Conceptualizing Algebraic Thinking for Undergraduate Mathematics Majors: An Integrated Framework and Pedagogical Implications
DOI:
https://doi.org/10.63561/fnas-jmse.v7i3.1170Keywords:
Algebraic Thinking, Undergraduate Mathematics Education, Structural Reasoning, Representational Fluency, CommognitionAbstract
mathematics majors is under-theorized. This paper synthesizes contemporary conceptual frameworks in order to propose an integrated multidimensional framework for algebraic thinking among undergraduate mathematics majors. Thematic synthesis was used to examine an integrative review of 35 peer-reviewed sources (2015-2025). Four interconnected dimensions were identified: generalization and abstraction, structural reasoning, representational fluency, and proof based algebraic argumentation. These dimensions draw upon cultural-semiotic theory, APOS theory, commognitive theory and Realistic Mathematics Education. The synthesis highlights four corresponding pedagogical approaches; inquiry-based learning, integration of digital technologies, discourse-rich pedagogy, and contextual problem-solving. Six major challenges are also identified, such as the school-university transition and assessment misalignment. The findings support a multidimensional teaching approach which prepares students to engage in advanced mathematical practice. The suggested framework is theoretical and needs to be empirically proven.
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