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This paper proposes embedding axiology (the study of values) as a foundational philosophical orientation alongside ontology, epistemology, and methodology. Through theoretical analysis and interpretive examination of contrasting research exemplars, we demonstrate how value commitments fundamentally shape scholarly inquiry across all dimensions of research practice whilst revealing dynamic, recursive relationships amongst values and other philosophical orientations. The research establishes the Axiological Reflexivity Framework (ARF) as a structured approach for examining how value commitments shape inquiry across five interconnected dimensions: axiological positioning, ontological engagement, epistemological reflection, methodological alignment, and interpretative consequences. By making value commitments explicit rather than implicit, this framework supports coherent alignment between researchers’ fundamental orientations and their scholarly practices whilst strengthening connections between research and social responsibility. Our findings suggest that axiologically conscious research practices enhance both methodological rigour and educational relevance by fostering critical reflexivity and facilitating constructive engagement across diverse theoretical positions within mathematics education.