Polish education system that covers teaching History does not provide efficient training for young people' living in informational society and knowledge-based economics of the 21st century. Skills important for further education and many modern occupations are weak points of many Polish graduates. Teaching History in a way adequate to present needs (that is, establishing necessary skills and competencies) should focus not as much on choosing problems with which pupils have to acknowledge, as on guaranteeing possibility for acting, that would result in increase of knowledge and skills. Learning of History in a present form is condemned for a slow marginalization because of its uselessness for pupils in their everyday life. Author states, that among various contemporary theories in pedagogy, two - constructivism and connectivism - seem to face challenges of present times and give the pupils chance to gain all above mentioned skills. Nevertheless, the problem is that noticeable failures of traditional teaching of History do not convince Polish Ministry of National Education to focus on new theories and implement them to a teaching plan, which should be done. In the article can be found propositions of subjects, that can be taught according to above mentioned theories.