HÁBITOS DE PENSAMIENTO MATEMÁTICO Y EL USO DE GEOGEBRA EN LA RESOLUCIÓN Y FORMULACIÓN DE PROBLEMAS DE OPTIMIZACIÓN - García Rodríguez, Dra. Martha Leticia (2025)
The objective of this work was to analyze the mathematical thinking habits that students develop when they work on solving and proposing optimization problems in a dynamic geometry environment. The resolution and formulation of mathematical problems is assumed as a route of thought in which the student shows habits, resources, strategies and a disposition to understand ideas and concepts. Currently, research on problem solving and formulation processes incorporates the use of digital technologies; therefore, it is interesting to know the mathematical activities derived from the use of these technologies. The process of problem solving and formulation carried out by six students enrolled in a calculus course in the first semester of a science degree program was analyzed, considering four phases: orientation, connection, generation and reflection. The data showed the mathematical thinking habits that emerged during problem solving and formulation. semester of a science degree program was analyzed, considering four phases: orientation, connection, generation and reflection. The data showed the mathematical thinking habits that emerged during problem solving and formulation. The principle of problematization contributed to the development of habits such as analyzing a problem from different approaches and formulating conjectures. The evidence collected through the construction protocols in GeoGebra made it possible to identify mathematical activities related to the use of technology, such as discovering relationships, testing and verifying conjectures, replacing extensive calculations with others performed with digital technologies, and confirming results obtained analytically.