Exploring the creative pathways: How a second-grader navigates multiplication and division without formal instruction

Purpose: This study addresses the gap in understanding how young learners develop self-invented strategies for multiplication and division without formal instruction. The purpose is to investigate the methods a second-grade student employs to solve problems, focusing on her reasoning processes and challenges. Method: A case study design was utilized, involving a second-grade student with no prior formal instruction in multiplication or division. Data collection included a series of problem-solving sessions, where the student tackled tasks using her strategies. Observational notes, student drawings, and verbal explanations were analyzed qualitatively to identify patterns and challenges in her approach. Findings: The student demonstrated a range of self-invented strategies, including repeated addition, visual representations, and intuitive reasoning. She showed progression from concrete methods to more abstract thinking, effectively addressing many problems. However, challenges such as confusion with the commutative property and difficulties with complex division tasks were noted. Despite limited formal exposure, her ability to articulate and apply mathematical concepts underscored the significance of prior informal learning experiences. Conclusion: The findings highlight the importance of recognizing and supporting self-constructed strategies in early mathematics education. By leveraging students’ intuitive methods and addressing conceptual gaps, educators can foster deeper mathematical understanding. Future research should examine how informal learning experiences contribute to early mathematical development and explore instructional approaches that integrate these self-invented strategies.