Design of tasks for assessment of generalization abilities of preservice teachers of elementary school mathematics

Generalization is considered to be an essential part of mathematical reasoning and proving, and it has many definitions in mathematics education research. Despite its centrality, teachers often have difficulty identifying and responding to generalization in students’ work. In this study, we focus on preservice teacher’s (PTs) ability to describe generalizations of student answers. This study uses a digital geometry environment to investigate the potential in the process of designing geometry dragging tasks in which students are asked to create one or more examples of a figure that fit the specified characteristics by dragging one point. As part of the task design, PTs were asked to describe visually the correct answers they expected from their students as areas or objects that represent certain characteristics. We characterize different levels of generalization in expected student answers, as described by PTs, and suggest that they can be used to enhance teacher's awareness and can serve as a potential design principle for professional development of PTs’.