Growing patterns invention by primary education students

Abstract

ABSTRACT This paper addresses the creation of patterns through an open-ended invention task. With a qualitative study, we aimed to characterise the written answers of 76 primary education students in fourth, fifth and sixth grades, identifying the type of pattern they invented. We analysed the representations they used and the structure followed in the sequences they created. In addition, we determined whether there were differences in the invention of patterns among the three school grades in the sample. Results showed that students prefer creating growing patterns using numerical and visual representations. They generally involved a numerical structure more frequently than a geometric one, using an increasing arithmetic progression. They usually formed the pattern by involving a geometric structure, building a figure based on an initial element to which they added more elements to complete a particular figure. In fourth grade, numerical representations were more common than pictorial ones, while in sixth grade, the opposite was true. As age increased, so did the frequency with which students invented a pattern. Results also provided information on the complexity of the types of geometric patterns invented.