Abstract
This study develops and evaluates a numeracy-focused didactical design that addresses high school students’ learning obstacles in Systems of Linear Inequalities in Two Variables (SLITV) through scaffolded instruction differentiated by Adversity Quotient (AQ) profiles. The investigation employed an exploratory sequential mixed-methods approach, combining Didactical Design Research (DDR) at one school (6 students for obstacle identification; 3 for metapedadidactic analysis) with a quasi-experimental design at another (80 students: 40 experimental and 40 control). The qualitative phase identified six learning obstacle types with distinct AQ-based manifestations. Among Quitters, psychological barriers such as mathematics anxiety and learned helplessness functioned as root causes through an “obstacle cascade” mechanism. Campers exhibited a self-imposed “good enough” mentality despite adequate capability, whilst only curriculum limitations emerged among Climbers. The study developed a Hypothetical Didactical Design integrating Brousseau’s Theory of Didactical Situations with a novel SCALE (Set up Goals, Contradict Adidactic, Anonymous Gallery, Lock-In, Evaluate/Extended) framework and three-tiered AQ-responsive scaffolding and iteratively refined it through metapedadidactic analysis, producing an Empirical Didactical Design with 16 new Didactical- Pedagogical Anticipations. The empirical design demonstrated strong effectiveness: Cohen’s d = 1.687, experimental normalised gain of 0.82 (high) versus control of 0.67 (medium), classical completeness at 85%, implementation fidelity of 97% and student responses at 95.91% (very positive). This study contributes the first integration of AQ-responsive differentiation within DDR specifically targeting numeracy competencies in algebraic domains.
Keywords: Adversity Quotient, Didactical Design Research, Learning Obstacles, Numeracy, Scaffolded Instruction.