct some typos and to improve the flow and readability of the text.

Finally, I would ask the authors if they considered possible differences between different levels of severity of ASD (based on DSM criteria) in math abilities and the cognitive processes related to math abilities. This could be a research question for future studies.

********** 

6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: Yes: Federica Somma

**********

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

10.1371/journal.pone.0310525.r002
Author response to Decision Letter 0
Submission Version1
18 Aug 2024

PONE-D-24-09141

Cognitive correlates of math abilities in autism spectrum disorder

PLOS ONE

Dear Dr. Tonizzi,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript by Aug 07 2024 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

• A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.

• A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.

• An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Laura Mandolesi

Academic Editor

PLOS ONE

We would like to thank very much the Editor and the Reviewers for the opportunity to revise the manuscript. We are particularly grateful for this opportunity, which allowed us to improve the quality of our paper. We reported our responses below each comment. All changes were highlighted in the revised version of the manuscript.

Reviewers'comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

________________________________________

2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

________________________________________

3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

________________________________________

4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

________________________________________

5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters.

Reviewer #1: First of all, I appreciate the opportunity to review the article entitled “Cognitive correlates of math abilities in autism spectrum disorder”. It's a commendable piece of work, demonstrating a meticulous and thorough methodological approach. The study's commitment to ensuring the reliability and validity of its findings is evident. Below are just some suggestions to further enhance its impact.

The introduction provides a comprehensive overview of previous literature on mathematics abilities in children with Autism Spectrum Disorder (ASD), including references to relevant studies and meta-analyses. It clearly outlines the objectives of the study, emphasizing the importance of understanding the strengths and weaknesses in mathematical learning in children with ASD and investigating the contributions of inhibitory control (IC) and working memory (WM) to these abilities. By addressing the gaps in existing research, it underscores the need for further investigation in this area.

On the other hand it presents dense information, potentially overwhelming readers and hindering clarity. Simplifying the language and condensing content could improve readability. For example, repetitive discussions on ASD heterogeneity and research limitations are evident, requiring streamlining to enhance coherence. While effectively summarizing existing knowledge, I suggest that the introduction could be strengthened by further emphasizing the contribution to knowledge of the proposed study. Explicit insights into how to fill existing gaps would strengthen its significance.

We would like to thank the reviewer for this observation. We have revised the text to make it clearer and more concise, eliminating redundant parts and highlighting the gaps that the study aims to fill

Regarding the study description, the author clearly outlines the two main aims of the study, providing context on the current state of research and the challenges encountered in analyzing mathematical abilities in children with Autism Spectrum Disorder (ASD). The methodological approach is well defined, intending to examine differences in mathematical abilities between individuals with ASD and typically developing ones through a series of specific mathematical tasks. The methods employed are robust and reflect a rigorous and accurate scientific approach to research.

However, some limitations should be highlighted, such as the representativeness of the samples and the generalizability of the results to larger populations, especially concerning the implications that these findings can have on the individualized interventions that should derive from them. I suggest delving deeper into this aspect (in the discussion or limitation section), citing some studies that highlight the difficulty of finding the most effective appropriate treatment considering the extreme phenotypic variability of autism, especially with reference to the practical and treatment implications, also in other areas of intervention, for example:

Simeoli, R., Cerasuolo, M., Nappo, R., Gallucci, M., Iovino, L., Frolli, A., & Rega, A. (2022). Examining predictors of different ABA treatments: A systematic review. Behavioral Sciences, 12(2), 267.;

Klinger, L. G., Cook, M. L., & Dudley, K. M. (2021). Predictors and Moderators of Treatment Efficacy in Children and Adolescents with Autism Spectrum Disorder. Journal of clinical child and adolescent psychology : the official journal for the Society of Clinical Child and Adolescent Psychology, American Psychological Association, Division 53, 50(4), 517–524. https://doi.org/10.1080/15374416.2020.1833735

Thank you for the valuable suggestions. We have delved into the recommended literature and expanded the section on the limitations and implications of the study, highlighting the extreme phenotypic variability of autism and the consequent difficulty in designing individualized interventions.

Results and general findings are well-supported by existing literature. The study extends previous literature by highlighting the differential contributions of verbal and visuospatial working memory to various math tasks, suggesting a nuanced relationship between cognitive processes and mathematical abilities.

Overall, the manuscript provides valuable insights into the cognitive correlates of math abilities in ASD, shedding light on potential intervention targets and informing educational practices for individuals with neurodevelopmental disorders. The thorough methodology and robust statistical analyses strengthen the study's contribution to the field of cognitive psychology and autism research. However, further discussion on the implications of these findings for educational interventions and future research directions would enhance the manuscript's impact and relevance

Thank you, we have expanded the section on implications

Reviewer #2: The article addresses the topic of math abilities in autism spectrum disorder (ASD), particularly focusing on the cognitive processes that can contribute to ASD math outcomes. This is an important topic, especially given the ongoing interest in individualized academic programs for students with neurodevelopmental disorders. However, several issues with the methods and analysis need to be addressed. Below are more specific comments by section:

Abstract

I recommend adding a short sentence regarding the theoretical framework that supports the study methods.

Thank you for the observation. We have included the reference to the multidimensional model in the abstract

Introduction

The research question (a) described from lines 206 to 208 should be more detailed, explaining better what kind of differences between the ASD and TD groups the authors aimed to analyze. Besides research questions, the authors have not presented the hypothesis of the current study. It is difficult for the reader to understand the scope of the study.

We fully agree with the reviewer and have accordingly revised the section on research questions. Specifically, we have clarified them further and added considerations regarding the hypotheses

Method

Regarding the method section, first, I point out that ASD participants’ diagnosis is based on DSM, ICD, SRS, and CARS, which are not gold standard measures for the diagnosis of ASD. This should be a limitation underlined in “Limitations” section.

Thank you. In the limitations section, we have highlighted the importance of using standardized measures for autism, such as ADOS and ADI, in future studies

Additionally, I recommend adding a power analysis to explain how the authors determined the sample size needed for analysis.

Thank you for the suggestion. We have highlighted in the limitations section the need to replicate the study with a larger sample, especially for the group with ASD. In addition, we report here the information regarding the power analysis conducted with jPower before starting the study: considering the average effect size of 0.50 identified in the previous meta-analysis, to achieve a power of at least 0.80, 51 participants per group would have been necessary. This number was reached only in the typical development group, but not in the group with ASD. However, the size of the group with ASD could be considered adequate if we consider the maximum effect size identified by the previous meta-analysis (0.77), which would require 22 participants per group to achieve a power of 0.80.

Third, from lines 238-242, I suggest briefly describe in narrative form (in the text) how the groups differ on the cognitive tasks mentioned.

We have revised the text to briefly describe the differences between the two groups in cognitive tasks.

Lastly, the method section is missing a crucial procedure: a description of how informed consent was obtained from participants and their parents, information on the ethics committee that approved the study, and a reference to the Declaration of Helsinki. I highly recommend including these details.

Thank you for the suggestion. We have included the section on informed consent and the reference to the Declaration of Helsinki

Analytic Strategy

From lines 377 to 380, it is reported: “To take the participants' different ages into account, we calculated residual scores for each cognitive process by running a series of regression analyses with age as the predictor and the raw score of each cognitive process as the dependent variable [62, 63].” However, it seems that these analyses are not reported in the results section.

We have included these analyses in the supplementary materials and added the reference in the text (Table S1)

Results

Regarding the “Zero Order (Pearson) correlations between math abilities and domain-general cognitive processes,” I recommend adding multiple corrections (e.g., Bonferroni or Holm-Bonferroni correction).

Thank you for the comment. We have included the Bonferroni correction in the correlation table

Discussions

Discussions of the study results seem complete and adequate.

General suggestions

I advise the authors to review the writing to correct some typos and to improve the flow and readability of the text.

Finally, I would ask the authors if they considered possible differences between different levels of severity of ASD (based on DSM criteria) in math abilities and the cognitive processes related to math abilities. This could be a research question for future studies.

This is definitely an interesting observation that merits further investigation. Since it would require a larger sample size, we have included it in the limitations section.

________________________________________

6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: Yes: Federica Somma

________________________________________

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

Attachment Submitted filename: Response to Reviewers.docx

10.1371/journal.pone.0310525.r003
Decision Letter 1
Mandolesi Laura Academic Editor
© 2024 Laura Mandolesi
2024
Laura Mandolesi
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Submission Version1
3 Sep 2024

Cognitive correlates of math abilities in autism spectrum disorder

PONE-D-24-09141R1

Dear Dr. Tonizzi

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

An invoice will be generated when your article is formally accepted. Please note, if your institution has a publishing partnership with PLOS and your article meets the relevant criteria, all or part of your publication costs will be covered. Please make sure your user information is up-to-date by logging into Editorial Manager at Editorial Manager® and clicking the ‘Update My Information' link at the top of the page. If you have any questions relating to publication charges, please contact our Author Billing department directly at authorbilling@plos.org.

If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

Kind regards,

Laura Mandolesi

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

10.1371/journal.pone.0310525.r004
Acceptance letter
Mandolesi Laura Academic Editor
© 2024 Laura Mandolesi
2024
Laura Mandolesi
https://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
6 Sep 2024

PONE-D-24-09141R1

PLOS ONE

Dear Dr. Tonizzi,

I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now being handed over to our production team.

At this stage, our production department will prepare your paper for publication. This includes ensuring the following:

* All references, tables, and figures are properly cited

* All relevant supporting information is included in the manuscript submission,

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If revisions are needed, the production department will contact you directly to resolve them. If no revisions are needed, you will receive an email when the publication date has been set. At this time, we do not offer pre-publication proofs to authors during production of the accepted work. Please keep in mind that we are working through a large volume of accepted articles, so please give us a few weeks to review your paper and let you know the next and final steps.

Lastly, if your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

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Thank you for submitting your work to PLOS ONE and supporting open access.

Kind regards,

PLOS ONE Editorial Office Staff

on behalf of

Professor Laura Mandolesi

Academic Editor

PLOS ONE
==== Refs
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8 Traverso L , Tonizzi I , Usai MC , Viterbori P . The relationship of working memory and inhibition with different number knowledge skills in preschool children. Journal of Experimental Child Psychology. 2021 Mar;203 :105014. doi: 10.1016/j.jecp.2020.105014 33232915
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