Making workplace mathematics visible: an analytical framework of vocational mathematical affordances in welding and fabrication in Ghana

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Introduction Workplace mathematics is often embedded in occupational processes, tools, materials, and artifacts rather than expressed through formal mathematical procedures, creating challenges for identifying and representing mathematics in Technical and Vocational Education and Training (TVET). This study examined mathematical affordances identifiable in welding and fabrication practices in Ghana and organized them into an analytical framework of vocational mathematical affordances. Methods An interpretive and exploratory qualitative design was employed. Sixty-one welding and fabrication activities were purposively documented across 11 commercial workshops using photographic records, structured observations, and descriptive activity records. Qualitative content analysis involved identifying mathematical affordances, open coding, category development, and framework construction. Four researchers independently coded the activities following calibration, yielding Krippendorff's α = 0.87. Results The analysis identified five interconnected domains: measurement and quantification, geometric reasoning, spatial reasoning and visualization, design and pattern formation, and structural and applied mathematics. Measurement and geometric reasoning were coded across the widest range of activities, whereas the other domains were coded within more specific subsets of the purposively selected corpus. Discussion The resulting Analytical Framework of Vocational Mathematical Affordances represents researcher-identified mathematical relationships in documented workplace processes and artifacts rather than demonstrated individual worker competence. The framework provides a workplacegrounded basis for further research on how vocational mathematical affordances might be recontextualized within TVET curriculum, teaching, and assessment.

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