Pre-service teachers using an app to generalize figural patterns through figural reasoning

To investigate a dynamic learning environment’s (DLE) facilitation of students’ figural generalization of figural patterns, this study scrutinizes 12 pre-service teachers’ efforts to generalize figural patterns using a DLE that offers dynamically adapting shapes. The shapes support identification of figural patterns’ figural commonalities. In video recorded task-based interviews, the pre-service teachers worked in pairs to solve figural pattern tasks using the DLE. Duval’s (2006) theory of semiotic representations is utilized to identify characteristics of the pre-service teachers’ conversions and treatments. Results show that they adopted an experimental approach and utilized the DLE to create multiple valid symbolic generalizations, and they used symbolic treatments to support some solutions. However, they would often treat only one exemplar of the figural pattern, weakening the basis for their generalizations, and they struggled to express verbally the figural patterns’ generalized structure. These results raise concerns about the algebraic thinking involved in their solution processes. Implications of this study include the identification of crucial factors of DLEs designed to support students’ exploration of figural patterns.