Proposal for a Didactic E-book on Optimization Integrating Technologies, Problem Solving and Operations Research

This work presents the proposal, under development, of creating a didactic e-book for High School with a focus on teaching optimization, aligned with the competencies and skills of the National Common Curricular Base (BNCC). The goal is to offer teachers a practical resource and students a solid and contextualized introduction to mathematical optimization. The material will include content such as optimization without derivatives (by geometric methods and classical designs), linear programming, evolutionary algorithms and a proposal for deepening in continuous optimization aimed at students with greater interest, such as Scientific Initiation participants. In addition, active methodologies will be valued, such as mathematical modeling and the use of digital technologies, especially GeoGebra and Python, to foster computational thinking and real problem solving. The research will be organized into three main axes: survey of dissertations from PROFMAT (Professional Master's Degree in Mathematics in National Network) on optimization; analysis of BNCC competencies related to problem solving, modeling, and use of technologies; and investigation of how the theme is addressed in high school textbooks. From this foundation, the e-book will be prepared, with contextualized activities, projects ready for application in the classroom and use of digital tools, providing complete material for the teacher