Analysis of algebraic errors university students make in solving geometry problems using Newman error analysis

Geometry word problems require students to integrate geometric concepts, algebraic reasoning, and procedural knowledge, yet many university students experience difficulties when solving such problems. This study examined the challenges students encounter, their perceptions of geometry word problems, and whether students’ performance differed significantly by gender. The study employed an explanatory sequential design. The quantitative phase involved 80 Level 100 Mathematics Education students, comprising 40 males and 40 females, selected through stratified random sampling from a target population of 240 students. Five students were purposively selected from the quantitative sample for the qualitative phase. Data were collected using a researcher-developed Geometry Word Problem Test consisting of three open-ended problems, with responses analysed across the five NEA stages: reading, comprehension, transformation, process skills, and encoding. Quantitative data were analysed using descriptive statistics while interview data were analysed thematically. The findings showed that process skill errors were the most frequent, followed by transformation errors, comprehension errors, encoding errors, and reading errors. These results indicate that students experienced greater difficulties with translating problem information into mathematical representations and executing appropriate mathematical procedures than with reading the problems. Qualitative findings revealed difficulties in understanding problem statements, translating verbal information into mathematical representations, performing algebraic manipulations, and constructing appropriate diagrams. The study concludes that instruction should place greater emphasis on strengthening students’ algebraic reasoning and comprehension through guided and integrated approaches to geometry problem solving.