The Relationship of Early Math Skills and Mathematical Literacy in the Middle and the End of Elementary School

The paper presents a study of the development of early mathematical skills. In the course of theoretical analysis it was shown what early mathematical skills predict further achievements in mathematics. Further, a theoretical model of the development of early mathematical skills was proposed. In the empirical part of the work using the tools of Item Response Theory (IRT) psychometric analysis of mathematics test iPIPS for children of the first and third grades of primary school in Russia was conducted. It has been proven that the results of both tests can be used to make a reliable assessment of the respondetns ability level, and, accordingly, for check hypotheses advanced in the theoretical part of the work. Hypotheses about the factor structure of the iPIPS test and the role of knowledge of numbers in the transition to formal calculations were confirmed. It was confirmed that the ability to calculate in the first class is a strong predictor of children's achievements in mathematics in the third grade. The expected hierarchy of task difficulty according to the theoretical model was not fully consistent with the empirical data. It was concluded that in order to interpret the iPIPS test results in terms of the level of mathematical skills development, it is necessary to improve a number of test tasks, as well as add the missing ones. The paper offers recommendations on how to improve a number of test tasks, and which tasks need to be added.