OPTI-ODE: Enhancing Problem-Solving and Decision-Making in Ordinary Differential Equations Through Visual Mind Mapping and Strategic Decision Trees

About the Project

Ordinary Differential Equations (ODEs) pose significant pedagogical challenges in undergraduate mathematics education due to the cognitive load arising from complex algebraic manipulations and obstacles in structural recognition. This study evaluates OPTI-ODE, a student-centered pedagogical innovation that integrates self-constructed visual mind maps and systematic decision trees into the workflow for solving first-order ordinary differential equations (ODEs). Using a pre-test/post-test mixed-methods framework involving 13 Diploma in Mathematical Sciences students (N = 13), the students' performance, confidence, and cognitive obstacles were assessed both quantitatively and qualitatively. The implementation resulted in an increase in absolute scores from a pre-test (baseline) mean of 64.08% to a post-test mean of 86.62%, representing an average individual score increase of 20.38 percentage points. Qualitative survey data indicate a very high level of agreement regarding the tool's effectiveness in distinguishing between types of differential equations and reducing cognitive inertia at the initial stage of problem-solving. This finding highlights visual mind mapping as a high-impact, low-cost intervention to reduce mathematics anxiety, support the use of metacognitive checklists, and optimize problem-solving efficiency within higher education mathematics curricula.