Geometric distance and semantic structure: A methodological innovation for mixed methods research with HUDAP and ATLAS.ti

This article presents a rigorous and replicable methodological alternative for articulating quantitative and qualitative analyses within mixed-methods research, contributing to interpretive coherence by relating quantitative proximity structures to inductively derived qualitative codes. The proposed approach integrates minimum-distance and mean-value analysis (employing WSSA1 and POSAC via HUDAP software) with qualitative content analysis in ATLAS.ti to construct cohesive interpretive categories. It enables the alignment and meaningful links of Euclidean clusters of quantitative variables with inductively derived qualitative codes, enhancing the interpretive coherence of complex datasets. Through a case study in Technology and Informatics teacher education, the article demonstrates how a didactic unit based on scientific instrument construction fosters professional competencies in pre-service educators. Grounded in abductive reasoning, this integrated strategy offers a methodological contribution to mixed-methods research by bridging geometric and semantic analyses within a transferable educational framework. • Provides a systematic, replicable model linking Euclidean clusters (HUDAP: WSSA1/POSAC) with inductively coded qualitative categories (ATLAS.ti). • Contributes to interpretive depth and internal validity through methodological triangulation. • Offers a transferable application for STEM teacher education by fostering competencies through hands-on instrument design.