Intuitive thinking in solving HOTS problems on sequences and series: A dual process theory perspective

Abstract

Higher Order Thinking Skills (HOTS) are a central focus in mathematics education; however, students' intuitive thinking in solving HOTS problems on Sequences and Series remains underexplored. This study aimed to describe students' intuitive thinking across the C4–C6 cognitive levels using the indicators of differentiating, attributing, checking, and formulating. A descriptive qualitative approach involved three purposively selected eleventh-grade students identified through HOTS tests and classroom observations. Data were collected through written tests, structured observations, and task-based semi-structured interviews conducted after each problem-solving session to explore students' thinking processes in depth. Data were analyzed through reduction, display, and conclusion drawing, with triangulation across all three sources to ensure validity. Dual Process Theory served as the analytical framework, specifically to examine how System 1 intuitive processes manifest across the four HOTS indicators of differentiating, attributing, checking, and formulating at the C4 to C6 cognitive levels. The findings reveal consistent System 1 dominance across all four indicators, where students bypassed information selection at the differentiating level, failed to connect procedures to contextual purpose at the attributing level, relied on affective judgment rather than logical diagnosis at the checking level, and substituted formula retrieval for original model construction at the formulating level. These patterns suggest that intuitive thinking persists beyond initial responses, extending through strategy selection, verification, and solution formulation. To address this, teachers are encouraged to implement prompted-justification tasks, cognitive-conflict problems, and structured verification routines. Findings are specific to the participants and context studied.