Reconstructing Students’ Understanding of Integer Addition and Subtraction: A Didactical Design Grounded in the Theory of Didactical Situations

Abstract

Mastering integer addition and subtraction is essential for further learning in mathematics. However, students often struggle with persistent conceptual misconceptions. This study goes beyond previous research that has merely documented difficulties or suggested instructional methods without thoroughly examining the underlying barriers. This study presents a didactical sequence based on Brousseau’s Theory of Didactical Situations (TDS). It views technology as an extension of cognition and applies this perspective through the IntuMath digital application. Employing a qualitative approach within interpretive–critical paradigms, data were collected through classroom observations, written assessments, and semi-structured interviews. The findings suggest that the proposed design effectively supports students in gradually developing their understanding, transitioning from concrete activities to abstract representations across the four key TDS situations: action, formulation, validation, and institutionalization. Furthermore, using IntuMath expands opportunities for practice and conceptual exploration beyond the classroom setting. TDS helps students progress from real-world experiences with Body-scale Snakes and Ladders (BSL) and Small Snakes and Ladders games to more abstract concepts. Findings show that students were able to construct their own knowledge independently. Additionally, the use of the IntuMath application served as a tool for extended cognition, enabling independent practice and improving conceptual understanding beyond the classroom.