Mathematical development during early childhood involves a dynamic interplay between domain-general and domain-specific cognitive skills, which evolve with age and learning complexity.
In an interview conducted on 12.11.2024 by Dr. Schmitt Pereira Anna for Magrid, two authors Dr. Ilse Coolen and Dr. Sixtine Omont-Lescieux, detailed and explained for us one of their recent studies, which was part of a project conducted under the supervision of Prof. André Knops*.This one explored how these skills contribute to mathematics abilities in children aged 3, 5, and 7 years, offering new insights into the age-specific predictors of mathematical success.
*Coolen, I. E. J. I., Omont- Lescieux, S., & Knops, A. (2023). Now You See It, Now You Don’t – Cognitive Skills and Their Contributions to Mathematics Across Early Development. Journal of Cognition, 6(1): 43, pp. 1–21. https://doi.org/10.5334/joc.309
Can you remind us what the objective of your study was?
The aim of this study was to investigate which skills contribute to children’s mathematics abilities and whether these are the same at every age during development.
A wide variety of domain-general and domain-specific cognitive skills* have been identified as predictors of success in mathematics. However, as the complexity of mathematics learning increases with age, and as the cognitive demands associated with this learning also increase, it can be assumed that predictors of mathematical success may vary with age. This study of children aged 3, 5, and 7 years aims to 1) identify the different skills contributing to mathematics abilities and 2) explore their dynamics during development.
*Some cognitive skills are called domain-general (e.g., spatial skills and inhibition) because they are involved in different types of learning, such as reading, writing, or mathematics. Other skills are called domain-specific because they are involved in a single type of learning. For instance, the ability to process or estimate quantities are skills involved only when learning mathematics.
What was lacking in the scientific literature before your study?
In the scientific literature, the various domain-general and domain-specific cognitive skills identified as predictors of mathematics were often studied separately. As a result, it was difficult to establish how these skills interacted individually in mathematical development. What’s more, the mathematics curriculum is specific to each stage of development and, therefore, to each age group, which is not always taken into account in previous studies, where mathematics abilities were generally measured using a standardised, global assessment.
This study, therefore, 1) tested the predictors hypothesised by age group based on the mathematics curriculum; and 2) explored the contribution of these domain-general and domain-specific cognitive skills in specific mathematics subcomponents.
What were your initial hypotheses and why?
The various hypotheses concerning predictors of success in mathematics are based on the French mathematics curriculum corresponding to the ages tested and on existing scientific literature.
In the first year of preschool (i.e., 3-4-year-olds), we expected to observe that visuospatial memory and the ability to compare non-symbolic quantities (e.g., comparing two sets of dots and deciding which one contains more dots) are predictors of mathematics ability. In other words, if 3-4-year-olds have good cognitive skills in visuospatial memory and quantity comparison, then we’ll observe that they’re good at mathematics.
Why is this? Activities in preschool classes involve 1) the use of visuo-spatial skills (e.g., constructions with 3D objects such as blocks or different shapes) and 2) the manipulation of quantities, with the learning of the notions “more than”, “less than”.
In the third and final year of preschool (i.e., 5-6-year-olds), we expected to observe that 1) visuospatial memory, spatial attention, and the ability to add non-symbolic quantities are strong predictors of mathematics ability.
Why is this? At the age of 5 years, we hypothesised that children would use spatial attention when counting or performing simple additions and subtractions by representing numbers (i.e., 1, 2, 3) on a mental number line with smaller numbers to the left of larger numbers. As they calculate, they move along this mental number line (Knops, Thirion, et al., 2009). They also use their visuospatial skills because when they count, they define the place of the number in the number sequence (e.g., 3 in 3rd place), and depending on their calculation strategies, they may use their fingers to help them count (Liu & Zhang, 2022). Furthermore, children begin to make simple additions from non-symbolic quantities (starting to learn additions with objects), meaning that we hypothesised that non-symbolic additions would become more important than non-symbolic comparisons.
Finally, depending on mathematical skills, inhibition may begin to have an impact. For example, when learning subtractions, children need to inhibit maladaptive strategies and automatic responses (e.g., seeing 2 and 3 together, create an automatic response of 5) used for additions in order to apply the correct strategies to solve subtractions (Bull & Scerif, 2001). Although, as subtractions are not usually learned until the end of preschool, inhibition might not play a role yet.
In the second year of primary school (i.e., 7-8-year-olds), we expected to observe that inhibition and non-symbolic addition skills are strong predictors of mathematics ability.
Why is this? At the age of 7 years, visuospatial skills, like spatial attention and spatial memory, tend to become less important as verbal memory (although not tested in this study) comes to play a more important role, particularly in the ability to retrieve arithmetic results (Coolen & Castronovo, 2023; De Smedt et al., 2009). Indeed, counting on fingers or counting up and down using a mental number line might become less frequent and are replaced by retrieving verbally-stored responses from memory. However, the role of inhibition increases with the increasing demand to adopt the right strategy for solving mathematical problems (e.g., adding instead of subtracting). Next, at this age, non-symbolic addition skills are hypothesised to be important in order to correctly manipulate the quantities used in symbolic arithmetic and obtain the correct expected result (Feigenson et al., 2013; Lourenco et al., 2012).
What were your study groups?
Typical children (without diagnosed disabilities) attending French-language public and private schools in Paris. Three different cohorts were tested: the youngest cohort was made up of children at the start of preschool, aged 3 to 4 years; the second cohort, aged 5 to 6 years, was in the third and final year of preschool; and children aged 7 to 8 years were in the second year of primary school. The parents came from relatively high socio-economic backgrounds, with an average of 2.75 on a scale of 4 in terms of parental education level (the scale being 1: primary education completed, 2: secondary education completed, 3: university education completed, 4: doctoral education completed), meaning that most households had at least one university degree.
What was your research methodology, and why did you choose this particular one?
The current study is based on the first data acquisition of a longitudinal design (assessing participants at several moments across time) in which we followed each child over a three-year period. In children aged 3, 5 and 7 years, we tested, on an individual basis in school, the various domain-general and domain-specific cognitive skills identified as predictors of mathematics, as well as their mathematical skills (different subtests of the TEDI-math, a standardised mathematics battery were used). Each child was tested over 2 or 3 sessions (depending on age) of 20 to 40 minutes each. To motivate the children, we designed a treasure map, and in order to reach the treasure and receive a small diploma, they had to complete all the short tests. At the end of each test, the child stuck a sticker on the treasure map over the image of the corresponding test.
What are your main results?
The overall aim of this study was to identify the contributions of domain-specific and domain-general cognitive skills and their interactions across mathematical development, taking into account mathematical activities carried out in the classroom at different ages: 3 years, 5 years and 7 years. In general, the skills of processing non-symbolic quantities (comparing quantities and adding quantities) appear to be important for mathematical development in all three age groups, with the exception of non-symbolic addition in the youngest cohort. Visuospatial skills seem most important at the age of 5 years, and no significant role was found for inhibition and spatial attention throughout mathematical development at all ages tested. A slightly more divergent view between age groups emerges when exploring the relations between cognitive skills and the different mathematics subtests taken separately.
Do they align with your research hypotheses? Are they consistent with the scientific literature or different?
In relation to our hypotheses, we found that they were over-optimistic with regard to the age ranges studied. However, the relations expected for a given age group seemed to be realised more in the age group above it (e.g., expected predictors at the age of 3 years were significant at the age of 5). This could be explained by the fact that our hypotheses were based on the school curriculum, which describes what children should have acquired by the end of the year without necessarily reflecting their learning process over the course of the year. It is possible that the expected predictors only become significant when the mathematical skills we thought would emerge at the start of learning are fully understood and acquired by the children.
In the first year of preschool (3-4-year-olds), children begin to learn the meaning of numbers and their corresponding values, as well as engage in pre-mathematical activities such as pattern and block building. We, therefore, hypothesised that visuospatial skills and quantity comparison abilities were important variables for mathematical competence at this age. However, only quantity comparison skills were significantly related to mathematical skills. This is probably due to the elements included in the mathematical task, which do not directly reflect the spatial components of mathematics (e.g., block building, pattern recognition). Although it has been suggested that promoting spatial skills through block building and pattern construction at preschool age is important for later mathematics (Wijns et al., 2020), this may be a link that is not yet formed in the first year of preschool age.
Third year of preschool (5-6-year-olds): At this age, children begin to understand the basics of numbers, such as Arabic digits and the counting sequence, and to perform simple calculations (e.g., 2 + 3). Our results showed that the ability to compare non-symbolic quantities, add non-symbolic quantities, and visuospatial short-term memory were all linked to mathematical performance. However, further analysis of the different mathematics subtests revealed that visuospatial short-term memory was the most important cognitive skill for tasks such as number comparison and arithmetic. Other measures, such as non-symbolic addition and comparison, did not show the same significant links. This is consistent with previous research (Coolen & Castronovo, 2023) that highlights the importance of visuospatial memory for mathematical learning at this age, suggesting that children still use visual strategies to solve problems, such as finger counting.
However, contrary to our expectations, inhibition and spatial attention were not significantly related to 5-year-olds’ mathematical skills. Children are already starting to use new strategies to solve mathematical problems, which may require inhibiting old methods, but most seem to have not yet integrated these new strategies. This indicates that by the end of preschool, children tend to rely on visuospatial approaches rather than more advanced verbal strategies. We had also assumed that spatial attention would play a role when using number representations on a mental line to perform calculations, but this was not reflected in our results. Nevertheless, other research suggests that automatic activation of a spatial representation of numbers does not occur until the age of 9 (Van Galen and Reitsma, 2008).
Second year of primary school (7-8-year-olds): At this age, students are learning to manipulate numbers up to three digits and need to memorise the addition, subtraction and multiplication tables. We, therefore, thought that visuospatial memory and attention skills would be less important, as verbal skills should play a more critical role. In addition, it was expected that inhibition – the ability to replace old strategies with new ones – would be significant in their mathematical learning.
However, our results show that only certain cognitive skills specific to mathematics, such as comparing non-symbolic quantities and non-symbolic addition, were linked to the 7-year-olds’ mathematical performance. Visuospatial memory was significantly related to arithmetic, and the ability to compare non-symbolic quantities was related to the symbolic number comparison task. These results support the idea that visuospatial skills help to acquire new mathematical skills, although they become less crucial once the skills have been mastered (Andersson, 2008).
Our hypothesis that inhibition plays an important role in the mathematical performance of 7-year-olds has not been confirmed. Previous research shows that links between inhibition and mathematics can vary, often due to age, the way tasks are measured, or the relevance of the inhibition tasks chosen (Lee & Lee, 2019). Thus, the lack of a link between inhibition and mathematical performance in our study could be due to the nature of the tasks tested, which did not require inhibiting old strategies or filtering out irrelevant information.
Has this research had practical implications for the school curriculum in France or on a broader educational level?
This study should be regarded above all as fundamental research, the results of which should be translated into teaching practice only with caution. For example, we must always bear in mind that the positive effects obtained by training cross-domain skills (e.g., working memory training to improve mathematics) lead to only very limited improvement. In addition, it should be borne in mind that our analyses always relate to the group as a whole, making it difficult to infer strategies at the individual level. Nevertheless, our results can contribute to the development of hypotheses in pedagogical practice. Teachers may prefer to target games or exercises that involve the domain-general and domain-specific cognitive skills identified as predictors of mathematics at a particular age.
What are your current research projects on children and mathematics?
Today, as part of our research, we have taken a closer look at the role of one of the domain-general cognitive skills called inhibition and its role in the development of symbolic (i.e. Arabic numerals) and non-symbolic arithmetic (addition and subtraction) skills in 5- and 7-year-old children (Omont-Lescieux et al., 2024).
Moreover, this cross-sectional study is part of a longitudinal study. We tested these 3-, 5- and 7-year-olds for 3 years, with the aim of better understanding the contribution of domain-general and domain-specific cognitive skills to mathematics learning across the ages of 3 to 9 years.
Would you like to add anything?
What’s important to note from these results is that we hypothesised that domain-general and domain-specific cognitive skills related to mathematics skills would differ by age, reflecting the mathematics skills acquired at that age. Although the results do not entirely match the hypotheses, differences in unique contributions to mathematics by age group can be seen.
The non-symbolic quantity comparison task is the only task that plays a consistently significant role in mathematics performance across the three age groups studied, although this role is less important when explored in separate mathematics subtests. Non-symbolic addition skills, which represent a skill somewhat separable from non-symbolic quantity comparison, as shown by the results of the present study and previous literature (Coolen et al., 2022; Gilmore et al., 2011), only begin to play a role in mathematics from the age of 5 years. In contrast, visuospatial memory plays an important role in mathematics and in most subtests from the age of 5 years.
This is in line with previous research demonstrating an important role for visuospatial memory in 5-year-olds, followed by a shift from visuospatial to verbal memory from the age of 6 years onwards (Coolen & Castronovo, 2023; De Smedt et al., 2009), reflecting the strategies used in mathematical tasks (e.g. visual finger counting or arithmetic retrieval from verbal memory).
What potential links or connections do you see with your study and the scientific studies conducted in relation to Magrid?
MAGRID is designed to enhance the development of early mathematical, visuospatial, and cognitive abilities in children through a language-neutral, tablet-based application. Research has demonstrated MAGRID’s effectiveness in measuring visuospatial and early numerical skills (Pazouki et al., 2018) as well as in fostering early visuospatial skills (Cornu et al., 2017) in young children. These studies align closely with our findings (Coolen et al., 2023), which emphasise a strong connection between visuospatial and mathematical skills from as early as 5 years of age.
The connection we identified between early visuospatial skills and mathematical abilities suggests that MAGRID’s focus on early intervention, targeting a critical period of cognitive development, is well-placed. By leveraging findings from both MAGRID-related studies and our research, MAGRID has the potential to broaden its pedagogical framework, supporting not only visuospatial and mathematical skills but also other cognitive abilities that underpin early learning.
Full reference: Coolen, I. E. J. I., Omont- Lescieux, S., & Knops, A. (2023). Now You See It, Now You Don’t – Cognitive Skills and Their Contributions to Mathematics Across Early Development. Journal of Cognition, 6(1): 43, pp. 1–21. https://doi.org/10.5334/joc.309
Who are the authors of this study?
Ilse Coolen, Dr., Marie Skłodowska-Curie Action Fellow at Parenting and Special Education Research Unit, KU Leuven, Belgium and Experimental Psychology at the University of Oxford, UK. Her main research is currently focusing on understanding the causal mechanisms behind spatial skills and mathematics in 5-7-year-old children.
Sixtine Omont-Lescieux, Dr., Postdoctoral Fellowship at Translational Neuroanatomy and Neuroimaging Laboratory (LN2T) – Neuroscience Institute in Université Libre de Bruxelles. She is currently working on the cerebral bases of early digital acquisitions using MEG and MRI in children aged 5-6 and adults.
Andre Knops, Prof., CNRS researcher (Directeur de recherche) at Université de Paris Cité, LaPsyDÉ, CNRS, F-75005 Paris, France. He currently leads the Numerical Cognition Group.
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