Minimax-Based Optimization of Instructional Strategies for Heterogeneous Learner Populations

Abstract

Different groups of learners will have differing amounts of prior knowledge, readiness levels, and requirements of support. Thus, an instruction plan that is optimal on average may generate a considerable learning deficit for some smaller subgroup. In this paper, we consider a simple minimax model for choosing an instruction plan that maximizes the smallest predicted group deficit. We define learner groups using readiness categories and use the group x strategy loss table as the description of each instructional plan. A mixed strategy involves distribution of instructional time between different strategies. The corresponding optimization model is formulated as a linear programming problem and generalized for loss estimates and resource restrictions under uncertainty. We provide a reproducible numerical example comparing the four models. In relation to the presumed loss matrix, average loss optimization leads to a minimum group loss of 40.00 points, while the mixture of minimax yields a minimum group loss of only 24.15 points. The minimum weighted average loss is higher at 23.30 points compared to the previous value of 18.70 points. The example shows the way the mathematical model behaves. It is not a proof obtained in a classroom setting. This mathematical model provides an intuitive basis to start with when designing teaching programs where there are different groups and estimates of their performances are uncertain. Further work should be done using education data.