Strategies and Challenges in Numeracy Problem-Solving: A Case Study of a Gifted Student

Abstract

This study investigates the strategies, challenges, and techniques employed by a gifted student, referred to as Iwan, in solving complex numeracy problems. Using a qualitative case study design, data were collected through task-based interviews involving problem types similar to those in international assessments such as PISA. Problems required graph interpretation, arithmetic operations, pattern recognition, estimation, and the use of scribbling techniques. Verbal responses were audio-recorded, transcribed verbatim, and complemented with observational field notes on non-verbal actions. Data were analyzed thematically following Braun and Clarke’s (2012) framework, with triangulation, peer review, member checking, and audit trail procedures ensuring credibility and trustworthiness. Findings revealed that Iwan integrated multiple strategies: (1) interpreting graphs as the initial step, followed by relevant arithmetic computations; (2) recognizing numerical patterns to expedite calculations; (3) using scribbling for rough work to reduce cognitive load; (4) applying estimation and scaling when exact values were unavailable; and (5) employing straightforward problem-solving by focusing only on essential data. However, obstacles emerged, including difficulties in balancing estimation and precision, interpreting scales across formats, and transitioning between representations. These challenges, alongside a tendency to overemphasize accuracy, limited flexibility in problem-solving. The study concludes that effective numeracy instruction should integrate graph literacy, arithmetic fluency, estimation skills, and flexible problem-solving approaches. Pedagogical recommendations include embedding pattern recognition, encouraging strategic use of rough work, and teaching adaptive reasoning for real-world numerical contexts. The findings contribute to both theory and practice by highlighting the cognitive strategies of gifted learners and offering insights for enhancing numeracy education.