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Rote counting skills have found to be a strong predictor of later arithmetic and reading fluency. However, knowledge of the underlying cognitive factors influencing counting skill is very limited. Present study examined to what extent language skills (phonology, vocabulary, and morphology), nonverbal reasoning skills, and memory at the age of five could explain counting skill at the beginning of first grade. Gender, parents’ education level and child’s persistence were included as control variables. The question was examined in a longitudinal sample (N = 101) with a structural equation model. Results showed that language skills together with memory, nonverbal reasoning skills and parent’s education explained only 22% of the variance in counting at the beginning of the first grade. Vocabulary, morphology, and verbal short-term memory were found to be interchangeable predictors, each explaining approximately 7%–9%, of counting skill. These findings challenge the interpretation of counting as a strongly language-based number skill. However, additional analysis among children with dyslexia revealed that memory and language skills, together with a child’s persistence and gender, had a rather strong predictive value, explaining 34%–46% of counting skill. Together these results suggest that verbal short-term memory and language skills at the age of five have not the same predictive value on counting skill at the beginning of school among a population-based sample as found in subjects with language impairment or learning difficulties, and thus, other cognitive factors should be taken into account in further research related to typical development of counting skill.

Rote counting—the ability to recite number words forward and backward—is an early number skill that starts to develop around the age of two years, and remarkable developmental steps are acquired before children enter formal education. The ability to recite number words can be considered as one of the core number skills, being an essential skill for the exact enumeration of quantities larger than five and a tool for mental calculation. From a theoretical and practical point of view, counting is an important skill because it has been found to be a strong predictor of later arithmetic fluency (

Despite the importance of counting as a predictor of later fluency in reading and arithmetic, the cognitive factors underlying the development of an individual’s counting skill are poorly understood. Yet only by understanding the cognitive processes and skills needed to perform well in counting tasks are we able to comprehend why counting serves as a good predictor. This, in turn, is the first critical step when trying to develop effective early support to provide good basic skills in calculation and reading. In the present study, we aimed to explore the proximal cognitive predictors of counting at school start, a time point before which no formal teaching for mathematics has been available for children. When examining cognitive correlates of counting, it’s important to know how it develops during early childhood. In the following chapters we will first describe the development of counting skills and then cognitive factors that have been found to associate with counting skills.

Learning to count in many languages, including Finnish, means acquiring rather arbitrary sequences of number words below 20 and knowledge of the syntax and grammar for the structure of higher numbers (

Despite the importance of counting as a predictor of later reading and arithmetic skill, only a few previous studies focused on the underlying cognitive skills required for counting (

There are several reasonable hypotheses for the possible links between counting and language that explain why deficiencies in language skills would result in a compromised counting skill. One possibility is phonology: the number words are phonologically coded in memory (e.g.,

Another reasonable hypothesis of underlying language-based factors are lexical skills, that is, receptive and productive vocabulary.

The third and fourth possible relevant language skills in counting are language comprehension and morphology. In a study by

Rote counting is a serial process requiring holding information in one’s memory while articulating items and retrieving the next; thus, verbal memory should be examined as a potential underlying factor influencing counting skill. According to

Besides language skills and memory, the relationship between nonverbal reasoning skills and counting has been examined in children with language impairment (see

Counting skill is not innate, but rather, it emerges and develops through individual learning and cultural transmission. Thus, factors such as parents’ socioeconomic status should be taken into account when trying to understand factors that influence the development of counting skill, especially before the phase of formal learning. There are several possible reasons why parents’ educational levels predict children’s later academic skills. One view is based on the assumption that parents learn something during schooling that influences the way in which they interact with their children regarding learning activities at home. Another view indicates that education influences parents’ skills, values, and knowledge of the educational system, as well as methods for educational practices at home, and children’s skills (for review, see

There are several meta-analyses showing that there are no gender differences in math and that the gender differences in math performance may have narrowed from the 1970s to now (see

Besides the child’s cognitive capacity and environmental factors, children’s orientations and persistence in task situations have been shown to be related to later academic learning. Previous research has shown that positive achievement-related behaviours, such as task-focused behaviours, are related to good academic outcomes, whereas negative behaviours, such as task-avoidant behaviours, are related to poor academic outcomes (e.g.,

Because of the lack of a comprehensive view of the cognitive background of counting skill, the present study aimed to model the relationships between various cognitive predictors measured concurrently at the age of 5 and counting skill measured 2 years later at the beginning of first grade. The associations were examined in a population-based sample, and thus, extending the previous literature which is mainly based on the findings in children with language difficulties. The specific research questions were as follows:

To what extent can language, memory, and nonverbal reasoning skills at age 5 predict rote counting skill at the beginning of the first grade?

Based on previous studies we expect that language and memory skills are significant predictors of later counting skill (

To what extent do the child’s task-orientation or persistence in preschool, gender, and parents’ educational levels explain the counting skill at the beginning of first grade in addition to cognitive skills?

Because differences between families in SES are relatively small in Finland (unlike to many countries like USA), SES has usually been found as a significant but typically not very strong predictor of academic achievement (for example see

All participants (

Trained testers assessed children’s skills individually in a laboratory setting; the children were 5 and 5.5 years old, and just beginning the first grade (age 7.2). In addition, children’s persistence in tasks was evaluated at age 6 by their kindergarten teachers. Composite scores (arithmetical means) for each skill using z-scored values were calculated and used when reporting correlative associations between skills (for full details of measures, see

The education of mothers and fathers was classified using a 7-point scale, taking into account both a basic level of education and advanced educational training (e.g., 1 = comprehensive school education without any vocational education; 7 = comprehensive school or upper secondary general school diploma combined with a master’s or doctoral degree). The parents’ educational distributions resembled that of the Finnish population (mothers:

At 5–5.5 years, a composite mean (Cronbach α = 0.75) was calculated from three different measures, including both receptive and expressive vocabulary: Peabody Picture Vocabulary Test–Revised (PPVT;

At 5.5 years, the composite mean was derived from performance in three tasks (Cronbach α = 0.66): from the word or pseudoword segmentation task, including both phoneme- and syllable-level segments (

At 5 years, mastery of the highly inflected Finnish morphology was measured with the Berko-type elicitation test (

At 5–5.5 years, a composite mean was calculated from three tasks (Cronbach α = 0.66): digit span (

At 5 years, a short form of the WPPSI-R (

At 6 years, children’s persistence was calculated from three items, with which their preschool teachers rated children’s behaviour using a 5-point Likert scale (1 = not at all this kind of behaviour, 5 = extremely often this kind of behaviour). The three questions used in this study were as follows:

In the first grade, at 7.2 years, a series of six items of counting was administered just after school started in August–September. Three measures of counting were calculated, each including three items: (a) counting forward included counting from 1 to 31 and counting by 10s from 10 up to 150, (b) counting backward entailed counting backward from 10 to 1 and from 23 to 1, and (c) counting challenging items included counting forward by twos (skip-counting) in multiples of 2 up to 30 and counting backward from 83 to 60. For each set of six items, error-free outcomes were allocated 2 points while 1 point was awarded for completing the item with up to two errors, and a score was given for more than two errors or a failure to complete the list within any item. The maximum was 4 points in all the three measures of counting, that is, counting forward, counting backward, and counting challenging items (see

Pearson correlations were used to examine the associations between the predictors and outcome measures, as well as between the predictors themselves. The relations between measures were further modelled in a structural equation model (SEM) framework using the Mplus 6.12 program (^{2} test, Comparative Fit Index (CFI), Tucker-Lewis Fit Index (TLI), Root Mean Square Error of Approximation (RMSEA), and Standardized Root Mean Square Residual (SRMR).

Descriptive statistics for all measures used in the latent factors are presented in

Measure | Range | Skewness ( |
||
---|---|---|---|---|

Vocabulary | ||||

PPVT | 22 – 120 | 73.10 | 22.26 | -0.06 (.24) |

Boston Naming | 23 – 46 | 35.52 | 5.59 | -0.39 (.24) |

WPPSI-R Vocabulary | 5 – 18 | 11.55 | 2.96 | -0.13 (.24) |

Morphological skills | ||||

Adjective inflections | 0 – 29 | 13.46 | 8.70 | -1.30 (.24) |

Verb inflections | 0 – 29 | 20.56 | 6.21 | 0.14 (.24) |

Noun inflections | 0 – 30 | 22.39 | 7.30 | -0.99 (.24) |

Phonology | ||||

Word / pseudoword segmentation | 5 – 20 | 13.79 | 2.87 | -0.26 (.24) |

First phoneme production | 2 – 9 | 7.52 | 1.50 | -1.24 (.24) |

Word segmentation, phoneme level | 0 – 24 | 11.98 | 5.07 | -0.50 (.26) |

Verbal short term memory | ||||

Digit span | 0 – 8 | 3.67 | 1.57 | -0.23 (.24) |

Syllable span | 0 – 6 | 2.74 | 1.25 | -0.12 (.24) |

Sentence repetition | 12 – 28 | 21.39 | 3.54 | -0.37 (.26) |

Performance IQ | ||||

WPPSI-R, Object assembly | 3 – 15 | 9.78 | 2.69 | -0.14 (.24) |

WPPSI-R, Picture completion | 4 – 15 | 11.11 | 2.46 | -0.52 (.24) |

WPPSI-R, Block design | 4 – 17 | 10.20 | 2.59 | 0.03 (.24) |

Task-orientation / persistence | ||||

Solving difficult tasks | 1 – 5 | 3.72 | 1.11 | -0.55 (.25) |

Persistence in pre-school tasks | 1 – 5 | 3.81 | 1.01 | 0.75 (.25) |

Giving up easily | 1 – 4 | 2.03 | 1.01 | -0.74 (.24) |

Parental education | ||||

Mothers’ education | 1 – 7 | 4.51 | 1.38 | 0.19 (.26) |

Fathers’ education | 1 – 7 | 3.84 | 1.48 | 0.37 (.26) |

Counting skill | ||||

Counting forward | 0 – 4 | 2.60 | 1.19 | -0.33 (.24) |

Counting backward | 1 – 4 | 3.34 | 0.82 | 0.00 (.24) |

Counting difficult items | 0 – 4 | 1.59 | 1.33 | 0.19 (.24) |

Measure | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|

1. Mother’s education | |||||||||

2. Father’s education | .36*** | ||||||||

3. Vocabulary | .08 | .16 | |||||||

4. Phonological awareness | .04 | .01 | .37*** | ||||||

5. Morphological skill | .07 | .08 | .40*** | .26** | |||||

6. Verbal short-term memory | .22* | -.01 | .49*** | .36*** | .37*** | ||||

7. Performance IQ | .06 | .00 | .36*** | .29** | .14 | .32** | |||

8. Persistence | .14 | .09 | .16 | .05 | .07 | .11 | .23* | ||

9. Counting skill | .19 | .28** | .21* | .18 | .25* | .19 | .13 | .17 | |

10. Gender | .16 | .19 | -.02 | -.13 | -.06 | -.03 | -.11 | -.15 | .20 |

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Associations between the cognitive predictors and counting skill were further inspected in an SEM framework to be able, first, to use latent factors of the skills instead of means of raw scores, second, estimate error variances in measures, and, third, see the simultaneous effects of each predictor on counting skill. Factor constructs, including loadings for each of the measures, are presented in

Factor constructs of the cognitive predictors at age of five, task-orientation and persistence, and counting skill.

The model with all significant paths of the language-related predictors and persistence included.

The final model, including language-related predictors, child’s persistence, and gender. All significant paths included.

All factor constructs were satisfactory. The significance of each of the latent cognitive factors as a predictor of counting skill was tested first. Vocabulary, morphology, and verbal short-term memory turned out to be significant predictors, explaining 9.3%, 9.9%, and 10.2% of counting skill 2 years later, whereas the predictive paths from phonological awareness and performance IQ turned out to be nonsignificant. Next, to assess the simultaneous effects of the cognitive predictors on counting skill, each was added one by one into a model where the best predictor (verbal short-term memory) predicted counting skill. In all cases, adding another cognitive predictor besides verbal short-term memory resulted in a reduction in the goodness-of-fit indices and produced situations where none of the predictive paths were significant. Thus, vocabulary, morphology, and verbal short-term memory turned out to be interchangeable predictors of counting skill, each explaining roughly 10% of its variance, but not fitting into the model at the same time.

Finally, to test the predictive power of children’s task-orientation and persistence, it was added into the model together with one of the significant cognitive predictors (vocabulary, morphology, or verbal short-term memory). The best goodness-of-fit indices and highest portion of explained variance in counting skill were reached with morphology and task-orientation and persistence as predictors. No more than 13.25% of the variance in counting skill could be explained with this final model. Morphological skill explained 8.41% of the outcome variance of counting in the final model. The predictive path of children’s task-orientation and persistence was barely significant (

Altogether, 21.6% of the variance in counting skill could be explained by morphology, child’s persistence, and gender. All three measures explained close to a similar portion of the outcome measure: 8.41%, 5.76%, and 7.29%, morphology, child’s persistence, and gender, respectively. What also was remarkable was that the significance of the predictive association from child’s persistence to counting skill sank below .05, i.e. to .029.

Because of the small amount of explained variance in counting observed in the population-based sample additional regression analyses were conducted in a sample including children with dyslexia (

In the present study, we examined to what extent language skills (phonology, vocabulary, and morphology), memory, and nonverbal reasoning skills at the age of 5 could explain counting skills 2 years later at the beginning of first grade. The question was examined in a population-based sample with a SEM, where each of the skills was represented by a latent factor constructed from three measures, allowing us to estimate the error variances as well. Despite using this sophisticated method, we were only able to explain 22% of the variance in counting at the beginning of first grade. Cognitive skills were found to be closely associated with each other, and vocabulary, morphology, and verbal short-term memory were found to be interchangeable predictors of counting skill. Child’s task-orientation and persistence explained an additional 5% and gender 7% when included in the model. Finally, the father’s educational level alone explained 10% of counting skills, but the fit of the model without cognitive predictors was unsatisfactory. Additional analysis among children with dyslexia revealed that memory and language skills, together with child’s persistence and gender, had stronger predictive value on counting skill explaining 34-46% of counting skill.

The low percentage of the variance in rote counting skill explained by the cognitive skills was surprising, and it challenges the previous literature as well as our hypothesis considering rote counting as a strongly language-based skill that requires verbal short-term memory resources to develop normally (e.g.,

The relation between morphology and counting skills could be explained by a similar kind of learning process. Learning the morphological structure of language happens quite early in children’s development and without explicit instruction, as is the case in the early developmental phase of counting. Moreover, mastering morphology in a highly inflectional language such as Finnish, where one must correctly inflect verbs, substantives, or adjectives, relies on processing sequential information and rule learning. It requires detecting the root of the word and its morphological endings (

Verbal short-term memory was also associated with counting, which had been found in previous studies (e.g.,

More surprisingly, phonological awareness at the age of 5 did not predict later counting skills. In previous studies, the role of phonological processing in the development of early number skills, especially in counting, has been strongly assumed. According to previous studies, number words are phonologically coded in memory (e.g.,

The second aim of the study was to examine whether the child’s task-orientation and persistence or parents’ educational level would explain the level of rote counting skill at the beginning of first grade. Children’s task-orientation and persistence was significant, explaining 5% of the variance in counting. This finding was in line with our hypothesis and similar to those found in previous studies (

Some limitations of the present study are worth mentioning. When generalising these findings across countries, the morphological structure of the language and specific features in the number word system should be considered. It should also be noticed that, because of a lack of standardised measures in Finland, we had only one measure of language comprehension, and it was not possible to create a latent factor, as was the case in other cognitive predictors. For this reason, language comprehension was not included in the models. However, its correlation with counting was not significant. Language should be measured using a wider battery of subskills in future.

Third, home numeracy was not included, and there is a need to examine this variable in future research. For example, the relation between parents’ number talk about large sets of present objects and children’s cardinal-number knowledge has found to be significant, even after controlling for factors such as parents’ socioeconomic status and other measures of parents’ number and non-number talk (

Rote counting skill has been suggested to be a language-based skill requiring verbal short-term memory, but this hypothesis has rarely been examined explicitly. Thus, empirical evidence is missing. The present study indicated that verbal short-term memory, together with vocabulary, phonological awareness, and morphology, measured at the age of 5 explains very little of the variance in rote counting skill at the beginning of the first grade. A rethinking of the nature of rote counting skill and empirical research are important in the future because rote counting has been shown to have a strong predictive power on later reading and arithmetic fluency and is an important early predictor of academic achievement.

It should be also considered that the relation between language skills and rote counting might differ depending on the sample. Our additional analysis showed that language and memory, together with child’s persistence and gender, explained twice the amount of the variance in counting among dyslexic children when compared to children without cognitive deficiencies. It seems that in a normal population, the associations are not as strong as among children with language impairment or dyslexia indicating that other factors are more important among 5- to 7-year old children with typical language development. However, it could be possible to find stronger relation of language and memory skills with counting skills among younger typically developing children. It could be assumed that requirements for verbal memory capacity would be stronger at the early developmental phase when children are practicing and learning rather arbitrary sequences of number words (Finnish number words below 20) in contrast to later developmental phase when children practice number words that in Finnish language start to be transparent with ten-base system (number words larger than 20). However, longitudinal studies following the early number skill development and their cognitive correlates is needed in order to exam this proposal. Moreover, cross-linguistic studies are needed as well because languages vary in how they grammatically mark number (e.g., in nouns, verbs, and so forth), and this has found to influence the development of early number word development (

This study was funded by Academy of Finland (264264, 292466).

The authors have declared that no competing interests exist.

The authors have no support to report.