Linking Creativity Levels to Problem-Solving Strategies in Number Pattern Tasks

Abstract

Mathematical creativity plays a pivotal role in preparing students for twenty-first-century challenges; however, systematic studies linking creativity levels with problem-solving strategies in the context of number patterns remain limited. This study addressed that gap by investigating relationships between students’ creativity levels and the strategies they used to solve number-pattern generalization tasks. We employed a qualitative case-study approach with 126 junior high school students who solved number-pattern problems. In addition to written work, 21 students representing three creativity levels were interviewed using stimulated recall. Data were analyzed via open, axial, and selective coding, yielding three overarching themes: (1) visual–numeric strategies dominated among students with low creativity, marked by procedural fluency without representational shifting or formal verification; (2) multi-representation integration among students with medium and high creativity, characterized by flexible movement among visual, tabular, and algebraic representations and explicit verification; and (3) deep elaboration as the hallmark of high creativity, including pattern restructuring, generation of multiple valid models, and connections to prior experiences. The findings revealed a developmental trajectory from single procedural strategies toward original, concept-rich approaches. The implication of this study includes the urgency for instructional designs that explicitly cultivate representational flexibility and originality through tasks that require multi-representation translation and cross-context application to support higher-order creative thinking in pattern generalization.