Students’ mathematical modelling with the aid of digital technologies: An Activity and Affordance Theory perspective

Abstract

Digital technologies in mathematical modelling activities are receiving increased attention in curriculum and policy documents in Norway and internationally. An important point arising from diverse interests in technology and students’ mathematical modelling activities is the various forms of interactions that emerge within students’ activities generated by digital technologies. However, the majority of research on technology-mediated activities in mathematical modelling is still approached from a cognitive perspective. This study takes another perspective, a socio-cultural perspective combining Cultural-Historical Activity Theory (CHAT) with Affordance Theory. This dissertation explored how secondary school students solve mathematical modelling tasks with the aid of digital technologies. This research study focuses on different forms of interactions within students’ mathematical modelling activities with the aid of digital technologies in group settings. Three subgoals were formulated from the aim of the study: Examining the various forms of interactions within the students’ activities; investigating the students’ working processes; and examining students’ interactions with digital technologies. The study is framed within a qualitative research paradigm and adopts an ethnographical case study research design. It involves four secondary schools in southern Norway. Empirical data were collected through video recordings, screen capture, fieldnotes and students’ worksheets. A combination of inductive and deductive approaches was used in the data analysis. The study highlights three major findings. Firstly, it shows that the elements of CHAT are seen as a collective system interacting with each other, in contrast to cognitive approaches focusing on heuristics and modelling processes. Secondly, the findings indicate that students’ activities in mathematical modelling can be categorized as modelling actions and operations towards the object of solving a mathematical modelling task, from a CHAT perspective. Digital technologies also played an essential role in the modelling actions that emerged. Thirdly, the findings highlight the emergence of technological, mathematical and socio-cultural affordances and constraints of the digital technologies in the students’ activities. The study contributes to research in mathematics education and draws various implications out of the major findings regarding students’ use of digital technologies in mathematical modelling activities. These implications include the potential influence of digital technologies in group interactions, students’ tendency in selecting or using particular digital technologies, the impact of different types of mathematical modelling tasks on interaction dynamics, and students’ roles in mathematical modelling activities. Future research is also suggested to explore the expansion of students’ mathematical modelling activities with the aid of digital technologies, teachers’ roles in the students’ activities, and considerations of other theoretical perspectives.