Bidirectional Relationships between Phonological Processing and Basic Number Knowledge in Kindergarten Children: A Longitudinal Study

Bidirectional Relationships between Phonological Processing and Basic Number Knowledge in Kindergarten Children: A Longitudinal Study | 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 Bidirectional Relationships between Phonological Processing and Basic Number Knowledge in Kindergarten Children: A Longitudinal Study Xin Chen, Chi Ma, Xiujie Yang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4660918/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 17 Jan, 2025 Read the published version in BMC Psychology → Version 1 posted 4 You are reading this latest preprint version Abstract An ongoing debate on the association of phonological processing and number knowledge concerns the extent to which they influence each other when children were at young ages. The current study aims at establishing the direction of the developmental relationship between these two kinds of abilities at an early age. Eighty-two Chinese kindergarten children were followed from 5 to 6 years old with a one-year interval. We investigated three phonological processing skills (phonological awareness, phonological memory, and rapid automatized naming) and two kinds of basic number knowledge (number identification and number comparison) at time 1 and time 2. Cross-lagged panel analyses revealed that the association between phonological awareness and number comparison was bidirectional. Specifically, early phonological awareness at time 1 could predict later number identification, and early number comparison at time 1 was a significant predictor of later phonological memory. In contrast, rapid automatized naming had no such predictive relations with other variables. The present findings are among the first to provide evidence that basic number knowledge could predict later phonological processing in kindergarten children. phonological awareness rapid automatized naming phonological memory number knowledge kindergarteners longitudinal study Figures Figure 1 Figure 2 Introduction Basic number knowledge is an important foundation of children’s performance on future mathematics (Cirino, 2011; Koponen et al., 2013 ; Krajewski & Schneider, 2009 ; LeFevre et al., 2010 ; Träff et al., 2020 ). Children’s development of basic symbolic number skills has been shown largely dependent upon phonological processing (e.g., Yang et al., 2021 ; Fuchs et al., 2010 ; Geary, 2013 ; LeFevre et al., 2010 ; von Aster & Shalev, 2007 ). However, rather few researchers have paid attention to whether basic number knowledge could also contribute to the development of phonological processing. The present study would investigate whether the relationship of phonological processing with basic number knowledge could be bidirectional over time in a longitudinal sample of children, using cross-lagged panel analyses. Krajewski and Schneider ( 2009 a) proposed the developmental levels of basic number knowledge (see also Krajewski & Schneider, 2009 ). The model described early development of quantity-number knowledge, and development could be divided into three level. Level 1 is the basic numerical skills. When children reached this stage, they can distinguish at least indiscrete amounts (quantity discrimination). For example, they can compare quantities with the terms of “more”, “less” or “same”. At level 2, children acquire the ability of linking quantities to numbers and the ability of understanding the meaning of number words. They can accurately compare the magnitude of two numbers (e.g. 3 and 8). At level 3, the children understand the decomposition and composition of numbers (e.g. 8 can be decomposed into 3 and 5; 3 and 5 compose 8). Considering the current study focuses on kindergarten children, we only examined the basic number knowledge that belongs to the Level 1 and Level 2: number identification and number comparison, respectively. Contributions of Phonological Processing to Basic Number Knowledge Phonological processing refers to the ability to use phonological information to decode linguistic information (Wagner & Torgesen, 1987 ; Kuzmina et al., 2019 ). Phonological processing includes three main components: phonological awareness, rapid automatic naming (hereafter, RAN) and phonological memory (Lu, 2003 ; Wagner & Torgesen, 1987 ). Phonological awareness is an awareness or understanding of the sound structure of spoken language and the ability to manipulate these sounds (Wagner & Torgesen, 1987 ; Milwidsky, 2008 ). It requires the skills of an individual to convert the spoken language into sound units and then recompose it into spoken language. RAN refers to children’s ability to record a visual word onto a sound-based representation by retrieving words which often measured by the speed of labeling common items (Blachman, 1984 ; Torgesen et al. 1990 ). Phonological memory emphasizes the short-term maintaining and rehearsing of verbal words and phrases (Cameron et al. 2005 ). When solving a math problem, we need select, implement, monitor strategies and store representations in the working memory. Therefore, these phonological processing skills might be very important. When children hear a number, they first have to convert the spoken language into sound units, a step where phonological awareness comes in to play. The RAN functions to facilitate retrieval speed when children retrieve phonological number codes in long term memory (Koponen et al., 2016 ). Finally, children need to store and rehearse the number information in mind when solving a math problem, in which phonological memory is required. Indeed, several longitudinal studies suggest that phonological processing should predict later basic number knowledge, such as number counting (Krajewski &Schneider, 2009 ; Koponen et al., 2016 ; LeFevre et al, 2010 ). A recent meta-analysis also revealed significant associations between earlier phonological processing and later basic number abilities (e.g., number identification, number comparison) (Peng et al., 2020 ). For example, a 3-year longitudinal study on 4.5- to 7.5-year-old children found that the phonological awareness independently contributed to future performance in number identification and number comparison (LeFevre et al, 2010 ). Koponen et al. ( 2016 ) followed 378 Finish children from kindergarten to Grade 3, and indicated that RAN predicted arithmetic fluency. The relationship remained even after controlling phonological awareness, vocabulary, phonological memory, working memory, number concept skill and mother’s education. Our own study tracked Filipino children at mean ages of 4.5, 5.0, and 5.5 years old and found that RAN explained significant variance in the growth rate of early numeracy (Yang et al., 2021 ). We therefore assume that phonological processing should predict later basic number knowledge. The Possible Role of Basic Number Knowledge in Phonological Processing Except for the role of phonological processing in basic number knowledge, there might be a reciprocal linkage between phonological processing and basic number knowledge. There are researchers indicating that mathematics development could contribute to specific math vocabulary knowledge that are stored in a language format (e.g., O’Halloran, 2005 ). For example, the numbers included phonemes/syllable information (e.g., one, two, three…), and when children learn to count numbers, they will manipulate the syllables. A recent meta-analysis conducted with 344 studies found a moderate relation between language (e.g., phonological awareness and RAN) and mathematics (e.g., basic number knowledge, geometry, calculations). They propose that the foundational mathematics could improve the thinking function of language via advanced mathematics (Peng et al., 2020 ). Therefore, higher performance in basic number knowledge might also promote children’s thinking function of phonological processing, and we deduced that higher performance in basic number knowledge could promote the development of phonological processing. Altogether, the influence of early phonological processing on later basic number knowledge has been largely established, but the effect of early basic number knowledge on later phonological processing has been mainly discussed at the theoretical level, lacking verification by empirical studies. Thus, the purpose of the present study was to investigate, in a longitudinal sample of Chinese children, whether the basic number knowledge, in addition to being influenced by phonological processing subskills, could also predict the development of phonological processing. The present study would conduct cross-lagged longitudinal path models to establish the direction of the interaction between phonological processing (phonological awareness, RAN, phonological memory) and basic number knowledge (number identification, number comparison). Methods Participants and Procedures A total of ninety kindergarten children from Henan mainland China took part in our study for twice with a 12-month time interval. Eight students failed to complete the tests at both time points mainly due to sick leave or transferring to other schools. Finally, eighty-two kindergarten children (45 males and 37 females; Mean age = 60 months, SD = 8 months, at the first time of measurement) were included in the analysis. All Children were native Mandarin Chinese speakers. Written permission for conducting the study was first obtained from parents’ written consent prior to testing at each measurement occasion. The study was also approved by the Ethics Committee of the University. Participants were tested individually in a quiet room in Mandarin by trained testers with a major in psychology or education. Rapid digit naming (DRAN), phonological awareness (PA), forward digit span (DSF), number identification (NI), and number comparison (NC) were measured at both time points. It took approximately 30 minutes to finish all measures, and children were allowed to have a 5-minute short break in their seats during the testing period. The order of the tasks was counterbalanced. Children received souvenirs as rewards after testing. Measures Rapid Automatized Naming. In the rapid digit naming test, which was from Denckla and Rudel ( 1974 ), an 8×5 array of digits printed on a single sheet of A4 paper. Child was asked to name the digits (2,4,6,7, and 9) in order from top to bottom and left to right as quickly as possible. A stopwatch was used to record the naming time (ms). Each child completed the task twice. Calculate the average of the two naming times as the final score. The Cronbach’s alpha of the task was 0.88 (wave 1) and 0.91 (wave 2). Phonological awareness. In line with the previous study of Chinese kindergarteners (Yang et al., 2019b ), the Chinese syllable deletion task was used to measure phonological awareness. There were 2 practice items and 22 test items. The experimenter verbally gave some syllables (i.e., 2–4 syllables) and asked the children to say the remaining syllables except for the deleted one. For example, the experimenter may ask: ‘what is left if we delete the (men2) syllable from (ta1 men2). One score was given for each correct answer (max = 22). Testing stopped after five consecutive failures. The Cronbach’s alpha of the task was 0.93 (wave 1) and 0.94 (wave 2). Phonological Memory Task. The digit forward span task of the Wechsler Intelligence Scale for Children-Fourth Edition (WISC-4; Wechsler, 2008 ) was used to assess phonological memory. Children were asked to listen to and repeat the series in the given order. Eight pairs of 2-digit to 8-digit items were included, for a total of 14 items (max = 14). One point was given for each item correctly answered. When children failed to repeat both items at one level, the task was discontinued. The Cronbach’s alpha of the task was 0.78 (wave 1) and 0.78 (wave 2). Number Identification. The number identification task was adapted from Göbel et al. ( 2014 ) (see also Peng et al., 2017 ). The tester verbally states the target number (e.g., "163") and the child was required to identify the matching Arabic number from the four or five options. The test includes one 1-digit number (6), four 2-digit numbers (14, 28, 52, 76) and three 3-digit numbers (163, 235, 427). One point for correctly identifying an Arabic number (max = 8). The Cronbach’s alpha of the task was 0.70 (wave 1) and 0.83(wave 2). Number Comparison. In the number comparison task, children were asked to choose the larger of the two digits. The test includes 1-digit number pairs (e.g., 2–3), two 2-digit number pairs (e.g., 12–13), and 3-digit number pairs (e.g., 263 − 245), with a total of 12 items. One point for each correct answer (max = 12). The Cronbach’s alpha of the task was 0.84 (wave 1) and 0.79 (wave 2). Analytic Strategies Preliminary data analyses were conducted using SPSS. Cross-lagged longitudinal path models were tested using Mplus 7.4 (Muthén & Muthén,1998–2015) to investigate the reciprocal relationships between phonological processing and basic number knowledge. with age and gender at wave 1 statistically controlled for. Because age and gender were found to affect early numeracy (Cheung et al., 2018 ), they would be statistically controlled for in the following analyses. Missing data was handled using Full information maximum likelihood (FIML) (Enders & Bandalos, 2001 ). The parameters of the models were estimated using the maximum likelihood of robust procedure. The following four indicators were used to assess the fit of the model (Hu & Bentler, 1999 ): Comparative Fit Index (CFI) ≥ .95, Tucker-Lewis Index (TLI) ≥ .95, Root Mean Square Error of Approximation (RMSEA) ≤ .06, and Standardized Root Mean Square Residual (SRMR) ≤ .08. Results Preliminary Analyses Table 1 shows the descriptive statistics of all variables involved in the current study. The mean levels of children’s phonological processing (i.e., rapid digit naming, phonological awareness, and digit forward span) and basic number knowledge (i.e., number comparison and number identification) showed enhancements from wave 1 to wave 2. Table 2 shows the correlations associated with all variables. The results showed significant relationships cross-sectionally between the three phonological processing tasks and the two basic number knowledge tasks (i.e., | r | = .33, p = .003 to .51, p < .001 at wave 1; | r | = .35, p = .001 to .56, p < .001 at wave 2). The longitudinally relationship between phonological processing and basic number knowledge were mostly significant (| r | = .26, p = .019 to .64, p < .001), except that between wave1 rapid digit naming and wave 2 number comparison ( r = − .19, p = .085), and that between wave 1number identification and wave 2 rapid digit naming ( r = − .22, p = .061) Table 1 Descriptive statistics for involved variables. Wave 1 Wave 2 Mean (SD) Range Skewness Kurtosis Mean (SD) Range Skewness Kurtosis DRAN 42.35 (11.56) 21.39–88.80 1.05 2.43 36.78 (10.83) 17.79–71.60 .41 .17 PA 4.96 (5.10) 0.00–19.00 1.24 .93 11.15 (7.27) 0.00–22.00 .24 -1.36 DSF 4.24 (2.31) 0.00–9.00 .05 − .55 6.41 (2.91) 1.00–14.00 .45 − .25 NC 7.98 (3.03) 0.00–12.00 − .55 − .67 10.06 (2.56) 0.00–12.00 -2.22 5.90 NI 3.48 (1.88) 0.00–8.00 .51 − .05 4.82 (1.86) 1.00–8.00 .07 .27 Note. DRAN: rapid digit naming, PA: phonological awareness, DSF: backward digit span, NI: number identification, NC: number comparison. Table 2 Correlations among involved variables. 1 2 3 4 5 6 7 8 9 10 1. DRAN T1 1.00 2. PA T1 − .19 1.00 3. DSF T1 − .32 ** .47 *** 1.00 4. NC T1 − .33 ** .41 *** .51 *** 1.00 5. NI T1 − .33 ** .33 ** .46 *** .40 *** 1.00 6. DRAN T2 .67 *** − .14 − .25 * − .33 ** − .22 1.00 7. PA T2 − .44 *** .46 *** .59 *** .64 *** .37 ** − .58 *** 1.00 8. DSF T2 − .31 ** .34 ** .54 *** .52 *** .37 ** − .54 *** .74 *** 1.00 9. NC T2 − .19 .38 *** .46 *** .53 *** .26 * − .35 ** .53 *** .56 *** 1.00 10. NI T2 − .26 * .30 ** .34 *** .46 *** .36 ** − .39 *** .56 *** .56 *** .38 *** 1.00 11. Age − .45 *** .05 .39 *** .37 ** .34 ** − .58 *** .56 *** .51 *** .35 ** .46 *** 12. Gender .25 * .22 * − .05 − .02 − .11 .20 − .07 − .08 − .09 − .01 Note. DRAN: rapid digit naming, PA: phonological awareness, DSF: backward digit span, NI: number identification, NC: number comparison. * p < .05. ** p < .01. *** p < .001. Cross-lagged Associations between Phonological Processing and Basic Number Knowledge Next, we examine the bidirectional relationships between phonological processing and the two basic number knowledge (i.e., number comparison and number identification) using cross-lagged models with consideration of covariates (i.e., age and gender). The model for number comparison (see Table 3 a and Fig. 1 ) fitted the data well, CFI = 1.00, TLI = 1.00, SRMR = .00, RMSEA = .00. As indicated, phonological awareness at wave 1 significantly predicted higher number comparison at wave 2 ( β = .24, p = .029), and number comparison at wave 1 significantly predicted higher phonological awareness at wave 2 ( β = .28, p = .002). Higher number comparison at wave 1significantly predicted higher digit forward span at wave 2 ( β = .21, p = .05); however, digit forward span did not predict later number comparison ( β = .12, p = .283). Rapid digit naming was unrelated to number comparison. The model for number identification fitted the data well, CFI = 1.00, TLI = 1.00, SRMR = .00, RMSEA = .00 (Table 3 b and Fig. 1 ) . As shown, phonological awareness at wave 1 significantly predicted number identification at wave 2 ( β = .25, p = .033); but number identification did not predict later phonological awareness ( β = − .05, p = .605). Digit forward span and rapid digit naming were not significantly associated with number identification. Table 3 a The cross-lagged path model summary for number comparison. Paths β (SE) p Stability Paths DRAN1→DRAN2 .50 (.08) < .001 PA1→PA2 .26 (.09) .003 DSF1→DSF2 .24 (.11) .027 NC1→NC2 .33 (.11) .003 Cross-lagged Paths PA1→NC2 .24 (.11) .029 NC1→PA2 .28 (.09) .002 DSF1→NC2 .12 (.11) .283 NC1→DSF2 .21 (.11) .05 DRAN1→NC2 .09 (.11) .390 NC1→DRAN2 − .03 (.10) .767 Note. DRAN = digit rapid automatized naming. PA = phonological awareness. DSF = digit span forward. NC = number comparison. Table 3 b The cross-lagged path model summary for number identification. T1-T2 NI β (SE) p Stability Paths DRAN1→DRAN2 .53 (.08) < .001 PA1→PA2 .34 (.09) < .001 DSF1→DSF2 .29 (.11) .007 NI1→NI2 .13 (.11) .247 Cross-lagged Paths DRAN1→NI2 .02 (.11) .837 NI1→DRAN2 .13 (.09) .147 PA1→NI2 .25 (.12) .033 NI1→PA2 − .05 (.09) .605 DSF1→NI2 .02 (.12) .869 NI1→DSF2 .04(.10) .717 Note. DRAN = rapid automatized naming. PA = phonological awareness. DSF = digit span forward. NI = number identification. When number identification and number comparison were included in the same model, (CFI = 1.00, TLI = 1.00, SRMR = .00, RMSEA = .00) (see Table 3 c and Fig. 2 ) , the bidirectional relationship between phonological awareness and number comparison continued to hold ( β = .26, p = .020 from PA1 to NC2 and β = .28, p = .001 from NC1 to PA2). However, unlike the previous models, wave 1 number comparison was only marginally significant in predicting subsequent digit forward span ( β = .20, p = .056), and so was wave 1 phonological awareness in predicting wave 2 number identification (i.e., β = .19, p = .108). Table 3 c The cross-lagged path model summary for number identification and number comparison. T1-T2 NI β (SE) p Stability Paths DRAN1→DRAN2 .52 (.08) < .001 PA1→PA2 .28 (.09) .002 DSF1→DSF2 .23 (.11) .035 NC→NC2 .34 (.11) .002 NI1→NI2 .11 (.11) .312 Cross-lagged Paths for NI DRAN1→NI2 .07 (.11) .312 NI1→DRAN2 .13 (.09) .139 PA1→NI2 .19 (.12) .108 NI1→PA2 − .07 (.09) .426 DSF1→NI2 .02 (.12) .826 NI1→DSF2 .13(.09) .139 Cross-lagged Paths for NC PA1→NC2 .26 (.11) .020 NC1→PA2 .28 (.09) .001 DSF1→NC2 .15 (.12) .205 NC1→DSF2 .20 (.11) .056 DRAN1→NC2 .08 (.11) .467 NC1→DRAN2 − .04 (.10) .677 Note. DRAN = digit rapid automatized naming. PA = phonological awareness. DSF = digit span forward. NI = number identification. NC = number comparison. Discussion Using a cross-lagged panel design, we examined whether the relationship between phonological processing and basic number knowledge could be bidirectional over time in a longitudinal sample of Chinese kindergarten children. Results showed that three phonological processing abilities were all significantly positively correlated to number comparison and number identification at concurrent time points. Furthermore, early number comparison predicted future phonological awareness and phonological memory, whereas early phonological awareness could predict later number identification and number comparison. The results highlighted that basic number knowledge significantly contributed to phonological processing, which was among the first findings to show that they could reinforce each other during children’s developmental stages of early number acquisitions. Consistent with previous studies indicating that phonological processing and math basic number knowledge have stable developmental trajectories over time (Peng et al., 2020 ), our results showed that phonological processing and basic number knowledge steadily increase from wave 1 to wave 2 in early childhood. The stability suggested that children with phonological processing or math basic number knowledge above their peers at one time point tended to have relatively higher scores on the same measure later on. In addition, we found moderate relations between phonological processing and basic number knowledge, in both wave 1 and wave 2, which further validated the results of previous cross-sectional studies (Cirino et al., 2016 ; de Smedt et al., 2010 ; Koponen et al., 2007 ; Krajewski & Schneider, 2009 ; Peng et al., 2020 ). More importantly, the present study revealed the longitudinal predictive effect of phonological processing on basic number knowledge. Specifically, children’s phonological awareness at wave 1 was significantly related to their number identification and number comparison at wave 2. Previous longitudinal studies have also found the significant effect of phonological awareness on basic number knowledge (e.g., Krajewski &Schneider, 2009 ; LeFevre et al, 2010 ; Träff et al., 2020 ; Yang et al., 2021 ). Considering that children often rely on verbal code representations when manipulating the pronunciations of number words (Krajewski & Schneider, 2009 a; Simmons & Singleton, 2008 ), it is expected that phonological awareness would have a significant effect on number identification. In addition, these studies also suggested that phonological awareness has only an indirect effect on higher levels of quantity to number-word linkage (i.e., when number words had to be linked with quantities such as number comparison) (Krajewski &Schneider, 2009 ; Träff et al., 2020 ). They argue that these higher-order quantity-number skills processes reflect a conceptual understanding to associate quantitative information with number words and their Arabic symbols, a process that relies more on visual-spatial abilities. The significant results of phonological awareness on both number comparison in this study may suggest that, at least for Chinese kindergarten children, digit comparison also involves the activation of verbal–phonological number codes. No significant predictive effect of RAN on basic number knowledge was found in this study. The time-limited measure might be more related to number fluency (De Jong & Vrielink, 2004 ; Yang et al., 2019b ), rather than number accuracy (i.e., number comparison) (Jacobson et al., 2004 ; Saavalainen et al., 2006 ). In this study, neither number identification nor number comparison require complex memory of quantitative information (Krajewski &Schneider, 2009 ); this may explain why phonological memory that emphasize short-term retention and rehearsal of verbal words and phrases is not necessary for basic number knowledge. Future research could test this by incorporating both basic number knowledge and more complex mathematical abilities in the model. Inspired by previous proposal that language is a tool for us to communicate mathematical knowledge with others (Bruner, 1966 ; Dehaene, 1992 ; Dehaene & Cohen, 1995 ; Fetzer & Tiedemann, 2018 ; Gersten et al., 2009 ; LeFevre et al., 2010 ), our results suggest that phonological processing may also played a role as a support tool in the development of basic number knowledge among Chinese kindergarten children, especially in the process of converting the spoken number words into sound units (Wagner & Torgesen, 1987 ; Milwidsky, 2008 ). We also found that early basic number knowledge could predict later phonological processing. Specifically, of the two components of basic number knowledge, number comparison was a significant predictor of subsequent phonological processing. Children’s number comparison at wave 1 was significantly related to their phonological awareness and phonological memory at wave 2. This was among the first longitudinal research evidence for the possible predictive relationship from increased math proficiency to increased phonological processing, which has also been suggested by previous studies (Peng et al., 2020 ; O’Halloran, 2005 ). In addition to the role of language as a communication tool in the learning of mathematical knowledge, researchers have proposed that the foundational mathematics could also improve the thinking function of language for performing more advanced mathematics (Peng et al., 2020 ). Our study stepped further by revealing that it is number comparison, rather than number identification, that promotes the development of phonological processing. That might be because number comparison involves more complex cognitive processes, including the manipulation of number pronunciation and also the orders of the numbers (Krajewski &Schneider, 2009 ). This extends the theory of the interaction between reading and mathematics during early numeracy development (e.g., Amland et al., 2021 ; Peng et al., 2020 ), showing that basic verbal and mathematical processing can influence each other. Nevertheless, there are several limitations of this study. First, we only used digit naming to measure RAN ability in children. Future studies might consider adding naming tasks for other stimuli, such as letter, object, animal, etc., to measure RAN more comprehensively. Second, the sample size and age range of the subjects can be expanded to explore the development process of the above variables with age change and whether the relationship is consistent in different age groups. In addition to focusing on basic number knowledge, other mathematical ability indicators might be involved in future, such as number sense, addition, subtraction, etc., so as to explore the relationships between phonological processing, foundational mathematics and advanced mathematics, and their internal mechanisms in a more specific way. Conclusions and Educational Implications This study was among the first revealing the bidirectional predictive relationship between phonological processing and basic number knowledge. Specifically, the basic number knowledge, in addition to being influenced by phonological processing subskills, could also predict the development of phonological processing. These findings prompt us to pay more attention to children with specific language disorders and math disabilities for the possibility of their co-morbidity in math and reading. These findings also have important implications for teachers designing mathematics and language instruction programs. In the current teaching of children, mathematics and language often taught as an independent subject. Our results suggested that integrating the teaching process of mathematical knowledge and linguistic knowledge might be beneficial. For example, teachers could consciously guide children to use phonological processing to retrieve the number information in mathematics. And some mathematical concepts can also be incorporated into language learning. In this way, children's learning of language and mathematics can be both taught in an effective way. Declarations Ethics approval and consent to participate: All subjects gave written informed consent in accordance with the Declaration of Helsinki. Within our ethics statement, the consent obtained from the parents of all research participants was both informed and written by the ethics committee of Faculty of Psychology, Beijing Normal University. Consent for publication: Written informed consent for publication was obtained from all participants. Availability of data and materials: The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request. Competing interests: We confirm that the manuscript has been read and approved by all named authors and that there are no other persons who satisfied the criteria for authorship but are not listed. We further confirm that the order of authors listed in the manuscript has been approved by all of us. We further confirm that any aspect of the work covered in this manuscript that has involved either experimental animals or human patients has been conducted with the ethical approval of all relevant bodies and that such approvals are acknowledged within the manuscript. Funding: This study was funded by the National Natural Science Foundation of China (32000757) to Xiujie Yang, the Science Foundation for the Excellent Youth Scholars from Faculty of Psychology, Beijing Normal University (2019004) to Xiujie Yang, Open Research Fund of the State Key Laboratory of Cognitive Neuroscience and Learning (CNLZD2105) to Xiujie Yang, and Beijing Education Science Planning of 14th Five-year (BEAA21030) to Xiujie Yang. Authors' contributions : X.C.: Conceptualization, Formal Analysis, Visualization, Methodology, Writing-Original Draft C.M.: Conceptualization, Investigation, Writing-Original Draft X.J.Y.: Conceptualization, Funding Acquisition, Supervision, Writing-Review & Editing Acknowledgements : We thank all the children for cooperating with this study, thank the school for the test site and thank the testers for their due diligence. References Amland, T., Lervåg, A., & Melby-Lervåg, M. (2021). Comorbidity between math and reading problems: Is phonological processing a mutual factor?. Frontiers in human neuroscience, 14 , 577304. Blachman, B. A. (1984). Relationship of rapid naming ability and language analysis skills to kindergarten and first grade reading achievement. Journal of Educational Psychology, 76 (4), 610-622. http://dx.doi.org/10.1037/0022-0663.76.4.610 Bruner, J. S. (1966). Toward a theory of instruction . Harvard University Press, Cambridge, MA. Cameron, K. A., Haarmann, H. J., Grafman, J., & Ruchkin, D. S. (2005). Long-term memory is the representational basis for semantic verbal short-term memory. Psychophysiology, 42 (6), 643-653. http://dx.doi.org/10.1111/j.14698986.2005.00357.x Cheung, S. K., Yang, X., Dulay, K. M., & McBride, C. (2018). Family and individual variables associated with young Filipino children’s numeracy interest and competence. British Journal of Developmental Psychology , 36, 334–353. Cirino, P. T., Tolar, T. D., Fuchs, L. S., & Huston-Warren, E. (2016). Cognitive and numerosity predictors of mathematical skills in middle school. Journal of Experimental Child Psychology, 145 , 95-119. http://dx.doi.org/10.1016/j.jecp.2015.12.010 De Jong, P. F., & Vrielink, L. O. (2004). Rapid automatic naming: Easy to measure, hard to improve (quickly). Annals of Dyslexia, 54(1), 65-88. http://dx.doi.org/10.1007/s11881-004-0004-1 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. http://dx.doi.org/10.1111/j.1467-7687.2009.00897.x Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44 (1-2), 1-42. http://dx.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, 83–120. Denckla, M. B., & Rudel, R. (1974). Rapid “automatized” naming of pictured objects, colors, letters and numbers by normal children. Cortex , 10 (2), 186-202. http://dx.doi.org/10.1016/S0010-9452(74)80009-2 Enders, C. K., & Bandalos, D. L. (2001). The relative performance of full information maximum likelihood estimation for missing data in structural equation models. Structural Equation Modeling, 8 (3), 430–457. doi:10.1207/s15328007sem0803_5 Fetzer M., Tiedemann K. (2018) The Interplay of Language and Objects in the Process of Abstracting. In: Moschkovich J., Wagner D., Bose A., Rodrigues Mendes J., Schütte M. (eds) Language and Communication in Mathematics Education. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-75055-2_8 Fuchs, L. S., Geary, D. C., Compton, D. L., Fuchs, D., Hamlett, C. L., Seethaler, P. M., Bryant, J. D., & Schatschneider, C. (2010). Do different types of school mathematics development depend on different constellations of numerical versus general cognitive abilities? Developmental Psychology, 46 (6), 1731-1746. http://dx.doi.org/10.1037/a0020662 Geary, D. C. (2013). Early foundations for mathematics learning and their relations to learning disabilities. Current Directions in Psychological Science, 22, 23–27. http://dx.doi.org/10.1177/0963721412469398 Gersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morphy, P., & Flojo, J. (2009). Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79, 1202–1242. http://dx.doi.org/10.3102/0034654309334431 Göbel, S. M., Watson, S. E., Lervåg, A., & Hulme, C. (2014). Children’s arithmetic development: It is number knowledge, not the approximate number sense, that counts. Psychological Science, 25 (3), 789-798. http://dx.doi.org/10.1177/0956797613516471 Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6 (1), 1-55. http://dx.doi.org/10.1080/10705519909540118 Jacobson, J. M., Nielsen, N. P., Minthon, L., Warkentin, S., & Wiig, E. H. (2004). Multiple Rapid Automatic Naming Measures of Cognition: Normal Performance and Effects of Aging. Perceptual and Motor Skills, 98 (3), 739-753. http://dx.doi.org/10.2466/PMS.98.3.739-753 Koponen, T., Aunola, K., Ahonen, T., & Nurmi, J. (2007). Cognitive predictors of single-digit and procedural calculation skills and their covariation with reading skill. Journal of Experimental Child Psychology, 97 (3), 220-241. http://dx.doi.org/10.1016/j.jecp.2007.03.001 Koponen, T., Salmi, P., Eklund, K., & Aro, T. (2013). Counting and RAN: Predictors of arithmetic calculation and reading fluency. Journal of educational psychology , 105 (1), 162. http://dx.doi.org/10.1037/a0029285 Koponen, T., Salmi, P., Torppa, M., Eklund, K., Aro, T., Aro, M., Poikkeus, A., Lerkkanen, M., & Nurmi, J. (2016). Counting and rapid naming predict the fluency of arithmetic and reading skills. Contemporary Educational Psychology, 44-45 , 83-94. http://dx.doi.org/10.1016/j.cedpsych.2016.02.004 Krajewski, K., & Schneider, W. (2009). Early development of quantity to number-word linkage as a precursor of mathematical school achievement and mathematical difficulties: Findings from a four-year longitudinal study. Learning and Instruction, 19 (6), 513-526. http://dx.doi.org/10.1016/j.learninstruc.2008.10.002 Krajewski, K., & Schneider, W. (2009a). Exploring the impact of phonological awareness, visual-spatial working memory, and preschool quantity-number competencies on mathematics achievement in elementary school: Findings from a 3-year longitudinal study. Journal of Experimental Child Psychology, 103 (4), 516-531. http://dx.doi.org/10.1016/j.jecp.2009.03.009 Kuzmina, Y., Ivanova, A., & Kaiky, D. (2019). The effect of phonological processing on mathematics performance in elementary school varies for boys and girls: Fixed‐effects longitudinal analysis. British Educational Research Journal, 45 (3), 640-661. http://dx.doi.org/10.1002/berj.3518 LeFevre, J., Fast, L., Skwarchuk, S., Smith-Chant, B., Bisanz, J., Kamawar, D., & Penner-Wilger, M. (2010). Pathways to mathematics: Longitudinal predictors of performance. Child Development, 81 (6), 1753-1767. http://dx.doi.org/10.1111/j.1467-8624.2010.01508.x Lu, T. (2003). The relationship of phonological processing (phonological awareness, verbal short -term memory, and rapid naming) and visual short -term memory to reading disabilities in Chinese children (Order No. 3088262). Available from ProQuest Dissertations & Theses Global. (305337245). https://www.proquest.com/dissertations-theses/relationship-phonological-processing-awareness/docview/305337245/se-2?accountid=8554 Milwidsky, C. (2008). Working Memory and Phonological Awareness . March . Muthén, L. K., & Muthén, B. O. 1998–2015. Mplus user’s guide, 7th ed. Los Angeles: Muthén & Muthén. O’Halloran, K. L. (2005). Mathematical discourse: Language, symbolism and visual images. New York, NY: Continuum. Peng, P., Lin, X., Ünal, Z. E., Lee, K., Namkung, J., Chow, J., & Sales, A. (2020). Examining the mutual relations between language and mathematics: A meta-analysis. Psychological Bulletin, 146 (7), 595-634. http://dx.doi.org/10.1037/bul0000231 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. http://dx.doi.org/10.1016/j.jecp.2016.12.011 Saavalainen, P., Luoma, L., Bowler, D., Timonen, T., Määttä, S., Laukkanen, E., & Herrgård, E. (2006). Naming skills of children born preterm in comparison with their term peers at the ages of 9 and 16 years. Developmental Medicine & Child Neurology, 48 (1), 28-32. http://dx.doi.org/10.1017/S0012162206000077 Simmons, F. R., & Singleton, C. (2008). Do weak phonological representations impact on arithmetic development? A review of research into arithmetic and dyslexia. Dyslexia: An International Journal of Research and Practice, 14 (2), 77-94. http://dx.doi.org/10.1002/dys.341 Torgesen, J. K., Wagner, R. K., Simmons, K., & Laughon, P. (1990). Identifying phonological coding problems in disabled readers: Naming, counting, or span measures? Learning Disability Quarterly, 13 (4), 236-243. http://dx.doi.org/10.2307/1510350 Träff, U., Olsson, L., Skagerlund, K., & Östergren, R. (2020). Kindergarten domain-specific and domain-general cognitive precursors of hierarchical mathematical development: A longitudinal study. Journal of Educational Psychology, 112 (1), 93-109. http://dx.doi.org/10.1037/edu0000369 von Aster, M. G., & Shalev, R. S. (2007). Number development and developmental dyscalculia. Developmental Medicine & Child Neurology, 49 (11), 868-873. http://dx.doi.org/10.1111/j.1469-8749.2007.00868.x Wagner, R. K., & Torgesen, J. K. (1987). The nature of phonological processing and its causal role in the acquisition of reading skills. Psychological Bulletin, 101 (2), 192-212. http://dx.doi.org/10.1037/0033-2909.101.2.192 Wechsler, D. (2008). WAIS–IV: Administration and scoring manual. San Antonio, TX: The Psychological Corporation. Yang, X., Dulay, K. M., McBride, C., & Cheung, S. K. (2021). How do phonological awareness, rapid automatized naming, and vocabulary contribute to early numeracy and print knowledge of Filipino children? Journal of Experimental Child Psychology, 209 , 105179. https://doi.org/10.1016/j.jecp.2021.105179 Yang, X., McBride, C., Ho, C. S. H., & Chung, K. K. H. (2019b). Longitudinal associations of phonological processing skills, Chinese word reading, and arithmetic. Reading and Writing , 1-21. https://doi.org/10.1007/s11145-019-09998-9. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 17 Jan, 2025 Read the published version in BMC Psychology → Version 1 posted Editorial decision: Revision requested 03 Jul, 2024 Editor assigned by journal 02 Jul, 2024 Submission checks completed at journal 02 Jul, 2024 First submitted to journal 29 Jun, 2024 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-4660918","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":322058306,"identity":"2afa1d96-ae0e-4380-9f95-2e83d0e8016a","order_by":0,"name":"Xin Chen","email":"","orcid":"","institution":"1.\tBeijing Key Laboratory of Applied Experimental Psychology, National Demonstration Center for Experimental Psychology Education, Faculty of Psychology, Beijing Normal University","correspondingAuthor":false,"prefix":"","firstName":"Xin","middleName":"","lastName":"Chen","suffix":""},{"id":322058307,"identity":"890e007e-81e6-4a7c-9cf1-bf036f7d22d5","order_by":1,"name":"Chi Ma","email":"","orcid":"","institution":"1.\tBeijing Key Laboratory of Applied Experimental Psychology, National Demonstration Center for Experimental Psychology Education, Faculty of Psychology, Beijing Normal University","correspondingAuthor":false,"prefix":"","firstName":"Chi","middleName":"","lastName":"Ma","suffix":""},{"id":322058308,"identity":"7a25c4b7-2dad-41b5-b7f2-8df0c1c55191","order_by":2,"name":"Xiujie Yang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0UlEQVRIiWNgGAWjYBADOQMwxUaCFmPStSRuIFoL/7QzZhI/d9Smb5fuMWD4UHaYgX92A34tErdzzCR7zxzP3TnnjAHjjHOHGSTuHCBgDVCLBG/bsdwNN3IMmHnbDjMYSCTg1yEPsuVv27F0A5CWv8RoMQBqkeZtq0kAa2EkRovh7bRia9m2A4Y7Z6QVHOw5l84jcYOAFrnbyRtvvm2rkzeXSN744EeZtRz/DAJaGBg4TCQYGA6DmQeAmIeQeiBgf/yBgaGOCIWjYBSMglEwYgEANz5EucwUd8YAAAAASUVORK5CYII=","orcid":"","institution":"1.\tBeijing Key Laboratory of Applied Experimental Psychology, National Demonstration Center for Experimental Psychology Education, Faculty of Psychology, Beijing Normal University","correspondingAuthor":true,"prefix":"","firstName":"Xiujie","middleName":"","lastName":"Yang","suffix":""}],"badges":[],"createdAt":"2024-06-30 01:53:23","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4660918/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4660918/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1186/s40359-025-02375-y","type":"published","date":"2025-01-17T15:57:43+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":61010244,"identity":"d8c40726-89c8-4c1d-b3e0-0e2f67465191","added_by":"auto","created_at":"2024-07-24 14:23:59","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":611028,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eThe relationships between rapid automatized naming (DRAN), phonological awareness (PA), digit span forward (DSF), and number identification (NI)/number comparison (NC) from K2 to K3.\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eNote. The results were based on the full model. For ease of presentation, baseline covariates and correlations, non-significant direct pathways, and correlations between within-year variable residuals not shown. All parameters are standardized coefficients. \u003c/em\u003e\u003csup\u003e\u003cem\u003e*\u003c/em\u003e\u003c/sup\u003e\u003cem\u003ep \u0026lt; .05. \u003c/em\u003e\u003csup\u003e\u003cem\u003e**\u003c/em\u003e\u003c/sup\u003e\u003cem\u003ep \u0026lt; .01.\u003c/em\u003e\u003csup\u003e\u003cem\u003e ***\u003c/em\u003e\u003c/sup\u003e\u003cem\u003ep \u0026lt; .001.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"Figure1.png","url":"https://assets-eu.researchsquare.com/files/rs-4660918/v1/f79b6dd16fd9146cc3722fd7.png"},{"id":61009105,"identity":"53dc0f59-709f-40a0-bfe6-81f4f2345f2b","added_by":"auto","created_at":"2024-07-24 14:15:59","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":574000,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eThe relationships between rapid automatized naming (DRAN), phonological awareness (PA), digit span forward (DSF), and number identification (NI) and number comparison (NC) from K2 to K3.\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eNote. \u003c/em\u003eThe results were based on the full model, for ease of presentation, baseline covariates and correlations, non-significant direct pathways, and correlations between within-year variable residuals not shown. All parameters are standardized coefficients.\u003c/p\u003e","description":"","filename":"Figure2.png","url":"https://assets-eu.researchsquare.com/files/rs-4660918/v1/21d1b6c064aba8792b589c9f.png"},{"id":74284827,"identity":"8866cc88-8b38-45cd-b0f3-762cb69f38d8","added_by":"auto","created_at":"2025-01-20 16:12:55","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2731189,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4660918/v1/4fb85b09-ac22-4d03-ba69-119f54430e2d.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Bidirectional Relationships between Phonological Processing and Basic Number Knowledge in Kindergarten Children: A Longitudinal Study","fulltext":[{"header":"Introduction","content":"\u003cp\u003eBasic number knowledge is an important foundation of children\u0026rsquo;s performance on future mathematics (Cirino, 2011; Koponen et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Krajewski \u0026amp; Schneider, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; LeFevre et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Tr\u0026auml;ff et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Children\u0026rsquo;s development of basic symbolic number skills has been shown largely dependent upon phonological processing (e.g., Yang et al., \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Fuchs et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Geary, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; LeFevre et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; von Aster \u0026amp; Shalev, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). However, rather few researchers have paid attention to whether basic number knowledge could also contribute to the development of phonological processing. The present study would investigate whether the relationship of phonological processing with basic number knowledge could be bidirectional over time in a longitudinal sample of children, using cross-lagged panel analyses.\u003c/p\u003e \u003cp\u003eKrajewski and Schneider (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2009\u003c/span\u003ea) proposed the developmental levels of basic number knowledge (see also Krajewski \u0026amp; Schneider, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). The model described early development of quantity-number knowledge, and development could be divided into three level. Level 1 is the basic numerical skills. When children reached this stage, they can distinguish at least indiscrete amounts (quantity discrimination). For example, they can compare quantities with the terms of \u0026ldquo;more\u0026rdquo;, \u0026ldquo;less\u0026rdquo; or \u0026ldquo;same\u0026rdquo;. At level 2, children acquire the ability of linking quantities to numbers and the ability of understanding the meaning of number words. They can accurately compare the magnitude of two numbers (e.g. 3 and 8). At level 3, the children understand the decomposition and composition of numbers (e.g. 8 can be decomposed into 3 and 5; 3 and 5 compose 8). Considering the current study focuses on kindergarten children, we only examined the basic number knowledge that belongs to the Level 1 and Level 2: number identification and number comparison, respectively.\u003c/p\u003e\n\u003ch3\u003eContributions of Phonological Processing to Basic Number Knowledge\u003c/h3\u003e\n\u003cp\u003ePhonological processing refers to the ability to use phonological information to decode linguistic information (Wagner \u0026amp; Torgesen, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e1987\u003c/span\u003e; Kuzmina et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Phonological processing includes three main components: phonological awareness, rapid automatic naming (hereafter, RAN) and phonological memory (Lu, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2003\u003c/span\u003e; Wagner \u0026amp; Torgesen, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e1987\u003c/span\u003e). \u003cem\u003ePhonological awareness\u003c/em\u003e is an awareness or understanding of the sound structure of spoken language and the ability to manipulate these sounds (Wagner \u0026amp; Torgesen, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e1987\u003c/span\u003e; Milwidsky, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). It requires the skills of an individual to convert the spoken language into sound units and then recompose it into spoken language. \u003cem\u003eRAN\u003c/em\u003e refers to children\u0026rsquo;s ability to record a visual word onto a sound-based representation by retrieving words which often measured by the speed of labeling common items (Blachman, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e1984\u003c/span\u003e; Torgesen et al. \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e1990\u003c/span\u003e). \u003cem\u003ePhonological memory\u003c/em\u003e emphasizes the short-term maintaining and rehearsing of verbal words and phrases (Cameron et al. \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2005\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eWhen solving a math problem, we need select, implement, monitor strategies and store representations in the working memory. Therefore, these phonological processing skills might be very important. When children hear a number, they first have to convert the spoken language into sound units, a step where phonological awareness comes in to play. The RAN functions to facilitate retrieval speed when children retrieve phonological number codes in long term memory (Koponen et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Finally, children need to store and rehearse the number information in mind when solving a math problem, in which phonological memory is required.\u003c/p\u003e \u003cp\u003eIndeed, several longitudinal studies suggest that phonological processing should predict later basic number knowledge, such as number counting (Krajewski \u0026amp;Schneider, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Koponen et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; LeFevre et al, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). A recent meta-analysis also revealed significant associations between earlier phonological processing and later basic number abilities (e.g., number identification, number comparison) (Peng et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). For example, a 3-year longitudinal study on 4.5- to 7.5-year-old children found that the phonological awareness independently contributed to future performance in number identification and number comparison (LeFevre et al, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). Koponen et al. (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) followed 378 Finish children from kindergarten to Grade 3, and indicated that RAN predicted arithmetic fluency. The relationship remained even after controlling phonological awareness, vocabulary, phonological memory, working memory, number concept skill and mother\u0026rsquo;s education. Our own study tracked Filipino children at mean ages of 4.5, 5.0, and 5.5 years old and found that RAN explained significant variance in the growth rate of early numeracy (Yang et al., \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). We therefore assume that phonological processing should predict later basic number knowledge.\u003c/p\u003e\n\u003ch3\u003eThe Possible Role of Basic Number Knowledge in Phonological Processing\u003c/h3\u003e\n\u003cp\u003eExcept for the role of phonological processing in basic number knowledge, there might be a reciprocal linkage between phonological processing and basic number knowledge. There are researchers indicating that mathematics development could contribute to specific math vocabulary knowledge that are stored in a language format (e.g., O\u0026rsquo;Halloran, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). For example, the numbers included phonemes/syllable information (e.g., one, two, three\u0026hellip;), and when children learn to count numbers, they will manipulate the syllables. A recent meta-analysis conducted with 344 studies found a moderate relation between language (e.g., phonological awareness and RAN) and mathematics (e.g., basic number knowledge, geometry, calculations). They propose that the foundational mathematics could improve the thinking function of language via advanced mathematics (Peng et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Therefore, higher performance in basic number knowledge might also promote children\u0026rsquo;s thinking function of phonological processing, and we deduced that higher performance in basic number knowledge could promote the development of phonological processing.\u003c/p\u003e \u003cp\u003eAltogether, the influence of early phonological processing on later basic number knowledge has been largely established, but the effect of early basic number knowledge on later phonological processing has been mainly discussed at the theoretical level, lacking verification by empirical studies. Thus, the purpose of the present study was to investigate, in a longitudinal sample of Chinese children, whether the basic number knowledge, in addition to being influenced by phonological processing subskills, could also predict the development of phonological processing. The present study would conduct cross-lagged longitudinal path models to establish the direction of the interaction between phonological processing (phonological awareness, RAN, phonological memory) and basic number knowledge (number identification, number comparison).\u003c/p\u003e"},{"header":"Methods","content":"\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003eParticipants and Procedures\u003c/h2\u003e \u003cp\u003eA total of ninety kindergarten children from Henan mainland China took part in our study for twice with a 12-month time interval. Eight students failed to complete the tests at both time points mainly due to sick leave or transferring to other schools. Finally, eighty-two kindergarten children (45 males and 37 females; Mean age\u0026thinsp;=\u0026thinsp;60 months, \u003cem\u003eSD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;8 months, at the first time of measurement) were included in the analysis. All Children were native Mandarin Chinese speakers. Written permission for conducting the study was first obtained from parents\u0026rsquo; written consent prior to testing at each measurement occasion. The study was also approved by the Ethics Committee of the University. Participants were tested individually in a quiet room in Mandarin by trained testers with a major in psychology or education. Rapid digit naming (DRAN), phonological awareness (PA), forward digit span (DSF), number identification (NI), and number comparison (NC) were measured at both time points. It took approximately 30 minutes to finish all measures, and children were allowed to have a 5-minute short break in their seats during the testing period. The order of the tasks was counterbalanced. Children received souvenirs as rewards after testing.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003eMeasures\u003c/h2\u003e \u003cp\u003e \u003cb\u003eRapid Automatized Naming.\u003c/b\u003e In the rapid digit naming test, which was from Denckla and Rudel (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e1974\u003c/span\u003e), an 8\u0026times;5 array of digits printed on a single sheet of A4 paper. Child was asked to name the digits (2,4,6,7, and 9) in order from top to bottom and left to right as quickly as possible. A stopwatch was used to record the naming time (ms). Each child completed the task twice. Calculate the average of the two naming times as the final score. The Cronbach\u0026rsquo;s alpha of the task was 0.88 (wave 1) and 0.91 (wave 2).\u003c/p\u003e \u003cp\u003e\u003cb\u003ePhonological awareness.\u003c/b\u003e In line with the previous study of Chinese kindergarteners (Yang et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2019b\u003c/span\u003e), the Chinese syllable deletion task was used to measure phonological awareness. There were 2 practice items and 22 test items. The experimenter verbally gave some syllables (i.e., 2\u0026ndash;4 syllables) and asked the children to say the remaining syllables except for the deleted one. For example, the experimenter may ask: \u0026lsquo;what is left if we delete the (men2) syllable from (ta1 men2). One score was given for each correct answer (max\u0026thinsp;=\u0026thinsp;22). Testing stopped after five consecutive failures. The Cronbach\u0026rsquo;s alpha of the task was 0.93 (wave 1) and 0.94 (wave 2).\u003c/p\u003e \u003cp\u003e \u003cb\u003ePhonological Memory Task.\u003c/b\u003e The digit forward span task of the Wechsler Intelligence Scale for Children-Fourth Edition (WISC-4; Wechsler, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) was used to assess phonological memory. Children were asked to listen to and repeat the series in the given order. Eight pairs of 2-digit to 8-digit items were included, for a total of 14 items (max\u0026thinsp;=\u0026thinsp;14). One point was given for each item correctly answered. When children failed to repeat both items at one level, the task was discontinued. The Cronbach\u0026rsquo;s alpha of the task was 0.78 (wave 1) and 0.78 (wave 2).\u003c/p\u003e \u003cp\u003e \u003cb\u003eNumber Identification.\u003c/b\u003e The number identification task was adapted from G\u0026ouml;bel et al. (\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) (see also Peng et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). The tester verbally states the target number (e.g., \"163\") and the child was required to identify the matching Arabic number from the four or five options. The test includes one 1-digit number (6), four 2-digit numbers (14, 28, 52, 76) and three 3-digit numbers (163, 235, 427). One point for correctly identifying an Arabic number (max\u0026thinsp;=\u0026thinsp;8). The Cronbach\u0026rsquo;s alpha of the task was 0.70 (wave 1) and 0.83(wave 2).\u003c/p\u003e \u003cp\u003e \u003cb\u003eNumber Comparison.\u003c/b\u003e In the number comparison task, children were asked to choose the larger of the two digits. The test includes 1-digit number pairs (e.g., 2\u0026ndash;3), two 2-digit number pairs (e.g., 12\u0026ndash;13), and 3-digit number pairs (e.g., 263\u0026thinsp;\u0026minus;\u0026thinsp;245), with a total of 12 items. One point for each correct answer (max\u0026thinsp;=\u0026thinsp;12). The Cronbach\u0026rsquo;s alpha of the task was 0.84 (wave 1) and 0.79 (wave 2).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003eAnalytic Strategies\u003c/h2\u003e \u003cp\u003ePreliminary data analyses were conducted using SPSS. Cross-lagged longitudinal path models were tested using Mplus 7.4 (Muth\u0026eacute;n \u0026amp; Muth\u0026eacute;n,1998\u0026ndash;2015) to investigate the reciprocal relationships between phonological processing and basic number knowledge. with age and gender at wave 1 statistically controlled for. Because age and gender were found to affect early numeracy (Cheung et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), they would be statistically controlled for in the following analyses. Missing data was handled using Full information maximum likelihood (FIML) (Enders \u0026amp; Bandalos, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2001\u003c/span\u003e). The parameters of the models were estimated using the maximum likelihood of robust procedure. The following four indicators were used to assess the fit of the model (Hu \u0026amp; Bentler, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e1999\u003c/span\u003e): Comparative Fit Index (CFI)\u0026thinsp;\u0026ge;\u0026thinsp;.95, Tucker-Lewis Index (TLI)\u0026thinsp;\u0026ge;\u0026thinsp;.95, Root Mean Square Error of Approximation (RMSEA)\u0026thinsp;\u0026le;\u0026thinsp;.06, and Standardized Root Mean Square Residual (SRMR)\u0026thinsp;\u0026le;\u0026thinsp;.08.\u003c/p\u003e \u003c/div\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec9\"\u003e\n \u003ch2\u003ePreliminary Analyses\u003c/h2\u003e\n \u003cp\u003eTable \u003cspan\u003e1\u003c/span\u003e shows the descriptive statistics of all variables involved in the current study. The mean levels of children\u0026rsquo;s phonological processing (i.e., rapid digit naming, phonological awareness, and digit forward span) and basic number knowledge (i.e., number comparison and number identification) showed enhancements from wave 1 to wave 2. Table \u003cspan\u003e2\u003c/span\u003e shows the correlations associated with all variables. The results showed significant relationships cross-sectionally between the three phonological processing tasks and the two basic number knowledge tasks (i.e., |\u003cem\u003er\u003c/em\u003e| = .33, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.003 to .51, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001 at wave 1; |\u003cem\u003er\u003c/em\u003e| = .35, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.001 to .56, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001 at wave 2). The longitudinally relationship between phonological processing and basic number knowledge were mostly significant (|\u003cem\u003er\u003c/em\u003e| = .26, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.019 to .64, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001), except that between wave1 rapid digit naming and wave 2 number comparison (\u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;.19, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.085), and that between wave 1number identification and wave 2 rapid digit naming (\u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;.22, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.061)\u003c/p\u003e\n \u003cdiv\u003e\n \u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 1\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003e\u003cem\u003eDescriptive statistics for involved variables.\u003c/em\u003e\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"9\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\" colspan=\"4\"\u003e\n \u003cp\u003eWave 1\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"4\"\u003e\n \u003cp\u003eWave 2\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\"\u003e\n \u003cp\u003eMean (SD)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRange\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eSkewness\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eKurtosis\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMean (SD)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRange\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eSkewness\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eKurtosis\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDRAN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e42.35 (11.56)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e21.39\u0026ndash;88.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e36.78 (10.83)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e17.79\u0026ndash;71.60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.17\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.96 (5.10)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00\u0026ndash;19.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.15 (7.27)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00\u0026ndash;22.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-1.36\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDSF\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.24 (2.31)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00\u0026ndash;9.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.41 (2.91)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.00\u0026ndash;14.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.25\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.98 (3.03)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00\u0026ndash;12.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.67\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.06 (2.56)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00\u0026ndash;12.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-2.22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.90\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNI\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.48 (1.88)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00\u0026ndash;8.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.82 (1.86)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.00\u0026ndash;8.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.27\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003ctfoot\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"9\"\u003e\u003cem\u003eNote.\u003c/em\u003e DRAN: rapid digit naming, PA: phonological awareness, DSF: backward digit span, NI: number identification, NC: number comparison.\u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tfoot\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cdiv\u003e\n \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\u003eCorrelations among involved variables.\u003c/em\u003e\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"11\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\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 \u003cth align=\"left\"\u003e\n \u003cp\u003e10\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. DRAN T1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.00\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 \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2. PA T1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.00\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\u003e3. DSF T1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.32\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.47\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.00\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\u003e4. NC T1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.33\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.41\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.51\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.00\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\u003e5. NI T1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.33\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.33\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.46\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.40\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.00\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\u003e6. DRAN T2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.67\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.25\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.33\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.00\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\u003e7. PA T2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.44\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.46\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.59\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.64\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.37\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.58\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.00\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\u003e8. DSF T2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.31\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.34\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.54\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.52\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.37\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.54\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.74\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.00\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\u003e9. NC T2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.38\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.46\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.53\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.26\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.35\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.53\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.56\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.00\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\u003e10. NI T2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.26\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.30\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.34\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.46\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.36\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.39\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.56\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.56\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.38\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11. Age\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.45\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.39\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.37\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.34\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.58\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.56\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.51\u003csup\u003e***\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.35\u003csup\u003e**\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.46\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\u003e12. Gender\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.25\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.22\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.01\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003ctfoot\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"11\"\u003eNote. DRAN: rapid digit naming, PA: phonological awareness, DSF: backward digit span, NI: number identification, NC: number comparison.\u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tfoot\u003e\n \u003c/table\u003e\n \u003c/div\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.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec10\"\u003e\n \u003ch2\u003eCross-lagged Associations between Phonological Processing and Basic Number Knowledge\u003c/h2\u003e\n \u003cp\u003eNext, we examine the bidirectional relationships between phonological processing and the two basic number knowledge (i.e., number comparison and number identification) using cross-lagged models with consideration of covariates (i.e., age and gender).\u003c/p\u003e\n \u003cp\u003eThe model for number comparison (see Table \u003cspan\u003e3\u003c/span\u003ea \u003cstrong\u003eand\u003c/strong\u003e Fig. \u003cspan\u003e1\u003c/span\u003e\u003cstrong\u003e)\u003c/strong\u003e fitted the data well, CFI\u0026thinsp;=\u0026thinsp;1.00, TLI\u0026thinsp;=\u0026thinsp;1.00, SRMR\u0026thinsp;=\u0026thinsp;.00, RMSEA\u0026thinsp;=\u0026thinsp;.00. As indicated, phonological awareness at wave 1 significantly predicted higher number comparison at wave 2 (\u003cem\u003e\u0026beta;\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.24, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.029), and number comparison at wave 1 significantly predicted higher phonological awareness at wave 2 (\u003cem\u003e\u0026beta;\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.28, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.002). Higher number comparison at wave 1significantly predicted higher digit forward span at wave 2 (\u003cem\u003e\u0026beta;\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.21, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.05); however, digit forward span did not predict later number comparison (\u003cem\u003e\u0026beta;\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.12, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.283). Rapid digit naming was unrelated to number comparison. The model for number identification fitted the data well, CFI\u0026thinsp;=\u0026thinsp;1.00, TLI\u0026thinsp;=\u0026thinsp;1.00, SRMR\u0026thinsp;=\u0026thinsp;.00, RMSEA\u0026thinsp;=\u0026thinsp;.00 (Table \u003cspan\u003e3\u003c/span\u003eb \u003cstrong\u003eand\u003c/strong\u003e Fig. \u003cspan\u003e1\u003c/span\u003e\u003cstrong\u003e)\u003c/strong\u003e. As shown, phonological awareness at wave 1 significantly predicted number identification at wave 2 (\u003cem\u003e\u0026beta;\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.25, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.033); but number identification did not predict later phonological awareness (\u003cem\u003e\u0026beta;\u003c/em\u003e = \u0026minus;\u0026thinsp;.05, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.605). Digit forward span and rapid digit naming were not significantly associated with number identification.\u003c/p\u003e\n \u003cdiv\u003e\n \u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 3\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003e\u003cstrong\u003ea\u003c/strong\u003e \u003cem\u003eThe cross-lagged path model summary for number comparison.\u003c/em\u003e\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"3\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ePaths\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026beta;\u003c/em\u003e (SE)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003ep\u003c/em\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\n \u003cp\u003e\u003cstrong\u003eStability Paths\u003c/strong\u003e\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\u003eDRAN1\u0026rarr;DRAN2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.50 (.08)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;\u0026thinsp;.001\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePA1\u0026rarr;PA2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.26 (.09)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.003\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDSF1\u0026rarr;DSF2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.24 (.11)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.027\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNC1\u0026rarr;NC2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.33 (.11)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.003\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eCross-lagged Paths\u003c/strong\u003e\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\u003e\u003cstrong\u003ePA1\u0026rarr;NC2\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e.24 (.11)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e.029\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eNC1\u0026rarr;PA2\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e.28 (.09)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e.002\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDSF1\u0026rarr;NC2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.12 (.11)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.283\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eNC1\u0026rarr;DSF2\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e.21 (.11)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e.05\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDRAN1\u0026rarr;NC2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.09 (.11)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.390\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNC1\u0026rarr;DRAN2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.03 (.10)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.767\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003e\u003cem\u003eNote. DRAN\u0026thinsp;=\u0026thinsp;digit rapid automatized naming. PA\u0026thinsp;=\u0026thinsp;phonological awareness. DSF\u0026thinsp;=\u0026thinsp;digit span forward. NC\u0026thinsp;=\u0026thinsp;number comparison.\u003c/em\u003e\u003c/p\u003e\n \u003cdiv\u003e\n \u003ctable id=\"Tab4\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 3\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003e\u003cstrong\u003eb\u003c/strong\u003e \u003cem\u003eThe cross-lagged path model summary for number identification.\u003c/em\u003e\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"3\"\u003e\u003c/colgroup\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\u003eT1-T2\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\u003eNI\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026beta;\u003c/em\u003e (SE)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003ep\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eStability Paths\u003c/strong\u003e\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\u003eDRAN1\u0026rarr;DRAN2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.53 (.08)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;\u0026thinsp;.001\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePA1\u0026rarr;PA2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.34 (.09)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;\u0026thinsp;.001\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDSF1\u0026rarr;DSF2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.29 (.11)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.007\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNI1\u0026rarr;NI2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.13 (.11)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.247\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eCross-lagged Paths\u003c/strong\u003e\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\u003eDRAN1\u0026rarr;NI2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.02 (.11)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.837\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNI1\u0026rarr;DRAN2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.13 (.09)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.147\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003ePA1\u0026rarr;NI2\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e.25 (.12)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e.033\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNI1\u0026rarr;PA2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.05 (.09)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.605\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDSF1\u0026rarr;NI2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.02 (.12)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.869\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNI1\u0026rarr;DSF2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.04(.10)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.717\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003ctfoot\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"3\"\u003e\u003cem\u003eNote. DRAN\u0026thinsp;=\u0026thinsp;rapid automatized naming. PA\u0026thinsp;=\u0026thinsp;phonological awareness. DSF\u0026thinsp;=\u0026thinsp;digit span forward. NI\u0026thinsp;=\u0026thinsp;number identification.\u003c/em\u003e\u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tfoot\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eWhen number identification and number comparison were included in the same model, (CFI\u0026thinsp;=\u0026thinsp;1.00, TLI\u0026thinsp;=\u0026thinsp;1.00, SRMR\u0026thinsp;=\u0026thinsp;.00, RMSEA\u0026thinsp;=\u0026thinsp;.00) (see Table \u003cspan\u003e3\u003c/span\u003ec \u003cstrong\u003eand\u003c/strong\u003e Fig. \u003cspan\u003e2\u003c/span\u003e\u003cstrong\u003e)\u003c/strong\u003e, the bidirectional relationship between phonological awareness and number comparison continued to hold (\u003cem\u003e\u0026beta;\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.26, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.020 from PA1 to NC2 and \u003cem\u003e\u0026beta;\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.28, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.001 from NC1 to PA2). However, unlike the previous models, wave 1 number comparison was only marginally significant in predicting subsequent digit forward span (\u003cem\u003e\u0026beta;\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.20, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.056), and so was wave 1 phonological awareness in predicting wave 2 number identification (i.e., \u003cem\u003e\u0026beta;\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.19, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.108).\u003c/p\u003e\n \u003cdiv\u003e\n \u003ctable id=\"Tab5\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 3\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003e\u003cstrong\u003ec\u003c/strong\u003e \u003cem\u003eThe cross-lagged path model summary for number identification and number comparison.\u003c/em\u003e\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"3\"\u003e\u003c/colgroup\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\u003eT1-T2\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\u003eNI\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026beta;\u003c/em\u003e (SE)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003ep\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eStability Paths\u003c/strong\u003e\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\u003eDRAN1\u0026rarr;DRAN2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.52 (.08)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026lt;\u0026thinsp;.001\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePA1\u0026rarr;PA2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.28 (.09)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.002\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDSF1\u0026rarr;DSF2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.23 (.11)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.035\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNC\u0026rarr;NC2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.34 (.11)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.002\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNI1\u0026rarr;NI2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.11 (.11)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.312\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eCross-lagged Paths for NI\u003c/strong\u003e\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\u003eDRAN1\u0026rarr;NI2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.07 (.11)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.312\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNI1\u0026rarr;DRAN2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.13 (.09)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.139\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePA1\u0026rarr;NI2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.19 (.12)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.108\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNI1\u0026rarr;PA2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.07 (.09)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.426\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDSF1\u0026rarr;NI2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.02 (.12)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.826\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNI1\u0026rarr;DSF2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.13(.09)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.139\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eCross-lagged Paths for NC\u003c/strong\u003e\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\u003e\u003cstrong\u003ePA1\u0026rarr;NC2\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e.26 (.11)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e.020\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eNC1\u0026rarr;PA2\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e.28 (.09)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e.001\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDSF1\u0026rarr;NC2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.15 (.12)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.205\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNC1\u0026rarr;DSF2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.20 (.11)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.056\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDRAN1\u0026rarr;NC2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.08 (.11)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.467\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNC1\u0026rarr;DRAN2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026minus;\u0026thinsp;.04 (.10)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e.677\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003ctfoot\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"3\"\u003e\u003cem\u003eNote.\u003c/em\u003e DRAN\u0026thinsp;=\u0026thinsp;digit rapid automatized naming. PA\u0026thinsp;=\u0026thinsp;phonological awareness. DSF\u0026thinsp;=\u0026thinsp;digit span forward. NI\u0026thinsp;=\u0026thinsp;number identification. NC\u0026thinsp;=\u0026thinsp;number comparison.\u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tfoot\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eUsing a cross-lagged panel design, we examined whether the relationship between phonological processing and basic number knowledge could be bidirectional over time in a longitudinal sample of Chinese kindergarten children. Results showed that three phonological processing abilities were all significantly positively correlated to number comparison and number identification at concurrent time points. Furthermore, early number comparison predicted future phonological awareness and phonological memory, whereas early phonological awareness could predict later number identification and number comparison. The results highlighted that basic number knowledge significantly contributed to phonological processing, which was among the first findings to show that they could reinforce each other during children’s developmental stages of early number acquisitions.\u003c/p\u003e \u003cp\u003eConsistent with previous studies indicating that phonological processing and math basic number knowledge have stable developmental trajectories over time (Peng et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), our results showed that phonological processing and basic number knowledge steadily increase from wave 1 to wave 2 in early childhood. The stability suggested that children with phonological processing or math basic number knowledge above their peers at one time point tended to have relatively higher scores on the same measure later on. In addition, we found moderate relations between phonological processing and basic number knowledge, in both wave 1 and wave 2, which further validated the results of previous cross-sectional studies (Cirino et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; de Smedt et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Koponen et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Krajewski \u0026amp; Schneider, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Peng et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eMore importantly, the present study revealed the longitudinal predictive effect of phonological processing on basic number knowledge. Specifically, children’s phonological awareness at wave 1 was significantly related to their number identification and number comparison at wave 2. Previous longitudinal studies have also found the significant effect of phonological awareness on basic number knowledge (e.g., Krajewski \u0026amp;Schneider, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; LeFevre et al, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Träff et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Yang et al., \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Considering that children often rely on verbal code representations when manipulating the pronunciations of number words (Krajewski \u0026amp; Schneider, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2009\u003c/span\u003ea; Simmons \u0026amp; Singleton, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2008\u003c/span\u003e), it is expected that phonological awareness would have a significant effect on number identification. In addition, these studies also suggested that phonological awareness has only an indirect effect on higher levels of quantity to number-word linkage (i.e., when number words had to be linked with quantities such as number comparison) (Krajewski \u0026amp;Schneider, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Träff et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). They argue that these higher-order quantity-number skills processes reflect a conceptual understanding to associate quantitative information with number words and their Arabic symbols, a process that relies more on visual-spatial abilities. The significant results of phonological awareness on both number comparison in this study may suggest that, at least for Chinese kindergarten children, digit comparison also involves the activation of verbal–phonological number codes.\u003c/p\u003e \u003cp\u003eNo significant predictive effect of RAN on basic number knowledge was found in this study. The time-limited measure might be more related to number fluency (De Jong \u0026amp; Vrielink, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Yang et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2019b\u003c/span\u003e), rather than number accuracy (i.e., number comparison) (Jacobson et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Saavalainen et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). In this study, neither number identification nor number comparison require complex memory of quantitative information (Krajewski \u0026amp;Schneider, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2009\u003c/span\u003e); this may explain why phonological memory that emphasize short-term retention and rehearsal of verbal words and phrases is not necessary for basic number knowledge. Future research could test this by incorporating both basic number knowledge and more complex mathematical abilities in the model. Inspired by previous proposal that language is a tool for us to communicate mathematical knowledge with others (Bruner, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e1966\u003c/span\u003e; Dehaene, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e1992\u003c/span\u003e; Dehaene \u0026amp; Cohen, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e1995\u003c/span\u003e; Fetzer \u0026amp; Tiedemann, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Gersten et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; LeFevre et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2010\u003c/span\u003e), our results suggest that phonological processing may also played a role as a support tool in the development of basic number knowledge among Chinese kindergarten children, especially in the process of converting the spoken number words into sound units (Wagner \u0026amp; Torgesen, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e1987\u003c/span\u003e; Milwidsky, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2008\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eWe also found that early basic number knowledge could predict later phonological processing. Specifically, of the two components of basic number knowledge, number comparison was a significant predictor of subsequent phonological processing. Children’s number comparison at wave 1 was significantly related to their phonological awareness and phonological memory at wave 2. This was among the first longitudinal research evidence for the possible predictive relationship from increased math proficiency to increased phonological processing, which has also been suggested by previous studies (Peng et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; O’Halloran, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). In addition to the role of language as a communication tool in the learning of mathematical knowledge, researchers have proposed that the foundational mathematics could also improve the thinking function of language for performing more advanced mathematics (Peng et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Our study stepped further by revealing that it is number comparison, rather than number identification, that promotes the development of phonological processing. That might be because number comparison involves more complex cognitive processes, including the manipulation of number pronunciation and also the orders of the numbers (Krajewski \u0026amp;Schneider, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). This extends the theory of the interaction between reading and mathematics during early numeracy development (e.g., Amland et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Peng et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), showing that basic verbal and mathematical processing can influence each other.\u003c/p\u003e \u003cp\u003eNevertheless, there are several limitations of this study. First, we only used digit naming to measure RAN ability in children. Future studies might consider adding naming tasks for other stimuli, such as letter, object, animal, etc., to measure RAN more comprehensively. Second, the sample size and age range of the subjects can be expanded to explore the development process of the above variables with age change and whether the relationship is consistent in different age groups. In addition to focusing on basic number knowledge, other mathematical ability indicators might be involved in future, such as number sense, addition, subtraction, etc., so as to explore the relationships between phonological processing, foundational mathematics and advanced mathematics, and their internal mechanisms in a more specific way.\u003c/p\u003e "},{"header":"Conclusions and Educational Implications","content":"\u003cp\u003eThis study was among the first revealing the bidirectional predictive relationship between phonological processing and basic number knowledge. Specifically, the basic number knowledge, in addition to being influenced by phonological processing subskills, could also predict the development of phonological processing. These findings prompt us to pay more attention to children with specific language disorders and math disabilities for the possibility of their co-morbidity in math and reading. These findings also have important implications for teachers designing mathematics and language instruction programs. In the current teaching of children, mathematics and language often taught as an independent subject. Our results suggested that integrating the teaching process of mathematical knowledge and linguistic knowledge might be beneficial. For example, teachers could consciously guide children to use phonological processing to retrieve the number information in mathematics. And some mathematical concepts can also be incorporated into language learning. In this way, children's learning of language and mathematics can be both taught in an effective way.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate:\u0026nbsp;\u003c/strong\u003eAll subjects gave written informed consent in accordance with the Declaration of Helsinki. Within\u0026nbsp;our\u0026nbsp;ethics statement, the consent obtained from the parents of all research participants was both informed and written by the ethics committee of Faculty of Psychology, Beijing Normal University.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication:\u003c/strong\u003e Written informed consent for publication was obtained from all participants.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials:\u0026nbsp;\u003c/strong\u003eThe datasets generated during and/or analyzed during the current study are available from the\u0026nbsp;corresponding\u0026nbsp;author on reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests:\u003c/strong\u003e We confirm that the manuscript has been read and approved by all named authors and that there are no other persons who satisfied the criteria for authorship but are not listed. We further confirm that the order of authors listed in the manuscript has been approved by all of us.\u0026nbsp;We further confirm that\u0026nbsp;any\u0026nbsp;aspect of the work covered in this manuscript that has involved either experimental animals or human patients has been conducted with the ethical approval of all relevant bodies and that such approvals are acknowledged within the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding:\u0026nbsp;\u003c/strong\u003eThis study was funded by the National Natural Science Foundation of China (32000757) to Xiujie Yang, the Science\u0026nbsp;Foundation\u0026nbsp;for the Excellent Youth Scholars from Faculty of Psychology, Beijing Normal University (2019004) to Xiujie Yang, Open Research Fund of the State Key Laboratory\u0026nbsp;of Cognitive Neuroscience and Learning\u0026nbsp;(CNLZD2105) to Xiujie Yang, and Beijing Education Science Planning of 14th Five-year (BEAA21030) to Xiujie Yang.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u0026apos; contributions\u003c/strong\u003e:\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eX.C.: Conceptualization, Formal Analysis, Visualization, Methodology, Writing-Original Draft\u003c/p\u003e\n\u003cp\u003eC.M.: Conceptualization, Investigation, Writing-Original Draft\u003c/p\u003e\n\u003cp\u003eX.J.Y.: Conceptualization, Funding Acquisition, Supervision, Writing-Review \u0026amp; Editing\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e: We thank all the children for cooperating with this study, thank the school for the test site and thank the testers for their due diligence.\u003cbr\u003e\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAmland, T., Lerv\u0026aring;g, A., \u0026amp; Melby-Lerv\u0026aring;g, M. (2021). Comorbidity between math and reading problems: Is phonological processing a mutual factor?. \u003cem\u003eFrontiers in human neuroscience, 14\u003c/em\u003e, 577304.\u003c/li\u003e\n\u003cli\u003eBlachman, B. A. (1984). Relationship of rapid naming ability and language analysis skills to kindergarten and first grade reading achievement.\u003cem\u003e Journal of Educational Psychology, 76\u003c/em\u003e(4), 610-622. http://dx.doi.org/10.1037/0022-0663.76.4.610\u003c/li\u003e\n\u003cli\u003eBruner, J. S. (1966). \u003cem\u003eToward a theory of instruction\u003c/em\u003e. Harvard University Press, Cambridge, MA.\u003c/li\u003e\n\u003cli\u003eCameron, K. A., Haarmann, H. J., Grafman, J., \u0026amp; Ruchkin, D. S. (2005). Long-term memory is the representational basis for semantic verbal short-term memory.\u003cem\u003e Psychophysiology, 42\u003c/em\u003e(6), 643-653. http://dx.doi.org/10.1111/j.14698986.2005.00357.x\u003c/li\u003e\n\u003cli\u003eCheung, S. K., Yang, X., Dulay, K. M., \u0026amp; McBride, C. (2018). Family and individual variables associated with young Filipino children\u0026rsquo;s numeracy interest and competence. \u003cem\u003eBritish Journal of Developmental Psychology\u003c/em\u003e, 36, 334\u0026ndash;353.\u003c/li\u003e\n\u003cli\u003eCirino, P. T., Tolar, T. D., Fuchs, L. S., \u0026amp; Huston-Warren, E. (2016). Cognitive and numerosity predictors of mathematical skills in middle school.\u003cem\u003e Journal of Experimental Child Psychology, 145\u003c/em\u003e, 95-119. http://dx.doi.org/10.1016/j.jecp.2015.12.010\u003c/li\u003e\n\u003cli\u003eDe Jong, P. F., \u0026amp; Vrielink, L. O. (2004). Rapid automatic naming: Easy to measure, hard to improve (quickly). Annals of Dyslexia, 54(1), 65-88. http://dx.doi.org/10.1007/s11881-004-0004-1\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\u0026apos;s arithmetic skills? \u003cem\u003eDevelopmental Science, 13\u003c/em\u003e(3), 508-520. http://dx.doi.org/10.1111/j.1467-7687.2009.00897.x\u003c/li\u003e\n\u003cli\u003eDehaene, S. (1992). Varieties of numerical abilities.\u003cem\u003e Cognition, 44\u003c/em\u003e(1-2), 1-42. http://dx.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\u003e Mathematical Cognition\u003c/em\u003e, 1, 83\u0026ndash;120.\u003c/li\u003e\n\u003cli\u003eDenckla, M. B., \u0026amp; Rudel, R. (1974). Rapid \u0026ldquo;automatized\u0026rdquo; naming of pictured objects, colors, letters and numbers by normal children. \u003cem\u003eCortex\u003c/em\u003e, \u003cem\u003e10\u003c/em\u003e(2), 186-202. http://dx.doi.org/10.1016/S0010-9452(74)80009-2\u003c/li\u003e\n\u003cli\u003eEnders, C. K., \u0026amp; Bandalos, D. L. (2001). The relative performance of full information maximum likelihood estimation for missing data in structural equation models.\u003cem\u003eStructural Equation Modeling, 8\u003c/em\u003e(3), 430\u0026ndash;457. doi:10.1207/s15328007sem0803_5\u003c/li\u003e\n\u003cli\u003eFetzer M., Tiedemann K. (2018) The Interplay of Language and Objects in the Process of Abstracting. In: Moschkovich J., Wagner D., Bose A., Rodrigues Mendes J., Sch\u0026uuml;tte M. (eds) Language and Communication in Mathematics Education. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-75055-2_8\u003c/li\u003e\n\u003cli\u003eFuchs, L. S., Geary, D. C., Compton, D. L., Fuchs, D., Hamlett, C. L., Seethaler, P. M., Bryant, J. D., \u0026amp; Schatschneider, C. (2010). Do different types of school mathematics development depend on different constellations of numerical versus general cognitive abilities? \u003cem\u003eDevelopmental Psychology, 46\u003c/em\u003e(6), 1731-1746. http://dx.doi.org/10.1037/a0020662\u003c/li\u003e\n\u003cli\u003eGeary, D. C. (2013). Early foundations for mathematics learning and their relations to learning disabilities. \u003cem\u003eCurrent Directions in Psychological Science, 22,\u003c/em\u003e 23\u0026ndash;27. http://dx.doi.org/10.1177/0963721412469398\u003c/li\u003e\n\u003cli\u003eGersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morphy, P., \u0026amp; Flojo, J. (2009). Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. \u003cem\u003eReview of Educational Research, 79, \u003c/em\u003e1202\u0026ndash;1242. http://dx.doi.org/10.3102/0034654309334431\u003c/li\u003e\n\u003cli\u003eG\u0026ouml;bel, S. M., Watson, S. E., Lerv\u0026aring;g, A., \u0026amp; Hulme, C. (2014). Children\u0026rsquo;s arithmetic development: It is number knowledge, not the approximate number sense, that counts.\u003cem\u003e Psychological Science, 25\u003c/em\u003e(3), 789-798. http://dx.doi.org/10.1177/0956797613516471\u003c/li\u003e\n\u003cli\u003eHu, L., \u0026amp; Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives.\u003cem\u003e Structural Equation Modeling, 6\u003c/em\u003e(1), 1-55. http://dx.doi.org/10.1080/10705519909540118\u003c/li\u003e\n\u003cli\u003eJacobson, J. M., Nielsen, N. P., Minthon, L., Warkentin, S., \u0026amp; Wiig, E. H. (2004). Multiple Rapid Automatic Naming Measures of Cognition: Normal Performance and Effects of Aging.\u003cem\u003e Perceptual and Motor Skills, 98\u003c/em\u003e(3), 739-753. http://dx.doi.org/10.2466/PMS.98.3.739-753\u003c/li\u003e\n\u003cli\u003eKoponen, T., Aunola, K., Ahonen, T., \u0026amp; Nurmi, J. (2007). Cognitive predictors of single-digit and procedural calculation skills and their covariation with reading skill.\u003cem\u003e Journal of Experimental Child Psychology, 97\u003c/em\u003e(3), 220-241. http://dx.doi.org/10.1016/j.jecp.2007.03.001\u003c/li\u003e\n\u003cli\u003eKoponen, T., Salmi, P., Eklund, K., \u0026amp; Aro, T. (2013). Counting and RAN: Predictors of arithmetic calculation and reading fluency. \u003cem\u003eJournal of educational psychology\u003c/em\u003e, \u003cem\u003e105\u003c/em\u003e(1), 162. http://dx.doi.org/10.1037/a0029285\u003c/li\u003e\n\u003cli\u003eKoponen, T., Salmi, P., Torppa, M., Eklund, K., Aro, T., Aro, M., Poikkeus, A., Lerkkanen, M., \u0026amp; Nurmi, J. (2016). Counting and rapid naming predict the fluency of arithmetic and reading skills.\u003cem\u003e Contemporary Educational Psychology, 44-45\u003c/em\u003e, 83-94. http://dx.doi.org/10.1016/j.cedpsych.2016.02.004\u003c/li\u003e\n\u003cli\u003eKrajewski, K., \u0026amp; Schneider, W. (2009). Early development of quantity to number-word linkage as a precursor of mathematical school achievement and mathematical difficulties: Findings from a four-year longitudinal study.\u003cem\u003e Learning and Instruction, 19\u003c/em\u003e(6), 513-526. http://dx.doi.org/10.1016/j.learninstruc.2008.10.002\u003c/li\u003e\n\u003cli\u003eKrajewski, K., \u0026amp; Schneider, W. (2009a). Exploring the impact of phonological awareness, visual-spatial working memory, and preschool quantity-number competencies on mathematics achievement in elementary school: Findings from a 3-year longitudinal study.\u003cem\u003e Journal of Experimental Child Psychology, 103\u003c/em\u003e(4), 516-531. http://dx.doi.org/10.1016/j.jecp.2009.03.009\u003c/li\u003e\n\u003cli\u003eKuzmina, Y., Ivanova, A., \u0026amp; Kaiky, D. (2019). The effect of phonological processing on mathematics performance in elementary school varies for boys and girls: Fixed‐effects longitudinal analysis.\u003cem\u003e British Educational Research Journal, 45\u003c/em\u003e(3), 640-661. http://dx.doi.org/10.1002/berj.3518\u003c/li\u003e\n\u003cli\u003eLeFevre, J., Fast, L., Skwarchuk, S., Smith-Chant, B., Bisanz, J., Kamawar, D., \u0026amp; Penner-Wilger, M. (2010). Pathways to mathematics: Longitudinal predictors of performance.\u003cem\u003e Child Development, 81\u003c/em\u003e(6), 1753-1767. http://dx.doi.org/10.1111/j.1467-8624.2010.01508.x\u003c/li\u003e\n\u003cli\u003eLu, T. (2003). \u003cem\u003eThe relationship of phonological processing (phonological awareness, verbal short -term memory, and rapid naming) and visual short -term memory to reading disabilities in Chinese children \u003c/em\u003e(Order No. 3088262). Available from ProQuest Dissertations \u0026amp; Theses Global. (305337245). https://www.proquest.com/dissertations-theses/relationship-phonological-processing-awareness/docview/305337245/se-2?accountid=8554\u003c/li\u003e\n\u003cli\u003eMilwidsky, C. (2008). \u003cem\u003eWorking Memory and Phonological Awareness\u003c/em\u003e. \u003cem\u003eMarch\u003c/em\u003e.\u003c/li\u003e\n\u003cli\u003eMuth\u0026eacute;n, L. K., \u0026amp; Muth\u0026eacute;n, B. O. 1998\u0026ndash;2015. Mplus user\u0026rsquo;s guide, 7th ed. Los Angeles: Muth\u0026eacute;n \u0026amp; Muth\u0026eacute;n.\u003c/li\u003e\n\u003cli\u003eO\u0026rsquo;Halloran, K. L. (2005). Mathematical discourse: Language, symbolism and visual images. New York, NY: Continuum.\u003c/li\u003e\n\u003cli\u003ePeng, P., Lin, X., \u0026Uuml;nal, Z. E., Lee, K., Namkung, J., Chow, J., \u0026amp; Sales, A. (2020). Examining the mutual relations between language and mathematics: A meta-analysis.\u003cem\u003e Psychological Bulletin, 146\u003c/em\u003e(7), 595-634. http://dx.doi.org/10.1037/bul0000231\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\u003e Journal of Experimental Child Psychology, 157\u003c/em\u003e, 111-124. http://dx.doi.org/10.1016/j.jecp.2016.12.011\u003c/li\u003e\n\u003cli\u003eSaavalainen, P., Luoma, L., Bowler, D., Timonen, T., M\u0026auml;\u0026auml;tt\u0026auml;, S., Laukkanen, E., \u0026amp; Herrg\u0026aring;rd, E. (2006). Naming skills of children born preterm in comparison with their term peers at the ages of 9 and 16 years.\u003cem\u003e Developmental Medicine \u0026amp; Child Neurology, 48\u003c/em\u003e(1), 28-32. http://dx.doi.org/10.1017/S0012162206000077\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\u003e Dyslexia: An International Journal of Research and Practice, 14\u003c/em\u003e(2), 77-94. http://dx.doi.org/10.1002/dys.341\u003c/li\u003e\n\u003cli\u003eTorgesen, J. K., Wagner, R. K., Simmons, K., \u0026amp; Laughon, P. (1990). Identifying phonological coding problems in disabled readers: Naming, counting, or span measures?\u003cem\u003e Learning Disability Quarterly, 13\u003c/em\u003e(4), 236-243. http://dx.doi.org/10.2307/1510350\u003c/li\u003e\n\u003cli\u003eTr\u0026auml;ff, U., Olsson, L., Skagerlund, K., \u0026amp; \u0026Ouml;stergren, R. (2020). Kindergarten domain-specific and domain-general cognitive precursors of hierarchical mathematical development: A longitudinal study.\u003cem\u003e Journal of Educational Psychology, 112\u003c/em\u003e(1), 93-109. http://dx.doi.org/10.1037/edu0000369\u003c/li\u003e\n\u003cli\u003evon Aster, M. G., \u0026amp; Shalev, R. S. (2007). Number development and developmental dyscalculia.\u003cem\u003e Developmental Medicine \u0026amp; Child Neurology, 49\u003c/em\u003e(11), 868-873. http://dx.doi.org/10.1111/j.1469-8749.2007.00868.x\u003c/li\u003e\n\u003cli\u003eWagner, R. K., \u0026amp; Torgesen, J. K. (1987). The nature of phonological processing and its causal role in the acquisition of reading skills.\u003cem\u003e Psychological Bulletin, 101\u003c/em\u003e(2), 192-212. http://dx.doi.org/10.1037/0033-2909.101.2.192\u003c/li\u003e\n\u003cli\u003eWechsler, D. (2008). WAIS\u0026ndash;IV: Administration and scoring manual. San Antonio, TX: The Psychological Corporation.\u003c/li\u003e\n\u003cli\u003eYang, X., Dulay, K. M., McBride, C., \u0026amp; Cheung, S. K. (2021). How do phonological awareness, rapid automatized naming, and vocabulary contribute to early numeracy and print knowledge of Filipino children? \u003cem\u003eJournal of Experimental Child Psychology, 209\u003c/em\u003e, 105179. https://doi.org/10.1016/j.jecp.2021.105179\u003c/li\u003e\n\u003cli\u003eYang, X., McBride, C., Ho, C. S. H., \u0026amp; Chung, K. K. H. (2019b). Longitudinal associations of phonological processing skills, Chinese word reading, and arithmetic. \u003cem\u003eReading and Writing\u003c/em\u003e, 1-21. https://doi.org/10.1007/s11145-019-09998-9. \u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"bmc-psychology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"psyo","sideBox":"Learn more about [BMC Psychology](http://bmcpsychology.biomedcentral.com/)","snPcode":"","submissionUrl":"","title":"BMC Psychology","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"phonological awareness, rapid automatized naming, phonological memory, number knowledge, kindergarteners, longitudinal study","lastPublishedDoi":"10.21203/rs.3.rs-4660918/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4660918/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAn ongoing debate on the association of phonological processing and number knowledge concerns the extent to which they influence each other when children were at young ages. The current study aims at establishing the direction of the developmental relationship between these two kinds of abilities at an early age. Eighty-two Chinese kindergarten children were followed from 5 to 6 years old with a one-year interval. We investigated three phonological processing skills (phonological awareness, phonological memory, and rapid automatized naming) and two kinds of basic number knowledge (number identification and number comparison) at time 1 and time 2. Cross-lagged panel analyses revealed that the association between phonological awareness and number comparison was bidirectional. Specifically, early phonological awareness at time 1 could predict later number identification, and early number comparison at time 1 was a significant predictor of later phonological memory. In contrast, rapid automatized naming had no such predictive relations with other variables. The present findings are among the first to provide evidence that basic number knowledge could predict later phonological processing in kindergarten children.\u003c/p\u003e","manuscriptTitle":"Bidirectional Relationships between Phonological Processing and Basic Number Knowledge in Kindergarten Children: A Longitudinal Study","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-07-24 14:15:55","doi":"10.21203/rs.3.rs-4660918/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-07-03T06:54:48+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-07-02T09:17:29+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-07-02T09:16:32+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Psychology","date":"2024-06-30T01:51:10+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"bmc-psychology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"psyo","sideBox":"Learn more about [BMC Psychology](http://bmcpsychology.biomedcentral.com/)","snPcode":"","submissionUrl":"","title":"BMC Psychology","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"c73e5eea-8909-46bb-adfd-b2aea6a7cb54","owner":[],"postedDate":"July 24th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-01-20T16:06:44+00:00","versionOfRecord":{"articleIdentity":"rs-4660918","link":"https://doi.org/10.1186/s40359-025-02375-y","journal":{"identity":"bmc-psychology","isVorOnly":false,"title":"BMC Psychology"},"publishedOn":"2025-01-17 15:57:43","publishedOnDateReadable":"January 17th, 2025"},"versionCreatedAt":"2024-07-24 14:15:55","video":"","vorDoi":"10.1186/s40359-025-02375-y","vorDoiUrl":"https://doi.org/10.1186/s40359-025-02375-y","workflowStages":[]},"version":"v1","identity":"rs-4660918","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4660918","identity":"rs-4660918","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}