FOSTERING FIGURAL-CONCEPTUAL COVARIATION: HOW GEOGEBRA TRANSFORMS UNDERSTANDING IN EUCLIDEAN-TAXICAB GEOMETRIC TRANSITIONS

This study investigates how university mathematics students develop geometric understanding when transitioning between Euclidean and Taxicab geometries using GeoGebra. Through structured activities that engage students as both learners and future teachers, we explore the emergence of "figural-conceptual covariation", a dynamic process where visual representations and theoretical understanding evolve simultaneously and the interconnected formation of an extension of Fischbein's figural concept theory to non-intuitive geometric systems. Our findings reveal that GeoGebra functions not merely as a visualization tool but as a catalyst for theoretical thinking, creating what we term "GeoTaxiGebra", an epistemologically enhanced learning environment where Taxicab geometry visualization and Euclidean understanding mutually reinforce each other.