TEACHING GEOMETRIC-METRIC THINKING THROUGH THE MKT MODEL AND AUGMENTED REALITY FOR PRE-SERVICE MATHEMATICS TEACHERS

Abstract

The article presents a systematic theoretical review that integrates the conceptual foundations of geometric-metric thinking, the Mathematical Knowledge for Teaching (MKT) framework, the Van Hiele theory of levels of geometric reasoning, and the potential of Augmented Reality (AR) as a didactic mediation in university-level geometry teaching. It analyzes the persistence of gaps between the formative goals of geometric education and traditional school practices, as evidenced in international, regional, and national assessments, which justifies examining geometric-metric thinking as a multidimensional construct articulated through processes of visualization, modeling, representation, and argumentation. The documentary review identifies relevant contributions regarding specialized teacher knowledge, highlighting that the MKT domains—particularly SCK, KCS, and HCK—are critical for understanding how future teachers interpret, explain, and mobilize geometric definitions, properties, and relationships. Likewise, recent findings are systematized, demonstrating that AR enhances spatial intelligence, supports active exploration of three-dimensional objects, and promotes representational fluency, thus acting as a mediation aligned with the cognitive demands of geometric-metric thinking. The comparative analysis reveals a scarcity of studies that integrate these three axes: geometric-metric thinking, specialized teacher knowledge, and immersive technologies within the initial training of mathematics teachers, which underscores the relevance and contribution of the present article as a theoretically and analytically integrated endeavor.