All articles

This paper reports on a case study which explores the co-creation of a zone of proximal development (ZPD) in a mathematics teaching-learning activity in a Norwegian kindergarten. To capture the complexity of teaching and learning mathematics in kindergarten the study uses qualitative methods within an interpretative paradigm. The findings illustrate how a five-year-old girl and a kindergarten teacher co-create a ZPD by expanding each other’s action possibilities, and how the co-creation is fundamentally based on mutual trust and responsibility. The results give insights into how mathematical learning possibilities may be promoted in kindergarten. The study illustrates the importance of being receptive to children’s contributions and, above all, to trust children’s abilities to take responsibility for moving mathematical teaching-learning activities forward.

Introduction. The authors show the necessity for preschool teachers to know how to develop the ideas of square, its measurement and the comparison of subject squares in preschoolers. The main preschool curriculums and a large body of literature on the problem were analyzed, which revealed the lack of methodological sources for the development of ideas about square. As a result, the authors have designed and described the appropriate methodology.

Methods. The section describes four stages of getting familiar with square for preschool-age children: 1) the development of an idea of the square of objects and their comparison through the method of imposition; 2) measuring and comparing square of figures using conditional measurements; 3) the determination of the dependence of the measurement results of the square on the size of the measurement; 4) familiarization with the generally accepted standard measures of measuring square in centimeters. At each stage, the features of introducing the new material are considered, and examples of tasks and exercises are given. The conditions for the effective development of ideas about the area of objects in preschoolers are described. Positive aspects of the development of preschool children are revealed when they get familiar with the mathematical concept of “square”.

Conclusions. The authors note that the designed methodology has been successfully applied by educators of preschoolers and senior preschool groups for schools in kindergartens in Stavropol. It is shown that the fulfillment by preschoolers of the relevant thematic tasks and exercises contributes to the development of their sensory abilities, logical thinking, coherent speech, attention, and memory, which will favorably influence further education in primary school and will be useful in practical activities.