Conceptual disruptions in the interpretations of linear function and affine function by graduates of an undergraduate program in mathematics in the Colombian Caribbean/ Disrupciones conceptuales en las interpretaciones de funcion lineal y funcion afin por parte de egresados de un programa de licenciatura en matematicas del Caribe Colombiano/ Interrupcoes conceituais nas interpretacoes de funcao linear e funcao afim por graduados de um programa de licenciatura em matematica no Caribe colombiano

To analyze the interpretation and conceptualization of linear and related functions by graduates of the Bachelor's degree program in Mathematics. The study highlights the need for graduates to integrate technology effectively into teaching practices, emphasizing the importance of pedagogical knowledge and the use of appropriate tools to enhance the learning experience of students. The research is based on the field of mathematics education and the theory of semiotic representations, focusing on the mental representations evoked when contemplating mathematical concepts. The study methodologically implemented a qualitative approach to facilitate reflection from both a subjective and objective perspective. The selected technique is data triangulation, which is used to analyze the information collected, examining categories such as the conceptualization of linear and related functions and the theory of semiotic representations. The findings indicate that graduates have difficulties in moving from natural language to algebraic representation, which causes deficiencies in data handling and affects cognitive activities related to mathematical formation and processing. The research emphasizes the importance of improving conceptual understanding in mathematics education, particularly in areas such as linear and related functions, to improve students' ability to interpret and work with mathematical concepts effectively.