Students' Learning Obstacles on Sequences and Series Viewed by Pirie Kieren's Theory

Abstract

Mathematical understanding develops through eight layers, as described by Pirie and Kieren: primitive knowing, image making, image having, property noticing, formalizing, observing, structuring, and inventizing. However, evidence indicates that many students encounter obstacles that hinder their progression through these layers. This study aims to identify and describe the learning obstacles students face in understanding sequences and series, utilizing Pirie and Kieren's theoretical framework. A descriptive qualitative research design was employed, purposive sampling to select participants from 30 Year 11 students in Malang, Indonesia. Data were gathered through tests and interviews and analyzed based on indicators of learning obstacles and the corresponding layers of mathematical understanding outlined by Pirie and Kieren. The findings reveal that many students experience significant difficulties in noticing and formalizing layers within the property. These challenges are attributed to inadequate foundational knowledge (ontogenic conceptual obstacles) and a lack of structured opportunities for developing deeper mathematical understanding (ontogenic instrumental, didactical, and epistemological obstacles). The results underscore the need for further research to address these learning barriers by focusing on enhancing students' foundational knowledge and designing educational experiences that foster the growth of mathematical understanding.