Inconsistencies and errors in traditional approaches to energy in our introductory courses.

We present a critical analysis of the classical approaches to energy subjects, based on the work-energy theorem and the conservation of mechanical energy proposed in the courses of the first years of tertiary education. We show how these approaches present a series of inconsistencies and errors that are a source of conceptual difficulties among students. We then analyze a modern treatment of mechanical courses based on the results of research in physics education over the last 40 years. We place special emphasis on the principle of conservation of energy as one of the fundamental principles of nature, prioritizing the concepts of system, surrounding, and energy transfer and transformation.