Students' Mathematical Understanding According to Kilpatrick and Findell: The Number Pattern Generalisation Process of Junior Secondary School Students

Abstract

Purpose – This study investigates how junior secondary school students generalise number patterns through Kilpatrick and Findell’s framework of mathematical understanding, focusing on the interaction among conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. Methodology – A qualitative descriptive design was conducted with 30 Year 8 students at an Islamic junior secondary school in Ambon, Indonesia. Screening tests, informal interviews, and repeated testing were used to identify students who consistently demonstrated indicators of mathematical understanding. Two students, coded WNF and FF, were selected for in-depth analysis. NVivo 12 Plus supported the mapping and visualisation of their reasoning processes, while data were analysed using the Miles and Huberman model of data collection, reduction, display, and conclusion drawing. Findings – Both students progressed from recursive reasoning based on differences between consecutive terms to correspondence-based symbolic generalisation. They expressed the nth term using arithmetic and quadratic forms. This transition reflected interconnected development in conceptual understanding, procedural fluency, strategic competence, and adaptive reasoning. Novelty – The study reveals how mathematical understanding operates within the transition from recursive to explicit generalisation, rather than treating pattern generalisation solely as a procedural outcome. Significance – The findings contribute to international research on early algebra by identifying a transferable reasoning trajectory from recursive pattern recognition to symbolic generalisation. This trajectory provides a basis for designing mathematics instruction that supports algebraic reasoning across diverse junior secondary educational contexts.