Core mathematical skills

Early numerical skills are highly important for later learning in school (Duncan et al., 2007). If the most essential skills in early development are prioritised, it might be possible to prevent or at least lower the likelihood of future learning difficulties in mathematics. There are several ways to define early mathematics skills, and some research-based models have been published about early mathematics development (Krajewski & Schneider, 2009; Purpura & Ganley, 2014; Purpura & Napoli, 2015; Sarama & Clements, 2009).

As part of the development work of the Finnish LukiMat web service for educators and parents about preventing mathematical learning difficulties, a research-based core factor model of mathematics skills development in children aged 5–8 years was developed. This model used longitudinal studies and published mathematics assessment batteries as the main data (Aunio & Räsänen, 2015). According to this model, mathematics skills can be divided into four core factors: symbolic and non-symbolic number sense, understanding mathematical relations, counting skills and basic arithmetic skills.

 Core Numerical Skills for Learning Mathematics in Children Aged 5–8 Years:

 Symbolic and non-symbolic number sense

Counting skills

  • Number word sequence skills
  • Knowledge of number symbols
  • Enumeration skills

Understanding mathematical relations

  • early mathematical-logical principles
  • operational symbols in mathematics

Basic skills in arithmetic

  • simple addition and subtraction skills



  • Aunio, P. & Räsänen, P. (2015). Core numerical skills for learning mathematics in children aged five to eight years – a working model for educators. European Early Childhood Education Research Journal, 24(5), 684–704.
  • Purpura, D. J. & Ganley, C. (2014). Working memory and language: Skill-specific or domain-general relations to mathematics? Journal of Experimental Child Psychology, 122, 104–121. doi:10.1016/j.jecp.2013.12.00
  • Purpura, D. J. & Napoli, A. R. (2015). Early numeracy and literacy: Untangling the relation between specific components. Mathematical Thinking and Learning, 17(2-3). Advance online publication. doi:10.1080/10986065.2015.1016817
  • Sarama, J. & Clements, D. H. (2009). Early childhood mathematics education research. Learning trajectories for young children. New York, NY: Routledge.