Abstract:

Figural patterns connect several aspects of mathematical activity central to the work of teaching mathematics. A number of studies has investigated pupils’ and pre-service mathematics teachers’ strategies of generalizing figural patterns, but as Kılıç (2017) has stated, generating figural patterns based on number patterns requiring translation between representations is not studied at all. The same is the case for students and pre-service mathematics teachers (PSETs) generating figural patterns based on algebraic formulas. In our study we investigated solutions of 16 PSETs performing a task in which they were asked to generate a figural pattern based on a given quadratic formula. PSETs were solving this task on a digital platform, which allowed us to look at their process of generating patterns and identify possible obstacles. In the paper we report on a solution process of one student who is repeatedly trying to fit the number of squares used in his generated pattern to a given formula. If we only had the final solution of the student, for instance a solution by pen and paper, we would not have been able to understand the challenges he met during the solution process, as well as not being able to adjust the instructions in the following teaching session.

Our results indicate that although the teacher education successfully trains PSETs to generalize figural patterns (Kohanová, Solstad, 2019), more attention to generating figural patterns can further improve the training of pre-service elementary teachers and their development of algebraic thinking.

Keywords:

Generalization, generating, prospective elementary teachers, algebraic thinking, figural patterns.