Abstract
Understanding the part-whole fraction subconstruct is essential for developing mathematical literacy, yet many students still struggle to coordinate fraction meanings across visual, symbolic and contextual representations. This study examined how epistemological, ontogenic and didactical obstacles interact in students’ representation of partwhole fractions within Brousseau’s Theory of Didactic Situations. An exploratory case study design was used, involving 187 Grade 7 students and 12 mathematics teachers from 12 schools in South Sulawesi, Indonesia. Data were collected through diagnostic tests, classroom observations and clinical interviews. Quantitative test data were analyzed using descriptive statistics and classroom-level comparisons, while qualitative data were analyzed through theory-driven coding and triangulation across data sources. The findings showed that 56.7% of students experienced epistemological obstacles, especially natural number bias, while 62.6% showed ontogenic obstacles related to developmental limitations in coordinating equal parts and whole-unit relationships. Didactical obstacles were identified in 91.7% of classroom teaching practices, mainly through representational monotony and premature institutionalization. Triangulation revealed four interaction mechanisms: representational monotony amplified context-bound understanding, didactic contract norms sustained natural number bias, premature division terminology triggered symbolic interference and limited action situations hindered the development of equipartitioning. This study contributes a systemic model explaining how milieu design, didactic contract norms and institutionalization timing shape persistent fraction errors, thereby shifting the focus from individual student deficits to didactic system redesign.
Keywords: Didactic Contract, Fraction Representation, Learning Obstacles, Natural Number Bias, Part-whole Fractions, Theory of Didactic Situations.