INTEGRATION OF DIGITAL FORMATIVE ASSESSMENT IN DIDACTIC DESIGN TO REDUCE STUDENTS' LEARNING OBSTACLES IN THE MATERIAL OF TWO-VARIABLE LINEAR INEQUALITY SYSTEM

Abstract

This research set out to characterise the learning obstacles experienced by students and to build a didactical design for the topic of Two-Variable Linear Inequality Systems (SPtLDV) combined with Digital Formative Assessment (DFA). It was prompted by observations that students commonly struggled with modelling contextual problems, locating boundary lines, sketching graphs, and pinpointing solution and intersection regions within SPtLDV. A qualitative Didactical Design Research (DDR) design guided the study, unfolding across three phases: analysis of the didactical situation, metapedadidactic analysis, and retrospective analysis. Grade X.5 students took part in the stage of identifying learning obstacles, while Grade X.3 students were involved in implementing the didactical design, both groups drawn from a state senior high school in Tegal City. Data collection combined diagnostic tests, interviews, classroom observation, and DFA tools comprising Google Form, Canva AI, and QR-code-based digital reflection. The findings indicate that epistemological obstacles predominated, marked by procedural understanding unaccompanied by conceptual grasp, alongside ontogenic obstacles evident in students' difficulty linking verbal, symbolic, and visual representations. These insights informed the design of a three-stage Hypothetical Learning Trajectory (HLT) together with Didactical and Pedagogical Anticipation (ADP) integrated with DFA. Across three teaching sessions, the implementation revealed close alignment between anticipated and actual student responses, accompanied by gains in students' ability to build mathematical models, sketch graphs, determine solution regions, and interpret their solutions. The study concludes that a didactical design grounded in identified learning obstacles and reinforced through DFA meaningfully supports students in developing a deeper understanding of SPtLDV.