A Van Hiele-Newman model analysis of geometric reasoning and problem-solving errors among final-year students in a...

This study examined students' geometric reasoning, geometric problem-solving errors, and the association between demonstrated Van Hiele reasoning levels and Newman error categories. A quantitative approach employing a cross-sectional descriptive-correlational design was adopted. The study involved 300 final-year students from a selected senior high school, who were selected through proportionate stratified random sampling. Data were collected using an adapted 20-item Geometry Test developed by Usiskin (1982) and a 12-item researcher-designed Geometry Problem-Solving Test aligned with the Ghanaian core mathematics curriculum. Descriptive statistics and category-specific binary logistic Generalized Estimating Equations (GEE) models were used for data analysis. Most students demonstrated lower levels of geometric reasoning, with Level 0 (visualization) and Level 1 (analysis) accounting for the largest proportions, while relatively few demonstrated Levels 2 (informal deduction) and 3 (deduction). Transformation errors were the most frequent, followed by comprehension errors, whereas reading errors were least frequent among the erroneous responses. The GEE analysis showed significant associations between demonstrated Van Hiele reasoning levels and comprehension, transformation, processing skill, and encoding errors, but not reading errors. The findings indicate that error patterns varied across demonstrated reasoning levels, highlighting the value of examining geometric problem-solving errors in relation to both the level of reasoning explicitly demonstrated and the stage at which difficulty was manifested. The study contributes an initial empirical examination of the proposed GRaPSE framework, which integrates these two dimensions for analyzing geometric problem-solving responses.