A model of teaching/learning is proposed based on a "problem-based structure" of the contents of the course, in combination with a training in paper and pencil problem solving that emphasizes discussion and quantitative analysis, rather than formulae plug-in. The aim is to reverse the high failure and attrition rate among engineering undergraduates taking physics. A number of tests and questionnaires were administered to a group of students following a traditional lecture-based instruction, as well as to another group that was following an instruction scheme based on the proposed approach and the teaching materials developed ad hoc. The results show that students following the new method can develop scientific reasoning habits in problem-solving skills, and show gains in conceptual learning, attitudes and interests, and that the effects of this approach on learning are noticeable several months after the course is over. (Contains 10 tables.)