Tracing Conceptual Errors in Grade 11 Students’ Reasoning About Sequences and Series

Abstract

Purpose – This study investigates conceptual errors in Grade 11 students’ solutions to sequences-and-series problems and examines the reasoning underlying these errors by distinguishing conceptual, procedural, and operational breakdowns. Methodology – A qualitative descriptive design involved 33 Grade 11 students from a public senior high school in Pekanbaru, Indonesia. Students completed a written diagnostic test, followed by semi-structured interviews with selected participants whose responses represented recurrent or analytically significant errors. Written solutions were examined step by step, while interview data were used to reconstruct students’ interpretations, formula choices, and reasoning. Error frequencies served as descriptive support for the qualitative analysis. Findings – Error patterns varied across test items. Procedural errors were most prominent in Item 1 (52%), operational errors in Item 2 (27%), while conceptual errors reached 45% in Item 3 and 76% in Item 5. Conceptual difficulties were particularly evident when students had to interpret contextual information, identify underlying mathematical structures, and select appropriate relationships or formulas. Similar incorrect answers were found to originate from different reasoning processes. Novelty – The study moves beyond classifying incorrect answers by tracing how errors emerge within students’ mathematical reasoning. Linking written solutions with interview explanations distinguishes conceptual misunderstanding from procedural breakdowns and computational inaccuracies. Significance – The findings provide a diagnostic basis for targeted instruction. They enable teachers to match remedial strategies to specific sources of difficulty rather than treating all incorrect responses as equivalent.