Numerical Quantitative Design of Assignments and Assessments to Facilitate Differentiated Instruction in Large Class Cohorts

Classroom learning has been used for centuries that helps to promote socialization, face-to-face interaction, and open exchange of ideas. We propose a new approach to classroom learning based on sequential numeral division. It builds on the concept of trichotomy – a division of students based on creamy-level, middle-level and weaker-level students -- proposed in a previous study. A sequenced series of formative assessments can map student progress and achievement, particularly in the case of weaker students. In the design of this model, we assume that the students are deeply engaged in learning activities and show their dedicated involvement in interacting with the group members. The idea behind the development of this model is to study if weak students perform better on critical-thinking tests in a collaborative learning setting rather than when they study individually. We propose a mathematical model to measure group activity/achievement, which is a complex function of several parameters. We collect data on different parameters for validation of the model in the near future.