An observational study of the 8Ps learning model in grade 12 differential calculus instruction

Achieving proficiency in fundamental differential calculus concepts remains a persistent challenge for grade 12 students, raising concerns among mathematics teachers and policymakers. Despite the widely acknowledged applications of differential calculus across diverse disciplines, global examination diagnostic reports consistently highlight students’ struggles to grasp core concepts, underscoring the urgent need for targeted educational interventions. In response, this study developed and evaluated the 8Ps learning model a structured pedagogical framework designed to address these challenges through collaborative problem-solving strategies. As part of a broader mixed-method research initiative, this qualitative study employed classroom observations to assess the model’s implementation in teaching stationary points in differential calculus. Data were processed using comparative and content analyses to identify differences between the 8Ps learning model and traditional teaching methods. The findings reveal distinct contrasts in instructional approaches: while traditional methods rely on teacher-centered instruction and passive student engagement, the 8Ps learning model organizes students into small, mixed-ability groups that collaboratively solve problems, engage in peer discussions, and employ creative reasoning with minimal teacher guidance. These findings suggest that the 8Ps model’s structured yet collaborative design may enhance differential calculus instruction by fostering active learning and deeper conceptual understanding.