Year: 2026 | Month: August | Volume: 13 | Issue: 8 | Pages: 417-421
DOI: https://doi.org/10.52403/ijrr.20260840
A Cognitive Method for Calculating Squares of Numbers
Amrinder Singh
Executive Officer, Central Public Sector Enterprise, ONGC, India.
ABSTRACT
Squaring of numbers is traditionally taught using standard long multiplication or algebraic expansion identities. While these methods are mathematically rigorous and universally accepted, they may appear cognitively demanding for some learners because they involve simultaneous management of multiplication, carrying operations, symbolic manipulation and larger numbers. This paper presents a method that attempts to reorganize squaring into smaller multiplications and sequential steps. The proposed method emerged empirically by observing square values across decadal intervals and subsequently attests algebraic confirmation. The paper outlines the method and provides algebraic justification for the same. It also shows that, while mathematically equivalent, the new approach emphasizes visual pattern recognition and may reduce cognitive load during calculation, suggesting potential value as a pedagogical supplement. The proposed approach makes the mental computation of squares of numbers easier, making it particularly suitable for students who respond more effectively to pattern-based reasoning than to formal symbolic computation or the memorization of large numerical values.
Keywords: Squaring Method, Cognitive mathematics, Pattern recognition, Pedagogical mathematics, Squares of numbers, Mental Calculation
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