<![CDATA[Fractions are abstract mathematical concepts that often challenge students due to their various representations. While fraction instruction in schools typically emphasizes area models, it is crucial to incorporate other models, such as length models and number lines. This study aims to 1) identify the learning obstacles students encounter in representing fractions with length and number line models, 2) develop didactic designs to address these learning obstacles, and 3) evaluate the effectiveness of the designs. Employing a qualitative approach grounded in the Didactical Design Research (DDR) framework, the study comprised three stages: prospective, metapedadidactic, and retrospective analysis. Data were collected through tests administered to 20 seventh-grade bilingual students, in-depth interviews with those experiencing difficulties, and an analysis of their learning resources. All the collected data on learning obstacles were then analyzed using the Miles & Huberman method, which involves the stages of data reduction, data display, and conclusion drawing. The findings indicate that students relied predominantly on area models due to limited instructional exposure, leading to learning obstacles when representing fractions using the length model and locating them on the number line. When asked to use the length model, students tended to revert to area representations, reflecting conceptual constraints. Based on these obstacles, a didactic design was developed in which the length model and number line were introduced sequentially and in an interconnected manner. The design proved effective, as no further learning obstacles were identified after its implementation. These findings suggest that systematically integrating both representations strengthens students’ conceptual understanding of fractions.]]>
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