The Ability of Pre-Service Primary Teachers to Produce Figural Patterns Based on Algebraic Formulas

In this study, the participants were asked to create figural patterns (figural representations) of two sequences, where the presentation is in the form of an algebraic formula. Those algebraic formulas were representing linear and quadratic (non-linear) patterns, in which pre-service primary teachers were asked to generate figural patterns based on those algebraic formulas. In total, 127 pre-service primary teachers participated in the study. The obtained data were analysed at two levels including both semantic and descriptive analyzes. The results of the study indicated that of 127 participants, 88 could generate a correct figural pattern of some kind for the given arithmetic sequence expressed via a linear function of n, while 72 were able to do so for the given non-linear sequence expressed via a quadratic function of n. Follow-up individual interviews were conducted with 9 volunteer participants, reflecting a cross-section of types of responses, including some who were unable to respond and had some issues.