Teacher profiles in rural contexts: Multivariate characterization of algebra teaching and its configuration in differentiated praxeologies

Abstract

The development of algebraic thinking from an early age is a priority in contemporary mathematics education, especially in rural contexts due to their structural and sociocultural conditions. Grounded in the Anthropological Theory of Didactics and hermeneutic phenomenology, this study aims to identify and characterize teacher profiles based on their algebra teaching practices and their perceptions of different types of mathematical thinking. A descriptive-exploratory multiple case study was conducted with empirical data from 16 teachers at a rural institution in western Colombia, analyzed using multivariate statistical techniques (cluster analysis, multiple correspondence analysis, and principal components analysis). Two teacher profiles were identified: one focused on digital technologies and problem-solving, and another that prioritizes traditional strategies. The findings underscore the importance of considering institutional and territorial conditions when designing contextualized pedagogical proposals that foster algebraic thinking in rural areas. Findings are transferable to similar contexts but not statistically generalizable to the broader teaching population.