Obstáculos epistemológicos y representaciones semióticas en pre-saberes de trigonometría: un enfoque de superación desde el Modelo BARRISO: Epistemological obstacles and semiotic representations in trigonometry prior knowledge: an approach to overcoming difficulties through the BARRISO model - Barrios Soto, Luis; Arrieta, Xiomara; Maradey Coronell, Juan (Quórum Académico, 2025)
In teaching mathematics, and particularly trigonometry, it is essential to build on students’ prior knowledge, as this allows learning to be guided and avoids the simple repetition of knowledge already acquired. However, practice often privileges the mechanical execution of exercises focused on the routine application of algorithms over problem solving, which requires comprehension, analysis, and decision-making. This tendency hinders the identification of conceptual errors, as well as the challenges that arise when moving across different forms of mathematical representation, such as numerical, algebraic, graphical, or verbal. The present study aims to analyze students’ prior knowledge in trigonometry, identifying the epistemological obstacles that interfere with their understanding and evaluating the influence of semiotic representations on learning. The research is grounded in the theoretical contributions of Bachelard (1996) and Duval (1993), in articulation with the BARRISO model proposed by Barrios and Delgado (2025). Methodologically, a qualitative approach is adopted with a phenomenological and interpretive-descriptive design, focused on the analysis of graphic representations produced by 30 secondary school students while solving trigonometry problems. The results reveal persistent difficulties in graphical construction, evidenced by errors in assigning values, locating angles, and representing figures consistent with the problem statement. It is concluded that these difficulties stem from the presence of epistemological obstacles and limitations in semiotic conversion processes, which reveals the need for new teaching approaches or pedagogical strategies, such as the BARRISO model, to overcome these barriers and promote a more rigorous and meaningful mathematical understanding.