Patterns of geometric problem-solving errors among pre-tertiary students across levels of geometric reasoning

Abstract

This study examined pre-tertiary students’ geometric problem-solving performance, the distribution of their errors across Van Hiele levels of geometric reasoning, and the nature of these errors using Newman's Error Hierarchical Model. A descriptive quantitative research design, complemented by qualitative content analysis of students’ written responses, was adopted. The sample comprised 300 final-year students selected through stratified random sampling. Data were collected using a researcher-designed Geometry Problem-Solving Test consisting of twelve open-ended items aligned with the senior high school geometry curriculum. Students’ responses were analysed using frequency and percentage distributions, while error patterns were classified using Newman's framework and mapped onto Van Hiele levels. The findings showed generally low performance in geometry problem solving, with most students scoring within the lower performance range. Error analysis indicated that students at lower Van Hiele levels, particularly visualisation and analysis, exhibited higher frequencies of comprehension and transformation errors. In contrast, students at higher reasoning levels showed fewer conceptual and representational difficulties but continued to experience process skills and encoding errors. The findings indicate different patterns of problem-solving errors observed among students demonstrating different levels of geometric reasoning. The results demonstrate the value of interpreting students’ geometric problem-solving through both the Van Hiele and Newman frameworks, providing complementary perspectives on students’ reasoning and the errors evident in their solution processes.