Perception of rectangular and skew structures in a row-column arrangement of figures

Abstract

The aim of the reported research is identification of difficulties and natural developmental limitations in understanding of a Row-Column Arrangement of Figures (RCAF) by 10-13 years old children. RCAF includes the arrangements made by regular distribution of any elements in rows and columns. These elements don’t have to be the same and adjoining. Analyzing school curricula shows that the multilateral understanding of RCAF is a prerequisite knowledge for many problems; e g. the product of two positive integers, the commutative law of multiplication, the idea of area, coordinates, matrices and various tables. In their tasks children had to construct and draw examples of RCAF. My research results show which elements of the given structure are important for children and which of them arc dominant in the children’s awareness. The research also proves that at the beginning of school, children do not possess well formed structures, necessary for the understanding of some mathematical ideas or operations, while the curriculum assumes their presence. The introduction of concepts based on unformed structures may lead to dramatic failures of some students.