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.
| Published in | Advances in Sciences and Humanities (Volume 11, Issue 3) |
| DOI | 10.11648/j.ash.20251103.11 |
| Page(s) | 52-68 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2025. Published by Science Publishing Group |
Cognitive Load Theory, Sequential Processing, Educational Theory, Mathematical Notation, PEMDAS
| [1] | Anderson, J. R., & Lebiere, C. (2003). The newell test for a theory of cognition. Behavioral and Brain Sciences, 26(5), 587-600. |
| [2] | Baddeley, A. (2012). Working memory: Theories, models, and controversies. Annual Review of Psychology, 63(1), 1-29. |
| [3] | Chen, L., & Martinez, R. (2023). Cognitive load in mathematical notation: A cross-cultural analysis. Journal of Educational Psychology, 45(3), 234-251. |
| [4] | Clark, R., Nguyen, F., Sweller, J., & Baddeley, M. (2006). Efficiency in learning: Evidence-based guidelines to manage cognitive load. Performance Improvement, 45(9), 46-47. |
| [5] | Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20(3-6), 487-506. |
| [6] | Geary, D. C. (2013). Early foundations for mathematics learning and their relations to learning disabilities. Current Directions in Psychological Science, 22(1), 23-27. |
| [7] | Ifrah, G. (2000). The universal history of numbers: From prehistory to the invention of the computer (First ed.). John Wiley & Sons. |
| [8] | Kalyuga, S. (2011). Cognitive load theory: How many types of load does it really need? Educational Psychology Review, 23(1), 1-19. |
| [9] | Kumar, S., Thompson, J., & Lee, M. (2024). Sequential processing in elementary mathematics: Preliminary findings. Educational Research Quarterly, 28(2), 112-128. |
| [10] | LeFevre, J., Fast, L., Skwarchuk, S., Smith‐Chant, B. L., Bisanz, J., Kamawar, D., & Penner‐Wilger, M. (2010). Pathways to mathematics: Longitudinal predictors of performance. Child Development, 81(6), 1753-1767. |
| [11] | Paas, F., & Sweller, J. (2011). An evolutionary upgrade of cognitive load theory: Using the human motor system and collaboration to support the learning of complex cognitive tasks. Educational Psychology Review, 24(1), 27-45. |
| [12] | Rodriguez, A., & Kim, H. (2024). Rethinking mathematical conventions: A pedagogical perspective. International Journal of Mathematical Education, 39(4), 445-462. |
| [13] | Sweller, J., van Merriënboer, J. G., & Paas, F. (2019). Cognitive architecture and instructional design: 20 years later. Educational Psychology Review, 31(2), 261-292. |
| [14] | Van de Walle, J., Karp, K., & Bay-Williams, J. (2022). Elementary and middle school mathematics: Teaching developmentally (11th ed.). Pearson. |
| [15] | Zhang, X., Koponen, T., Räsänen, P., Aunola, K., Lerkkanen, M., & Nurmi, J. (2013). Linguistic and spatial skills predict early arithmetic development via counting sequence knowledge. Child Development, 85(3), 1091-1107. |
APA Style
Ouanhlee, T. (2025). Beyond PEMDAS: A Cognitive Theory of Sequential Mathematical Processing. Advances in Sciences and Humanities, 11(3), 52-68. https://doi.org/10.11648/j.ash.20251103.11
ACS Style
Ouanhlee, T. Beyond PEMDAS: A Cognitive Theory of Sequential Mathematical Processing. Adv. Sci. Humanit. 2025, 11(3), 52-68. doi: 10.11648/j.ash.20251103.11
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Download@article{10.11648/j.ash.20251103.11,
author = {Thanakit Ouanhlee},
title = {Beyond PEMDAS: A Cognitive Theory of Sequential Mathematical Processing
},
journal = {Advances in Sciences and Humanities},
volume = {11},
number = {3},
pages = {52-68},
doi = {10.11648/j.ash.20251103.11},
url = {https://doi.org/10.11648/j.ash.20251103.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ash.20251103.11},
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.},
year = {2025}
}
TY - JOUR T1 - Beyond PEMDAS: A Cognitive Theory of Sequential Mathematical Processing AU - Thanakit Ouanhlee Y1 - 2025/07/23 PY - 2025 N1 - https://doi.org/10.11648/j.ash.20251103.11 DO - 10.11648/j.ash.20251103.11 T2 - Advances in Sciences and Humanities JF - Advances in Sciences and Humanities JO - Advances in Sciences and Humanities SP - 52 EP - 68 PB - Science Publishing Group SN - 2472-0984 UR - https://doi.org/10.11648/j.ash.20251103.11 AB - 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. VL - 11 IS - 3 ER -
Doctoral Research Department, California Intercontinental University, Irvine, U.S.A. Analysis Management Department, Thipsamai Institute, Bangkok, Thailand
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