Arguments are presented to explain why the usual approach to the teaching of introductory quantum mechanics, as well as some newer ones, in general seems to fail to achieve any profound understanding of the subject. An alternative approach is suggested which, although not new, has hardly been adopted anywhere, for reasons which are analyzed. A course which has been based on this approach is described. The main aim of the article is to contribute to, and hopefully stimulate, a debate on the various approaches used to introduce quantum mechanics and the psychological and didactic premises on which they are based.