Density in different contexts: what undergraduate students think
Video lessons; real numbers; Density of real numbers
Motivated by the ongoing debate on the use of technology in education, the growing relevance of video lessons, and their potential to facilitate the understanding of complex mathematical concepts, this study aims to explore the perceptions of mathematics pre-service teachers regarding different notions of density. It seeks to foster a deeper understanding of this concept while reflecting on the possibilities of teaching it through video lessons. To support the research, a literature review was conducted on the topics of video lessons and density. The review revealed a scarcity of studies focusing on the educational use of video lessons and none that explicitly connect video lessons with the teaching of density. The research adopts the Design-Based Research (DBR) methodology due to its interactive and interventionist nature. In terms of teaching strategies, brainstorming was employed to elicit participants’ prior conceptions of density, and mathematical modeling was used to contextualize real-life problems involving density. Both strategies were implemented during fieldwork activities with the participants. The design of the tasks was based on the mathematical modeling framework proposed by Bassanezi (2002), combined with investigative scenarios described by Skovsmose (2000) and classroom inquiry approaches outlined by Ponte (2005). As a final outcome, the study aims to develop a video lesson that models a real-world problem involving density, provides its mathematical solution, and undergoes refinement through iterative feedback cycles with the pre-service teachers.