Edited by: Natasha Kirkham, Birkbeck College, UK
Reviewed by: Natasha Kirkham, Birkbeck College, UK; Stefan Heim, RWTH Aachen University, Germany
*Correspondence: Júlia B. Lopes-Silva, Developmental Neuropsychology Laboratory, Department of Psychology (FAFICH), Universidade Federal de Minas Gerais, Antônio Carlos Avenue, 6627, 31270-901, Belo Horizonte, MG, Brazil e-mail:
This article was submitted to Developmental Psychology, a section of the journal Frontiers in Psychology.
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Although verbal and numerical abilities have a well-established interaction, the impact of phonological processing on numeric abilities remains elusive. The aim of this study is to investigate the role of phonemic awareness in number processing and to explore its association with other functions such as working memory and magnitude processing. One hundred seventy-two children in 2nd grade to 4th grade were evaluated in terms of their intelligence, number transcoding, phonemic awareness, verbal and visuospatial working memory and number sense (non-symbolic magnitude comparison) performance. All of the children had normal intelligence. Among these measurements of magnitude processing, working memory and phonemic awareness, only the last was retained in regression and path models predicting transcoding ability. Phonemic awareness mediated the influence of verbal working memory on number transcoding. The evidence suggests that phonemic awareness significantly affects number transcoding. Such an association is robust and should be considered in cognitive models of both dyslexia and dyscalculia.
Mastering reading and writing numbers in their verbal and Arabic forms is an essential skill for daily life (Lochy and Censabella,
The verbal number system is linguistically structured and, although it may differ among languages, there are some common basic principles and regularities (Fayol and Seron,
The Arabic code is more complex and is acquired later in development (Geary,
One preeminent model of number transcoding is ADAPT (A Developmental, Asemantic, and Procedural model for Transcoding from verbal to Arabic numerals; Barrouillet et al.,
The ADAPT model is the only cognitive model of number transcoding which makes testable predictions regarding both working memory capacity and phonological/lexical representations and their respective roles in the typical and atypical development of transcoding abilities. Moreover, even though it is not explicitly stated in the original publication (Barrouillet et al.,
Short-term memory and working memory (thereafter WM) are involved in the temporary storage of verbal information, lexical retrieval, and the execution of the manipulations to generate the Arabic output. Working memory representations are also involved in creating a sequence of digits and possibly blank spaces to be filled with subsequent procedures. It has been consistently related to number transcoding performance and error patterns (Camos,
Another cognitive mechanism that may be involved in number transcoding is phonemic awareness. Phonemic awareness is the subcomponent of phonological processing which is related to the ability to perceive and manipulate the phonemes that constitute words (Wagner and Torgesen,
Krajewski and Schneider (
In view of the above, the aim of this study is to investigate the role of specific cognitive mechanisms underlying number transcoding such as general cognitive ability, verbal and non-verbal short-term and working memory, magnitude representation, and phonemic awareness. More specifically, our main goal was to investigate the relative impact of phonemic awareness on number transcoding. Phonemic awareness is related to reading and spelling skills (Wagner and Torgesen,
Two main hypotheses will be addressed in the present study: First, based on the central role assigned by the ADAPT model to working memory capacity (Barrouillet et al.,
The study was approved by the local research ethics committee (COEP–UFMG) and is in line with the Declaration of Helsinki. Children participated only after informed consent was obtained. Informed consent was obtained in written form from parents and orally from children.
A total of 487 children in grades 2–4 were invited from public schools in Belo Horizonte, Brazil. Of these children, 207 (42%) children agreed to take part in this study. Testing was conducted in the children's own schools. The various tasks were presented in four different pseudo-random orders during one session that lasted approximately 1 h.
We excluded five children from the sample due to low intelligence (performance on Raven's Colored Progressive Matrices below one standard deviation). One child did not complete the entire battery and was also excluded from the analysis. Twenty-nine children were excluded from further analyses because either they had a poor R2 on the fitting procedure to calculate their internal Weber fraction on the non-symbolic comparison task (
The following instruments were used in the cognitive assessment: Raven's Colored Progressive Matrices, Digit Span, Corsi Blocks, Non-symbolic magnitude comparison task, Phoneme Elision and Arabic number writing task.
Raven's Colored Progressive Matrices: general intelligence was assessed with the age-appropriate Brazilian validated version of Raven's Colored Matrices (Angelini et al.,
Digit Span: Verbal short-term and working memory were assessed with the Brazilian WISC-III Digit Span subtest (Figueiredo,
Corsi Blocks: This test is a measure of the visuospatial component of short-term and working memory. It consists of a set of nine blocks, which the examiner taps in a certain sequence. The test starts with sequences of two blocks and can reach a maximum of nine blocks. We used the forward and backward orders according to Kessels et al. (
Non-symbolic magnitude comparison task: In this task, the participants were instructed to compare two simultaneously presented sets of dots, indicating which one contained the larger number. Black dots were presented on a white circle over a black background. In each trial, one of the two white circles contained 32 dots (reference numerosity) and the other contained 20, 23, 26, 29, 35, 38, 41, or 44 dots. Each magnitude of dot sets was presented eight times. The task comprised 8 learning trials and 64 experimental trials. Perceptual variables were varied such that in half of the trials the individual dot size was held constant, while in the other half, the size of the area occupied by the dots was held constant (see exact procedure descriptions in Dehaene et al.,
Phoneme Elision: This is a widely accepted measure of phonemic awareness (Wagner and Torgesen,
Arabic number writing task: To evaluate number transcoding, children were instructed to write the Arabic forms of dictated numbers. This task consists of 40 items, up to 4 digits (3 one-digit numbers, 9 two-digit numbers, 10 three-digit numbers and 18 four-digit numbers). The one- and two- digit numbers were classified as “lexical items” (12 items), and the other 28 items require the use of algorithm-based rules in order to be written (Barrouillet et al.,
The differential impact of phonemic awareness and working memory on number transcoding was investigated in a hierarchical regression analysis with Arabic number writing as the dependent variable. Age and intelligence were entered first, and working memory and the Weber fraction in a second step, using the stepwise method. The phoneme elision task was entered in the model in a third step, also using the stepwise method. This allowed us to investigate the specific contribution of phonemic awareness to number transcoding performance after working memory variance was taken into account.
As a complement, path analyses, including all measures of age, intelligence, working memory and phonemic awareness were calculated, to determine the specific contribution of phonemic awareness as a mediator of the effect of working memory on number transcoding.
Thirty-three percent of the children did not commit any errors in the number transcoding task. Ninety-three percent of the children did not commit any errors on the numbers that can be lexically retrieved (items 1–12). According to what is suggested by the ADAPT model, errors rates increased with the number of rules required for number transcoding. In the numbers that required 3 transcoding rules, 50% of the children committed errors, in the 4-rules, 71.6% presented some errors, in the 5-rules, 73.3% and, finally in the more complex items (6 and 7 rules), 84.5% of the children committed, at least, one error.
Since one-third of the sample did not commit any error in the transcoding task, one may argue that they should be excluded from the sample to avoid biases in the estimation of the covariance matrix, particularly with regard to the association between transcoding performance and other cognitive functions. To investigate the occurrence of bias, regression and path analyses were performed in the full sample and in the sample without the children with perfect score in the transcoding task. Results were numerically comparable in both regression and path analyses and their interpretation was exactly the same. For this reason, we decided to report the results obtained by analysing the full sample.
First, the specific impact of the different cognitive mechanisms on number transcoding was evaluated by means of hierarchical regression models. To approximate a normal distribution, error rates of the Arabic number writing task were arcsine transformed. Initially, we examined the general association between these measures through Pearson's correlations. Inspection of Table
1. Age (in months) | 1 | |||||||
2. Raven | −0.23 |
1 | ||||||
3. Digit span-Forward | 0.19 |
0.19 |
1 | |||||
4. Digit span-Backward | 0.05 | 0.34 |
0.18 |
1 | ||||
5. Corsi blocks Forward | 0.19 |
0.28 |
0.15 |
0.20 |
1 | |||
6. Corsi blocks Backward | 0.01 | 0.34 |
0.14 | 0.36 |
0.36 |
1 | ||
7. Weber fraction | −0.19 |
−0.11 | −0.17 |
−0.19 |
−0.16 |
−0.13 | 1 | |
8. Phoneme elision | 0.11 | 0.36 |
0.23 |
0.36 |
0.24 |
0.25 |
−0.13 | 1 |
9. Number transcoding | −0.11 | −0.17 |
−0.11 | −0.15 |
−0.10 | −0.13 | 0.21 |
−0.36 |
To investigate in more detail the specific impact of phonemic awareness on transcoding abilities, a hierarchical regression model was calculated (Table
Intercept | 10.14 | <0.001 | ||
Age (months) | −0.404 | −6.487 | <0.001 | 0.305 |
Raven | −0.225 | −3.282 | 0.001 | |
Digit span−backward | −0.089 | −1.358 | 0.176 | Excluded |
Weber fraction | 0.095 | 1.545 | 0.124 | Excluded |
Digit span−forward | −0.056 | −0.885 | 0.378 | Excluded |
Corsi blocks−backward | −0.035 | −0.529 | 0.598 | Excluded |
Corsi blocks−forward | −0.003 | −0.051 | 0.959 | Excluded |
Phoneme elision | −0.337 | −5.038 | <0.001 | 0.088 |
The regression model reveals that after removing the effects of age and intelligence in step 1, verbal working memory remains a significant predictor of transcoding performance in step 2. Nevertheless, the addition of phonemic awareness to the model in step 3 leads to the exclusion of verbal working memory. Phonemic awareness, along with age and intelligence, was a significant predictor of number transcoding and absorbed the impact of verbal working memory on transcoding performance. The model explains a moderate amount of variance (Table
The reason to employ a hierarchical regression model in this analysis is to demonstrate the validity of the present experimental setup. By entering the measures of working memory in the regression model first we are able to replicate previous studies and thereby show that our measures of working memory were well-chosen and are associated to transcoding abilities. After completing this step of validation of well-established results, we continue the investigation showing that phonemic awareness absorbs the impact of measures of working memory on transcoding capacity. We have also calculated a regression model allowing the effect of phonemic awareness to vary simultaneously to measures of working memory, that is, with no hierarchical distinction between these variables. Results were largely comparable with those reported previously: only phonemic awareness is retained in the model along with intelligence and age (
As shown in the previous section, the influence of the verbal working memory on number transcoding is shared with phonemic awareness. Therefore, as a complement to the previous findings, path analyses including both working memory and phonemic awareness, as well as Weber fraction, were calculated in order to investigate the interplay of these variables in number transcoding.
To determine the strength of the effect of phonemic awareness on number transcoding, a sequence of models was calculated and compared. Chi-square and the approximate fit indexes root mean square residual (RMR), goodness of fit index (GFI), adjusted goodness of fit index (AGFI), comparative fit index (CFI) and root mean square error of approximation (RMSEA) were used to evaluate model quality. A non-significant chi-square indicates no significant discrepancy between model and data. The RMR measures the ratio of residuals in comparison to the covariances expressed by the models. Values smaller than 0.10 are considered adequate. GFI, AGFI, and CFI evaluate the degree of misspecification present in the model. Usually, the best acceptable values are greater than 0.90. Finally, the Root Mean Square Error of Approximation, or RMSEA, considers the model complexity when evaluating the model fit. The RMSEA is considered acceptable when it is lower than 0.05. The Chi-square difference between models was employed to compare models with increasing numbers of free parameters. Models were calculated in the software AMOS v.19 using the maximum likelihood estimation function.
To control for the influence of developmental and intellectual levels on the path models, we calculated the unstandardized residuals of the independent variables (short-term and working memory, Weber fraction and phonemic awareness), in which the portion of variance due to age (in months) and/or intelligence was removed. These adjusted values of working memory, magnitude processing and phonemic awareness were entered as the exogenous variables in the path analyses. All the covariances between the exogenous variables were set as free (Figure
Those variables with negative standardized values indicate that higher scores in these predictors lead to lower error rates in the number transcoding task. The only exception is the Weber Fraction path, in which higher values indicate poorer magnitude representation acuity and, hence, more errors in number transcoding.
Fit statistics of path models are shown in Table
ALL PATHS | 0.793 | 3 | 0.851 | 1.066 | 0.999 | 0.988 | 1.000 | 0.000 |
NO VISUOSPATIAL | 0.953 | 5 | 0.966 | 1.067 | 0.998 | 0.991 | 1.000 | 0.000 |
NO ANS | 2.396 | 6 | 0.880 | 1.067 | 0.996 | 0.981 | 1.000 | 0.000 |
MEDIATION PATH | 4.156 | 8 | 0.843 | 1.071 | 0.993 | 0.976 | 1.000 | 0.000 |
NO MEDIATION | 30.654 | 9 | <0.001 | 3.388 | 0.954 | 0.858 | 0.563 | 0.119 |
First, the NO VISUOSPATIAL model removed the paths from visuospatial memory to transcoding. Accordingly, the NO ANS model also suppressed the path from the Weber fraction to transcoding. In one further step, two models were calculated. In the first (MEDIATION PATH), the contribution of verbal working memory to transcoding is partially mediated by phonemic awareness. Finally, to determine the relevance of phonemic awareness for transcoding, in the last model, the path from Phoneme elision to Number transcoding was removed, while the direct paths from verbal working memory to transcoding were retained (NO MEDIATION). If the exclusion of any of these paths leads to a statistically significant decrease in model fit, one may conclude that the specific parameters removed from the more parsimonious version of the path model contribute substantially to model fit.
Inspection of Table
Overall, the model that presented the worst fit indices was the one that excluded the Phoneme Elision-mediation path and assumed that Digit Span has a direct influence on number transcoding (NO MEDIATION). Model comparisons corroborate these results because the model NO MEDIATION presented statistically poorer fit than all other models. Its chi-square was statistically significant, and the model did not present any adequate fix indexes (Table
The present study investigated the impact of phonological skills on a number transcoding task, and it is, to our knowledge, the first to simultaneously evaluate the relative impact of short-term and working memory, number sense and phonemic awareness on number transcoding. Our results revealed two main findings. First, we confirmed previous evidence of a verbal working memory effect on number transcoding, and, more importantly, we provided evidence of a relationship between number transcoding and phonemic awareness. Our second main finding is that the well-established relationship between verbal working memory capacity and number transcoding is mediated by phonemic awareness abilities. In the following sections, these topics will be discussed in more detail.
The performance of children in the number writing task was far from being flawless. They present many errors on the more complex two-, three-, and four-digit items, which require more than three transcoding rules, according to ADAPT. These findings are in accordance to what has been reported in the literature regarding transcoding skills of school aged children (Moura et al.,
Working memory plays an important role in the algorithmic-based procedures of number transcoding (Camos,
Raghubar et al. (
The first step of writing Arabic numbers from dictation proposed by the ADAPT model (Barrouillet et al.,
Another aim of the present study was to clarify the influence of phonemic awareness on number transcoding. We aimed to investigate whether there is a direct influence of verbal working memory on number transcoding or if this association would be mediated by phonemic awareness. Our results presented evidence showing that phonemic awareness mediates the influence of verbal working memory in number transcoding, even after controlling for the effects of age and intelligence. In the path analyses, the removal of the Phoneme Elision-mediation path had a deleterious effect on model fit, which suggests that this parameter contributes crucially to improve the model fit.
This finding is consistent with the ADAPT model, which postulates that the first step in number transcoding would be the encoding of the verbal string into its phonological form (Barrouillet et al.,
A plausible explanation for the association between phonemic awareness and the influence of verbal working memory in number transcoding is the “weak phonological representation hypothesis” (Simmons and Singleton,
The performance in verbal working memory and phonemic awareness depend on the same underlying and latent phonological representations (Hecht et al.,
Evidence indicates that the influences of phonemic awareness and verbal working memory on literacy acquisition are both shared and unique (Mann and Liberman,
Another dimension adding complexity to the relationship between phonemic awareness and verbal working memory is the child's individual level of development, which may be characterized as the degree of automatization in phonological processing. Before the child acquires expertise with phonemic awareness, a task such as phoneme elision may impose heavy demands on the central executive. As the child progressively acquires experience with phonological processing, this task can be solved in a more automatic way, freeing working memory resources for other tasks relevant for more advanced operations. If, however, the child does not acquire abilities of accurately and automatically processing the phonemic units, precious working memory resources will be less available for numerical transcoding. Accurate and automatic phonemic processing liberates sparse processing resources necessary to solve more complex tasks.
Disclosing a complex relationship among working memory, phonemic awareness and transcoding has important consequences for math achievement in general and for its disorders. School achievement in reading and/or mathematics depends on a complex interaction between general and specific cognitive factors. As the child acquires expertise in specific domains, such as phonemic and/or quantitative representations, processing resources are liberated to work in increasingly more complex activities. The accurate and automatic nature of more basic sound and quantitative representations may thus influence the whole process of school learning, explaining variances both in achievement and in working memory. Johnson (
There have been few studies that directly addressed the relationship between verbal memory and phonemic awareness during the performance of arithmetic tasks. Leather and Henry (
Our findings are in accordance to what was reported by Michalczyk et al. (
Mathematics encompasses a range of several different competences, such as numerical estimation, word problems, fact retrieval and number transcoding. Standardized arithmetic tasks usually assess these different abilities simultaneously and do not tap their specificities. It is important to investigate the distinct cognitive mechanisms that are associated with each of these mathematical skills. In our study, we concluded that phonemic awareness and verbal memory are directly connected to number transcoding, being important pathways between the verbal input and the transcription of the Arabic output.
The acuity of number sense, as measured by the Weber Fraction, did not influence number writing, suggesting that the assessment of numerical magnitude is not a necessary step in number transcoding. The acuity of number sense has been considered an important predictor of arithmetic performance (Halberda et al.,
Although we did not explicitly assess children with learning disabilities, our results provide additional support to the hypothesis that phonemic awareness might be a cognitive mechanism that underlies both dyslexia and dyscalculia. Epidemiological studies describe high comorbidity rates between reading and mathematical difficulties: approximately 40% of dyslexics also have arithmetical difficulties (Lewis et al.,
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
The research by Vitor G. Haase during the elaboration of this paper was funded by grants from CAPES/DAAD Probral Program, Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq, 307006/2008-5, 401232/2009-3) and Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG, APQ-02755-SHA, APQ-03289-10). Guilherme Wood is supported by a FWF research project (no. P22577).