Analysis of Students' Errors in Solving Recurrence Relation Word Problems Based on Newman's Procedure

Although Newman’s Error Analysis (NEA) has been widely applied to mathematical word problems, contextual recurrence relation problems in undergraduate Discrete Mathematics remain underexamined. This study analysed the types, frequencies, and characteristics of students’ errors in solving a recurrence relation word problem using Newman’s procedure. A qualitative descriptive approach with a document analysis design was employed, examining examination scripts from all 32 students enrolled in a Discrete Mathematics course through total sampling. Written responses to a single contextual savings problem were analysed using NEA-based coding, frequency tabulation, and qualitative description. Only one student (3.1%) produced a complete and correct response, while 59.4% failed before constructing a valid model. The largest decline in successful progression occurred at the comprehension stage. The most frequent error indicators were failure to interpret the result in context (43.8%) and failure to construct a recurrence model (28.1%). The findings suggest that the principal difficulties in this task concerned translating verbal information into mathematical models and interpreting mathematical results within the original context. The study contributes a task-specific account of modelling errors to NEA research in higher education. Instructional implications include explicitly linking temporal expressions to mathematical indices, incorporating contextual validation into assessment rubrics, and designing realistic contextual problems. Further research should triangulate written-response analysis with interviews to clarify the reasoning underlying the observed errors.