From paper to software: Teaching polygon-separability problems using BichromaticSolver

Abstract

This paper examines how bichromatic separability problems, a classic topic in computational geometry, can be adapted for secondary mathematics education through the use of BichromaticSolver. The software computes simple or convex polygons that separate two finite sets of points under different optimisation criteria, including maximum area, minimum area, maximum perimeter, or minimum perimeter. Unlike traditional approaches, the number of polygon sides k is not fixed in advance but chosen by the user, enabling the exploration of diverse and potentially more effective configurations. Three classroom tasks were designed in which students alternated between paper-and-pencil methods and digital exploration with the software. This two-phase structure encouraged them to verify constructions, compare alternative outcomes, and refine their strategies. Classroom observations from this exploratory study document how these activities created opportunities for students to express and refine geometric reasoning while making computational thinking (CT)-related practices visible, for example decomposition, abstraction, strategic planning, and comparative evaluation of solutions. The findings suggest that integrating computational geometry problems with digital tools can enrich traditional mathematics instruction, highlight the relevance of geometry in authentic contexts, and offer a promising and transferable context for developing CT alongside core geometry content in secondary mathematics education.