Didactic-Mathematical Knowledge and Instructional Design in Blended Mathematics Teaching Under Conditions of Unequal Digital Access: A Multiple Case Study in Central America

Abstract

This study examined how secondary school classrooms, within a higher education training context mathematics teachers participating in the Diploma in Mathematics Education Applied to Secondary Education (EMAS), conceived as a blended professional development environment, mobilized didactic-mathematical knowledge and competencies when designing, implementing, assessing, and redesigning instruction under unequal conditions of digital access and participation. Grounded in the Didactic-Mathematical Knowledge and Competencies model and the criteria of didactic suitability and complemented by the TPACK-XK framework and the Theory of Instrumental Genesis, the study adopted a qualitative, interpretive multiple-case design. Three teachers, identified as A, B, and G, were analyzed through their didactic sequences, classroom implementation videos and transcripts, classroom evidence, teacher reflections, and redesign proposals. Findings revealed a shared professional basis across the three cases, but also important differences in the enactment of blended instruction. Case A showed more restricted blended enactment and limited integration of the virtual component; Case B displayed a more balanced profile, with digital resources serving as bridging elements between virtual and face-to-face work; and Case G presented the strongest evidence of blended enactment, with digital tools fully integrated into participation, feedback, and instructional adjustment. The results suggest that differences in digital access and participation shape not only the visibility of blended learning practices, but also the ways teachers sustain instructional continuity across modalities. The study highlights the importance of designing blended teacher education environments that support coherent pedagogical pathways under unequal participation conditions.