Constructing Advanced Mathematical Thinking on Function Limits through Cognitive Styles and APOS-Based Scaffolding: A Qualitative Case Study
DOI:
https://doi.org/10.33394/j-ps.v14i2.19936Keywords:
Cognitive style, APOS theory, Scaffolding, Advanced mathematical thinking, Function limitsAbstract
This study examines patterns of advanced mathematical thinking (AMT) in learning function limits through students’ cognitive styles and APOS-based scaffolding. Although previous studies have investigated APOS theory and cognitive styles separately, limited research has explored how both interact in the development of AMT within calculus learning, particularly in the concept of function limits. Adopting a qualitative case study design, data were generated through semi-structured interviews, classroom observations, and document analysis involving 24 mathematics education students at Universitas Islam An Nur Lampung. In this study, cognitive style refers to field-dependent and field-independent learning tendencies, while AMT is represented through indicators of reasoning, abstraction, representation, proof, and problem posing. The analysis employed thematic coding to identify patterns emerging from students’ learning experiences during APOS-based scaffolding activities. The findings reveal three interrelated themes. First, students with field-independent cognitive styles demonstrated more flexible and self-directed reasoning when solving limit problems, whereas field-dependent students relied more on guided explanations, visual representations, and collaborative support. Second, the APOS-based scaffolding sequence of action, process, object, and schema illustrated students’ gradual movement from procedural manipulation toward conceptual interpretation of limits. Third, collaborative scaffolding activities created opportunities for peer explanation and collective meaning-making that supported mathematical generalization. Across the AMT indicators, reasoning obtained the highest average score (3.6), while proof showed the lowest average score (2.9), indicating that students experienced greater difficulty in constructing formal mathematical justification. These findings indicate patterns showing that students’ advanced mathematical thinking emerged through the interaction between individual cognitive tendencies and instructional scaffolding rather than through isolated instructional techniques alone. The study highlights the importance of aligning scaffolding practices with learners’ cognitive characteristics in calculus instruction and contributes qualitative insights into the development of AMT in higher mathematics learning.
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