Where functions go wrong: Analyzing students’ misconceptions and errors through Newman’s lens

Abstract

Functions are a fundamental concept in mathematics, yet many students struggle with their operations and applications. This qualitative descriptive study investigated the types of mathematical errors committed by Grade 11 students from two senior high schools in Davao del Norte, Philippines, focusing on performing operations on functions and solving related problems. Ten purposively selected students identified as struggling in mathematics took a 10-item validated test, followed by interviews. Data were analyzed using Newman’s Error Analysis, covering reading, comprehension, transformation, process skills, and encoding errors. Results showed persistent errors across all categories, with common difficulties in interpreting mathematical symbols, composing and operating functions, translating problems into equations, applying correct procedures, and accurately presenting final answers. Contributing factors included limited conceptual understanding, inadequate problem-solving practice, insufficient prior knowledge, and incomplete curriculum coverage. The study highlights the need for targeted instructional interventions to develop both conceptual and procedural fluency in functions, offering implications for teachers, curriculum designers, and policymakers aiming to improve mathematics learning outcomes.

Keywords: Conceptual understanding; functions; mathematics education; procedural fluency; student errors.