Proportional Relations When Programming Using Scratch: The Case of Pre-Service Elementary School Teachers

Programming activities provide learners with opportunities to implement both computational and mathematical thinking while developing abstraction, which lies at the core of both domains. Although abstraction is fundamental to both computational and mathematical thinking, it is conceptualized and interpreted differently in each, as explained below. This study examines changes in level of abstract thinking among 41 pre-service elementary school teachers as they use the Scratch environment to produce animations in sequence of six tasks. These tasks were designed to provide repeated opportunities for abstracting proportional relations, including direct and inverse relations between motion and time. To analyze the data, we defined three levels of abstraction that capture these relations in the scripts of each task. We examined the extent to which pre-service elementary school teachers’ scripts demonstrated shifts in levels of abstraction across the sequence of programming tasks. The findings reveal gradual shifts in pre-service elementary school teachers’ levels of abstraction for both direct and inverse relations. This study extends prior research on the relations between computational and mathematical abstract thinking by focusing on proportional relations and offering a novel approach for assessing levels of abstraction in programming.