Students' Mathematical Representation in PISA Space and Shape Tasks Across Gregorc's Thinking Styles

Abstract

This qualitative descriptive study investigates high school students' mathematical representation ability in solving PISA Space and Shape problems, analyzed through Gregorc’s thinking style model. Eight tenth-grade students at Islamic High Secondary School DDI Takkalasi (2025/2026 academic year) were purposively selected based on a Gregorc Thinking Style Questionnaire, representing two students per style: Concrete Sequential (CS), Abstract Sequential (AS), Concrete Random (CR), and Abstract Random (AR). Data gathered through questionnaires, a six-item mathematical representation test adapted from PISA released items, and semi-structured interviews were analyzed using Miles, Huberman, and Saldaña’s framework, with credibility ensured via source triangulation. Results demonstrate distinct representation profiles across styles: CS students systematically integrated verbal, visual, and symbolic representations; AS students prioritized conceptual understanding by linking visual confirmation to symbolic formalization through verbal justification; CR students utilized visual representation for exploration but struggled with accurate symbolic translation; and AR students relied on mental visualization and intuition, leaving key reasoning unverified. These findings indicate that thinking styles systematically influence mathematical representation behaviors and suggest that evaluating representation ability solely through written work risks underestimating conceptual understanding, particularly in random-oriented thinkers. The study provides critical insights for developing differentiated instructional strategies that align mathematical task design with students' dominant cognitive processing styles.