Cognitive Dimensions of Mathematical Problem-Solving-A Theoretical Study of Completeness, Pattern Recognition, Mental Processing, and Observational Insight

Authors:

Geetha T, Dr. N. Johnson

Pages: 27-29

Abstract:

Problem-solving ability is central to mathematical learning and cognitive development. Contemporary research highlights heuristics, metacognition, and working memory as key contributors to effective problem solving; however, ancient mathematical frameworks offer parallel cognitive insights that remain underexplored. This theoretical study examines four cognitive abilities derived from Vedic Mathematics—Nikhilam (Completeness Ability), Anurupya (Pattern Recognition Ability), Samskara (Mental Processing Ability), and Vilokanam (Observation Ability)—as foundational components of mathematical problem solving. Rather than interpreting these sutras as computational techniques, the paper conceptualizes them as problem-solving abilities that support holistic understanding, strategic reasoning, mental efficiency, and insight formation. A conceptual model is proposed linking these abilities with modern cognitive theories of problem solving. The study suggests that integrating these abilities into mathematics instruction may enhance learners’ adaptability, reasoning depth, and transfer of knowledge. The paper contributes a novel theoretical perspective suitable for future empirical validation.