ENSURING CONTINUITY IN THE STUDY OF FRACTIONS: MATHEMATICAL AND METHODOLOGICAL ASPECTS

Abstract

The article is devoted to the problem of continuity in teaching mathematics, in particular, the topic of "Fractions". The study highlights the importance of ensuring continuity between the main stages of learning, examines the definition of this diverse pedagogical phenomenon, and explores the possibilities of maintaining continuity at various levels: general didactic, subject-specific, methodological, and personal. The article describes the importance of expanding the set of nonnegative integers to include fractions, highlighting their applicability in various sciences and emphasizing their fundamental nature. In addition to the thorough mathematical applications, the importance of fractions in everyday life is also described. It is concluded that they influence the development of critical thinking and serve as an important tool for making informed decisions. The problem of the adaptation period in learning fractions, which occurs during the transition from primary to basic secondary school, is described, along with the main difficulties in overcoming it. The study explores the potential of introducing propaedeutic familiarization with parts of the whole in preschool education, and describes the properties and patterns that preschool children can understand. The main issues addressed by the current primary and basic secondary school curricula in relation to the study of fractions are analyzed, and typical difficulties and causes of students' mistakes are described. The main focus is on methods for overcoming these difficulties and the possibility of correcting the acquired knowledge and skills of students. The main stages of studying the topic and the relevant mathematical materials, including fraction models, are highlighted, along with the models that will be appropriate for each stage. The main differences between integers and fractions are described, which students should be familiar with in order to generalize or correct their knowledge and skills. Effective forms of processing educational material related to fractions, the educational strategy of scaffolding, which should be followed by the teacher for effective learning, are presented. The importance of combining traditional methods of teaching mathematics and modern technologies, such as gaming, digital technologies, augmented and virtual reality, and gamification, in the educational process of primary and basic secondary schools is emphasized.