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There are differences in the mathematic abilities of children even before they enter primary school. Students who start with greater difficulties maintain, and even tend to increase, the gap from their peers over the years. Might families contribute to every child having a better point of departure? A recent study demonstrated how more informal mathematical activities between parents and children raise their formal mathematical abilities in pre-school.


Mathematical abilities in the first years of school, such as counting skills, are strong predictors of the subsequent performance in mathematics and reading. Developing efficient strategies for mathematical learning essentially requires the identification of just which factors and predictors underpin higher levels of acquisition of these capacities.

Recently, a team led by the Chinese researcher Xiao Zhang studied the involvement of parents in pre-school maths activities as a potential factor driving mathematics learning in the first year of schooling.


Just what mathematics do parents actually do with their children?

According to an idea long since proposed by the Russian psychologist Lev Vygotsky, among others, culture, community and social interactions are essential to learning and child development. Indeed, various studies have demonstrated the connection between the household environment and, on the one hand, various aspects of activities between parents and their children and, on the other hand, the initial learning phases of children, especially literacy. However, there has been less research focus on studying the impact of these activities ongoing between parents and children in terms of mathematics.

Parents, in their interactions with their children, may undertake two types of maths activities: formal and informal. In the case of the formal, the parents directly and intentionally teach their children mathematics through activities that may be numeric (such as counting objects and writing down numbers) or reading (for example, reading stories with numbers). In the informal cases, they play number based games (card or board games) and applied real world tasks (cooking, shopping) in which the acquisition of mathematics is a secondary factor.

This distinguishes between two types of mathematical knowledge: the symbolic, or formal, which involve the entire numeric system (for example, the writing of Arabic numerals), and the non-symbolic, or informal, which include all the representations and manipulations of quantities without any associated symbols (for example, operations with objects).

What activities nurture mathematic abilities?

A study by the Chinese researcher Xiao Zhang and his team set out to evaluate how formal and informal mathematical activities lead to both immediate and long lasting effects on the formal (symbolic) and informal (non-symbolic) mathematic abilities of children. To this end, they accompanied 192 Chinese children from pre-school to the first year of schooling and, at three different stages in time, applied a standardised test that differentiates between formal and informal mathematics.

This thereby discovered a new and important relationship between the initial mathematics activities in the family environment and the mathematical skills of children. The frequency of formal mathematics activities between parents and children did not interlink with the formal or informal mathematics development trajectories of these children. Hence, the formal activities of parents and children did not generate any effect. In addition, the greater the frequency of informal mathematics activities (especially numerical games and applied activities) associates with higher levels of formal mathematics skills in pre-school children even when controlling for the effect of variables such as child age, gender, the socioeconomic status of the family and positive and negative parental practices. Finally, the involvement of the parents in informal activities in the pre-school years emerged as a significant predictor of the rate of growth of formal mathematics abilities in the first year of schooling.


How do we explain how these informal activities foster formal mathematical abilities?

This finding suggests that informal activities, especially games with numbers and applied activities, foster the active learning of mathematics; for example, playing cards or looking at a clock, in an informal context, motivates children to learn the Arabic numerals. In this context, parents are not taking on the traditional role of a teacher but rather providing support.

Multiple informal activities, such as telling the time or going shopping, contain a great deal of information about the symbolic numeric system. Involving children in these activities provides them with the opportunity to learn numeric and arithmetic symbols. The informal activities that do not include the symbolic numeric system (for example, comparing lines and sets) may help in grasping the non-symbolic nature of quantities that children apply to make the connection between numeric and arithmetic symbols and non-symbolic quantities.

Furthermore, applied informal activities (examples include, as seen above, cooking and shopping) returned the greatest effect on the mathematical abilities of first year students. The study sets out four reasons for this outcome.

Firstly, applied informal activities provide opportunities to interact with content related to life and fosters useful learning, enhancing the retention of information.

Secondly, numbers and quantities form part of daily life. The involvement of parents leads the children to spontaneously focus on numeracy even when their parents are absent. For example, this includes how talking about money when doing the shopping may lead children to read the pricing labels in supermarkets.

Thirdly, these applied informal activities may boost the motivation and interest of children, leading to their continued involvement and exploring with objectives.

Finally, the parents who get involved with their children in these activities at an early stage are those who display greater subsequent involvement, which may well lead to their children turning in better results over the course of time.


In summary…

Because the mathematical abilities of children in the first year of schooling influence their subsequent development, pre-school age children benefit from their families carrying out:

— informal applied mathematics learning activities: using calendars or agendas, adding up shopping prices with a calculator;

— numerical games: timed maths games, board games, sticker collection, among other activities.

These games and activities help children to appreciate the utility of mathematical concepts in the real world and return persistent benefits to the development of their abilities.


Sénéchal, M., & LeFevre, J. A. (2014). Continuity and change in the home literacy environment as predictors of growth in vocabulary and reading. Child Development, 85, 1552-1568.

Skwarchuk, S. L., Sowinski, C., & LeFevre, J. A. (2014). Formal and informal home learning activities in relation to children’s early numeracy and literacy skills: The development of a home numeracy model. Journal of Experimental Child Psychology, 121, 63-84.

Vygotsky, L. S. (1978). Mind in Society: The Development of Higher Psychological Processes. Harvard University.

Zhang, X., Hu, B. Y., Zou, X., & Ren, L. (2020). Parent-child number application activities predict children’s math trajectories from preschool to primary school. Journal of Educational Psychology, 112(8), 1521-1531.



Sandra Fernandes

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