Development of the non-symbolic and symbolic numerical sense

The issue of early predictors of mathematical achievement has been actively discussed in national and international literature lately. The numerical sense, mental representation of quantitative data, appears to be one of such predictors, specific to mathematics. The paper is a review of studies of symbolic and non-symbolic aspects of the numerical sense, specifics of their functioning and development. Varying versions of tests involving comparison and recognition of identities used in research, such as proportion of correct answers and Weber's fraction, were chosen as instruments of assessing the non-symbolic numerical sense. In order to analyze the symbolic numerical sense the authors discuss research findings obtained with the help of the test of the numerical line which reflects, among other things, the link between perception of quantity and that of space. Effects of interrelation (distance) and size were studied for symbolic and non-symbolic representation of quantity. The non-symbolic sense of number was also studied on the material of the congruence effect reflecting the link between assessment of quantity in non-symbolic form and assessment of visual characteristics of objects. The paper also discusses connection between the symbolic and non-symbolic numerical sense and a person's education, interaction of the symbolic and non-symbolic numerical sense in the course of individual development and research data pertaining to the link between the numerical sense and mathematical achievement in children of different ages.