Students' Engagement in a Mathematical Investigation through Online Problem-Based Learning

The core components of mathematical activity are involved in mathematical investigation: problem formulation, processing of conditions for which there is no clear solution, formulation and justification of conjectures, and generalization. However, introducing mathematical investigation to students is a challenging activity. A crucial aspect of the student's learning and understanding of the process is the kind and degree of their engagement in the learning activity. This phenomenological study sought to describe how pre-service teachers engaged in an online problem-based learning (PBL) while doing a mathematical investigation (MI). The researcher explored the cognitive, behavioral, and affective components of the 35 pre-service mathematics education students who had their first-hand experience of MI through online PBL. The students were given two contextualized, ill-structured problems, worked in groups, and proposed solutions to the problem. Data from the teachers' observation notes, students' learning logs, and the transcripts of the focus group discussions were gathered. Qualitative data analysis suggests that students were involved in peer-to-peer learning that included task-related conflicts, pattern recognition, self-regulation, critical analysis, participation in the learning activity, attention to the tasks, and interaction with the learning community which led to their enjoyment and motivation in conducting MI. The extent of their engagement during the presentation and analysis of the problem, planning and developing a solution, presenting and assessing solution, and summary and debriefing were further analyzed. The findings revealed that while students were initially puzzled at the start of their investigation, they shared, welcomed new information, analyzed it, and valued different approaches to a challenging mathematical problem as they progress with their inquiry. The results also revealed respondents' perspectives on how to manage online PBL. These findings can help teachers design collaborative online activities.