From Tiles to Worksheet: Exploring Concreteness Fading in Learning Vector Addition

Teaching vector addition seems challenging in secondary-level mathematics education. Vector addition requires both geometric and algebraic understandings, and the overreliance on abstract representations causes students difficulties in learning this complex mathematics skill. The concreteness fading framework is promising for effectively teaching complex mathematical topics in a progressive way. This study explores the contribution of concreteness fading to learning by implementing an instructional intervention for eighth graders on vector addition. Through a grounded theory method, this research reveals key concreteness fading mechanisms: (1) consistent design elements establish inter-task connections; (2) the fading task facilitates the co-building of operational and procedural knowledge; and (3) unfamiliar symbols within tasks promote mathematical sense-making. These findings suggest the potential for future studies to incorporate concreteness fading as a valuable strategy for enhancing the learning experience on complex mathematical subjects.