Spatial-Algebraic Cognitive Barriers in Solving Ellipse and Hyperbola Problems: An Analysis Using Polya’s Heuristics and Cognitive Load Theory

David Pratama; Aditya Prihandhika; Rafiq Zulkarnaen; Novia Nurlatifah; Putri Hoeriyah; Seli Mauludani

doi:10.58421/misro.v5i3.2027

DOI:

https://doi.org/10.58421/misro.v5i3.2027

Authors

David Pratama Universitas Singaperbangsa Karawang
Aditya Prihandhika Universitas Singaperbangsa Karawang https://orcid.org/0000-0002-6355-4006
Rafiq Zulkarnaen Universitas Singaperbangsa Karawang
Novia Nurlatifah Universitas Singaperbangsa Karawang
Putri Hoeriyah Universitas Singaperbangsa Karawang
Seli Mauludani Universitas Singaperbangsa Karawang

Keywords:

Cognitive barriers, Polya’s heuristics, Cognitive load theory, Problem-solving, Spatial algebraic representation

Abstract

Ellipse and hyperbola problems require students to coordinate geometric, spatial, and algebraic representations, which may generate cognitive barriers. This qualitative preliminary study aims to characterise students’ cognitive barriers when solving conic section tasks by integrating Polya’s heuristics with Cognitive Load Theory (CLT) as an analytical lens, without directly measuring empirical cognitive load states. Participants included 25 undergraduate students across two groups (4A and 4B). Data were collected from students’ written metacognitive reflections following a final examination alongside their problem-solving artefacts. Data were analysed using integrative coding across Polya’s four stages and qualitatively interpreted through intrinsic, extraneous, and germane cognitive load dimensions. Among the recurring patterns identified in hyperbola tasks, students frequently struggled to coordinate the centre, vertex, and focus to determine curve orientation and key parameters and . In ellipse tasks, barriers were commonly observed during general-to-standard equation transformations, specifically in grouping terms and completing the square. Procedural complexity, time constraints, and schema retrieval difficulties further interrupted problem-solving trajectories. These findings suggest that conic-section problem-solving difficulties reflect complex interactions between spatial-algebraic coordination and cognitive demands. Consequently, this study conceptualises the spatial-algebraic cognitive barrier as a preliminary analytical concept rather than an established psychological construct, offering pedagogical insights for analytic geometry instruction.

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