Understanding mathematical relations

The study of how children learn early mathematical-logical principles began with Piaget (1965) and continued with neo-Piagetian researchers (Case, 1996; Smith, 2002). Early mathematical-logical principles refer to skills such as seriation, classification, comparison and one-to-one correspondence (Aunio & Räsänen, 2015). Seriation skills are needed to understand number word sequences and their ordinality features. A young child can be asked to line order his or her toys based on their size. The ability to classify items is highly important in mathematical problem solving. For example, classifying toys by type (i.e. cars, dolls, balls) or colour is an early sign of this skill. Comparison skills are needed, for instance, when a child decides which of two dice has more dots. Young children are quite good at saying who has more candy. One-to-one correspondence refers to the ability to make connections between the entities in one set and those in another. Enumeration tasks are an instance in which one-to-one correspondence becomes necessary (e.g. how many balls are there in this box?). Here, a child makes a connection between the number word sequence and the pointing act and between the pointing act and the items to be counted.

Understanding operational symbols in mathematics is an important skill since it enables the child to follow mathematics instruction in school. In many cultures, during the kindergarten year (usually six years of age), children learn to understand basic mathematical symbols such as < (less than), > (more than) and (equal to), which reveal the relationship between two entities.



  • 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.
  • Case, R. (1996). Reconceptualising the nature of children’s conceptual structures and their development in middle childhood. In R. Case & Y. Okamoto (Eds.), The role of central conceptual structures in the development of children’s thought. Monographs of the Society for Research in Child Development,61(1-2), 1–26. Serial No. 246.
  • Smith, L. (2002). Reasoning by mathematical induction in children’s arithmetic.Oxford, UK: Pergamon Press.