Open mathematical tasks conceived, designed, and reflected upon by preservice elementary teachers

As part of the research on mathematical tasks, the literature on the advantages of using open tasks has been steadily growing. However, limited research exists on the types of open mathematical tasks considered by elementary preservice teachers and their abilities to create those tasks. This study explores the preconceptions of open mathematical tasks held by 56 preservice elementary teachers, as reflected in a survey where they described the characteristics and design of such tasks. The study also examines their reflections on implementing open mathematical tasks in one-on-one interviews with elementary students. Our analysis found that elementary preservice teachers described characteristics of open mathematical tasks that match aspects identified in the literature. They also showed the ability to create an open task to a certain degree. However, the open tasks they designed were predominantly procedural and focused on a few aspects of task openness. This finding indicates that the preservice teachers prefer a narrower spectrum of openness when creating open tasks compared to their preconceptions. Preservice teachers also reported challenges they faced when implementing the open tasks with elementary students. These findings suggest the need for mathematics teacher education to provide opportunities where future teachers design a broad spectrum of open mathematical tasks, while addressing on-the-ground challenges in classroom settings.