Creating Triangle Construction Exercises as Interactive GeoGebra Applets with Automatic Verification, Hints, and Feedback

Abstract

With the growing significance of technology-based education and the advancements in Computer Algebra and Dynamic Geometry systems, automated tools for interactive learning have attracted significant attention. Nonetheless, the scarcity of interactive open-source online tools for geometric construction problems that offer feedback has hindered their wider implementation within the educational system. The primary reason for this absence is that geometric construction problems necessitate a constructed object as a solution rather than a numerical one. This feature renders the evaluation of geometric construction problems to be particularly challenging for machine evaluation (solutions cannot be copied into answer boxes) and time-consuming for teacher evaluation. In this work, the focus will be on triangle construction problems within the broader topic of geometric constructions. Emphasis will be placed on methods for creating interactive triangle construction applets in the widely popular GeoGebra software. The necessary steps will be outlined to enable mathematics teachers to create interactive GeoGebra applets with automatic verification that offer feedback for a diverse range of triangle construction problems.