Differential Contributions of Working Memory Components and Visual Attention to Young Children’s Varieties of Basic Number Processing

Differential Contributions of Working Memory Components and Visual Attention to Young Children’s Varieties of Basic Number Processing | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Differential Contributions of Working Memory Components and Visual Attention to Young Children’s Varieties of Basic Number Processing Yuhan Wang, Zihan Yang, Xiao Yu, Yue Qi, Xiujie Yang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4746725/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Previous research has found that domain-general cognitive abilities, especially working memory and visual selective attention, play crucial roles in primary children’s mathematical performance, while little is known about their roles in basic number processing in kindergarten children at earlier years. The current study investigated whether working memory components and visual selective attention would make significant contributions to children’s basic number processing. A total of 110 Chinese children ( M ± SD = 6.28 ± 0.41 years old) were examined with the phonological loop, the visuospatial sketchpad, the central executive, visual selective attention and three number processing tasks (i.e., numerosity estimation, number line estimation and numerical magnitude comparison tasks). Results revealed that the phonological loop accounted for unique variance in children’s performance on numerosity estimation, number line estimation, and numerical magnitude comparison. Both the visuospatial sketchpad and the central executive significantly contributed to numerical magnitude comparison, whereas visual selective attention explained unique variance in children’s performance of numerosity estimation and number line estimation. Our findings suggest that three components of working memory and visual selective attention have differentiated associations with varied basic number processing skills. number processing working memory visual selective attention multivariate multiple regression Figures Figure 1 Figure 2 Background Before formal mathematical education, the capacities to make sense of quantities have been shown to lay a foundation for later mathematical learning [ 1 – 3 ]. Although working memory and visual selective attention have been shown to be important for numerical skills [ 4 , 5 ], few studies have empirically addressed various early number processing abilities in relation to them. Examining the associations of working memory components and visual selective attention with basic number processing skills would contribute to the identification of children at risk of mathematics difficulties, and developing relevant training programs to support children’s early math learning. Compared to many western languages, Chinese number word system has a transparent base-10 structure; this could promote better number counting performances and better precision on number line estimation [ 6 – 8 ]. Chinese language system is more orthographic and less phonological, which may make Chinese children process numbers in different ways [ 9 ]. However, most studies conducted in mainland China mainly found how working memory and visual attention respectively related to children’s formal mathematical achievements [ 10 , 11 ], rather than how they were altogether associated with different basic number processing skills. To fill the gaps, the purpose of this present study was to investigate how components of working memory and visual selective attention would predict young children’s performance on a variety of basic number processing tasks in Chinese contexts. Varieties of Basic Number Processing Number processing, according to the triple-code model, recruits an analogical magnitude representation, a verbal word form, and a visual Arabic number form [ 12 ]. Much behavioral evidence has revealed the importance of these basic forms of number processing in children’s later mathematical achievement [ 13 , 14 ]. First, the analogical magnitude representation holds and manipulates nonsymbolic magnitudes [ 15 ]. To assess the analogical magnitude representation, the numerosity estimation task has been typically administered in young children [ 3 , 16 – 17 ]. In this task, children are shown arrays of dots or objects in a short time, and children are asked to orally report the number of dots or objects in the array (see example in [ 18 ]). To perform this task, children should employ analogical magnitude representation to hold and manipulate non-symbolic numerical information. Previous work has shown that children possess an analogical mental number line that could be nonsymbolic in nature [ 19 , 20 ], which enables their representation and manipulation of nonsymbolic numerical stimuli. With age increasing, children would map symbolic numbers onto nonsymbolic numeriosities, incorporating symbolic forms of numbers into early analogical representations. Their analogical codes of representation are relied on and further developed to help them possess an advanced level of magnitude representation. Second, in the verbal word form, numerals are represented lexically, phonologically, and syntactically; this is associated with a semantic representation of numerical quantity and much like any other type of words [ 21 ]. The verbal system of number processing could be assessed with the numerical magnitude comparison task in which children are presented with two digits and are required to say which digit is larger [ 22 – 24 ]. To solve this task, children should encode the numerical information presented visually and verbally, manipulate mental magnitudes and finally report their answer with verbal digits. To transform visual forms of Arabic numbers into verbal representations and answers, stored verbal codes of Arabic digits should be activated and employed. And given that this process also involves visual Arabic number forms, it is likely that both verbal codes and visual codes of numerical representation are involved in performing these processes. Third, in the visual Arabic number form, quantities can be automatically encoded as strings of Arabic numerals [ 21 ]. It can be assessed with the number line estimation task in which children are presented a horizontal number line and then asked to perform number-to-position or position-to-number estimations [ 25 – 27 ]. Based on evidence from typically developed participants, the number line is assumed to follow Weber’s Law, with the representation of larger numbers becoming increasingly imprecise [ 28 ]. With development, greater exposure to visual Arabic numbers in the modern mathematics education would promote transformations of numerical representational of symbolic numbers [ 25 ]. Previous results reveal that number line estimation performance in first graders on the range of 0-100 were better modelled with a logarithmic function, while students at second grade could estimate numbers within 100 by a linear scale [ 27 ]. To further illuminate how children visually represent symbolic numbers, it was also found that on the 0-1000 range second graders have difficulty representing them linearly, however, fourth graders could do so [ 25 , 29 ]. Thus, to learn symbolic mathematics fluently, children transform their logarithmic representation to a linear representation for visual symbolic numbers, starting with small ones and stretching towards larger numbers with accumulated experience with visual symbolic numbers. These three components of basic number processing could be further divided into non-symbolic and symbolic abilities, with numerosity estimation as non-symbolic and numerical magnitude comparison and number line estimation as symbolic. It is agreed that non-symbolic abilities have innate evolutionary origins, shared among human infants and other species, laying the foundation for the development of symbolic skills and later mathematical performance [ 30 ]. Symbolic abilities are characterized by integrating numerical symbolic system with non-symbolic numerosities [ 31 , 32 ], which enables performance in more complex math problem solving presented in symbolic formats. Altogether, these non-symbolic and symbolic number processing abilities are domain-specific numerical skills, focusing on representing and manipulating numerical information of various formats. Children’s later mathematical performance is facilitated by increasingly mature domain-specific numerical abilities to precisely represent non-symbolic quantities, mapping non-symbolic quantities to symbolic magnitudes, and forming a more linear representation of magnitudes. The validity of triple-code model has been partially supported and revised by recent neural evidence. There are functionally dissociated brain areas associated with each code of representation, while it is also revealed that overlapping areas in the fronto-parietal network are activated for different forms of representation [ 33 – 35 ]. This overlapping could reflect a more complex picture of the relation among three codes of representation. On the other hand, it could suggest that domain-general cognitive abilities are associated with number processing performance. When solving arithmetic problems presented in non-symbolic formats, previous studies found elicited neural activities in frontal areas, and it was suggested that this reflected involvement of working memory and attentional processes in performing visual representation of quantities [ 36 , 37 ]. Also for the verbal component, it was found that parts of the mentalizing network and hippocampus which are responsible for recognizing and retrieving numerical facts from memory systems are involved [ 33 ]. However, little behavioral evidence has showed domain-general associates with young children’s varied number processing in the framework of triple-code model. Therefore, more complex relationships across these three components of number processing could be further captured by investigating core domain-general cognitive abilities which would underlie these representations in children who are in the very process of developing their number processing skills. Working Memory Components and Basic Number Processing Our study also lies in this assumption that development of domain-specific number processing abilities is supported by domain-general cognitive development. This could be suggested by previous studies revealing that children’s domain-general cognitive abilities could significantly predict number-processing skills and later mathematical performance [ 10 , 38 , 39 ]. Among various domain-general abilities, working memory components should make unique contributions, given their storing and manipulating components that organize the representation and usage of environmental information [ 40 ]. Working memory is composed of multiple components, including the visuospatial sketchpad, phonological loop and central executive. They work together to encode environmental inputs, temporarily store messages, and combine the information to serve behavioral outcomes [ 40 ]. Phonological loop, the articulatory component in the working memory model, could be mapped onto the verbal component in the triple-code model; that general ability to store verbal information could be related to rehearsal of number-specific verbal magnitudes. Visuospatial sketchpad, on the other hand, could be related to visual and analogical components in the triple-code model, that domain-specific ability to automatically code the quantities of visual objects as strings of Arabic numerals and organize numerical magnitudes onto spatially presented number lines could be related to domain-general ability to store visuospatial inputs. Besides these representational components, central executive in the working memory model, acting with the organizing role, could facilitate manipulation of domain-specific numerical information in number processing tasks [ 41 ]. It would be interesting to see how these three working memory components would be associated with early domain-specific number processing performance. Visual Selective Attention and Basic Number Processing In the current study, we are also interested in the role of visual selective attention in domain-specific number processing. Visual selective attention, as another core domain-general ability, has been claimed to facilitate rehearsal of stored information and more efficient processing of visual information [ 42 – 45 ]. According to the Pathways model, visual attention should be very important to the symbolic number system and numerical magnitude processes [ 46 ]. As a top-down process to directly focus people on certain aspect of surrounding environments [ 45 ], visual selective attention may be especially important in children’s ability to process numerical magnitudes and manage the complex demands of mathematical tasks [ 47 ]. In LeFevre et al.’s study [ 46 ], visual attention was found to be independently associated with two early numeracy skill measures. Children who were better at visual selective attention could name written Arabic numbers more correctly and performed better on a nonlinguistic arithmetic task that requires representing and manipulating visual quantity information. The importance of visual selective attention could also be suggested by evidence that numbers and spaces are inherently interweaved in human mind representations, that children’s number line representation is predicted by spatial processing skills [ 48 , 49 ]. The Present Study The purpose of the current study was to examine the contributions of working memory and visual selective attention to basic number processing. The current study recruited children who were 5- to 8-years old as participants because this is the critical period during which children getting increasingly exposed to extensive experience with numbers, both in formal math and informal math activities [ 50 – 52 ]. In this age range, their representation of magnitudes revealed great improvements, and they formed better linear representation of integers. In the present study, three basic numeracy tasks were employed to assess children’s number-processing abilities: numerosity estimation, number line estimation, and numerical magnitude comparison. Three components of working memory (the phonological loop, visuospatial sketchpad and central executive) were separately examined by the digit recall task, visual matrix task, and Flanker task. Visual selective attention was examined by asking children to search for a specific target in limited time. Several hypotheses were proposed. First, the weak phonological representation hypothesis proposes that number processing that relates to manipulating verbal codes of quantity involves a high level of phonological processing, while nonverbal representation is not influenced by phonological skills [ 53 ]. It was therefore hypothesized that the phonological loop would be more associated with children’s performance in the numerical magnitude comparison task and number line estimation than in the numerosity estimation task. Second, according to the triple-code model [ 12 ], we would like to find significant predictions of the visuospatial sketchpad for the numerosity estimation and number line estimation tasks since a visual linear representation of numerical information can facilitate magnitude estimation performance [ 48 , 54 ]. In addition, attention to visual stimuli is engaged in visual processing of the Arabic number form [ 21 ]. We therefore anticipated that visual selective attention would be related to performance on visually presented tasks including numerosity estimation and number line estimation tasks. Methods Participants The participants were 110 children (50 girls, mean age of 6.28 years, 5.37–7.86 years old, SD = 0.41 years) from Fujian Province and Henan Province in China. They were native Chinese speakers, and all children are not diagnosed with mathematical difficulties. Most of them came from middle SES families and all had normal or corrected-to-normal vision and hearing. According to the national statistics data (National Bureau of Statistics of the People’s Republic of China, 2020; State Council of the People’s Republic of China, 2020), the average disposable income in Fujian and Henan was both comparable to that of the middle-income group (State Council of the People’s Republic of China, 2020), which reflects that most of the children in our study came from middle SES families. For children’s school experience and residence, all children in our study were in kindergartens and resided in urban areas. General Procedure There were seven tasks in the current study, and Fig. 1 presents a schematic representation of the seven tasks. All the tasks are available on the website http://www.dweipsy.com/ . Because of the Covid-19 pandemic, we had no choice but to ask children to complete the tasks with trained experimenters monitoring the screen online. Previous studies have administered the tasks in similar ways [ 55 , 56 ]. During all tasks, children did most of the tasks themselves with parents and teachers sitting around silently. All what parents and teachers did was to mark down what the children did for completing the number line estimation task, the visual selective attention task, and the visuospatial sketchpad task, especially for young kids who are less familiar with handling the computer mouse. For all the processes, trained experimenters could observe the parents and teachers’ behaviors through the monitors. Once parents scheduled their sessions, experimenters provided parents and teachers with information to prepare them for their first session. This included information on preparing devices and information on dos and don’ts. For example, experimenters stressed the importance of not providing input during all tasks. At the start of the testing session, parents and teachers were again instructed by the test administrator not to provide answers or hints during these tasks, and test administrators monitored the whole process. We believe the results of the remote assessment were reliable because we have minimized the involvement of parents and teachers. Besides, recent work has also found that online testing of cognitive tasks reveals little difference from those administered offline [ 55 , 56 ]. The sequence of these tasks was counterbalanced between participants. The test administration lasted for approximately 40 to 50 minutes with a short break. Measures Visual-Spatial Sketchpad. The visual matrix task was adapted from the study by Wei et al. [ 57 ] to assess the ability of participants to remember visual sequences within a matrix. Participants were presented with a series of dots in a 3×3 lattice on the screen. Each dot was shown on the screen for 1000 ms, and the interval in between dot presentations was 1000 ms. When the last dot disappeared from the screen, participants were asked to click the sequence of positions in the lattice where the dots that had been shown disappeared. The number of dots ranged from 3 to 10, with 3 items at each difficulty level. In the practice experiment, children received feedback. There was no feedback to participants during the formal experiment. The test was ended when children consecutively and incorrectly answered all 3 items of a specific difficulty level. The final score was the total number of correct trials. Cronbach’s alpha coefficient on this task was 0.95. Phonological loop. The task with the digit recall forward and the digit recall backward adapted from the Wechsler Intelligence Scale [ 58 ], was used to assess phonological loop [ 11 , 59 , 60 ]. Participants were presented with a series of digits aurally through earphones. The length of the sound for each digit was standardized to 200 ms. In the forward digit span task, participants were asked to remember the order of the digits. In the backward digit span task, children were required to remember the reverse order of the digits. For both parts, children were asked to voice out what they have heard after listening to the sound. The test began with 3 digits and increased gradually until children failed to type them correctly three times consecutively. Experimenters recorded children’s answers in the spreadsheet. One score was given for each correctly answered item. The final score was the total number of correct trials on both recall tasks. Cronbach’s alpha coefficient for this measure was 0.68. Central executive. The Flanker task was used to measure children’s central executive, which was adapted from Fan et al. [ 61 ]. Flanker task has been used frequently to index central executive in the working memory [ 62 – 64 ]. Children were presented with five arrows in one line on the screen. In this task, children were asked to distinguish the direction of the arrow in the middle by pressing the “Q” key for left or pressing the “P” key for right. There were two conditions: the congruent condition and the incongruent condition. In the congruent condition, the middle arrows’ directions were the same as those of the other arrows. In the incongruent condition, the middle arrows’ directions were opposite to the directions of the other arrows. The arrow line was presented for 1700 ms or until participants pressed a key. There were totally 48 trials in this task. The final score was the number of correct trials minus the number of incorrect trials. Cronbach’s alpha coefficient of this task was 0.86. Visual selective attention. Visual search task was used to measure participants’ visual selective attention, which adapted from the study by Trick & Enns [ 65 ]. There were rows of combined graphics on the screen that could be viewed, and these combined graphics were automatically controlled to appear on the screen from bottom to top with the speed of one row of ten stimuli per four seconds. Children were required to select a combined graphic consisting of a circle and a square among all target and distractor graphics, and distractors consisted of other combinations of two basic figures (e.g. triangles, trapezoids, sectors). The task was limited to 4 minutes. Each correct click on the target figure was recorded as 1, while a missed target was recorded as 0 and wrong click was recorded as -1. The points were then added up to give a final score. The Cronbach’s alpha coefficient on this task was 0.97. Number line estimation. This task was used to evaluate children’s mental representation of visual symbolic numbers and thus provided an indicator of developing number-processing skills [ 66 ]. Children were shown a digit on a physical number line with fixed endpoints (0-100) without interim numbers or marks and were asked to mark the line with a cross to indicate the location of the shown digit. Children received feedback in the practice experiment, while there was no feedback presented to children in the formal experiment. Children had to put the numeral in the right place on the number line by pointing out the position, and parents and teachers would help click the position on the line. Then, the position children clicked was transferred to and recorded as the corresponding number on the standard number line. The score of each trial was calculated as 100–100 |response-standard answer|/(standard answer + |response-standard answer|), in which ‘response’ refers to the participants’ answer and ‘standard answer’ refers to the correct number [ 67 ]. The final score was the average score of the 20 trials (rounding to a whole number). Cronbach’s alpha coefficient on this task was 0.97. Numerosity estimation. The estimation of numerosity task required participants to estimate the number of dots from dot arrays consisting of 11 to 99 dots [ 57 ]. Dot arrays were presented on the screen for 200 ms. The dot arrays were created with all dot arrays occupying the same total area. Dots in a dot array were randomly distributed within a circle with varying sizes. The envelope area/convex hull varied little from trial to trial. Participants orally reported their estimated number for each array, and experimenters typed their answers into the computer with the keypad. After each trial, feedback was shown on the screen. The participants could not change their entries because the feedback in the formal trials was demonstrated very fast with complicated Chinese characters. Children at this age level could not catch up with it. In contrast, children would obtain clear feedback in the practice trials to ensure they understand how this task was administered. There were 28 trials in the formal test. The final score was calculated following the same rule as was used for the number line estimation task. Cronbach’s alpha coefficient on this task was 0.87. Numerical magnitude comparison. This task asked children to judge which of the two presented single-digit numbers was larger in magnitude [ 57 , 68 , 69 ]; this task was adapted from the classic number Stroop task [ 70 ]. The two numbers were presented on the screen side-by-side. Children made the judgment by pressing “Q” when the number on the left side was larger or pressing “P” when the number on the right side was larger. Small numbers were 1.6° in horizontal visual angle and 2.4° in vertical visual angle. Large numbers had horizontal and vertical visual angles of 2.0° and 2.9°, respectively. There were three conditions in the task. In the neutral condition, both numbers were of the same physical size (either small or large). In the congruent condition, numerically smaller numbers were also physically smaller. In the incongruent condition, the numerically smaller number was physically larger. The formal task contained 84 trials, with 28 trials for each condition. The final score was the number of correct trials. Cronbach’s alpha coefficient on this task was 0.99. Data Analysis First, a preliminary analysis was conducted to compute the means, standard deviations and correlations among the main variables. Second, we tried to answer our main question about the roles of working memory and visual selective attention on the three number processing tasks. Given that estimating separate models for the three dependent measures might lead to increased Type I error, we followed what has been done in previous relevant research by including all independent measures in a single model [ 71 – 73 ]. The variance each of those predictors explained in number processing could be calculated with each standardized coefficient squared. A multivariate multiple regression (MMR) model was developed to evaluate the effects of visual selective attention, the phonological loop, the visuospatial sketchpad and the central executive on children’s performance on numerosity estimation, number line estimation and numerical magnitude comparison tasks after considering demographic covariates, including age and gender. Mplus 7 was used to develop the MMR model, which permits handling missing data without listwise or pairwise deletion of incomplete cases [ 74 ]. Results We first excluded data points which are 3 SD beyond the mean score. Regarding missing data, we conducted the Little’s MCAR test and it indicated that the data was not missing completely at random, χ 2 = 72.02, p = .10 [ 75 ]. Table 1 presents means, standard deviations, ranges, skewness and kurtosis of non-standardized variables. Descriptive statistics and correlations among standardized variables are displayed in Table 2 . To adjust for a certain degree of nonnormality, we used the standardized scores to conduct the formal analysis [ 57 ]. Table 1 Descriptive Statistics among Observed Variables. Range Mean SD Skewness Kurtosis Age 5.37-7.86 6.28 0.41 0.79 1.61 Gender a 1-2 1.45 0.50 0.20 -1.96 Visual Selective Attention -18-83 24.84 20.64 0.52 0.26 Central Executive -4-48 36.76 12.05 -1.28 0.96 Phonological Loop 0-17 8.00 3.30 0.08 0.36 Visuospatial Sketchpad 0-27 10.05 5.78 0.30 -0.17 Numerosity Estimation 53-88 70.93 7.98 -0.36 -0.43 Number Line Estimation 59-90 76.98 7.92 -0.36 -0.82 Numerical Magnitude Comparison 0-76 42.54 15.79 -0.87 0.80 Note. a Dummy coded: 1 = boys, 2 = girls. Table 2 Descriptive statistics and correlations among the involved variables Variable 1 2 3 4 5 6 7 8 9 1.Age — 2.Gender a − .008 — 3.Visual Selective Attention b .005 .070 — 4.Central Executive c .023 − .074 .160 — 5.Phonological Loop d .011 .038 .234 * .099 — 6.Visuospatial Sketchpad e .033 − .047 .291 ** .098 .085 — 7. Numerosity Estimation f .030 − .020 .338 ** .212 * .236 ** .245 * — 8.Number Line Estimation g .078 * − .094 .417 *** .222 * .280 *** .306 ** .597 *** — 9.Numerical Magnitude Comparison h .098 * − .024 .240 * .308 ** .247 ** .380 *** .294 ** 0.369 *** — Note. a Dummy coded: 1 = boys, 2 = girls. b, c, d, e, f, g, h Standardized scores of visual selective attention, central executive, phonological loop, visuospatial sketchpad, numerosity estimation, number line estimation and numerical magnitude comparison. * p < .05, ** p < .01, *** p < .001, two-tailed. We then examined the path analysis model mentioned above to evaluate the extent to which visual selective attention, the phonological loop, the visuospatial sketchpad and the central executive accounted for children’s performance on numerosity estimation, number line estimation and numerical magnitude comparison tasks after considering demographic covariates. The model revealed a good fit [ χ ² ( df = 8) = 10.288, p = .245, CFI = 0.980, TLI = 0.946, RMSEA = 0.051 (90% CI = [.000, .130]), SRMR = 0.042]. The amount of variance of the three outcome variables explained by predictors were all significant and above 20% (numerosity estimation: R ² = 0.208; number line estimation: R ² = 0.369; numerical magnitude comparison: R ² = 0.333; all p s < .05). Figure 2 shows the paths, and Table 3 shows the standardized and unstandardized coefficients of the paths from the six predictors (age, gender, visual selective attention, central executive, phonological loop, and visuospatial sketchpad) to the three outcome variables (numerosity estimation, number line estimation and numerical magnitude comparison). Age served as a significant predictor of performance on the numerical magnitude comparison task ( p = .018) and was a marginal predictor of performance on the number line estimation task ( p = .066), while was it not significantly related to performance on the numerosity estimation task ( p = .604). There was an effect of gender on number line estimation performance ( p = .007), and boys performed better than girls. Additionally, visual selective attention explained unique variance in the numerosity estimation and number line estimation tasks (numerosity estimation: p = .021; number line estimation: p < .001). Importantly, the phonological loop significantly explained unique variance in all three tasks, including numerosity estimation ( p = .045), number line estimation ( p = .001), and numerical magnitude comparison tasks ( p = .027). Last, the central executive and visuospatial sketchpad significantly predicted performance on the numerical magnitude comparison task (central executive: p = .001; visuospatial sketchpad: p < .001). Table 3 MMR model predicting individual differences in numerosity estimation, number line estimation and numerical magnitude comparison Numerosity Estimation f Number Line Estimation g Numerical Magnitude Comparison h ( R ² = .208, p = .016) ( R ² = .369, p < .001) ( R ² = .333, p < .001) Variable Coef. (S.E.) Stand.(S.E.) Coef. (S.E.) Stand.(S.E.) Coef. (S.E.) Stand.(S.E.) Age .097 (.186) .040 (.078) .359 (.193) .149 (.081) .457 (.183) * .191 (.081) * Gender a − .093 (.187) − .047 (.094) − .430 (.162) ** − .215 (.080) ** .017 (.172) .009 (.087) Visual Selective Attention b .219 (.094) * .218 (.094) * .322 (.088) *** .318 (.088) *** .032 (.082) .032 (.083) Central Executive c .162 (.113) .145 (.096) .112 (.131) .099 (.113) .304 (.104) ** .273 (.085) *** Phonological Loop d .254 (.126) * .201 (.100) * .314 (.091) *** .248 (.073) *** .288 (.132) * .229 (.104) * Visuospatial Sketchpad e .148 (.098) .142 (.093) .153 (.100) .147 (.098) .330 (.089) *** .319 (.074) *** Note. a Dummy coded: 1 = boys, 2 = girls. b, c, d, e, f, g, h Standardized scores of visual selective attention, central executive, phonological loop, visuospatial sketchpad, numerosity estimation, number line estimation and numerical magnitude comparison. Coef. = estimate of unstandardized path coefficient; Stand. = estimate of standardized path coefficient. * p < .05, ** p < .01, *** p < .001, two-tailed. Discussion The purpose of this present study was to investigate whether component(s) of working memory and visual selective attention could predict performance on a variety of basic number-processing tasks in young Chinese children. Findings revealed that the phonological loop accounted for unique variance in children’s performance on all three number-processing tasks, while the visuospatial sketchpad uniquely contributed to the numerical magnitude comparison task. In addition, we found that performance on the numerical magnitude comparison task was significantly explained by the central executive. Visual selective attention, on the other hand, was associated with children’s performance on numerosity estimation and number line estimation tasks. Phonological Loop and Basic Number Processing The current study showed that the phonological loop was significantly associated with this verbal system of number processing. Previous studies have revealed that the phonological loop enables the acquisition of the phonological structure of verbal Arabic numerals [ 73 , 76 – 78 ]. Indeed, to successfully compare magnitude information of two orally presented Arabic numbers (such as “3” and “5”), children should first retrieve the verbal codes of the digits in mind. After receiving the two pieces of sensory verbal numerical information, children may employ phonological memory to maintain the temporary phonological numerical information [ 79 – 81 ]. By incorporating these pieces of numerical information with existing numerical knowledge, the following magnitude comparison process could be executed. Therefore, through these mental processes, storing phonological numerical information is critical in solving this magnitude comparison problem. In addition, we also demonstrated a significant predictive effect of the phonological loop on performance on numerosity estimation and number line estimation tasks, both of which involve visual and analogical number processing. When inspecting the relative significant values and effect sizes of the three effects that phonological loop is involved, we found that phonological loop played a greater role in the two tasks which involve verbal representation (numerosity estimation, p = .045; number line estimation, p = .001; numerical magnitude comparison, p = .027). When performing the numerosity estimation task, children were required to estimate numerosity and report it in verbal digits. Children not only need to extract visual numerosity information from the dot arrays but also need to transform the numerosity information into verbal numeral answers. This indicated that children not only need to rely on analogical representation of quantities, but also should integrate their number word knowledge and phonological storage ability to estimate numerosity arrays [ 82 ]. However, some studies argue that the use of numeric stimuli in the phonological loop task tapped into similar (numeric) processes involved in the magnitude comparison task. Future studies are needed to replace the digit span task with other stimuli while assessing phonological memory. Visuospatial Sketchpad and Basic Number Processing The results demonstrated that the visuospatial sketchpad failed to significantly predict performance on numerosity estimation and number line estimation tasks, while it accounted for variance in performance on the numerical magnitude comparison task. Given the importance of a visual linear organization of numerical information in facilitating estimation performance [ 48 , 54 ], we were curious to explain the current results. The predictive effect of the visuospatial sketchpad on performance on the numerical magnitude comparison task could be due to involvement of visual representation of magnitudes. In the numerical magnitude comparison task, children were shown written Arabic digits and asked to compare their magnitudes. The mental processes in solving the comparison task could largely have involved visual representations of numerical magnitudes, when children of this age could have not completely mapped their verbal counting words to innate visual numerosities and could not activate verbal codes automatically to solve this comparison problem [ 31 , 32 , 83 ]. To accurately compare the magnitudes, children could retrieve visual digit knowledge and maintain visual quantity information for later comparison rather than merely relying on the hypothesized verbal system of representation. Therefore, the numerical magnitude comparison task could activate the visual system of number processing, which requires visual processing skills to manipulate strings of Arabic numerals [ 12 , 21 ]. Central Executive and Basic Number Processing The current findings also revealed strong associations between the central executive and numerical magnitude comparison performance. This might be due to the requirements of this task (e.g., presentation formats and trial composition) in the current study. In the numerical magnitude comparison task, children were shown the written Arabic digits that supplemented the verbally presented ones. When the relative physical positions of the two numbers and the magnitude relations of the two numbers did not align with the left-small and right-large associations, it is possible that children need to consciously inhibit selecting the larger number by instinctively pressing the key that was on the right side [ 15 , 84 , 85 ]. Given that our numerical magnitude comparison task included congruent and incongruent trials between magnitude and physical sizes, the strong correlation between the central executive and performance on the numerical magnitude comparison task could be unsurprising ([ 86 – 88 ], for the role of inhibitory control in numerosity magnitude comparison tasks). The Flanker task required children to inhibit responding to the directions of peripheral arrows, and the incongruent numerical magnitude comparison trials required inhibition of judging the relative physical sizes of numbers. Both these tasks highlighted the inhibition component of the central executive. Given these possible confounding mental processes, we are uncertain about whether the central executive plays a crucial role in purely numerical magnitude comparison processes. Future studies could explore this further by adopting single verbal-presented numerical magnitude comparison tasks. Visual Selective Attention and Basic Number Processing As predicted, visual selective attention was shown to be important in numerosity estimation and number line estimation performance. Visual selective attention is responsible for selecting locations in visual space [ 89 ]. Indeed, to estimate numerosity in a visually displayed array, children should first receive and process the visual sensory inputs by attending to the dots that are scattered in their visual field. Only by successfully encoding these visual inputs could children later perform internal estimation operations. This first visual attending process in numerosity estimation is conceptually similar to the visual search task in which children were required to select patterns that consisted of a circle and a square among several patterns in their visual field. Both of these tasks are closely related to the visual selective attention ability of selecting relevant visual information from noisy visual inputs [ 89 ]. Therefore, to accurately estimate numerosity information that is heavily visually loaded, visual selective attention that enables visually attending to locations in visual space could play a crucial role. On the other hand, to solve the number line estimation task, children were required to place Arabic numbers accurately on the number lines. To accomplish this, they should first encode the quantity information from the written digits with their existing visual digit knowledge. Importantly, estimating quantity accurately on the number line further relies on a visually ordered mental number line [ 48 , 54 , 90 ]. Employment of visual processing could facilitate this spatial representation of numbers along a visual number line, and this linear order of quantity information facilitates accurate estimations [ 48 , 54 ]. Serving as a mental blackboard, visual-spatial processing could translate math-related problems into its spatial descriptions [ 91 – 93 ]. Combining the roles of the visuospatial sketchpad and visual selective attention in basic number processing, we suspect that the low predictive effect of the visuospatial sketchpad on estimation tasks could be due to a high overlap between the visuospatial sketchpad and visual selective attention ( r = .29, p = .003), which has also been suggested in previous studies [ 46 , 94 ]. Indeed, after removing visual selective attention measure from the model, we found that visuospatial sketchpad significantly predicted performance on both numerosity estimation ( β = .21, p = .026) and number line estimation ( β = .25, p = .007). The visuospatial sketchpad is responsible for visual and spatial representations of visual-spatial relations among various objects [ 40 ], and visual selective attention is responsible for selecting locations in visual space [ 89 ]. They could both highlight shared components of visual processing of numerical information. In the study by Zhou et al. [ 95 ], visuospatial processing was found to mediate the relation between numerosity performance and early arithmetic performance; however, this relation was not revealed in subsequent research that controlled for visual attention [ 96 ]. It is possible that, by facilitating a linear organization of magnitudes, the visuospatial sketchpad and visual selective attention, both of which highlight visual processing skills, facilitate basic number processing. Besides, our results also revealed that children’s age was correlated with their performance on number line estimation and numerical magnitude comparison tasks. This accords with previous literature revealing growth in children’s precision in representing numerical magnitudes as they are exposed to more formal mathematical education on the symbolic number system and engaged in more mathematical activities which promote understanding magnitudes [ 25 , 71 , 97 , 98 ]. Of the three number processing tasks, we only observed the gender difference in number line estimation performance, which is both revealed in bivariate correlations and in the model. And this is congruent with previous literature revealing gender differences on this specific number processing task [ 99 – 102 ]. On the one hand, gender stereotypes about mathematical ability could be transmitted to children subtly, which could influence girls’ confidence in performing math relevant tasks [ 101 , 103 , 104 ]. On the other hand, performance on the number line estimation task require precise representation of symbolic magnitudes onto spatial dimensions, which is largely dependent on visuospatial abilities. And it has been shown that visuospatial processing which males take an advantage plays a great role in this task [ 48 , 105 ]. Limitations and Future Directions There are several limitations in the current study. First, we acknowledge that the digit span task revealed unsatisfactory reliability in the current study. This might be because the social distance rule during COVID-19 influenced the administration, especially when our participants were young kids. Second, in the numerical magnitude comparison task, children were also visually presented numerical digits whose physical sizes were congruent or incongruent with their magnitudes. As mentioned above, this may have introduced some confounding mental processes in solving this task. Third, other domain general cognitive abilities, such as linguistic abilities [ 11 , 106 ], could influence the results. Future studies could investigate how these abilities should be statistically controlled for while investigating the associates with various number processing performance. Finally, we acknowledge the limitation of our sample and measured covariate demographic variables. We only included Chinese children, and since the Chinese number system is different from many other number systems such as the English system, it remains unclear whether the contributions of working memory and visual selective attention to early number-processing skills in Chinese children revealed in the current study can be generalized to other populations. And given that our sample was mainly drawn from middle SES families and high parental education, we could not speak firmly whether results from the current study could be equally generalizable to populations varying on different levels of family backgrounds. Future studies could recruit more diverse samples on a variety of demographic dimensions, to further examine cognitive precursors to children’s early number processing abilities. Altogether, the current study investigated whether working memory components and visual selective attention demonstrated predictive effects on performance on different kinds of basic number-processing in young Chinese children. The results suggested that three components of working memory, including the phonological loop, visuospatial sketchpad and central executive, and visual selective attention showed differentiated associations with performance on various number-processing tasks. The present results highlighted potential implications for Chinese mathematical education and practices. Standardized assessments and training protocols of working memory and visual attention could be developed by researchers and examined their effects for screening children at risk of mathematics deficits and promoting children’s number processing. Regarding spatial ability, previous studies have developed assessments for spatial ability and successfully performed systematic spatial training to improve children’s mathematical performance [ 107 , 108 ]. Similarly, future research from both our study and others focusing on improving early number processing ability could be more directed to interventional practices of assessing and training on working memory and visual selective attention [ 109 , 110 ], and empirically examine their effects among children from highly controlled to more naturalistic learning contexts (laboratories, classrooms, homes). Declarations Ethics approval and consent to participate The study procedure was approved by the Ethics Committee of the faculty of psychology, Beijing Normal University. In compliance with the Helsinki Declaration, all subjects provided written informed consent. All research participants’ parents gave informed written consent that was included in our ethics statement. Consent for publication Not applicable. Availability of data and materials The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request. Competing interests The authors declare that they have no competing interests. Funding This study was funded by Ministry of Science and Technology Foundation of China (2022ZD0211300), the National Natural Science Foundation of China (32000757), and Beijing Municipal Social Science Foundation (23JYC016) to Xiujie Yang. Authors' contributions Yuhan Wang, Zihan Yang, Xiao Yu, and Yue Qi contributed to the experimental design, the interpretation of the results, drafting and editing the manuscript. Xiujie Yang contributed to experimental design, interpretation of the results, drafting and editing the manuscript and foundation providing. Xiujie Yang and Zihan Yang were responsible for the revision of the manuscript. All authors reviewed the manuscript. Acknowledgements We are especially grateful to the schools, parents, and students for their willingness to participate and their commitment to the study. References Andersson, U. (2007). The contribution of working memory to children's mathematical word problem solving. Applied Cognitive Psychology, 21 (9), 1201-1216. https://doi.org/10.1002/acp.1317 Andersson, U., & Lyxell, B. (2007). Working memory deficit in children with mathematical difficulties: A general or specific deficit? Journal of Experimental Child Psychology , 96 (3), 197-228. https://doi.org/10.1016/j.jecp.2006.10.001 Awh, E., Anllo-Vento, L., & Hillyard, S. A. (2000). The role of spatial selective attention in working memory for locations: Evidence from event-related potentials. Journal of Cognitive Neuroscience, 12 (5), 840-847. https://doi.org/10.1162/089892900562444 Awh, E., & Jonides, J. (2001). Overlapping mechanisms of attention and spatial working memory. Trends in Cognitive Sciences, 5 (3), 119-126. https://doi.org/10.1016/S1364-6613(00)01593-X Awh, E., Jonides, J., & Reuter-Lorenz, P. A. (1998). Rehearsal in spatial working memory. Journal of Experimental Psychology: Human Perception and Performance, 24 (3), 780-790. https://doi.org/10.1037/0096-1523.24.3.780 Baddeley, A. (1992). Working memory. Science, 255 (5044), 556. https://doi.org/10.1126/science.1736359 Baddeley, A. (1996). Exploring the central executive. The Quarterly Journal of Experimental Psychology, 49 (1), 5-28. https://doi.org/10.1080/713755608 Baddeley, A., Gathercole, S., & Papagno, C. (1998). The phonological loop as a language learning device. Psychological Review, 105 (1), 158-173. https://doi.org/10.1037/0033-295X.105.1.158 Baroody, A. J., & Gatzke, M. R. (1991). The estimation of set size by potentially gifted kindergarten-age children. Journal for Research in Mathematics Education, 22 (1), 59-68. https://doi.org/10.2307/749554 Berch, D. B. (2005). Making sense of number sense: Implications for children with mathematical disabilities. Journal of learning disabilities, 38 (4), 333-339. https://doi.org/10.1177/00222194050380040901 Booth, J. L., & Siegler, R. S. (2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 42 (1), 189-201. https://doi.org/10.1037/0012-1649.41.6.189 Bulf, H., de Hevia, M. D., & Macchi Cassia, V. (2016). Small on the left, large on the right: numbers orient visual attention onto space in preverbal infants. Developmental Science, 19 (3), 394-401. https://doi.org/10.1111/desc.12315 Bull, R., Cleland, A. A., & Mitchell, T. (2013). Sex differences in the spatial representation of number. Journal of Experimental Psychology: General, 142 (1), 181-192. https://doi.org/10.1037/a0028387 Bull, R., Espy, K. A., & Wiebe, S. A. (2008). Short-term memory, working memory, and executive functioning in preschoolers: Longitudinal predictors of mathematical achievement at age 7 years. Developmental Neuropsychology, 33 (3), 205-228. https://doi.org/10.1080/87565640801982312 Carrasco, M. (2011). Visual attention: The past 25 years. Vision Research , 51 (13), 1484-1525. https://doi.org/10.1016/j.visres.2011.04.012 Chan, W. W. L. (2020). Counting enhances kindergarteners’ mappings of number words onto numerosities. Frontiers in Psychology, 11 (153). https://doi.org/10.3389/fpsyg.2020.00153 Cheng, Y.-L., & Mix, K. S. (2014). Spatial training improves children's mathematics ability. Journal of Cognition and Development, 15 (1), 2-11. https://doi.org/10.1080/15248372.2012.725186 Chesney, D., Bjalkebring, P., & Peters, E. (2015). How to estimate how well people estimate: Evaluating measures of individual differences in the approximate number system. Attention, Perception, & Psychophysics , 77 (8), 2781-2802. https://doi.org/10.3758/s13414-015-0974-6 Clark, C. A. C., Pritchard, V. E., & Woodward, L. J. (2010). Preschool executive functioning abilities predict early mathematics achievement. Developmental Psychology, 46 (5), 1176-1191. https://doi.org/10.1037/a0019672 Clayton, S., & Gilmore, C. (2015). Inhibition in dot comparison tasks. ZDM, 47 (5), 759-770. https://doi.org/10.1007/s11858-014-0655-2 Cui, J., Zhang, Y., Cheng, D., Li, D., & Zhou, X. (2017). Visual form perception can be a cognitive correlate of lower level math categories for teenagers. Frontiers in Psychology, 8 (1336). https://doi.org/10.3389/fpsyg.2017.01336 de Hevia, M. D., & Spelke, E. S. (2009). Spontaneous mapping of number and space in adults and young children. Cognition, 110 (2), 198-207. https://doi.org/10.1016/j.cognition.2008.11.003 De Smedt, B., Taylor, J., Archibald, L., & Ansari, D. (2010). How is phonological processing related to individual differences in children’s arithmetic skills? Developmental Science, 13 (3), 508-520. https://doi.org/10.1111/j.1467-7687.2009.00897.x De Smedt, B., Verschaffel, L., & Ghesquière, P. (2009). The predictive value of numerical magnitude comparison for individual differences in mathematics achievement. Journal of Experimental Child Psychology, 103 (4), 469-479. https://doi.org/10.1016/j.jecp.2009.01.010 Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44 (1), 1-42. https://doi.org/10.1016/0010-0277(92)90049-N Dehaene, S., & Cohen, L. (1995). Towards an anatomical and functional model of number processing. Mathematical Cognition, 1 (1), 83-120. Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122 (3), 371-396. https://doi.org/10.1037/0096-3445.122.3.371 Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20 (3-6), 487-506. https://doi.org/10.1080/02643290244000239 Durand, M., Hulme, C., Larkin, R., & Snowling, M. (2005). The cognitive foundations of reading and arithmetic skills in 7- to 10-year-olds. Journal of Experimental Child Psychology, 91 (2), 113-136. https://doi.org/10.1016/j.jecp.2005.01.003 Estes, Z., & Felker, S. (2012). Confidence mediates the sex difference in mental rotation performance. Archives of Sexual Behavior, 41 (3), 557-570. https://doi.org/10.1007/s10508-011-9875-5 Fan, J., McCandliss, B. D., Sommer, T., Raz, A., & Posner, M. I. (2002). Testing the efficiency and independence of attentional networks. Journal of Cognitive Neuroscience, 14 (3), 340-347. https://doi.org/10.1162/089892902317361886 Fazio, L. K., Bailey, D. H., Thompson, C. A., & Siegler, R. S. (2014). Relations of different types of numerical magnitude representations to each other and to mathematics achievement. Journal of Experimental Child Psychology, 123 , 53-72. https://doi.org/10.1016/j.jecp.2014.01.013 Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Science, 8 (7), 307-314. https://doi.org/10.1016/j.tics.2004.05.002 Friso-van den Bos, I., Kroesbergen, E. H., & van Luit, J. E. H. (2014). Number sense in kindergarten children: Factor structure and working memory predictors. Learning and Individual Differences, 33 , 23-29. https://doi.org/10.1016/j.lindif.2014.05.003 Fuhs, M. W., Hornburg, C. B., & McNeil, N. M. (2016). Specific early number skills mediate the association between executive functioning skills and mathematics achievement. Developmental Psychology, 52 (8), 1217-1235. https://doi.org/10.1037/dev0000145 Gazzaley, A., & Nobre, A. C. (2012). Top-down modulation: bridging selective attention and working memory. Trends in Cognitive Sciences, 16 (2), 129-135. https://doi.org/10.1016/j.tics.2011.11.014 Geary, D. C. (2004). Mathematics and learning disabilities. Journal of learning disabilities , 37(1), 4-15. https://doi.org/10.1177/00222194040370010201 Geary, D. C., Hoard, M. K., Byrd-Craven, J., Nugent, L., & Numtee, C. (2007). Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child Development, 78 (4), 1343-1359. https://doi.org/10.1111/j.1467-8624.2007.01069.x Geary, D. C., Hoard, M. K., Nugent, L., & Byrd-Craven, J. (2008). Development of number line representations in children with mathematical learning disability. Developmental Neuropsychology, 33 (3), 277-299. https://doi.org/10.1080/87565640801982361 Gelman, R., & Butterworth, B. (2005). Number and language: how are they related? Trends in Cognitive Sciences, 9 (1), 6-10. https://doi.org/10.1016/j.tics.2004.11.004 Georges, C., Hoffmann, D., & Schiltz, C. (2017). Mathematical abilities in elementary school: Do they relate to number–space associations? Journal of Experimental Child Psychology, 161 , 126-147. https://doi.org/10.1016/j.jecp.2017.04.011 Georgiou, G. K., Tziraki, N., Manolitsis, G., & Fella, A. (2013). Is rapid automatized naming related to reading and mathematics for the same reason(s)? A follow-up study from kindergarten to Grade 1. Journal of Experimental Child Psychology, 115 (3), 481-496. https://doi.org/10.1016/j.jecp.2013.01.004 Gilmore, C., Attridge, N., Clayton, S., Cragg, L., Johnson, S., Marlow, N., Simms, V., & Inglis, M. (2013). Individual differences in inhibitory control, not non-verbal number acuity, correlate with mathematics achievement. PLoS One, 8 (6), e67374. https://doi.org/10.1371/journal.pone.0067374 Girelli, L., Lucangeli, D., & Butterworth, B. (2000). The development of automaticity in accessing number magnitude. Journal of Experimental Child Psychology, 76 (2), 104-122. https://doi.org/10.1006/jecp.2000.2564 Gross, S. I., Gross, C. A., Kim, D., Lukowski, S. L., Thompson, L. A., & Petrill, S. A. (2018). A comparison of methods for assessing performance on the number line estimation task. Journal of Numerical Cognition, 4 (3), 554-571. https://doi.org/10.5964/jnc.v4i3.120 Gunderson, E. A., Hamdan, N., Hildebrand, L., & Bartek, V. (2019). Number line unidimensionality is a critical feature for promoting fraction magnitude concepts. Journal of Experimental Child Psychology, 187 , 104657. https://doi.org/10.1016/j.jecp.2019.06.010 Gunderson, E. A., Ramirez, G., Beilock, S. L., & Levine, S. C. (2012a). The relation between spatial skill and early number knowledge: The role of the linear number line. Developmental Psychology, 48 (5), 1229-1241. https://doi.org/10.1037/a0027433 Gunderson, E. A., Ramirez, G., Levine, S. C., & Beilock, S. L. (2012b). The role of parents and teachers in the development of gender-related math attitudes. Sex roles, 66 (3), 153-166. https://doi.org/10.1007/s11199-011-9996-2 Kolkman, M. E., Hoijtink, H. J. A., Kroesbergen, E. H., & Leseman, P. P. M. (2013). The role of executive functions in numerical magnitude skills. Learning and Individual Differences, 24 , 145-151. https://doi.org/10.1016/j.lindif.2013.01.004 Halberda, J., Mazzocco, M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455 (7213), 665-668. https://doi.org/10.1038/nature07246 Hamdan, N., & Gunderson, E. A. (2017). The number line is a critical spatial-numerical representation: Evidence from a fraction intervention. Developmental Psychology, 53 (3), 587-596. https://doi.org/10.1037/dev0000252 Hansen, N., Jordan, N. C., Fernandez, E., Siegler, R. S., Fuchs, L., Gersten, R., & Micklos, D. (2015). General and math-specific predictors of sixth-graders’ knowledge of fractions. Cognitive Development, 35 , 34-49. https://doi.org/10.1016/j.cogdev.2015.02.001 Hecht, S. A., Torgesen, J. K., Wagner, R. K., & Rashotte, C. A. (2001). The relations between phonological processing abilities and emerging individual differences in mathematical computation skills: A longitudinal study from second to fifth grades. Journal of Experimental Child Psychology, 79 (2), 192-227. https://doi.org/10.1006/jecp.2000.2586 Hoffmann, D., Pigat, D., & Schiltz, C. (2014). The impact of inhibition capacities and age on number–space associations. Cognitive Processing, 15 (3), 329-342. https://doi.org/10.1007/s10339-014-0601-9 Honzel, N., Justus, T., & Swick, D. (2014). Posttraumatic stress disorder is associated with limited executive resources in a working memory task. Cognitive, Affective, & Behavioral Neuroscience, 14 (2), 792-804. https://doi.org/10.3758/s13415-013-0219-x Howell, S. C., & Kemp, C. R. (2010). Assessing preschool number sense: Skills demonstrated by children prior to school entry. Educational Psychology, 30 (4), 411-429. https://doi.org/10.1080/01443411003695410 Huang, Q., Zhang, X., Liu, Y., Yang, W., & Song, Z. (2017). The contribution of parent–child numeracy activities to young Chinese children's mathematical ability. British Journal of Educational Psychology, 87 (3), 328-344. https://doi.org/10.1111/bjep.12152 Huo, S., Zhang, X., & Law, Y. K. (2021). Pathways to word reading and calculation skills in young Chinese children: From biologically primary skills to biologically secondary skills. Journal of Educational Psychology, 113 (2), 230-247. https://doi.org/10.1037/edu0000647 Hutchison, J. E., Lyons, I. M., & Ansari, D. (2019). More similar than different: gender differences in children's basic numerical skills are the exception not the rule. Child Development, 90 (1), e66-e79. https://doi.org/10.1111/cdev.13044 Jordan, N. C., Kaplan, D., Nabors Oláh, L., & Locuniak, M. N. (2006). Number sense growth in kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. Child Development, 77 (1), 153-175. https://doi.org/10.1111/j.1467-8624.2006.00862.x Kaufmann, L., Wood, G., Rubinsten, O., & Henik, A. (2011). Meta-analyses of developmental fMRI studies investigating typical and atypical trajectories of number processing and calculation. Developmental Neuropsychology, 36 (6), 763-787. https://doi.org/10.1080/87565641.2010.549884 Klein, E., Suchan, J., Moeller, K., Karnath, H.-O., Knops, A., Wood, G., Nuerk, H.-C., & Willmes, K. (2016). Considering structural connectivity in the triple-code model of numerical cognition: differential connectivity for magnitude processing and arithmetic facts. Brain Structure and Function, 221 (2), 979-995. https://doi.org/10.1007/s00429-014-0951-1 Korpipää, H., Koponen, T., Aro, M., Tolvanen, A., Aunola, K., Poikkeus, A.-M., Lerkkanen, M.-K., & Nurmi, J.-E. (2017). Covariation between reading and arithmetic skills from Grade 1 to Grade 7. Contemporary Educational Psychology, 51 , 131-140. https://doi.org/10.1016/j.cedpsych.2017.06.005 Kroesbergen, E. H., Van Luit, J. E. H., Van Lieshout, E. C. D. M., Van Loosbroek, E., & Van de Rijt, B. A. M. (2009). Individual differences in early numeracy: The role of executive functions and subitizing. Journal of Psychoeducational Assessment, 27 (3), 226-236. https://doi.org/10.1177/0734282908330586 Kroesbergen, E. H., van 't Noordende, J. E., & Kolkman, M. E. (2014). Training working memory in kindergarten children: Effects on working memory and early numeracy. Child Neuropsychology, 20 (1), 23-37. https://doi.org/10.1080/09297049.2012.736483 Lee, K., Ng, S. F., Pe, M. L., Ang, S. Y., Hasshim, M. N. A. M., & Bull, R. (2012). The cognitive underpinnings of emerging mathematical skills: Executive functioning, patterns, numeracy, and arithmetic. British Journal of Educational Psychology, 82 (1), 82-99. https://doi.org/10.1111/j.2044-8279.2010.02016.x LeFevre, J.-A., Fast, L., Skwarchuk, S.-L., Smith-Chant, B. L., Bisanz, J., Kamawar, D., & Penner-Wilger, M. (2010). Pathways to mathematics: Longitudinal predictors of performance. Child Development, 81 (6), 1753-1767. https://doi.org/10.1111/j.1467-8624.2010.01508.x LeFevre, J.-A., Skwarchuk, S.-L., Smith-Chant, B. L., Fast, L., Kamawar, D., & Bisanz, J. (2009). Home numeracy experiences and children’s math performance in the early school years. Canadian Journal of Behavioural Science / Revue canadienne des sciences du comportement, 41 (2), 55-66. https://doi.org/10.1037/a0014532 Linn, M. C., & Petersen, A. C. (1985). Emergence and characterization of sex differences in spatial ability: A meta-analysis. Child Development, 56 (6), 1479-1498. https://doi.org/10.2307/1130467 Little, R. J. A. (1988). A test of missing completely at random for multivariate data with missing values. Journal of the American Statistical Association, 83 (404), 1198-1202. https://doi.org/10.1080/01621459.1988.10478722 Lipton, J. S., & Spelke, E. S. (2005). Preschool children's mapping of number words to nonsymbolic numerosities. Child Development, 76 (5), 978-988. https://doi.org/10.1111/j.1467-8624.2005.00891.x Logie, R. H. (1995). Visuo-spatial working memory . Psychology Press. Logie, R. H., Gilhooly, K. J., & Wynn, V. (1994). Counting on working memory in arithmetic problem solving. Memory & Cognition, 22 (4), 395-410. https://doi.org/10.3758/BF03200866 Luo, Y., Wang, J., Wu, H., Zhu, D., & Zhang, Y. (2013). Working-memory training improves developmental dyslexia in Chinese children. Neural regeneration research, 8 (5), 452-460. https://doi.org/10.3969/j.issn.1673-5374.2013.05.009 McKenzie, B., Bull, R., & Gray, C. (2003). The effects of phonological and visual-spatial interference on children's arithmetical performance. Educational and Child Psychology, 20 (3), 93-108. Mejias, S., Mussolin, C., Rousselle, L., Grégoire, J., & Noël, M.-P. (2012). Numerical and nonnumerical estimation in children with and without mathematical learning disabilities. Child Neuropsychology, 18 (6), 550-575. https://doi.org/10.1080/09297049.2011.625355 Mejias, S., & Schiltz, C. (2013). Estimation abilities of large numerosities in Kindergartners. Frontiers in Psychology, 4 (518). https://doi.org/10.3389/fpsyg.2013.00518 Michalczyk, K., Krajewski, K., Preβler, A.-L., & Hasselhorn, M. (2013). The relationships between quantity-number competencies, working memory, and phonological awareness in 5- and 6-year-olds. British Journal of Developmental Psychology, 31 (4), 408-424. https://doi.org/10.1111/bjdp.12016 Mix, K. S., Levine, S. C., Cheng, Y.-L., Stockton, J. D., & Bower, C. (2021). Effects of spatial training on mathematics in first and sixth grade children. Journal of Educational Psycho logy, 113 (2), 304-314. https://doi.org/10.1037/edu0000494 Mix, K. S., Levine, S. C., Cheng, Y.-L., Young, C. J., Hambrick, D. Z., & Konstantopoulos, S. (2017). The latent structure of spatial skills and mathematics: A replication of the two-factor model. Journal of Cognition and Development, 18 (4), 465-492. https://doi.org/10.1080/15248372.2017.1346658 Miyake, A., Friedman, N. P., Rettinger, D. A., Shah, P., & Hegarty, M. (2001). How are visuospatial working memory, executive functioning, and spatial abilities related? A latent-variable analysis. Journal of Experimental Psychology: General, 130 (4), 621-640. http://dx.doi.org/10.1037/0096-3445.130.4.621 Moeller, K., Willmes, K., & Klein, E. (2015). A review on functional and structural brain connectivity in numerical cognition. Frontiers in Human Neuroscience, 9 (227). https://doi.org/10.3389/fnhum.2015.00227 Mundy, E., & Gilmore, C. K. (2009). Children’s mapping between symbolic and nonsymbolic representations of number. Journal of Experimental Child Psychology, 103 (4), 490-502. https://doi.org/10.1016/j.jecp.2009.02.003 Mutaf Yıldız, B., Sasanguie, D., De Smedt, B., & Reynvoet, B. (2018). Frequency of home numeracy activities is differentially related to basic number processing and calculation skills in kindergartners. Frontiers in Psychology, 9 (340). https://doi.org/10.3389/fpsyg.2018.00340 Muthén, L. K., & Muthén, B. O. (2012). 1998–2012. Mplus user’s guide. Los Angeles: Muthen & Muthen . Noël, M.-P., Seron, X., & Trovarelli, F. (2004). Working memory as a predictor of addition skills and addition strategies in children. Cahiers de Psychologie Cognitive/Current Psychology of Cognition, 22 (1), 3-25. Opfer, J. E., & Siegler, R. S. (2007). Representational change and children’s numerical estimation. Cognitive Psychology, 55 (3), 169-195. https://doi.org/10.1016/j.cogpsych.2006.09.002 Passolunghi, M. C., & Lanfranchi, S. (2012). Domain-specific and domain-general precursors of mathematical achievement: A longitudinal study from kindergarten to first grade. British Journal of Educational Psychology, 82 (1), 42-63. https://doi.org/10.1111/j.2044-8279.2011.02039.x Passolunghi, M. C., Lanfranchi, S., Altoè, G., & Sollazzo, N. (2015). Early numerical abilities and cognitive skills in kindergarten children. Journal of Experimental Child Psychology, 135 , 25-42. https://doi.org/10.1016/j.jecp.2015.02.001 Passolunghi, M. C., & Siegel, L. S. (2001). Short-term memory, working memory, and inhibitory control in children with difficulties in arithmetic problem solving. Journal of Experimental Child Psychology, 80 (1), 44-57. https://doi.org/10.1006/jecp.2000.2626 Peng, P., Yang, X., & Meng, X. (2017). The relation between approximate number system and early arithmetic: The mediation role of numerical knowledge. Journal of Experimental Child Psychology, 157 , 111-124. https://doi.org/10.1016/j.jecp.2016.12.011 Peters, L., Polspoel, B., Op de Beeck, H., & De Smedt, B. (2016). Brain activity during arithmetic in symbolic and non-symbolic formats in 9–12 year old children. Neuropsychologia, 86 , 19-28. https://doi.org/10.1016/j.neuropsychologia.2016.04.001 Prager, E. O., Sera, M. D., & Carlson, S. M. (2016). Executive function and magnitude skills in preschool children. Journal of Experimental Child Psychology, 147 , 126-139. https://doi.org/10.1016/j.jecp.2016.01.002 Price, G. R., & Fuchs, L. S. (2016). The mediating relation between symbolic and nonsymbolic foundations of math competence. PLoS One , 11 (2), e0148981. https://doi.org/10.1371/journal.pone.0148981 Reinert, R. M., Huber, S., Nuerk, H.-C., & Moeller, K. (2017). Sex differences in number line estimation: The role of numerical estimation. British Journal of Psychology, 108 (2), 334-350. https://doi.org/10.1111/bjop.12203 Rivers, M. L., Fitzsimmons, C. J., Fisk, S. R., Dunlosky, J., & Thompson, C. A. (2021). Gender differences in confidence during number-line estimation. Metacognition and Learning, 16 (1), 157-178. https://doi.org/10.1007/s11409-020-09243-7 Scharinger, C., Soutschek, A., Schubert, T., & Gerjets, P. (2015). When flanker meets the n-back: What EEG and pupil dilation data reveal about the interplay between the two central-executive working memory functions inhibition and updating. Psychophysiology, 52 (10), 1293-1304. https://doi.org/10.1111/psyp.12500 Siegler, R. S. (2009). Improving the numerical understanding of children from low-income families. Child Development Perspectives, 3 (2), 118-124. https://doi.org/10.1111/j.1750-8606.2009.00090.x Siegler, R. S., & Booth, J. L. (2004). Development of numerical estimation in young children. Child Development, 75 (2), 428-444. https://doi.org/10.1111/j.1467-8624.2004.00684.x Siegler, R. S., & Ramani, G. B. (2009). Playing linear number board games—but not circular ones—improves low-income preschoolers’ numerical understanding. Journal of Educational Psychology, 101 (3), 545-560. https://doi.org/10.1037/a0014239 Siegler, R. S., Thompson, C. A., & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62 (4), 273-296. https://doi.org/10.1016/j.cogpsych.2011.03.001 Sigmundsson, H., Anholt, S. K., & Talcott, J. B. (2010). Are poor mathematics skills associated with visual deficits in temporal processing? Neuroscience Letters, 469 (2), 248-250. https://doi.org/10.1016/j.neulet.2009.12.005 Simmons, F., Singleton, C., & Horne, J. (2008). Brief report—Phonological awareness and visual-spatial sketchpad functioning predict early arithmetic attainment: Evidence from a longitudinal study. European Journal of Cognitive Psychology, 20 (4), 711-722. https://doi.org/10.1080/09541440701614922 Simmons, F. R., & Singleton, C. (2008). Do weak phonological representations impact on arithmetic development? A review of research into arithmetic and dyslexia. Dyslexia, 14 (2), 77-94. https://doi.org/10.1002/dys.341 Simmons, F. R., Willis, C., & Adams, A.-M. (2012). Different components of working memory have different relationships with different mathematical skills. Journal of Experimental Child Psychology, 111 (2), 139-155. https://doi.org/10.1016/j.jecp.2011.08.011 Skagenholt, M., Träff, U., Västfjäll, D., & Skagerlund, K. (2018). Examining the Triple Code Model in numerical cognition: An fMRI study. PLoS One, 13 (6), e0199247. https://doi.org/10.1371/journal.pone.0199247 Swanson, H. L. (2004). Working memory and phonological processing as predictors of children’s mathematical problem solving at different ages. Memory & cognition, 32 (4), 648-661. https://doi.org/10.3758/BF03195856 Szucs, D., Devine, A., Soltesz, F., Nobes, A., & Gabriel, F. (2013). Developmental dyscalculia is related to visuo-spatial memory and inhibition impairment. Cortex, 49 (10), 2674-2688. https://doi.org/10.1016/j.cortex.2013.06.007 Thompson, C. A., & Opfer, J. E. (2008). Costs and benefits of representational change: Effects of context on age and sex differences in symbolic magnitude estimation. Journal of Experimental Child Psychology, 101 (1), 20-51. https://doi.org/10.1016/j.jecp.2008.02.003 Trick, L. M., & Enns, J. T. (1998). Lifespan changes in attention: the visual search task. Cognitive Development , 13 (3), 369-386. https://doi.org/10.1016/S0885-2014(98)90016-8 Tosto, M. G., Hanscombe, K. B., Haworth, C. M. A., Davis, O. S. P., Petrill, S. A., Dale, P. S., Malykh, S., Plomin, R., & Kovas, Y. (2014). Why do spatial abilities predict mathematical performance? Developmental Science, 17 (3), 462-470. https://doi.org/10.1111/desc.12138 Träff, U. (2013). The contribution of general cognitive abilities and number abilities to different aspects of mathematics in children. Journal of Experimental Child Psychology, 116 (2), 139-156. https://doi.org/10.1016/j.jecp.2013.04.007 Uttal, D. H., Meadow, N. G., Tipton, E., Hand, L. L., Alden, A. R., Warren, C., & Newcombe, N. S. (2013). The malleability of spatial skills: A meta-analysis of training studies. Psychological Bulletin, 139 (2), 352-402. https://doi.org/10.1037/a0028446 Vuilleumier, P., Ortigue, S., & Brugger, P. (2004). The number space and neglect. Cortex, 40 (2), 399-410. https://doi.org/10.1016/S0010-9452(08)70134-5 Wechsler, D. (1974). Wechsler intelligence scale for children-revised . Psychological Corporation. Wei, W., Yuan, H., Chen, C., & Zhou, X. (2012). Cognitive correlates of performance in advanced mathematics. British Journal of Educational Psychology, 82 (1), 157-181. https://doi.org/10.1111/j.2044-8279.2011.02049.x Yang, X., Chung, K. K. H., & McBride, C. (2019). Longitudinal contributions of executive functioning and visual-spatial skills to mathematics learning in young Chinese children. Educational Psychology, 39 (5), 678-704. https://doi.org/10.1080/01443410.2018.1546831 Yang, X., & McBride, C. (2020). How do phonological processing abilities contribute to early Chinese reading and mathematics? Educational Psychology , 1-19. https://doi.org/10.1080/01443410.2020.1771679 Yang, X., McBride, C., Ho, C. S.-H., & Chung, K. K. H. (2020). Longitudinal associations of phonological processing skills, Chinese word reading, and arithmetic. Reading and Writing , 33 (7), 1679-1699. https://doi.org/10.1007/s11145-019-09998-9 Yang, X., & Meng, X. (2020). Visual processing matters in Chinese reading acquisition and early mathematics. Frontiers in Psychology, 11 (462). https://doi.org/10.3389/fpsyg.2020.00462 Yang, X., Zhang, X., Huo, S., & Zhang, Y. (2020). Differential contributions of cognitive precursors to symbolic versus non-symbolic numeracy in young Chinese children. Early Childhood Research Quarterly, 53 , 208-216. https://doi.org/10.1016/j.ecresq.2020.04.003 Zhang, X. (2016). Linking language, visual-spatial, and executive function skills to number competence in very young Chinese children. Early Childhood Research Quarterly, 36 , 178-189. https://doi.org/10.1016/j.ecresq.2015.12.010 Zhang, X., Hu, B. Y., Zou, X., & Ren, L. (2020). Parent–child number application activities predict children’s math trajectories from preschool to primary school. Journal of Educational Psychology, 112 (8), 1521-1531. https://doi.org/10.1037/edu0000457 Zhang, X., & Lin, D. (2017). Does growth rate in spatial ability matter in predicting early arithmetic competence? Learning and Instruction, 49 , 232-241. https://doi.org/10.1016/j.learninstruc.2017.02.003 Zhang, X., & Lin, D. (2018). Cognitive precursors of word reading versus arithmetic competencies in young Chinese children. Early Childhood Research Quarterly, 42 , 55-65. https://doi.org/10.1016/j.ecresq.2017.08.006 Zhang, X., Räsänen, P., Koponen, T., Aunola, K., Lerkkanen, M.-K., & Nurmi, J.-E. (2017). Knowing, applying, and reasoning about arithmetic: Roles of domain-general and numerical skills in multiple domains of arithmetic learning. Developmental Psychology, 53 (12), 2304-2318. https://doi.org/10.1037/dev0000432 Zhou, X., Chen, Y., Chen, C., Jiang, T., Zhang, H., & Dong, Q. (2007). Chinese kindergartners’ automatic processing of numerical magnitude in Stroop-like tasks. Memory & Cognition, 35 (3), 464-470. https://doi.org/10.3758/BF03193286 Zhou, X., Wei, W., Zhang, Y., Cui, J., & Chen, C. (2015). Visual perception can account for the close relation between numerosity processing and computational fluency. Frontiers in Psychology, 6 (1364). https://doi.org/10.3389/fpsyg.2015.01364 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4746725","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":329237398,"identity":"f884fd73-1cc5-4c0d-a82a-95e388a9dcae","order_by":0,"name":"Yuhan Wang","email":"","orcid":"","institution":"Beijing Normal University","correspondingAuthor":false,"prefix":"","firstName":"Yuhan","middleName":"","lastName":"Wang","suffix":""},{"id":329237399,"identity":"ad5d179a-da0f-43b5-b3b5-810e454c59bd","order_by":1,"name":"Zihan Yang","email":"","orcid":"","institution":"Beijing Normal University","correspondingAuthor":false,"prefix":"","firstName":"Zihan","middleName":"","lastName":"Yang","suffix":""},{"id":329237400,"identity":"aeb9c797-6d18-49e3-8322-b86f8c7a8113","order_by":2,"name":"Xiao Yu","email":"","orcid":"","institution":"Beijing Forestry University","correspondingAuthor":false,"prefix":"","firstName":"Xiao","middleName":"","lastName":"Yu","suffix":""},{"id":329237401,"identity":"b79326eb-d410-4a66-96dc-d0f6f95c3bc8","order_by":3,"name":"Yue Qi","email":"","orcid":"","institution":"Beijing Normal University","correspondingAuthor":false,"prefix":"","firstName":"Yue","middleName":"","lastName":"Qi","suffix":""},{"id":329237402,"identity":"b39cc18b-ad92-4fad-9ada-6866551ace67","order_by":4,"name":"Xiujie Yang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAtklEQVRIiWNgGAWjYDACHgglx8befoA0LcZ8PGcSSNOSOE/CwYA4HeY8ZwwYfuYcTm+TYEhg+FGxjbAWy94eA8bebYdz26QbDzD2nLlNWIvBeR4DBl6QFpkDCcyMbURqYfy77XA6m0SCAZFazvYYMANtSSBei2XPsQJm2W3phm3AQD5IlF/MeZI3ML7dZi0v395+8MGPCmIcxsDA/oOBoRnMOUBYPUQLCNQRpXgUjIJRMApGKAAAnlQ5c3YcphgAAAAASUVORK5CYII=","orcid":"","institution":"Beijing Normal University","correspondingAuthor":true,"prefix":"","firstName":"Xiujie","middleName":"","lastName":"Yang","suffix":""}],"badges":[],"createdAt":"2024-07-16 03:38:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4746725/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4746725/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":62658797,"identity":"63bef9e0-086a-4515-a13c-7543e516b6c7","added_by":"auto","created_at":"2024-08-17 02:19:28","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":41569,"visible":true,"origin":"","legend":"\u003cp\u003eExamples of stimuli for all cognitive tasks.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eNote: \u003c/em\u003eFor the phonological loop task, the Chinese words mean “After inputting the answer, press the ‘Enter’ key.” For the numerosity estimation task, the Chinese words mean “Your estimated number of dots is: _______”\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-4746725/v1/059891dcc36574c7dd4a38d5.png"},{"id":62657612,"identity":"5e22c313-5ac6-4a53-8cc7-a72143310651","added_by":"auto","created_at":"2024-08-17 02:11:28","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":54068,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eVisual description of the Multivariate Multiple Regression (MMR) model\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eNote. \u003c/em\u003eThe estimates of standardized path coefficient and unstandardized path coefficient are shown in Table 2.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-4746725/v1/4d16451202460694316c91f1.png"},{"id":84597432,"identity":"35dca307-b680-473b-b12b-893f326e7579","added_by":"auto","created_at":"2025-06-14 07:16:50","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1216695,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4746725/v1/7e2f2264-61ee-4bb7-940e-9774e2f74c55.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Differential Contributions of Working Memory Components and Visual Attention to Young Children’s Varieties of Basic Number Processing","fulltext":[{"header":"Background","content":"\u003cp\u003eBefore formal mathematical education, the capacities to make sense of quantities have been shown to lay a foundation for later mathematical learning [\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Although working memory and visual selective attention have been shown to be important for numerical skills [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e], few studies have empirically addressed various early number processing abilities in relation to them. Examining the associations of working memory components and visual selective attention with basic number processing skills would contribute to the identification of children at risk of mathematics difficulties, and developing relevant training programs to support children\u0026rsquo;s early math learning.\u003c/p\u003e \u003cp\u003eCompared to many western languages, Chinese number word system has a transparent base-10 structure; this could promote better number counting performances and better precision on number line estimation [\u003cspan additionalcitationids=\"CR7\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Chinese language system is more orthographic and less phonological, which may make Chinese children process numbers in different ways [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. However, most studies conducted in mainland China mainly found how working memory and visual attention respectively related to children\u0026rsquo;s formal mathematical achievements [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], rather than how they were altogether associated with different basic number processing skills. To fill the gaps, the purpose of this present study was to investigate how components of working memory and visual selective attention would predict young children\u0026rsquo;s performance on a variety of basic number processing tasks in Chinese contexts.\u003c/p\u003e\n\u003ch3\u003eVarieties of Basic Number Processing\u003c/h3\u003e\n\u003cp\u003eNumber processing, according to the triple-code model, recruits an analogical magnitude representation, a verbal word form, and a visual Arabic number form [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Much behavioral evidence has revealed the importance of these basic forms of number processing in children\u0026rsquo;s later mathematical achievement [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eFirst, the analogical magnitude representation holds and manipulates nonsymbolic magnitudes [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. To assess the analogical magnitude representation, the numerosity estimation task has been typically administered in young children [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. In this task, children are shown arrays of dots or objects in a short time, and children are asked to orally report the number of dots or objects in the array (see example in [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]). To perform this task, children should employ analogical magnitude representation to hold and manipulate non-symbolic numerical information. Previous work has shown that children possess an analogical mental number line that could be nonsymbolic in nature [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e], which enables their representation and manipulation of nonsymbolic numerical stimuli. With age increasing, children would map symbolic numbers onto nonsymbolic numeriosities, incorporating symbolic forms of numbers into early analogical representations. Their analogical codes of representation are relied on and further developed to help them possess an advanced level of magnitude representation.\u003c/p\u003e \u003cp\u003eSecond, in the verbal word form, numerals are represented lexically, phonologically, and syntactically; this is associated with a semantic representation of numerical quantity and much like any other type of words [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. The verbal system of number processing could be assessed with the numerical magnitude comparison task in which children are presented with two digits and are required to say which digit is larger [\u003cspan additionalcitationids=\"CR23\" citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. To solve this task, children should encode the numerical information presented visually and verbally, manipulate mental magnitudes and finally report their answer with verbal digits. To transform visual forms of Arabic numbers into verbal representations and answers, stored verbal codes of Arabic digits should be activated and employed. And given that this process also involves visual Arabic number forms, it is likely that both verbal codes and visual codes of numerical representation are involved in performing these processes.\u003c/p\u003e \u003cp\u003eThird, in the visual Arabic number form, quantities can be automatically encoded as strings of Arabic numerals [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. It can be assessed with the number line estimation task in which children are presented a horizontal number line and then asked to perform number-to-position or position-to-number estimations [\u003cspan additionalcitationids=\"CR26\" citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. Based on evidence from typically developed participants, the number line is assumed to follow Weber\u0026rsquo;s Law, with the representation of larger numbers becoming increasingly imprecise [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. With development, greater exposure to visual Arabic numbers in the modern mathematics education would promote transformations of numerical representational of symbolic numbers [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Previous results reveal that number line estimation performance in first graders on the range of 0-100 were better modelled with a logarithmic function, while students at second grade could estimate numbers within 100 by a linear scale [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. To further illuminate how children visually represent symbolic numbers, it was also found that on the 0-1000 range second graders have difficulty representing them linearly, however, fourth graders could do so [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. Thus, to learn symbolic mathematics fluently, children transform their logarithmic representation to a linear representation for visual symbolic numbers, starting with small ones and stretching towards larger numbers with accumulated experience with visual symbolic numbers.\u003c/p\u003e \u003cp\u003eThese three components of basic number processing could be further divided into non-symbolic and symbolic abilities, with numerosity estimation as non-symbolic and numerical magnitude comparison and number line estimation as symbolic. It is agreed that non-symbolic abilities have innate evolutionary origins, shared among human infants and other species, laying the foundation for the development of symbolic skills and later mathematical performance [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Symbolic abilities are characterized by integrating numerical symbolic system with non-symbolic numerosities [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e], which enables performance in more complex math problem solving presented in symbolic formats. Altogether, these non-symbolic and symbolic number processing abilities are domain-specific numerical skills, focusing on representing and manipulating numerical information of various formats. Children\u0026rsquo;s later mathematical performance is facilitated by increasingly mature domain-specific numerical abilities to precisely represent non-symbolic quantities, mapping non-symbolic quantities to symbolic magnitudes, and forming a more linear representation of magnitudes.\u003c/p\u003e \u003cp\u003eThe validity of triple-code model has been partially supported and revised by recent neural evidence. There are functionally dissociated brain areas associated with each code of representation, while it is also revealed that overlapping areas in the fronto-parietal network are activated for different forms of representation [\u003cspan additionalcitationids=\"CR34\" citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. This overlapping could reflect a more complex picture of the relation among three codes of representation. On the other hand, it could suggest that domain-general cognitive abilities are associated with number processing performance. When solving arithmetic problems presented in non-symbolic formats, previous studies found elicited neural activities in frontal areas, and it was suggested that this reflected involvement of working memory and attentional processes in performing visual representation of quantities [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. Also for the verbal component, it was found that parts of the mentalizing network and hippocampus which are responsible for recognizing and retrieving numerical facts from memory systems are involved [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. However, little behavioral evidence has showed domain-general associates with young children\u0026rsquo;s varied number processing in the framework of triple-code model. Therefore, more complex relationships across these three components of number processing could be further captured by investigating core domain-general cognitive abilities which would underlie these representations in children who are in the very process of developing their number processing skills.\u003c/p\u003e\n\u003ch3\u003eWorking Memory Components and Basic Number Processing\u003c/h3\u003e\n\u003cp\u003eOur study also lies in this assumption that development of domain-specific number processing abilities is supported by domain-general cognitive development. This could be suggested by previous studies revealing that children\u0026rsquo;s domain-general cognitive abilities could significantly predict number-processing skills and later mathematical performance [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. Among various domain-general abilities, working memory components should make unique contributions, given their storing and manipulating components that organize the representation and usage of environmental information [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]. Working memory is composed of multiple components, including the visuospatial sketchpad, phonological loop and central executive. They work together to encode environmental inputs, temporarily store messages, and combine the information to serve behavioral outcomes [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e Phonological loop, the articulatory component in the working memory model, could be mapped onto the verbal component in the triple-code model; that general ability to store verbal information could be related to rehearsal of number-specific verbal magnitudes. Visuospatial sketchpad, on the other hand, could be related to visual and analogical components in the triple-code model, that domain-specific ability to automatically code the quantities of visual objects as strings of Arabic numerals and organize numerical magnitudes onto spatially presented number lines could be related to domain-general ability to store visuospatial inputs. Besides these representational components, central executive in the working memory model, acting with the organizing role, could facilitate manipulation of domain-specific numerical information in number processing tasks [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. It would be interesting to see how these three working memory components would be associated with early domain-specific number processing performance.\u003c/p\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eVisual Selective Attention and Basic Number Processing\u003c/h2\u003e \u003cp\u003eIn the current study, we are also interested in the role of visual selective attention in domain-specific number processing. Visual selective attention, as another core domain-general ability, has been claimed to facilitate rehearsal of stored information and more efficient processing of visual information [\u003cspan additionalcitationids=\"CR43 CR44\" citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e]. According to the Pathways model, visual attention should be very important to the symbolic number system and numerical magnitude processes [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAs a top-down process to directly focus people on certain aspect of surrounding environments [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e], visual selective attention may be especially important in children\u0026rsquo;s ability to process numerical magnitudes and manage the complex demands of mathematical tasks [\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e]. In LeFevre et al.\u0026rsquo;s study [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e], visual attention was found to be independently associated with two early numeracy skill measures. Children who were better at visual selective attention could name written Arabic numbers more correctly and performed better on a nonlinguistic arithmetic task that requires representing and manipulating visual quantity information. The importance of visual selective attention could also be suggested by evidence that numbers and spaces are inherently interweaved in human mind representations, that children\u0026rsquo;s number line representation is predicted by spatial processing skills [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e, \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003eThe Present Study\u003c/h2\u003e \u003cp\u003eThe purpose of the current study was to examine the contributions of working memory and visual selective attention to basic number processing. The current study recruited children who were 5- to 8-years old as participants because this is the critical period during which children getting increasingly exposed to extensive experience with numbers, both in formal math and informal math activities [\u003cspan additionalcitationids=\"CR51\" citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e]. In this age range, their representation of magnitudes revealed great improvements, and they formed better linear representation of integers. In the present study, three basic numeracy tasks were employed to assess children\u0026rsquo;s number-processing abilities: numerosity estimation, number line estimation, and numerical magnitude comparison. Three components of working memory (the phonological loop, visuospatial sketchpad and central executive) were separately examined by the digit recall task, visual matrix task, and Flanker task. Visual selective attention was examined by asking children to search for a specific target in limited time.\u003c/p\u003e \u003cp\u003eSeveral hypotheses were proposed. First, the weak phonological representation hypothesis proposes that number processing that relates to manipulating verbal codes of quantity involves a high level of phonological processing, while nonverbal representation is not influenced by phonological skills [\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e]. It was therefore hypothesized that the phonological loop would be more associated with children\u0026rsquo;s performance in the numerical magnitude comparison task and number line estimation than in the numerosity estimation task. Second, according to the triple-code model [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e], we would like to find significant predictions of the visuospatial sketchpad for the numerosity estimation and number line estimation tasks since a visual linear representation of numerical information can facilitate magnitude estimation performance [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e, \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e]. In addition, attention to visual stimuli is engaged in visual processing of the Arabic number form [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. We therefore anticipated that visual selective attention would be related to performance on visually presented tasks including numerosity estimation and number line estimation tasks.\u003c/p\u003e \u003c/div\u003e"},{"header":"Methods","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003eParticipants\u003c/h2\u003e \u003cp\u003eThe participants were 110 children (50 girls, mean age of 6.28 years, 5.37\u0026ndash;7.86 years old, \u003cem\u003eSD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.41 years) from Fujian Province and Henan Province in China. They were native Chinese speakers, and all children are not diagnosed with mathematical difficulties. Most of them came from middle SES families and all had normal or corrected-to-normal vision and hearing. According to the national statistics data (National Bureau of Statistics of the People\u0026rsquo;s Republic of China, 2020; State Council of the People\u0026rsquo;s Republic of China, 2020), the average disposable income in Fujian and Henan was both comparable to that of the middle-income group (State Council of the People\u0026rsquo;s Republic of China, 2020), which reflects that most of the children in our study came from middle SES families. For children\u0026rsquo;s school experience and residence, all children in our study were in kindergartens and resided in urban areas.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eGeneral Procedure\u003c/h2\u003e \u003cp\u003eThere were seven tasks in the current study, and Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e presents a schematic representation of the seven tasks. All the tasks are available on the website \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://www.dweipsy.com/\u003c/span\u003e\u003cspan address=\"http://www.dweipsy.com/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e. Because of the Covid-19 pandemic, we had no choice but to ask children to complete the tasks with trained experimenters monitoring the screen online. Previous studies have administered the tasks in similar ways [\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e, \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e]. During all tasks, children did most of the tasks themselves with parents and teachers sitting around silently. All what parents and teachers did was to mark down what the children did for completing the number line estimation task, the visual selective attention task, and the visuospatial sketchpad task, especially for young kids who are less familiar with handling the computer mouse. For all the processes, trained experimenters could observe the parents and teachers\u0026rsquo; behaviors through the monitors. Once parents scheduled their sessions, experimenters provided parents and teachers with information to prepare them for their first session. This included information on preparing devices and information on dos and don\u0026rsquo;ts. For example, experimenters stressed the importance of not providing input during all tasks.\u003c/p\u003e \u003cp\u003eAt the start of the testing session, parents and teachers were again instructed by the test administrator not to provide answers or hints during these tasks, and test administrators monitored the whole process. We believe the results of the remote assessment were reliable because we have minimized the involvement of parents and teachers. Besides, recent work has also found that online testing of cognitive tasks reveals little difference from those administered offline [\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e, \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e]. The sequence of these tasks was counterbalanced between participants. The test administration lasted for approximately 40 to 50 minutes with a short break.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003eMeasures\u003c/h2\u003e \u003cp\u003e \u003cb\u003eVisual-Spatial Sketchpad.\u003c/b\u003e The visual matrix task was adapted from the study by Wei et al. [\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e] to assess the ability of participants to remember visual sequences within a matrix. Participants were presented with a series of dots in a 3\u0026times;3 lattice on the screen. Each dot was shown on the screen for 1000 ms, and the interval in between dot presentations was 1000 ms. When the last dot disappeared from the screen, participants were asked to click the sequence of positions in the lattice where the dots that had been shown disappeared. The number of dots ranged from 3 to 10, with 3 items at each difficulty level. In the practice experiment, children received feedback. There was no feedback to participants during the formal experiment. The test was ended when children consecutively and incorrectly answered all 3 items of a specific difficulty level. The final score was the total number of correct trials. Cronbach\u0026rsquo;s alpha coefficient on this task was 0.95.\u003c/p\u003e \u003cp\u003e \u003cb\u003ePhonological loop.\u003c/b\u003e The task with the digit recall forward and the digit recall backward adapted from the Wechsler Intelligence Scale [\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e], was used to assess phonological loop [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e, \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e60\u003c/span\u003e]. Participants were presented with a series of digits aurally through earphones. The length of the sound for each digit was standardized to 200 ms. In the forward digit span task, participants were asked to remember the order of the digits. In the backward digit span task, children were required to remember the reverse order of the digits. For both parts, children were asked to voice out what they have heard after listening to the sound. The test began with 3 digits and increased gradually until children failed to type them correctly three times consecutively. Experimenters recorded children\u0026rsquo;s answers in the spreadsheet. One score was given for each correctly answered item. The final score was the total number of correct trials on both recall tasks. Cronbach\u0026rsquo;s alpha coefficient for this measure was 0.68.\u003c/p\u003e \u003cp\u003e \u003cb\u003eCentral executive.\u003c/b\u003e The Flanker task was used to measure children\u0026rsquo;s central executive, which was adapted from Fan et al. [\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e]. Flanker task has been used frequently to index central executive in the working memory [\u003cspan additionalcitationids=\"CR63\" citationid=\"CR62\" class=\"CitationRef\"\u003e62\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e64\u003c/span\u003e]. Children were presented with five arrows in one line on the screen. In this task, children were asked to distinguish the direction of the arrow in the middle by pressing the \u0026ldquo;Q\u0026rdquo; key for left or pressing the \u0026ldquo;P\u0026rdquo; key for right. There were two conditions: the congruent condition and the incongruent condition. In the congruent condition, the middle arrows\u0026rsquo; directions were the same as those of the other arrows. In the incongruent condition, the middle arrows\u0026rsquo; directions were opposite to the directions of the other arrows. The arrow line was presented for 1700 ms or until participants pressed a key. There were totally 48 trials in this task. The final score was the number of correct trials minus the number of incorrect trials. Cronbach\u0026rsquo;s alpha coefficient of this task was 0.86.\u003c/p\u003e \u003cp\u003e \u003cb\u003eVisual selective attention.\u003c/b\u003e Visual search task was used to measure participants\u0026rsquo; visual selective attention, which adapted from the study by Trick \u0026amp; Enns [\u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e65\u003c/span\u003e]. There were rows of combined graphics on the screen that could be viewed, and these combined graphics were automatically controlled to appear on the screen from bottom to top with the speed of one row of ten stimuli per four seconds. Children were required to select a combined graphic consisting of a circle and a square among all target and distractor graphics, and distractors consisted of other combinations of two basic figures (e.g. triangles, trapezoids, sectors). The task was limited to 4 minutes. Each correct click on the target figure was recorded as 1, while a missed target was recorded as 0 and wrong click was recorded as -1. The points were then added up to give a final score. The Cronbach\u0026rsquo;s alpha coefficient on this task was 0.97.\u003c/p\u003e \u003cp\u003e \u003cb\u003eNumber line estimation.\u003c/b\u003e This task was used to evaluate children\u0026rsquo;s mental representation of visual symbolic numbers and thus provided an indicator of developing number-processing skills [\u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e66\u003c/span\u003e]. Children were shown a digit on a physical number line with fixed endpoints (0-100) without interim numbers or marks and were asked to mark the line with a cross to indicate the location of the shown digit. Children received feedback in the practice experiment, while there was no feedback presented to children in the formal experiment. Children had to put the numeral in the right place on the number line by pointing out the position, and parents and teachers would help click the position on the line. Then, the position children clicked was transferred to and recorded as the corresponding number on the standard number line. The score of each trial was calculated as 100\u0026ndash;100 |response-standard answer|/(standard answer + |response-standard answer|), in which \u0026lsquo;response\u0026rsquo; refers to the participants\u0026rsquo; answer and \u0026lsquo;standard answer\u0026rsquo; refers to the correct number [\u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e67\u003c/span\u003e]. The final score was the average score of the 20 trials (rounding to a whole number). Cronbach\u0026rsquo;s alpha coefficient on this task was 0.97.\u003c/p\u003e \u003cp\u003e\u003cb\u003eNumerosity estimation.\u003c/b\u003e The estimation of numerosity task required participants to estimate the number of dots from dot arrays consisting of 11 to 99 dots [\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e]. Dot arrays were presented on the screen for 200 ms. The dot arrays were created with all dot arrays occupying the same total area. Dots in a dot array were randomly distributed within a circle with varying sizes. The envelope area/convex hull varied little from trial to trial. Participants orally reported their estimated number for each array, and experimenters typed their answers into the computer with the keypad. After each trial, feedback was shown on the screen. The participants could not change their entries because the feedback in the formal trials was demonstrated very fast with complicated Chinese characters. Children at this age level could not catch up with it. In contrast, children would obtain clear feedback in the practice trials to ensure they understand how this task was administered. There were 28 trials in the formal test. The final score was calculated following the same rule as was used for the number line estimation task. Cronbach\u0026rsquo;s alpha coefficient on this task was 0.87.\u003c/p\u003e \u003cp\u003e \u003cb\u003eNumerical magnitude comparison.\u003c/b\u003e This task asked children to judge which of the two presented single-digit numbers was larger in magnitude [\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e, \u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e68\u003c/span\u003e, \u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e69\u003c/span\u003e]; this task was adapted from the classic number Stroop task [\u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e70\u003c/span\u003e]. The two numbers were presented on the screen side-by-side. Children made the judgment by pressing \u0026ldquo;Q\u0026rdquo; when the number on the left side was larger or pressing \u0026ldquo;P\u0026rdquo; when the number on the right side was larger. Small numbers were 1.6\u0026deg; in horizontal visual angle and 2.4\u0026deg; in vertical visual angle. Large numbers had horizontal and vertical visual angles of 2.0\u0026deg; and 2.9\u0026deg;, respectively. There were three conditions in the task. In the neutral condition, both numbers were of the same physical size (either small or large). In the congruent condition, numerically smaller numbers were also physically smaller. In the incongruent condition, the numerically smaller number was physically larger. The formal task contained 84 trials, with 28 trials for each condition. The final score was the number of correct trials. Cronbach\u0026rsquo;s alpha coefficient on this task was 0.99.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003eData Analysis\u003c/h2\u003e \u003cp\u003eFirst, a preliminary analysis was conducted to compute the means, standard deviations and correlations among the main variables. Second, we tried to answer our main question about the roles of working memory and visual selective attention on the three number processing tasks. Given that estimating separate models for the three dependent measures might lead to increased Type I error, we followed what has been done in previous relevant research by including all independent measures in a single model [\u003cspan additionalcitationids=\"CR72\" citationid=\"CR71\" class=\"CitationRef\"\u003e71\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e73\u003c/span\u003e]. The variance each of those predictors explained in number processing could be calculated with each standardized coefficient squared. A multivariate multiple regression (MMR) model was developed to evaluate the effects of visual selective attention, the phonological loop, the visuospatial sketchpad and the central executive on children\u0026rsquo;s performance on numerosity estimation, number line estimation and numerical magnitude comparison tasks after considering demographic covariates, including age and gender. Mplus 7 was used to develop the MMR model, which permits handling missing data without listwise or pairwise deletion of incomplete cases [\u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e74\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e"},{"header":"Results","content":"\u003cp\u003eWe first excluded data points which are 3 \u003cem\u003eSD\u003c/em\u003e beyond the mean score. Regarding missing data, we conducted the Little\u0026rsquo;s MCAR test and it indicated that the data was not missing completely at random, \u003cem\u003e\u0026chi;\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;72.02, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.10 [\u003cspan\u003e75\u003c/span\u003e]. Table \u003cspan\u003e1\u003c/span\u003e presents means, standard deviations, ranges, skewness and kurtosis of non-standardized variables. Descriptive statistics and correlations among standardized variables are displayed in Table \u003cspan\u003e2\u003c/span\u003e. To adjust for a certain degree of nonnormality, we used the standardized scores to conduct the formal analysis [\u003cspan\u003e57\u003c/span\u003e].\u003c/p\u003e\n\u003cdiv\u003e\n \u003cp\u003e\u003cstrong\u003eTable 1\u0026nbsp;\u003c/strong\u003e\u003cem\u003eDescriptive Statistics among Observed Variables.\u003c/em\u003e\u003c/p\u003e\n \u003cdiv\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"767\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"36.28088426527958%\" valign=\"top\"\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.743823146944083%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003eRange\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.743823146944083%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003eMean\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.743823146944083%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003eSD\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.743823146944083%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003eSkewness\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.743823146944083%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003eKurtosis\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"36.422976501305484%\" valign=\"top\"\u003e\n \u003cp\u003eAge\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" valign=\"top\"\u003e\n \u003cp\u003e5.37-7.86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e6.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e0.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e0.79\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e1.61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"0.26109660574412535%\"\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"36.422976501305484%\" valign=\"top\"\u003e\n \u003cp\u003eGender \u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" valign=\"top\"\u003e\n \u003cp\u003e1-2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e1.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e0.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e0.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e-1.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"0.26109660574412535%\"\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"36.422976501305484%\" valign=\"top\"\u003e\n \u003cp\u003eVisual Selective Attention\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" valign=\"top\"\u003e\n \u003cp\u003e-18-83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e24.84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e20.64\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e0.52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e0.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"0.26109660574412535%\"\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"36.422976501305484%\" valign=\"top\"\u003e\n \u003cp\u003eCentral Executive\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" valign=\"top\"\u003e\n \u003cp\u003e-4-48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e36.76\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e12.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e-1.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e0.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"0.26109660574412535%\"\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"36.422976501305484%\" valign=\"top\"\u003e\n \u003cp\u003ePhonological Loop\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" valign=\"top\"\u003e\n \u003cp\u003e0-17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e8.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e3.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e0.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e0.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"0.26109660574412535%\"\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"36.422976501305484%\" valign=\"top\"\u003e\n \u003cp\u003eVisuospatial Sketchpad\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" valign=\"top\"\u003e\n \u003cp\u003e0-27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e10.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e5.78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e0.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e-0.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"0.26109660574412535%\"\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"36.422976501305484%\" valign=\"top\"\u003e\n \u003cp\u003eNumerosity Estimation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" valign=\"top\"\u003e\n \u003cp\u003e53-88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e70.93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e7.98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e-0.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e-0.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"0.26109660574412535%\"\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"36.422976501305484%\" valign=\"top\"\u003e\n \u003cp\u003eNumber Line Estimation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" valign=\"top\"\u003e\n \u003cp\u003e59-90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e76.98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e7.92\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e-0.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e-0.82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"0.26109660574412535%\"\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"36.422976501305484%\" valign=\"top\"\u003e\n \u003cp\u003eNumerical Magnitude Comparison\u003csup\u003e\u0026nbsp;\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" valign=\"top\"\u003e\n \u003cp\u003e0-76\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e42.54\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e15.79\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e-0.87\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.663185378590079%\" colspan=\"2\" valign=\"top\"\u003e\n \u003cp\u003e0.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"0.26109660574412535%\"\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cdiv align=\"left\"\u003e\u003cem\u003eNote.\u003c/em\u003e \u003csup\u003ea\u0026nbsp;\u003c/sup\u003eDummy coded: 1 = boys, 2 = girls.\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv\u003e \u0026nbsp;\u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 2\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003e\u003cem\u003eDescriptive statistics and correlations among the involved variables\u003c/em\u003e\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eVariable\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.Age\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026mdash;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.Gender\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.008\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026mdash;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.Visual Selective Attention \u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.005\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.070\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026mdash;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.Central Executive \u003csup\u003ec\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.023\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.074\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.160\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026mdash;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.Phonological Loop \u003csup\u003ed\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.011\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.038\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.234\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.099\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026mdash;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.Visuospatial Sketchpad \u003csup\u003ee\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.033\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.047\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.291\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.098\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.085\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026mdash;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7. Numerosity Estimation \u003csup\u003ef\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.030\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.020\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.338\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.212\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.236\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.245\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026mdash;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.Number Line Estimation \u003csup\u003eg\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.078\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.094\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.417\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.222\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.280\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.306\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.597\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026mdash;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.Numerical Magnitude Comparison \u003csup\u003eh\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.098\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.024\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.240\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.308\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.247\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.380\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.294\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.369\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026mdash;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003ctfoot\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"10\"\u003e\u003cem\u003eNote.\u003c/em\u003e \u003csup\u003ea\u003c/sup\u003e Dummy coded: 1\u0026thinsp;=\u0026thinsp;boys, 2\u0026thinsp;=\u0026thinsp;girls.\u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tfoot\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003csup\u003eb, c, d, e, f, g, h\u003c/sup\u003e Standardized scores of visual selective attention, central executive, phonological loop, visuospatial sketchpad, numerosity estimation, number line estimation and numerical magnitude comparison.\u003c/p\u003e\n\u003cp\u003e\u003csup\u003e*\u003c/sup\u003e \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.05, \u003csup\u003e**\u003c/sup\u003e \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.01, \u003csup\u003e***\u003c/sup\u003e \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001, two-tailed.\u003c/p\u003e\n\u003cp\u003eWe then examined the path analysis model mentioned above to evaluate the extent to which visual selective attention, the phonological loop, the visuospatial sketchpad and the central executive accounted for children\u0026rsquo;s performance on numerosity estimation, number line estimation and numerical magnitude comparison tasks after considering demographic covariates. The model revealed a good fit [\u003cem\u003e\u0026chi;\u003c/em\u003e\u0026sup2; (\u003cem\u003edf\u003c/em\u003e\u0026thinsp;=\u0026thinsp;8)\u0026thinsp;=\u0026thinsp;10.288, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.245, CFI\u0026thinsp;=\u0026thinsp;0.980, TLI\u0026thinsp;=\u0026thinsp;0.946, RMSEA\u0026thinsp;=\u0026thinsp;0.051 (90% CI = [.000, .130]), SRMR\u0026thinsp;=\u0026thinsp;0.042]. The amount of variance of the three outcome variables explained by predictors were all significant and above 20% (numerosity estimation: \u003cem\u003eR\u003c/em\u003e\u0026sup2; = 0.208; number line estimation: \u003cem\u003eR\u003c/em\u003e\u0026sup2; = 0.369; numerical magnitude comparison: \u003cem\u003eR\u003c/em\u003e\u0026sup2; = 0.333; all \u003cem\u003ep\u003c/em\u003es\u0026thinsp;\u0026lt;\u0026thinsp;.05). Figure 2 shows the paths, and Table \u003cspan\u003e3\u003c/span\u003e shows the standardized and unstandardized coefficients of the paths from the six predictors (age, gender, visual selective attention, central executive, phonological loop, and visuospatial sketchpad) to the three outcome variables (numerosity estimation, number line estimation and numerical magnitude comparison).\u003c/p\u003e\n\u003cp\u003eAge served as a significant predictor of performance on the numerical magnitude comparison task (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.018) and was a marginal predictor of performance on the number line estimation task (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.066), while was it not significantly related to performance on the numerosity estimation task (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.604). There was an effect of gender on number line estimation performance (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.007), and boys performed better than girls. Additionally, visual selective attention explained unique variance in the numerosity estimation and number line estimation tasks (numerosity estimation: \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.021; number line estimation: \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001). Importantly, the phonological loop significantly explained unique variance in all three tasks, including numerosity estimation (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.045), number line estimation (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.001), and numerical magnitude comparison tasks (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.027). Last, the central executive and visuospatial sketchpad significantly predicted performance on the numerical magnitude comparison task (central executive: \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.001; visuospatial sketchpad: \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001).\u003c/p\u003e\n\u003cdiv\u003e \u0026nbsp;\u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 3\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003e\u003cem\u003eMMR model predicting individual differences in numerosity estimation, number line estimation and numerical magnitude comparison\u003c/em\u003e\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eNumerosity Estimation \u003csup\u003ef\u003c/sup\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eNumber Line Estimation \u003csup\u003eg\u003c/sup\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eNumerical Magnitude Comparison \u003csup\u003eh\u003c/sup\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e(\u003cem\u003eR\u003c/em\u003e\u0026sup2; = .208, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.016)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e(\u003cem\u003eR\u003c/em\u003e\u0026sup2; = .369, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003e(\u003cem\u003eR\u003c/em\u003e\u0026sup2; = .333, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eVariable\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eCoef. (S.E.)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eStand.(S.E.)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eCoef. (S.E.)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eStand.(S.E.)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eCoef. (S.E.)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eStand.(S.E.)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAge\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.097 (.186)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.040 (.078)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.359 (.193)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.149 (.081)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.457 (.183) \u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.191 (.081) \u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGender \u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.093 (.187)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.047 (.094)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.430 (.162) \u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.215 (.080) \u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.017 (.172)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.009 (.087)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eVisual Selective Attention \u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.219 (.094) \u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.218 (.094) \u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.322 (.088) \u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.318 (.088) \u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.032 (.082)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.032 (.083)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCentral Executive \u003csup\u003ec\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.162 (.113)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.145 (.096)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.112 (.131)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.099 (.113)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.304 (.104) \u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.273 (.085) \u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePhonological Loop \u003csup\u003ed\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.254 (.126) \u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.201 (.100) \u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.314 (.091) \u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.248 (.073) \u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.288 (.132) \u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.229 (.104) \u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eVisuospatial Sketchpad \u003csup\u003ee\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.148 (.098)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.142 (.093)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.153 (.100)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.147 (.098)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.330 (.089) \u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.319 (.074) \u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003ctfoot\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"7\"\u003e\u003cem\u003eNote.\u003c/em\u003e \u003csup\u003ea\u003c/sup\u003e Dummy coded: 1\u0026thinsp;=\u0026thinsp;boys, 2\u0026thinsp;=\u0026thinsp;girls.\u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tfoot\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003csup\u003eb, c, d, e, f, g, h\u003c/sup\u003e Standardized scores of visual selective attention, central executive, phonological loop, visuospatial sketchpad, numerosity estimation, number line estimation and numerical magnitude comparison. \u003cem\u003eCoef.\u003c/em\u003e = estimate of unstandardized path coefficient; \u003cem\u003eStand.\u003c/em\u003e = estimate of standardized path coefficient.\u003c/p\u003e\n\u003cp\u003e\u003csup\u003e*\u003c/sup\u003e \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.05, \u003csup\u003e**\u003c/sup\u003e \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.01, \u003csup\u003e***\u003c/sup\u003e \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001, two-tailed.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThe purpose of this present study was to investigate whether component(s) of working memory and visual selective attention could predict performance on a variety of basic number-processing tasks in young Chinese children. Findings revealed that the phonological loop accounted for unique variance in children\u0026rsquo;s performance on all three number-processing tasks, while the visuospatial sketchpad uniquely contributed to the numerical magnitude comparison task. In addition, we found that performance on the numerical magnitude comparison task was significantly explained by the central executive. Visual selective attention, on the other hand, was associated with children\u0026rsquo;s performance on numerosity estimation and number line estimation tasks.\u003c/p\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003ePhonological Loop and Basic Number Processing\u003c/h2\u003e \u003cp\u003e The current study showed that the phonological loop was significantly associated with this verbal system of number processing. Previous studies have revealed that the phonological loop enables the acquisition of the phonological structure of verbal Arabic numerals [\u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e73\u003c/span\u003e, \u003cspan additionalcitationids=\"CR77\" citationid=\"CR76\" class=\"CitationRef\"\u003e76\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e78\u003c/span\u003e]. Indeed, to successfully compare magnitude information of two orally presented Arabic numbers (such as \u0026ldquo;3\u0026rdquo; and \u0026ldquo;5\u0026rdquo;), children should first retrieve the verbal codes of the digits in mind. After receiving the two pieces of sensory verbal numerical information, children may employ phonological memory to maintain the temporary phonological numerical information [\u003cspan additionalcitationids=\"CR80\" citationid=\"CR79\" class=\"CitationRef\"\u003e79\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR81\" class=\"CitationRef\"\u003e81\u003c/span\u003e]. By incorporating these pieces of numerical information with existing numerical knowledge, the following magnitude comparison process could be executed. Therefore, through these mental processes, storing phonological numerical information is critical in solving this magnitude comparison problem.\u003c/p\u003e \u003cp\u003eIn addition, we also demonstrated a significant predictive effect of the phonological loop on performance on numerosity estimation and number line estimation tasks, both of which involve visual and analogical number processing. When inspecting the relative significant values and effect sizes of the three effects that phonological loop is involved, we found that phonological loop played a greater role in the two tasks which involve verbal representation (numerosity estimation, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.045; number line estimation, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.001; numerical magnitude comparison, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.027). When performing the numerosity estimation task, children were required to estimate numerosity and report it in verbal digits. Children not only need to extract visual numerosity information from the dot arrays but also need to transform the numerosity information into verbal numeral answers. This indicated that children not only need to rely on analogical representation of quantities, but also should integrate their number word knowledge and phonological storage ability to estimate numerosity arrays [\u003cspan citationid=\"CR82\" class=\"CitationRef\"\u003e82\u003c/span\u003e]. However, some studies argue that the use of numeric stimuli in the phonological loop task tapped into similar (numeric) processes involved in the magnitude comparison task. Future studies are needed to replace the digit span task with other stimuli while assessing phonological memory.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003eVisuospatial Sketchpad and Basic Number Processing\u003c/h2\u003e \u003cp\u003eThe results demonstrated that the visuospatial sketchpad failed to significantly predict performance on numerosity estimation and number line estimation tasks, while it accounted for variance in performance on the numerical magnitude comparison task. Given the importance of a visual linear organization of numerical information in facilitating estimation performance [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e, \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e], we were curious to explain the current results. The predictive effect of the visuospatial sketchpad on performance on the numerical magnitude comparison task could be due to involvement of visual representation of magnitudes. In the numerical magnitude comparison task, children were shown written Arabic digits and asked to compare their magnitudes. The mental processes in solving the comparison task could largely have involved visual representations of numerical magnitudes, when children of this age could have not completely mapped their verbal counting words to innate visual numerosities and could not activate verbal codes automatically to solve this comparison problem [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e, \u003cspan citationid=\"CR83\" class=\"CitationRef\"\u003e83\u003c/span\u003e]. To accurately compare the magnitudes, children could retrieve visual digit knowledge and maintain visual quantity information for later comparison rather than merely relying on the hypothesized verbal system of representation. Therefore, the numerical magnitude comparison task could activate the visual system of number processing, which requires visual processing skills to manipulate strings of Arabic numerals [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003eCentral Executive and Basic Number Processing\u003c/h2\u003e \u003cp\u003eThe current findings also revealed strong associations between the central executive and numerical magnitude comparison performance. This might be due to the requirements of this task (e.g., presentation formats and trial composition) in the current study. In the numerical magnitude comparison task, children were shown the written Arabic digits that supplemented the verbally presented ones. When the relative physical positions of the two numbers and the magnitude relations of the two numbers did not align with the left-small and right-large associations, it is possible that children need to consciously inhibit selecting the larger number by instinctively pressing the key that was on the right side [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR84\" class=\"CitationRef\"\u003e84\u003c/span\u003e, \u003cspan citationid=\"CR85\" class=\"CitationRef\"\u003e85\u003c/span\u003e]. Given that our numerical magnitude comparison task included congruent and incongruent trials between magnitude and physical sizes, the strong correlation between the central executive and performance on the numerical magnitude comparison task could be unsurprising ([\u003cspan additionalcitationids=\"CR87\" citationid=\"CR86\" class=\"CitationRef\"\u003e86\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR88\" class=\"CitationRef\"\u003e88\u003c/span\u003e], for the role of inhibitory control in numerosity magnitude comparison tasks). The Flanker task required children to inhibit responding to the directions of peripheral arrows, and the incongruent numerical magnitude comparison trials required inhibition of judging the relative physical sizes of numbers. Both these tasks highlighted the inhibition component of the central executive. Given these possible confounding mental processes, we are uncertain about whether the central executive plays a crucial role in purely numerical magnitude comparison processes. Future studies could explore this further by adopting single verbal-presented numerical magnitude comparison tasks.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003eVisual Selective Attention and Basic Number Processing\u003c/h2\u003e \u003cp\u003eAs predicted, visual selective attention was shown to be important in numerosity estimation and number line estimation performance. Visual selective attention is responsible for selecting locations in visual space [\u003cspan citationid=\"CR89\" class=\"CitationRef\"\u003e89\u003c/span\u003e]. Indeed, to estimate numerosity in a visually displayed array, children should first receive and process the visual sensory inputs by attending to the dots that are scattered in their visual field. Only by successfully encoding these visual inputs could children later perform internal estimation operations. This first visual attending process in numerosity estimation is conceptually similar to the visual search task in which children were required to select patterns that consisted of a circle and a square among several patterns in their visual field. Both of these tasks are closely related to the visual selective attention ability of selecting relevant visual information from noisy visual inputs [\u003cspan citationid=\"CR89\" class=\"CitationRef\"\u003e89\u003c/span\u003e]. Therefore, to accurately estimate numerosity information that is heavily visually loaded, visual selective attention that enables visually attending to locations in visual space could play a crucial role. On the other hand, to solve the number line estimation task, children were required to place Arabic numbers accurately on the number lines. To accomplish this, they should first encode the quantity information from the written digits with their existing visual digit knowledge. Importantly, estimating quantity accurately on the number line further relies on a visually ordered mental number line [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e, \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e, \u003cspan citationid=\"CR90\" class=\"CitationRef\"\u003e90\u003c/span\u003e]. Employment of visual processing could facilitate this spatial representation of numbers along a visual number line, and this linear order of quantity information facilitates accurate estimations [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e, \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e]. Serving as a mental blackboard, visual-spatial processing could translate math-related problems into its spatial descriptions [\u003cspan additionalcitationids=\"CR92\" citationid=\"CR91\" class=\"CitationRef\"\u003e91\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR93\" class=\"CitationRef\"\u003e93\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eCombining the roles of the visuospatial sketchpad and visual selective attention in basic number processing, we suspect that the low predictive effect of the visuospatial sketchpad on estimation tasks could be due to a high overlap between the visuospatial sketchpad and visual selective attention (\u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.29, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.003), which has also been suggested in previous studies [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e, \u003cspan citationid=\"CR94\" class=\"CitationRef\"\u003e94\u003c/span\u003e]. Indeed, after removing visual selective attention measure from the model, we found that visuospatial sketchpad significantly predicted performance on both numerosity estimation (\u003cem\u003eβ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.21, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.026) and number line estimation (\u003cem\u003eβ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.25, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.007). The visuospatial sketchpad is responsible for visual and spatial representations of visual-spatial relations among various objects [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e], and visual selective attention is responsible for selecting locations in visual space [\u003cspan citationid=\"CR89\" class=\"CitationRef\"\u003e89\u003c/span\u003e]. They could both highlight shared components of visual processing of numerical information. In the study by Zhou et al. [\u003cspan citationid=\"CR95\" class=\"CitationRef\"\u003e95\u003c/span\u003e], visuospatial processing was found to mediate the relation between numerosity performance and early arithmetic performance; however, this relation was not revealed in subsequent research that controlled for visual attention [\u003cspan citationid=\"CR96\" class=\"CitationRef\"\u003e96\u003c/span\u003e]. It is possible that, by facilitating a linear organization of magnitudes, the visuospatial sketchpad and visual selective attention, both of which highlight visual processing skills, facilitate basic number processing.\u003c/p\u003e \u003cp\u003eBesides, our results also revealed that children\u0026rsquo;s age was correlated with their performance on number line estimation and numerical magnitude comparison tasks. This accords with previous literature revealing growth in children\u0026rsquo;s precision in representing numerical magnitudes as they are exposed to more formal mathematical education on the symbolic number system and engaged in more mathematical activities which promote understanding magnitudes [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e71\u003c/span\u003e, \u003cspan citationid=\"CR97\" class=\"CitationRef\"\u003e97\u003c/span\u003e, \u003cspan citationid=\"CR98\" class=\"CitationRef\"\u003e98\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eOf the three number processing tasks, we only observed the gender difference in number line estimation performance, which is both revealed in bivariate correlations and in the model. And this is congruent with previous literature revealing gender differences on this specific number processing task [\u003cspan additionalcitationids=\"CR100 CR101\" citationid=\"CR99\" class=\"CitationRef\"\u003e99\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR102\" class=\"CitationRef\"\u003e102\u003c/span\u003e]. On the one hand, gender stereotypes about mathematical ability could be transmitted to children subtly, which could influence girls\u0026rsquo; confidence in performing math relevant tasks [\u003cspan citationid=\"CR101\" class=\"CitationRef\"\u003e101\u003c/span\u003e, \u003cspan citationid=\"CR103\" class=\"CitationRef\"\u003e103\u003c/span\u003e, \u003cspan citationid=\"CR104\" class=\"CitationRef\"\u003e104\u003c/span\u003e]. On the other hand, performance on the number line estimation task require precise representation of symbolic magnitudes onto spatial dimensions, which is largely dependent on visuospatial abilities. And it has been shown that visuospatial processing which males take an advantage plays a great role in this task [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e, \u003cspan citationid=\"CR105\" class=\"CitationRef\"\u003e105\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003eLimitations and Future Directions\u003c/h2\u003e \u003cp\u003eThere are several limitations in the current study. First, we acknowledge that the digit span task revealed unsatisfactory reliability in the current study. This might be because the social distance rule during COVID-19 influenced the administration, especially when our participants were young kids. Second, in the numerical magnitude comparison task, children were also visually presented numerical digits whose physical sizes were congruent or incongruent with their magnitudes. As mentioned above, this may have introduced some confounding mental processes in solving this task. Third, other domain general cognitive abilities, such as linguistic abilities [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR106\" class=\"CitationRef\"\u003e106\u003c/span\u003e], could influence the results. Future studies could investigate how these abilities should be statistically controlled for while investigating the associates with various number processing performance. Finally, we acknowledge the limitation of our sample and measured covariate demographic variables. We only included Chinese children, and since the Chinese number system is different from many other number systems such as the English system, it remains unclear whether the contributions of working memory and visual selective attention to early number-processing skills in Chinese children revealed in the current study can be generalized to other populations. And given that our sample was mainly drawn from middle SES families and high parental education, we could not speak firmly whether results from the current study could be equally generalizable to populations varying on different levels of family backgrounds. Future studies could recruit more diverse samples on a variety of demographic dimensions, to further examine cognitive precursors to children\u0026rsquo;s early number processing abilities.\u003c/p\u003e \u003cp\u003eAltogether, the current study investigated whether working memory components and visual selective attention demonstrated predictive effects on performance on different kinds of basic number-processing in young Chinese children. The results suggested that three components of working memory, including the phonological loop, visuospatial sketchpad and central executive, and visual selective attention showed differentiated associations with performance on various number-processing tasks. The present results highlighted potential implications for Chinese mathematical education and practices. Standardized assessments and training protocols of working memory and visual attention could be developed by researchers and examined their effects for screening children at risk of mathematics deficits and promoting children\u0026rsquo;s number processing. Regarding spatial ability, previous studies have developed assessments for spatial ability and successfully performed systematic spatial training to improve children\u0026rsquo;s mathematical performance [\u003cspan citationid=\"CR107\" class=\"CitationRef\"\u003e107\u003c/span\u003e, \u003cspan citationid=\"CR108\" class=\"CitationRef\"\u003e108\u003c/span\u003e]. Similarly, future research from both our study and others focusing on improving early number processing ability could be more directed to interventional practices of assessing and training on working memory and visual selective attention [\u003cspan citationid=\"CR109\" class=\"CitationRef\"\u003e109\u003c/span\u003e, \u003cspan citationid=\"CR110\" class=\"CitationRef\"\u003e110\u003c/span\u003e], and empirically examine their effects among children from highly controlled to more naturalistic learning contexts (laboratories, classrooms, homes).\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003e\u003cem\u003eEthics approval and consent to participate\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe study procedure was approved by the Ethics Committee of the faculty of psychology, Beijing Normal University. In compliance with the Helsinki Declaration, all subjects provided written informed consent. All research participants\u0026rsquo; parents gave informed written consent that was included in our ethics statement.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eConsent for publication\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eAvailability of data and materials\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eCompeting interests\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eFunding\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study was funded by Ministry of Science and Technology Foundation of China (2022ZD0211300), the National Natural Science Foundation of China (32000757), and Beijing Municipal Social Science Foundation (23JYC016) to Xiujie Yang.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eAuthors\u0026apos; contributions\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eYuhan Wang, Zihan Yang, Xiao Yu, and Yue Qi contributed to the experimental design, the interpretation of the results, drafting and editing the manuscript.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eXiujie Yang contributed to experimental design, interpretation of the results, drafting and editing the manuscript and foundation providing.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eXiujie Yang and Zihan Yang were responsible for the revision of the manuscript.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAll authors reviewed the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eAcknowledgements\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe are especially grateful to the schools, parents, and students for their willingness to participate and their commitment to the study.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eAndersson, U. (2007). The contribution of working memory to children\u0026apos;s mathematical word problem solving. \u003cem\u003eApplied Cognitive Psychology, 21\u003c/em\u003e(9), 1201-1216. https://doi.org/10.1002/acp.1317 \u003c/li\u003e\n \u003cli\u003eAndersson, U., \u0026amp; Lyxell, B. (2007). Working memory deficit in children with mathematical difficulties: A general or specific deficit? \u003cem\u003eJournal of Experimental Child Psychology\u003c/em\u003e, \u003cem\u003e96\u003c/em\u003e(3), 197-228. https://doi.org/10.1016/j.jecp.2006.10.001\u003c/li\u003e\n \u003cli\u003eAwh, E., Anllo-Vento, L., \u0026amp; Hillyard, S. A. (2000). The role of spatial selective attention in working memory for locations: Evidence from event-related potentials. \u003cem\u003eJournal of Cognitive Neuroscience, 12\u003c/em\u003e(5), 840-847. https://doi.org/10.1162/089892900562444 \u003c/li\u003e\n \u003cli\u003eAwh, E., \u0026amp; Jonides, J. (2001). Overlapping mechanisms of attention and spatial working memory. \u003cem\u003eTrends in Cognitive Sciences, 5\u003c/em\u003e(3), 119-126. https://doi.org/10.1016/S1364-6613(00)01593-X\u003c/li\u003e\n \u003cli\u003eAwh, E., Jonides, J., \u0026amp; Reuter-Lorenz, P. A. (1998). Rehearsal in spatial working memory. \u003cem\u003eJournal of Experimental Psychology: Human Perception and Performance, 24\u003c/em\u003e(3), 780-790. https://doi.org/10.1037/0096-1523.24.3.780\u003c/li\u003e\n \u003cli\u003eBaddeley, A. (1992). Working memory. \u003cem\u003eScience, 255\u003c/em\u003e(5044), 556. https://doi.org/10.1126/science.1736359 \u003c/li\u003e\n \u003cli\u003eBaddeley, A. (1996). Exploring the central executive. \u003cem\u003eThe Quarterly Journal of Experimental Psychology, 49\u003c/em\u003e(1), 5-28. https://doi.org/10.1080/713755608 \u003c/li\u003e\n \u003cli\u003eBaddeley, A., Gathercole, S., \u0026amp; Papagno, C. (1998). The phonological loop as a language learning device. \u003cem\u003ePsychological Review, 105\u003c/em\u003e(1), 158-173. https://doi.org/10.1037/0033-295X.105.1.158 \u003c/li\u003e\n \u003cli\u003eBaroody, A. J., \u0026amp; Gatzke, M. R. (1991). The estimation of set size by potentially gifted kindergarten-age children. \u003cem\u003eJournal for Research in Mathematics Education, 22\u003c/em\u003e(1), 59-68. https://doi.org/10.2307/749554 \u003c/li\u003e\n \u003cli\u003eBerch, D. B. (2005). Making sense of number sense: Implications for children with mathematical disabilities. \u003cem\u003eJournal of learning disabilities, 38\u003c/em\u003e(4), 333-339. https://doi.org/10.1177/00222194050380040901 \u003c/li\u003e\n \u003cli\u003eBooth, J. L., \u0026amp; Siegler, R. S. (2006). Developmental and individual differences in pure numerical estimation. \u003cem\u003eDevelopmental Psychology, 42\u003c/em\u003e(1), 189-201. https://doi.org/10.1037/0012-1649.41.6.189 \u003c/li\u003e\n \u003cli\u003eBulf, H., de Hevia, M. D., \u0026amp; Macchi Cassia, V. (2016). Small on the left, large on the right: numbers orient visual attention onto space in preverbal infants. \u003cem\u003eDevelopmental Science, 19\u003c/em\u003e(3), 394-401. https://doi.org/10.1111/desc.12315 \u003c/li\u003e\n \u003cli\u003eBull, R., Cleland, A. A., \u0026amp; Mitchell, T. (2013). Sex differences in the spatial representation of number. \u003cem\u003eJournal of Experimental Psychology: General, 142\u003c/em\u003e(1), 181-192. https://doi.org/10.1037/a0028387 \u003c/li\u003e\n \u003cli\u003eBull, R., Espy, K. A., \u0026amp; Wiebe, S. A. (2008). Short-term memory, working memory, and executive functioning in preschoolers: Longitudinal predictors of mathematical achievement at age 7 years. \u003cem\u003eDevelopmental Neuropsychology, 33\u003c/em\u003e(3), 205-228. https://doi.org/10.1080/87565640801982312 \u003c/li\u003e\n \u003cli\u003eCarrasco, M. (2011). Visual attention: The past 25 years. \u003cem\u003eVision Research\u003c/em\u003e, \u003cem\u003e51\u003c/em\u003e(13), 1484-1525. https://doi.org/10.1016/j.visres.2011.04.012\u003c/li\u003e\n \u003cli\u003eChan, W. W. L. (2020). Counting enhances kindergarteners\u0026rsquo; mappings of number words onto numerosities. \u003cem\u003eFrontiers in Psychology, 11\u003c/em\u003e(153). https://doi.org/10.3389/fpsyg.2020.00153 \u003c/li\u003e\n \u003cli\u003eCheng, Y.-L., \u0026amp; Mix, K. S. (2014). Spatial training improves children\u0026apos;s mathematics ability. \u003cem\u003eJournal of Cognition and Development, 15\u003c/em\u003e(1), 2-11. https://doi.org/10.1080/15248372.2012.725186 \u003c/li\u003e\n \u003cli\u003eChesney, D., Bjalkebring, P., \u0026amp; Peters, E. (2015). How to estimate how well people estimate: Evaluating measures of individual differences in the approximate number system. \u003cem\u003eAttention, Perception, \u0026amp; Psychophysics\u003c/em\u003e, \u003cem\u003e77\u003c/em\u003e(8), 2781-2802. https://doi.org/10.3758/s13414-015-0974-6\u003c/li\u003e\n \u003cli\u003eClark, C. A. C., Pritchard, V. E., \u0026amp; Woodward, L. J. (2010). Preschool executive functioning abilities predict early mathematics achievement. \u003cem\u003eDevelopmental Psychology, 46\u003c/em\u003e(5), 1176-1191. https://doi.org/10.1037/a0019672 \u003c/li\u003e\n \u003cli\u003eClayton, S., \u0026amp; Gilmore, C. (2015). Inhibition in dot comparison tasks. \u003cem\u003eZDM, 47\u003c/em\u003e(5), 759-770. https://doi.org/10.1007/s11858-014-0655-2 \u003c/li\u003e\n \u003cli\u003eCui, J., Zhang, Y., Cheng, D., Li, D., \u0026amp; Zhou, X. (2017). Visual form perception can be a cognitive correlate of lower level math categories for teenagers. \u003cem\u003eFrontiers in Psychology, 8\u003c/em\u003e(1336). https://doi.org/10.3389/fpsyg.2017.01336 \u003c/li\u003e\n \u003cli\u003ede Hevia, M. D., \u0026amp; Spelke, E. S. (2009). Spontaneous mapping of number and space in adults and young children. \u003cem\u003eCognition, 110\u003c/em\u003e(2), 198-207. https://doi.org/10.1016/j.cognition.2008.11.003 \u003c/li\u003e\n \u003cli\u003eDe Smedt, B., Taylor, J., Archibald, L., \u0026amp; Ansari, D. (2010). How is phonological processing related to individual differences in children\u0026rsquo;s arithmetic skills? \u003cem\u003eDevelopmental Science, 13\u003c/em\u003e(3), 508-520. https://doi.org/10.1111/j.1467-7687.2009.00897.x \u003c/li\u003e\n \u003cli\u003eDe Smedt, B., Verschaffel, L., \u0026amp; Ghesqui\u0026egrave;re, P. (2009). The predictive value of numerical magnitude comparison for individual differences in mathematics achievement. \u003cem\u003eJournal of Experimental Child Psychology, 103\u003c/em\u003e(4), 469-479. https://doi.org/10.1016/j.jecp.2009.01.010 \u003c/li\u003e\n \u003cli\u003eDehaene, S. (1992). Varieties of numerical abilities. \u003cem\u003eCognition, 44\u003c/em\u003e(1), 1-42. https://doi.org/10.1016/0010-0277(92)90049-N \u003c/li\u003e\n \u003cli\u003eDehaene, S., \u0026amp; Cohen, L. (1995). Towards an anatomical and functional model of number processing. \u003cem\u003eMathematical Cognition, 1\u003c/em\u003e(1), 83-120. \u003c/li\u003e\n \u003cli\u003eDehaene, S., Bossini, S., \u0026amp; Giraux, P. (1993). The mental representation of parity and number magnitude. \u003cem\u003eJournal of Experimental Psychology: General, 122\u003c/em\u003e(3), 371-396. https://doi.org/10.1037/0096-3445.122.3.371 \u003c/li\u003e\n \u003cli\u003eDehaene, S., Piazza, M., Pinel, P., \u0026amp; Cohen, L. (2003). Three parietal circuits for number processing. \u003cem\u003eCognitive Neuropsychology, 20\u003c/em\u003e(3-6), 487-506. https://doi.org/10.1080/02643290244000239 \u003c/li\u003e\n \u003cli\u003eDurand, M., Hulme, C., Larkin, R., \u0026amp; Snowling, M. (2005). The cognitive foundations of reading and arithmetic skills in 7- to 10-year-olds. \u003cem\u003eJournal of Experimental Child Psychology, 91\u003c/em\u003e(2), 113-136. https://doi.org/10.1016/j.jecp.2005.01.003 \u003c/li\u003e\n \u003cli\u003eEstes, Z., \u0026amp; Felker, S. (2012). Confidence mediates the sex difference in mental rotation performance. \u003cem\u003eArchives of Sexual Behavior, 41\u003c/em\u003e(3), 557-570. https://doi.org/10.1007/s10508-011-9875-5 \u003c/li\u003e\n \u003cli\u003eFan, J., McCandliss, B. D., Sommer, T., Raz, A., \u0026amp; Posner, M. I. (2002). Testing the efficiency and independence of attentional networks. \u003cem\u003eJournal of Cognitive Neuroscience, 14\u003c/em\u003e(3), 340-347. https://doi.org/10.1162/089892902317361886\u003c/li\u003e\n \u003cli\u003eFazio, L. K., Bailey, D. H., Thompson, C. A., \u0026amp; Siegler, R. S. (2014). Relations of different types of numerical magnitude representations to each other and to mathematics achievement. \u003cem\u003eJournal of Experimental Child Psychology, 123\u003c/em\u003e, 53-72. https://doi.org/10.1016/j.jecp.2014.01.013 \u003c/li\u003e\n \u003cli\u003eFeigenson, L., Dehaene, S., \u0026amp; Spelke, E. (2004). Core systems of number. \u003cem\u003eTrends in Cognitive Science, 8\u003c/em\u003e(7), 307-314. https://doi.org/10.1016/j.tics.2004.05.002 \u003c/li\u003e\n \u003cli\u003eFriso-van den Bos, I., Kroesbergen, E. H., \u0026amp; van Luit, J. E. H. (2014). Number sense in kindergarten children: Factor structure and working memory predictors. \u003cem\u003eLearning and Individual Differences, 33\u003c/em\u003e, 23-29. https://doi.org/10.1016/j.lindif.2014.05.003 \u003c/li\u003e\n \u003cli\u003eFuhs, M. W., Hornburg, C. B., \u0026amp; McNeil, N. M. (2016). Specific early number skills mediate the association between executive functioning skills and mathematics achievement. \u003cem\u003eDevelopmental Psychology, 52\u003c/em\u003e(8), 1217-1235. https://doi.org/10.1037/dev0000145 \u003c/li\u003e\n \u003cli\u003eGazzaley, A., \u0026amp; Nobre, A. C. (2012). Top-down modulation: bridging selective attention and working memory. \u003cem\u003eTrends in Cognitive Sciences, 16\u003c/em\u003e(2), 129-135. https://doi.org/10.1016/j.tics.2011.11.014 \u003c/li\u003e\n \u003cli\u003eGeary, D. C. (2004). Mathematics and learning disabilities.\u003cem\u003e Journal of learning disabilities\u003c/em\u003e, 37(1), 4-15. https://doi.org/10.1177/00222194040370010201\u003c/li\u003e\n \u003cli\u003eGeary, D. C., Hoard, M. K., Byrd-Craven, J., Nugent, L., \u0026amp; Numtee, C. (2007). Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. \u003cem\u003eChild Development, 78\u003c/em\u003e(4), 1343-1359. https://doi.org/10.1111/j.1467-8624.2007.01069.x \u003c/li\u003e\n \u003cli\u003eGeary, D. C., Hoard, M. K., Nugent, L., \u0026amp; Byrd-Craven, J. (2008). Development of number line representations in children with mathematical learning disability. \u003cem\u003eDevelopmental Neuropsychology, 33\u003c/em\u003e(3), 277-299. https://doi.org/10.1080/87565640801982361 \u003c/li\u003e\n \u003cli\u003eGelman, R., \u0026amp; Butterworth, B. (2005). Number and language: how are they related? \u003cem\u003eTrends in Cognitive Sciences, 9\u003c/em\u003e(1), 6-10. https://doi.org/10.1016/j.tics.2004.11.004 \u003c/li\u003e\n \u003cli\u003eGeorges, C., Hoffmann, D., \u0026amp; Schiltz, C. (2017). Mathematical abilities in elementary school: Do they relate to number\u0026ndash;space associations? \u003cem\u003eJournal of Experimental Child Psychology, 161\u003c/em\u003e, 126-147. https://doi.org/10.1016/j.jecp.2017.04.011 \u003c/li\u003e\n \u003cli\u003eGeorgiou, G. K., Tziraki, N., Manolitsis, G., \u0026amp; Fella, A. (2013). Is rapid automatized naming related to reading and mathematics for the same reason(s)? A follow-up study from kindergarten to Grade 1. \u003cem\u003eJournal of Experimental Child Psychology, 115\u003c/em\u003e(3), 481-496. https://doi.org/10.1016/j.jecp.2013.01.004 \u003c/li\u003e\n \u003cli\u003eGilmore, C., Attridge, N., Clayton, S., Cragg, L., Johnson, S., Marlow, N., Simms, V., \u0026amp; Inglis, M. (2013). Individual differences in inhibitory control, not non-verbal number acuity, correlate with mathematics achievement. \u003cem\u003ePLoS One, 8\u003c/em\u003e(6), e67374. https://doi.org/10.1371/journal.pone.0067374 \u003c/li\u003e\n \u003cli\u003eGirelli, L., Lucangeli, D., \u0026amp; Butterworth, B. (2000). The development of automaticity in accessing number magnitude. \u003cem\u003eJournal of Experimental Child Psychology, 76\u003c/em\u003e(2), 104-122. https://doi.org/10.1006/jecp.2000.2564 \u003c/li\u003e\n \u003cli\u003eGross, S. I., Gross, C. A., Kim, D., Lukowski, S. L., Thompson, L. A., \u0026amp; Petrill, S. A. (2018). A comparison of methods for assessing performance on the number line estimation task. \u003cem\u003eJournal of Numerical Cognition, 4\u003c/em\u003e(3), 554-571. https://doi.org/10.5964/jnc.v4i3.120 \u003c/li\u003e\n \u003cli\u003eGunderson, E. A., Hamdan, N., Hildebrand, L., \u0026amp; Bartek, V. (2019). Number line unidimensionality is a critical feature for promoting fraction magnitude concepts. \u003cem\u003eJournal of Experimental Child Psychology, 187\u003c/em\u003e, 104657. https://doi.org/10.1016/j.jecp.2019.06.010 \u003c/li\u003e\n \u003cli\u003eGunderson, E. A., Ramirez, G., Beilock, S. L., \u0026amp; Levine, S. C. (2012a). The relation between spatial skill and early number knowledge: The role of the linear number line. \u003cem\u003eDevelopmental Psychology, 48\u003c/em\u003e(5), 1229-1241. https://doi.org/10.1037/a0027433 \u003c/li\u003e\n \u003cli\u003eGunderson, E. A., Ramirez, G., Levine, S. C., \u0026amp; Beilock, S. L. (2012b). The role of parents and teachers in the development of gender-related math attitudes. \u003cem\u003eSex roles, 66\u003c/em\u003e(3), 153-166. https://doi.org/10.1007/s11199-011-9996-2 \u003c/li\u003e\n \u003cli\u003eKolkman, M. E., Hoijtink, H. J. A., Kroesbergen, E. H., \u0026amp; Leseman, P. P. M. (2013). The role of executive functions in numerical magnitude skills. \u003cem\u003eLearning and Individual Differences, 24\u003c/em\u003e, 145-151. https://doi.org/10.1016/j.lindif.2013.01.004 \u003c/li\u003e\n \u003cli\u003eHalberda, J., Mazzocco, M. M., \u0026amp; Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. \u003cem\u003eNature, 455\u003c/em\u003e(7213), 665-668. https://doi.org/10.1038/nature07246 \u003c/li\u003e\n \u003cli\u003eHamdan, N., \u0026amp; Gunderson, E. A. (2017). The number line is a critical spatial-numerical representation: Evidence from a fraction intervention. \u003cem\u003eDevelopmental Psychology, 53\u003c/em\u003e(3), 587-596. https://doi.org/10.1037/dev0000252 \u003c/li\u003e\n \u003cli\u003eHansen, N., Jordan, N. C., Fernandez, E., Siegler, R. S., Fuchs, L., Gersten, R., \u0026amp; Micklos, D. (2015). General and math-specific predictors of sixth-graders\u0026rsquo; knowledge of fractions. \u003cem\u003eCognitive Development, 35\u003c/em\u003e, 34-49. https://doi.org/10.1016/j.cogdev.2015.02.001 \u003c/li\u003e\n \u003cli\u003eHecht, S. A., Torgesen, J. K., Wagner, R. K., \u0026amp; Rashotte, C. A. (2001). The relations between phonological processing abilities and emerging individual differences in mathematical computation skills: A longitudinal study from second to fifth grades. \u003cem\u003eJournal of Experimental Child Psychology, 79\u003c/em\u003e(2), 192-227. https://doi.org/10.1006/jecp.2000.2586 \u003c/li\u003e\n \u003cli\u003eHoffmann, D., Pigat, D., \u0026amp; Schiltz, C. (2014). The impact of inhibition capacities and age on number\u0026ndash;space associations. \u003cem\u003eCognitive Processing, 15\u003c/em\u003e(3), 329-342. https://doi.org/10.1007/s10339-014-0601-9 \u003c/li\u003e\n \u003cli\u003eHonzel, N., Justus, T., \u0026amp; Swick, D. (2014). Posttraumatic stress disorder is associated with limited executive resources in a working memory task. \u003cem\u003eCognitive, Affective, \u0026amp; Behavioral Neuroscience, 14\u003c/em\u003e(2), 792-804. https://doi.org/10.3758/s13415-013-0219-x \u003c/li\u003e\n \u003cli\u003eHowell, S. C., \u0026amp; Kemp, C. R. (2010). Assessing preschool number sense: Skills demonstrated by children prior to school entry. \u003cem\u003eEducational Psychology, 30\u003c/em\u003e(4), 411-429. https://doi.org/10.1080/01443411003695410\u003c/li\u003e\n \u003cli\u003eHuang, Q., Zhang, X., Liu, Y., Yang, W., \u0026amp; Song, Z. (2017). The contribution of parent\u0026ndash;child numeracy activities to young Chinese children\u0026apos;s mathematical ability. \u003cem\u003eBritish Journal of Educational Psychology, 87\u003c/em\u003e(3), 328-344. https://doi.org/10.1111/bjep.12152 \u003c/li\u003e\n \u003cli\u003eHuo, S., Zhang, X., \u0026amp; Law, Y. K. (2021). Pathways to word reading and calculation skills in young Chinese children: From biologically primary skills to biologically secondary skills. \u003cem\u003eJournal of Educational Psychology, 113\u003c/em\u003e(2), 230-247. https://doi.org/10.1037/edu0000647 \u003c/li\u003e\n \u003cli\u003eHutchison, J. E., Lyons, I. M., \u0026amp; Ansari, D. (2019). More similar than different: gender differences in children\u0026apos;s basic numerical skills are the exception not the rule. \u003cem\u003eChild Development, 90\u003c/em\u003e(1), e66-e79. https://doi.org/10.1111/cdev.13044 \u003c/li\u003e\n \u003cli\u003eJordan, N. C., Kaplan, D., Nabors Ol\u0026aacute;h, L., \u0026amp; Locuniak, M. N. (2006). Number sense growth in kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. \u003cem\u003eChild Development, 77\u003c/em\u003e(1), 153-175. https://doi.org/10.1111/j.1467-8624.2006.00862.x \u003c/li\u003e\n \u003cli\u003eKaufmann, L., Wood, G., Rubinsten, O., \u0026amp; Henik, A. (2011). Meta-analyses of developmental fMRI studies investigating typical and atypical trajectories of number processing and calculation. \u003cem\u003eDevelopmental Neuropsychology, 36\u003c/em\u003e(6), 763-787. https://doi.org/10.1080/87565641.2010.549884 \u003c/li\u003e\n \u003cli\u003eKlein, E., Suchan, J., Moeller, K., Karnath, H.-O., Knops, A., Wood, G., Nuerk, H.-C., \u0026amp; Willmes, K. (2016). Considering structural connectivity in the triple-code model of numerical cognition: differential connectivity for magnitude processing and arithmetic facts. \u003cem\u003eBrain Structure and Function, 221\u003c/em\u003e(2), 979-995. https://doi.org/10.1007/s00429-014-0951-1 \u003c/li\u003e\n \u003cli\u003eKorpip\u0026auml;\u0026auml;, H., Koponen, T., Aro, M., Tolvanen, A., Aunola, K., Poikkeus, A.-M., Lerkkanen, M.-K., \u0026amp; Nurmi, J.-E. (2017). Covariation between reading and arithmetic skills from Grade 1 to Grade 7. \u003cem\u003eContemporary Educational Psychology, 51\u003c/em\u003e, 131-140. https://doi.org/10.1016/j.cedpsych.2017.06.005 \u003c/li\u003e\n \u003cli\u003eKroesbergen, E. H., Van Luit, J. E. H., Van Lieshout, E. C. D. M., Van Loosbroek, E., \u0026amp; Van de Rijt, B. A. M. (2009). Individual differences in early numeracy: The role of executive functions and subitizing. \u003cem\u003eJournal of Psychoeducational Assessment, 27\u003c/em\u003e(3), 226-236. https://doi.org/10.1177/0734282908330586 \u003c/li\u003e\n \u003cli\u003eKroesbergen, E. H., van \u0026apos;t Noordende, J. E., \u0026amp; Kolkman, M. E. (2014). Training working memory in kindergarten children: Effects on working memory and early numeracy. \u003cem\u003eChild Neuropsychology, 20\u003c/em\u003e(1), 23-37. https://doi.org/10.1080/09297049.2012.736483 \u003c/li\u003e\n \u003cli\u003eLee, K., Ng, S. F., Pe, M. L., Ang, S. Y., Hasshim, M. N. A. M., \u0026amp; Bull, R. (2012). The cognitive underpinnings of emerging mathematical skills: Executive functioning, patterns, numeracy, and arithmetic. \u003cem\u003eBritish Journal of Educational Psychology, 82\u003c/em\u003e(1), 82-99. https://doi.org/10.1111/j.2044-8279.2010.02016.x \u003c/li\u003e\n \u003cli\u003eLeFevre, J.-A., Fast, L., Skwarchuk, S.-L., Smith-Chant, B. L., Bisanz, J., Kamawar, D., \u0026amp; Penner-Wilger, M. (2010). Pathways to mathematics: Longitudinal predictors of performance. \u003cem\u003eChild Development, 81\u003c/em\u003e(6), 1753-1767. https://doi.org/10.1111/j.1467-8624.2010.01508.x \u003c/li\u003e\n \u003cli\u003eLeFevre, J.-A., Skwarchuk, S.-L., Smith-Chant, B. L., Fast, L., Kamawar, D., \u0026amp; Bisanz, J. (2009). Home numeracy experiences and children\u0026rsquo;s math performance in the early school years. \u003cem\u003eCanadian Journal of Behavioural Science / Revue canadienne des sciences du comportement, 41\u003c/em\u003e(2), 55-66. https://doi.org/10.1037/a0014532 \u003c/li\u003e\n \u003cli\u003eLinn, M. C., \u0026amp; Petersen, A. C. (1985). Emergence and characterization of sex differences in spatial ability: A meta-analysis. \u003cem\u003eChild Development, 56\u003c/em\u003e(6), 1479-1498. https://doi.org/10.2307/1130467 \u003c/li\u003e\n \u003cli\u003eLittle, R. J. A. (1988). A test of missing completely at random for multivariate data with missing values. \u003cem\u003eJournal of the American Statistical Association, 83\u003c/em\u003e(404), 1198-1202. https://doi.org/10.1080/01621459.1988.10478722 \u003c/li\u003e\n \u003cli\u003eLipton, J. S., \u0026amp; Spelke, E. S. (2005). Preschool children\u0026apos;s mapping of number words to nonsymbolic numerosities. \u003cem\u003eChild Development, 76\u003c/em\u003e(5), 978-988. https://doi.org/10.1111/j.1467-8624.2005.00891.x \u003c/li\u003e\n \u003cli\u003eLogie, R. H. (1995). \u003cem\u003eVisuo-spatial working memory\u003c/em\u003e. Psychology Press. \u003c/li\u003e\n \u003cli\u003eLogie, R. H., Gilhooly, K. J., \u0026amp; Wynn, V. (1994). Counting on working memory in arithmetic problem solving. \u003cem\u003eMemory \u0026amp; Cognition, 22\u003c/em\u003e(4), 395-410. https://doi.org/10.3758/BF03200866 \u003c/li\u003e\n \u003cli\u003eLuo, Y., Wang, J., Wu, H., Zhu, D., \u0026amp; Zhang, Y. (2013). Working-memory training improves developmental dyslexia in Chinese children. \u003cem\u003eNeural regeneration research, 8\u003c/em\u003e(5), 452-460. https://doi.org/10.3969/j.issn.1673-5374.2013.05.009 \u003c/li\u003e\n \u003cli\u003eMcKenzie, B., Bull, R., \u0026amp; Gray, C. (2003). The effects of phonological and visual-spatial interference on children\u0026apos;s arithmetical performance. \u003cem\u003eEducational and Child Psychology, 20\u003c/em\u003e(3), 93-108. \u003c/li\u003e\n \u003cli\u003eMejias, S., Mussolin, C., Rousselle, L., Gr\u0026eacute;goire, J., \u0026amp; No\u0026euml;l, M.-P. (2012). Numerical and nonnumerical estimation in children with and without mathematical learning disabilities. \u003cem\u003eChild Neuropsychology, 18\u003c/em\u003e(6), 550-575. https://doi.org/10.1080/09297049.2011.625355 \u003c/li\u003e\n \u003cli\u003eMejias, S., \u0026amp; Schiltz, C. (2013). Estimation abilities of large numerosities in Kindergartners. \u003cem\u003eFrontiers in Psychology, 4\u003c/em\u003e(518). https://doi.org/10.3389/fpsyg.2013.00518 \u003c/li\u003e\n \u003cli\u003eMichalczyk, K., Krajewski, K., Pre\u0026beta;ler, A.-L., \u0026amp; Hasselhorn, M. (2013). The relationships between quantity-number competencies, working memory, and phonological awareness in 5- and 6-year-olds. \u003cem\u003eBritish Journal of Developmental Psychology, 31\u003c/em\u003e(4), 408-424. https://doi.org/10.1111/bjdp.12016 \u003c/li\u003e\n \u003cli\u003eMix, K. S., Levine, S. C., Cheng, Y.-L., Stockton, J. D., \u0026amp; Bower, C. (2021). Effects of spatial training on mathematics in first and sixth grade children. \u003cem\u003eJournal of Educational Psycho\u003c/em\u003e\u003cem\u003elogy, 113\u003c/em\u003e(2), 304-314. https://doi.org/10.1037/edu0000494 \u003c/li\u003e\n \u003cli\u003eMix, K. S., Levine, S. C., Cheng, Y.-L., Young, C. J., Hambrick, D. Z., \u0026amp; Konstantopoulos, S. (2017). The latent structure of spatial skills and mathematics: A replication of the two-factor model. \u003cem\u003eJournal of Cognition and Development, 18\u003c/em\u003e(4), 465-492. https://doi.org/10.1080/15248372.2017.1346658 \u003c/li\u003e\n \u003cli\u003eMiyake, A., Friedman, N. P., Rettinger, D. A., Shah, P., \u0026amp; Hegarty, M. (2001). How are visuospatial working memory, executive functioning, and spatial abilities related? A latent-variable analysis. \u003cem\u003eJournal of Experimental Psychology: General, 130\u003c/em\u003e(4), 621-640. http://dx.doi.org/10.1037/0096-3445.130.4.621 \u003c/li\u003e\n \u003cli\u003eMoeller, K., Willmes, K., \u0026amp; Klein, E. (2015). A review on functional and structural brain connectivity in numerical cognition. \u003cem\u003eFrontiers in Human Neuroscience, 9\u003c/em\u003e(227). https://doi.org/10.3389/fnhum.2015.00227 \u003c/li\u003e\n \u003cli\u003eMundy, E., \u0026amp; Gilmore, C. K. (2009). Children\u0026rsquo;s mapping between symbolic and nonsymbolic representations of number. \u003cem\u003eJournal of Experimental Child Psychology, 103\u003c/em\u003e(4), 490-502. https://doi.org/10.1016/j.jecp.2009.02.003 \u003c/li\u003e\n \u003cli\u003eMutaf Yıldız, B., Sasanguie, D., De Smedt, B., \u0026amp; Reynvoet, B. (2018). Frequency of home numeracy activities is differentially related to basic number processing and calculation skills in kindergartners. \u003cem\u003eFrontiers in Psychology, 9\u003c/em\u003e(340). https://doi.org/10.3389/fpsyg.2018.00340 \u003c/li\u003e\n \u003cli\u003eMuth\u0026eacute;n, L. K., \u0026amp; Muth\u0026eacute;n, B. O. (2012). 1998\u0026ndash;2012. Mplus user\u0026rsquo;s guide. \u003cem\u003eLos Angeles: Muthen \u0026amp; Muthen\u003c/em\u003e. \u003c/li\u003e\n \u003cli\u003eNo\u0026euml;l, M.-P., Seron, X., \u0026amp; Trovarelli, F. (2004). Working memory as a predictor of addition skills and addition strategies in children. \u003cem\u003eCahiers de Psychologie Cognitive/Current Psychology of Cognition, 22\u003c/em\u003e(1), 3-25. \u003c/li\u003e\n \u003cli\u003eOpfer, J. E., \u0026amp; Siegler, R. S. (2007). Representational change and children\u0026rsquo;s numerical estimation. \u003cem\u003eCognitive Psychology, 55\u003c/em\u003e(3), 169-195. https://doi.org/10.1016/j.cogpsych.2006.09.002\u003c/li\u003e\n \u003cli\u003ePassolunghi, M. C., \u0026amp; Lanfranchi, S. (2012). Domain-specific and domain-general precursors of mathematical achievement: A longitudinal study from kindergarten to first grade. \u003cem\u003eBritish Journal of Educational Psychology, 82\u003c/em\u003e(1), 42-63. https://doi.org/10.1111/j.2044-8279.2011.02039.x \u003c/li\u003e\n \u003cli\u003ePassolunghi, M. C., Lanfranchi, S., Alto\u0026egrave;, G., \u0026amp; Sollazzo, N. (2015). Early numerical abilities and cognitive skills in kindergarten children. \u003cem\u003eJournal of Experimental Child Psychology, 135\u003c/em\u003e, 25-42. https://doi.org/10.1016/j.jecp.2015.02.001 \u003c/li\u003e\n \u003cli\u003ePassolunghi, M. C., \u0026amp; Siegel, L. S. (2001). Short-term memory, working memory, and inhibitory control in children with difficulties in arithmetic problem solving. \u003cem\u003eJournal of Experimental Child Psychology, 80\u003c/em\u003e(1), 44-57. https://doi.org/10.1006/jecp.2000.2626 \u003c/li\u003e\n \u003cli\u003ePeng, P., Yang, X., \u0026amp; Meng, X. (2017). The relation between approximate number system and early arithmetic: The mediation role of numerical knowledge. \u003cem\u003eJournal of Experimental Child Psychology, 157\u003c/em\u003e, 111-124. https://doi.org/10.1016/j.jecp.2016.12.011 \u003c/li\u003e\n \u003cli\u003ePeters, L., Polspoel, B., Op de Beeck, H., \u0026amp; De Smedt, B. (2016). Brain activity during arithmetic in symbolic and non-symbolic formats in 9\u0026ndash;12 year old children. \u003cem\u003eNeuropsychologia, 86\u003c/em\u003e, 19-28. https://doi.org/10.1016/j.neuropsychologia.2016.04.001 \u003c/li\u003e\n \u003cli\u003ePrager, E. O., Sera, M. D., \u0026amp; Carlson, S. M. (2016). Executive function and magnitude skills in preschool children. \u003cem\u003eJournal of Experimental Child Psychology, 147\u003c/em\u003e, 126-139. https://doi.org/10.1016/j.jecp.2016.01.002 \u003c/li\u003e\n \u003cli\u003ePrice, G. R., \u0026amp; Fuchs, L. S. (2016). The mediating relation between symbolic and nonsymbolic foundations of math competence. \u003cem\u003ePLoS One\u003c/em\u003e, \u003cem\u003e11\u003c/em\u003e(2), e0148981. https://doi.org/10.1371/journal.pone.0148981\u003c/li\u003e\n \u003cli\u003eReinert, R. M., Huber, S., Nuerk, H.-C., \u0026amp; Moeller, K. (2017). Sex differences in number line estimation: The role of numerical estimation. \u003cem\u003eBritish Journal of Psychology, 108\u003c/em\u003e(2), 334-350. https://doi.org/10.1111/bjop.12203 \u003c/li\u003e\n \u003cli\u003eRivers, M. L., Fitzsimmons, C. J., Fisk, S. R., Dunlosky, J., \u0026amp; Thompson, C. A. (2021). Gender differences in confidence during number-line estimation. \u003cem\u003eMetacognition and Learning, 16\u003c/em\u003e(1), 157-178. https://doi.org/10.1007/s11409-020-09243-7 \u003c/li\u003e\n \u003cli\u003eScharinger, C., Soutschek, A., Schubert, T., \u0026amp; Gerjets, P. (2015). When flanker meets the n-back: What EEG and pupil dilation data reveal about the interplay between the two central-executive working memory functions inhibition and updating. \u003cem\u003ePsychophysiology, 52\u003c/em\u003e(10), 1293-1304. https://doi.org/10.1111/psyp.12500 \u003c/li\u003e\n \u003cli\u003eSiegler, R. S. (2009). Improving the numerical understanding of children from low-income families. \u003cem\u003eChild Development Perspectives, 3\u003c/em\u003e(2), 118-124. https://doi.org/10.1111/j.1750-8606.2009.00090.x\u003c/li\u003e\n \u003cli\u003eSiegler, R. S., \u0026amp; Booth, J. L. (2004). Development of numerical estimation in young children. \u003cem\u003eChild Development, 75\u003c/em\u003e(2), 428-444. https://doi.org/10.1111/j.1467-8624.2004.00684.x \u003c/li\u003e\n \u003cli\u003eSiegler, R. S., \u0026amp; Ramani, G. B. (2009). Playing linear number board games\u0026mdash;but not circular ones\u0026mdash;improves low-income preschoolers\u0026rsquo; numerical understanding. \u003cem\u003eJournal of Educational Psychology, 101\u003c/em\u003e(3), 545-560. https://doi.org/10.1037/a0014239 \u003c/li\u003e\n \u003cli\u003eSiegler, R. S., Thompson, C. A., \u0026amp; Schneider, M. (2011). An integrated theory of whole number and fractions development. \u003cem\u003eCognitive Psychology, 62\u003c/em\u003e(4), 273-296. https://doi.org/10.1016/j.cogpsych.2011.03.001 \u003c/li\u003e\n \u003cli\u003eSigmundsson, H., Anholt, S. K., \u0026amp; Talcott, J. B. (2010). Are poor mathematics skills associated with visual deficits in temporal processing? \u003cem\u003eNeuroscience Letters, 469\u003c/em\u003e(2), 248-250. https://doi.org/10.1016/j.neulet.2009.12.005 \u003c/li\u003e\n \u003cli\u003eSimmons, F., Singleton, C., \u0026amp; Horne, J. (2008). Brief report\u0026mdash;Phonological awareness and visual-spatial sketchpad functioning predict early arithmetic attainment: Evidence from a longitudinal study. \u003cem\u003eEuropean Journal of Cognitive Psychology, 20\u003c/em\u003e(4), 711-722. https://doi.org/10.1080/09541440701614922 \u003c/li\u003e\n \u003cli\u003eSimmons, F. R., \u0026amp; Singleton, C. (2008). Do weak phonological representations impact on arithmetic development? A review of research into arithmetic and dyslexia. \u003cem\u003eDyslexia, 14\u003c/em\u003e(2), 77-94. https://doi.org/10.1002/dys.341 \u003c/li\u003e\n \u003cli\u003eSimmons, F. R., Willis, C., \u0026amp; Adams, A.-M. (2012). Different components of working memory have different relationships with different mathematical skills. \u003cem\u003eJournal of Experimental Child Psychology, 111\u003c/em\u003e(2), 139-155. https://doi.org/10.1016/j.jecp.2011.08.011 \u003c/li\u003e\n \u003cli\u003eSkagenholt, M., Tr\u0026auml;ff, U., V\u0026auml;stfj\u0026auml;ll, D., \u0026amp; Skagerlund, K. (2018). Examining the Triple Code Model in numerical cognition: An fMRI study. \u003cem\u003ePLoS One, 13\u003c/em\u003e(6), e0199247. https://doi.org/10.1371/journal.pone.0199247 \u003c/li\u003e\n \u003cli\u003eSwanson, H. L. (2004). Working memory and phonological processing as predictors of children\u0026rsquo;s mathematical problem solving at different ages. \u003cem\u003eMemory \u0026amp; cognition, 32\u003c/em\u003e(4), 648-661. https://doi.org/10.3758/BF03195856 \u003c/li\u003e\n \u003cli\u003eSzucs, D., Devine, A., Soltesz, F., Nobes, A., \u0026amp; Gabriel, F. (2013). Developmental dyscalculia is related to visuo-spatial memory and inhibition impairment. \u003cem\u003eCortex, 49\u003c/em\u003e(10), 2674-2688. https://doi.org/10.1016/j.cortex.2013.06.007 \u003c/li\u003e\n \u003cli\u003eThompson, C. A., \u0026amp; Opfer, J. E. (2008). Costs and benefits of representational change: Effects of context on age and sex differences in symbolic magnitude estimation. \u003cem\u003eJournal of Experimental Child Psychology, 101\u003c/em\u003e(1), 20-51. https://doi.org/10.1016/j.jecp.2008.02.003 \u003c/li\u003e\n \u003cli\u003eTrick, L. M., \u0026amp; Enns, J. T. (1998). Lifespan changes in attention: the visual search task. \u003cem\u003eCognitive Development\u003c/em\u003e, \u003cem\u003e13\u003c/em\u003e(3), 369-386. https://doi.org/10.1016/S0885-2014(98)90016-8\u003c/li\u003e\n \u003cli\u003eTosto, M. G., Hanscombe, K. B., Haworth, C. M. A., Davis, O. S. P., Petrill, S. A., Dale, P. S., Malykh, S., Plomin, R., \u0026amp; Kovas, Y. (2014). Why do spatial abilities predict mathematical performance? \u003cem\u003eDevelopmental Science, 17\u003c/em\u003e(3), 462-470. https://doi.org/10.1111/desc.12138 \u003c/li\u003e\n \u003cli\u003eTr\u0026auml;ff, U. (2013). The contribution of general cognitive abilities and number abilities to different aspects of mathematics in children. \u003cem\u003eJournal of Experimental Child Psychology, 116\u003c/em\u003e(2), 139-156. https://doi.org/10.1016/j.jecp.2013.04.007\u003c/li\u003e\n \u003cli\u003eUttal, D. H., Meadow, N. G., Tipton, E., Hand, L. L., Alden, A. R., Warren, C., \u0026amp; Newcombe, N. S. (2013). The malleability of spatial skills: A meta-analysis of training studies. \u003cem\u003ePsychological Bulletin, 139\u003c/em\u003e(2), 352-402. https://doi.org/10.1037/a0028446 \u003c/li\u003e\n \u003cli\u003eVuilleumier, P., Ortigue, S., \u0026amp; Brugger, P. (2004). The number space and neglect. \u003cem\u003eCortex, 40\u003c/em\u003e(2), 399-410. https://doi.org/10.1016/S0010-9452(08)70134-5\u003c/li\u003e\n \u003cli\u003eWechsler, D. (1974). \u003cem\u003eWechsler intelligence scale for children-revised\u003c/em\u003e. Psychological Corporation.\u003c/li\u003e\n \u003cli\u003eWei, W., Yuan, H., Chen, C., \u0026amp; Zhou, X. (2012). Cognitive correlates of performance in advanced mathematics. \u003cem\u003eBritish Journal of Educational Psychology, 82\u003c/em\u003e(1), 157-181. https://doi.org/10.1111/j.2044-8279.2011.02049.x \u003c/li\u003e\n \u003cli\u003eYang, X., Chung, K. K. H., \u0026amp; McBride, C. (2019). Longitudinal contributions of executive functioning and visual-spatial skills to mathematics learning in young Chinese children. \u003cem\u003eEducational Psychology, 39\u003c/em\u003e(5), 678-704. https://doi.org/10.1080/01443410.2018.1546831 \u003c/li\u003e\n \u003cli\u003eYang, X., \u0026amp; McBride, C. (2020). How do phonological processing abilities contribute to early Chinese reading and mathematics? \u003cem\u003eEducational Psychology\u003c/em\u003e, 1-19. https://doi.org/10.1080/01443410.2020.1771679 \u003c/li\u003e\n \u003cli\u003eYang, X., McBride, C., Ho, C. S.-H., \u0026amp; Chung, K. K. H. (2020). Longitudinal associations of phonological processing skills, Chinese word reading, and arithmetic. \u003cem\u003eReading and Writing\u003c/em\u003e, \u003cem\u003e33\u003c/em\u003e(7), 1679-1699. https://doi.org/10.1007/s11145-019-09998-9\u003c/li\u003e\n \u003cli\u003eYang, X., \u0026amp; Meng, X. (2020). Visual processing matters in Chinese reading acquisition and early mathematics. \u003cem\u003eFrontiers in Psychology, 11\u003c/em\u003e(462). https://doi.org/10.3389/fpsyg.2020.00462 \u003c/li\u003e\n \u003cli\u003eYang, X., Zhang, X., Huo, S., \u0026amp; Zhang, Y. (2020). Differential contributions of cognitive precursors to symbolic versus non-symbolic numeracy in young Chinese children. \u003cem\u003eEarly Childhood Research Quarterly, 53\u003c/em\u003e, 208-216. https://doi.org/10.1016/j.ecresq.2020.04.003 \u003c/li\u003e\n \u003cli\u003eZhang, X. (2016). Linking language, visual-spatial, and executive function skills to number competence in very young Chinese children. \u003cem\u003eEarly Childhood Research Quarterly, 36\u003c/em\u003e, 178-189. https://doi.org/10.1016/j.ecresq.2015.12.010 \u003c/li\u003e\n \u003cli\u003eZhang, X., Hu, B. Y., Zou, X., \u0026amp; Ren, L. (2020). Parent\u0026ndash;child number application activities predict children\u0026rsquo;s math trajectories from preschool to primary school. \u003cem\u003eJournal of Educational Psychology, 112\u003c/em\u003e(8), 1521-1531. https://doi.org/10.1037/edu0000457 \u003c/li\u003e\n \u003cli\u003eZhang, X., \u0026amp; Lin, D. (2017). Does growth rate in spatial ability matter in predicting early arithmetic competence? \u003cem\u003eLearning and Instruction, 49\u003c/em\u003e, 232-241. https://doi.org/10.1016/j.learninstruc.2017.02.003 \u003c/li\u003e\n \u003cli\u003eZhang, X., \u0026amp; Lin, D. (2018). Cognitive precursors of word reading versus arithmetic competencies in young Chinese children. \u003cem\u003eEarly Childhood Research Quarterly, 42\u003c/em\u003e, 55-65. https://doi.org/10.1016/j.ecresq.2017.08.006 \u003c/li\u003e\n \u003cli\u003eZhang, X., R\u0026auml;s\u0026auml;nen, P., Koponen, T., Aunola, K., Lerkkanen, M.-K., \u0026amp; Nurmi, J.-E. (2017). Knowing, applying, and reasoning about arithmetic: Roles of domain-general and numerical skills in multiple domains of arithmetic learning. \u003cem\u003eDevelopmental Psychology, 53\u003c/em\u003e(12), 2304-2318. https://doi.org/10.1037/dev0000432 \u003c/li\u003e\n \u003cli\u003eZhou, X., Chen, Y., Chen, C., Jiang, T., Zhang, H., \u0026amp; Dong, Q. (2007). Chinese kindergartners\u0026rsquo; automatic processing of numerical magnitude in Stroop-like tasks. \u003cem\u003eMemory \u0026amp; Cognition, 35\u003c/em\u003e(3), 464-470. https://doi.org/10.3758/BF03193286 \u003c/li\u003e\n \u003cli\u003eZhou, X., Wei, W., Zhang, Y., Cui, J., \u0026amp; Chen, C. (2015). Visual perception can account for the close relation between numerosity processing and computational fluency. \u003cem\u003eFrontiers in Psychology, 6\u003c/em\u003e(1364). https://doi.org/10.3389/fpsyg.2015.01364\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"number processing, working memory, visual selective attention, multivariate multiple regression","lastPublishedDoi":"10.21203/rs.3.rs-4746725/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4746725/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003ePrevious research has found that domain-general cognitive abilities, especially working memory and visual selective attention, play crucial roles in primary children\u0026rsquo;s mathematical performance, while little is known about their roles in basic number processing in kindergarten children at earlier years. The current study investigated whether working memory components and visual selective attention would make significant contributions to children\u0026rsquo;s basic number processing. A total of 110 Chinese children (\u003cem\u003eM\u003c/em\u003e\u0026thinsp;\u0026plusmn;\u0026thinsp;SD\u0026thinsp;=\u0026thinsp;6.28\u0026thinsp;\u0026plusmn;\u0026thinsp;0.41 years old) were examined with the phonological loop, the visuospatial sketchpad, the central executive, visual selective attention and three number processing tasks (i.e., numerosity estimation, number line estimation and numerical magnitude comparison tasks). Results revealed that the phonological loop accounted for unique variance in children\u0026rsquo;s performance on numerosity estimation, number line estimation, and numerical magnitude comparison. Both the visuospatial sketchpad and the central executive significantly contributed to numerical magnitude comparison, whereas visual selective attention explained unique variance in children\u0026rsquo;s performance of numerosity estimation and number line estimation. Our findings suggest that three components of working memory and visual selective attention have differentiated associations with varied basic number processing skills.\u003c/p\u003e","manuscriptTitle":"Differential Contributions of Working Memory Components and Visual Attention to Young Children’s Varieties of Basic Number Processing","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-08-17 02:11:23","doi":"10.21203/rs.3.rs-4746725/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"00546188-57ce-49d0-b213-079d5761a65b","owner":[],"postedDate":"August 17th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-10-22T17:38:22+00:00","versionOfRecord":[],"versionCreatedAt":"2024-08-17 02:11:23","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4746725","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4746725","identity":"rs-4746725","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}