Foundational Mathematical Errors that Affect Learning of Mathematics and Related Subjects in Higher Institutions

Abstract: Mathematics forms the foundation for logical reasoning, scientific inquiry, and technological advancement in higher education. However, many students entering higher institutions struggle with persistent foundational errors that significantly hinder their academic progress. This study examines the nature, prevalence, and impact of foundational mathematical errors that affect learning of mathematics and related subjects in higher institutions. Using a descriptive survey design, data were collected from 68 respondents through structured items covering number work, logical reasoning, contextual problem-solving, and creative sketching. The findings revealed strong performance in routine procedural tasks such as number notation (88% correct), but notable weaknesses in conceptual understanding, critical thinking, and application of knowledge to real-life contexts. For instance, only 50% correctly defined a composite number, while responses to contextual problems (e.g., boiling eggs and birds on a tree) showed over-reliance on assumptions and limited analytical reasoning. Additionally, 80% of respondents produced elementary-level sketches in a creativity task, indicating low development of spatial and design thinking skills. The findings suggest the need for pedagogical reforms that emphasize higher-order thinking, contextual learning, and learner-centered instructional strategies. The findings reveal that while many students demonstrate procedural competence in routine tasks, they exhibit deep-rooted misconceptions in fundamental areas such as number sense, operations, proportional reasoning, algebraic structure, and interpretation of mathematical language. Overall, the study highlights a dominance of algorithmic and examination-oriented learning approaches at the expense of deep conceptual understanding, interdisciplinary reasoning, and creativity. Keywords: foundational errors, mathematical errors, conceptual skills, procedural competence. Title: Foundational Mathematical Errors that Affect Learning of Mathematics and Related Subjects in Higher Institutions Author: Dr. Gabriel S. Akakpo, Raymond Cudjoe International Journal of Mathematics and Physical Sciences Research ISSN 2348-5736 (Online) Vol. 13, Issue 2, October 2025 - March 2026 Page No: 74-86 Research Publish Journals Website: www.researchpublish.com Published Date: 26-March-2026 DOI: https://doi.org/10.5281/zenodo.19233396 Paper Download Link (Source) https://www.researchpublish.com/papers/foundational-mathematical-errors-that-affect-learning-of-mathematics-and-related-subjects-in-higher-institutions