Preschool education is considered to be a key factor in preparing children for the commencement of school education. However, the recognition of the crucial role of this kind of education has been accompanied by discussions on how to organize preschool education so that, on the one hand, it reflects current trends in education and upbringing and, on the other hand, helps children to acquire a compendium of basic skills necessary for future school education. Apart from scientific discussions on the role of preschool education, the evaluation and parents’ expectations with regard to this first stage of education are of equal importance. Identifying parents’ opinion on how preschools fulfill their fundamental responsibility for preparing children to achieve school readiness for reading and writing led to the performance of a survey among parents of preschool children. The research was conducted among parents of children from selected preschools in the town and municipality of Biała Podlaska, Lublin province. The research method of a diagnostic survey, with the use of a questionnaire, was employed. The results made it possible to learn the opinion of the surveyed group of parents with respect to the objective pursued. The research confirmed that, on the one hand, parents are positive about the work of preschool and didactic activities of teachers who, while implementing the Core curriculum for preschool education, take due account of all required skills. The parents, at the same time, expect preschools to lay even greater emphasis on teaching reading and writing to children. Those skills are considered by parents to be especially important in further school education. The research results also reveal that almost all parents work with their children at home on improving the skills.