Mathematical Activity of Playing in Joint Liability Mechanisms: An Ethnomathematical Study of Group Loan Feasibility Simulations in Microfinance Institutions

Group lending schemes in microfinance institutions commonly employ joint liability mechanisms, locally known as tanggung renteng, in which the repayment burden of a defaulting borrower may be redistributed among the remaining members of the group. While ethnomathematics studies have extensively explored mathematical practices embedded in traditional cultural activities, mathematical practices within modern professional and institutional settings remain relatively underexplored. This study examines the mathematical activity of playing, as conceptualized by Bishop, in the simulation of loan feasibility and explores how simulative reasoning extends from individual financial assessment to collective joint liability mechanisms. The study constitutes a focused reanalysis of descriptive qualitative data obtained through an in-depth interview with an Account Officer and document analysis of Debt Burden Ratio (DBR) records from a four-member borrower group at a microfinance institution in Makale, Indonesia. Two contrasting cases were examined: a borrower with adequate financial capacity and a borrower with limited repayment capacity. The findings indicate that playing emerges conditionally when uncertainty regarding repayment capacity requires the Account Officer to explore alternative loan ceilings and corresponding installment amounts. This activity takes the form of bounded exploration because the possible alternatives are constrained by institutional rules and standardized installment tables. Furthermore, a similar simulative pattern appears at the group level when the repayment obligation of a potentially defaulting borrower is projected and redistributed among the remaining members. This study introduces the notion of distributed playing to describe the extension of individual mathematical simulation into collective financial reasoning. The findings contribute to institutional ethnomathematics by demonstrating that mathematical activity in professional settings not only supports administrative decision-making but also contributes to the maintenance of collective solidarity and risk management within group lending systems.