Students' Divergent Thinking Ability in Terms of Field Dependent and Field Independent Cognitive Styles in Solving Open-Ended Problems on Arithmetic Sequences and Series

This study analyzes students' divergent thinking skills in solving open-ended problems on arithmetic sequences and series in terms of field dependent and field independent cognitive styles at SMA Negeri 1 Sinunukan. The background of this research is the need to develop higher-order thinking skills in the era of globalization, contrasted with the reality that mathematics learning in schools remains procedural and outcome-oriented. The objectives of this study are: 1) To describe the divergent thinking skills of field dependent students in solving open-ended problems on arithmetic sequences and series, and 2) To describe the divergent thinking skills of field independent students in solving open-ended problems on arithmetic sequences and series. This research employs a descriptive qualitative approach. Subjects were selected using purposive sampling technique, consisting of 4 students from a total of 32 tenth-grade students in the odd semester of the 2025/2026 academic year, comprising 2 field dependent students and 2 field independent students. The research instruments included the GEFT (Group Embedded Figure Test), divergent thinking test, interview guidelines, and documentation. Data analysis used the Miles, Huberman, and Saldana model with stages of data collection, data condensation, data display, and conclusion drawing. The results showed that students with field dependent cognitive style only fulfilled the fluency aspect, but have not yet fulfilled the flexibility and originality aspects. Field dependent students were able to generate solution ideas appropriate to the problem fluently, but only used one solution idea and were not yet able to produce unique ideas. Meanwhile, students with field independent cognitive style fulfilled all three aspects of divergent thinking: fluency, flexibility, and originality. Field independent students were able to generate various arithmetic sequences, use different solution perspectives, and discover unique ideas different from other students. The implication of this research is the need for learning strategies that consider students' cognitive style differences to optimize divergent thinking skills.