Research Article
Beyond PEMDAS: A Cognitive Theory of Sequential Mathematical Processing
Thanakit Ouanhlee*
Issue:
Volume 11, Issue 3, September 2025
Pages:
52-68
Received:
19 June 2025
Accepted:
2 July 2025
Published:
23 July 2025
DOI:
10.11648/j.ash.20251103.11
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Abstract: Background: Contemporary mathematical pedagogy relies fundamentally on hierarchical operation sequences codified through mnemonic devices such as PEMDAS and BODMAS, yet these conventions emerged through historical contingency rather than cognitive optimization or mathematical necessity. Current operational precedence hierarchies may systematically conflict with natural cognitive processing patterns, creating unnecessary cognitive burdens for developing learners while offering limited compensatory advantages in foundational arithmetic contexts. Objective: This investigation aims to develop a comprehensive theoretical framework proposing sequential left-to-right processing as a cognitively superior alternative for elementary mathematics education, integrating insights from cognitive psychology, educational theory, and historical analysis. Method: This theoretical investigation employs systematic literature synthesis and framework development, integrating established research across cognitive science, educational psychology, and mathematical pedagogy to construct a unified theoretical model. The approach follows established protocols for developing a theoretical framework in educational research, emphasizing systematic integration, logical consistency, and predictive capacity to guide future empirical investigations. Result: The sequential processing theoretical framework demonstrates that current conventions prioritize notational efficiency over cognitive accessibility, creating a fundamental misalignment between mathematical systems and human learning processes. The framework reveals four core theoretical advantages: the elimination of arbitrary precedence rules reduces cognitive load, alignment with natural reading patterns creates processing fluency, consistent procedural patterns facilitate the development of automaticity, and explicit notation supports mathematical communication and error detection. Sequential systems eliminate implicit hierarchies in favor of explicit structural notation, making all computational decisions transparent through notational structure rather than requiring the recall of arbitrary precedence rules. Conclusion: The sequential processing framework offers transformative potential for reconceptualizing mathematical notation systems to better serve human cognitive architecture and learning processes across diverse educational contexts. This theoretical contribution provides a systematic foundation for future empirical validation and educational innovation, suggesting that mathematical education could evolve toward approaches that optimize human potential while maintaining mathematical precision and effective communication.
Abstract: Background: Contemporary mathematical pedagogy relies fundamentally on hierarchical operation sequences codified through mnemonic devices such as PEMDAS and BODMAS, yet these conventions emerged through historical contingency rather than cognitive optimization or mathematical necessity. Current operational precedence hierarchies may systematically ...
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