Nowadays, when the changes that appear in programming paradigms and in software process development methodologies are extremely frequent, teaching Computer Science throughout all levels of study has become a demanding task. To all these are added changes caused by the dynamics of the society and the traits of the current learners and how they learn. A new era of education has just begun. To cope with the challenges mentioned above, teachers from three levels of study had been invited to share their experience in teaching sorting algorithms, through questionnaires, in order to achieve teaching efficiency for students. Thus, the paper proposes a framework for a unitary approach of sorting algorithms. Its contribution is twofold: firstly, it frames a pedagogical approach defined as a conceptual framework in teaching sorting algorithms by mining and investigating contents and aspects taught at three curriculum levels, following the Revised Bloom’s Taxonomy. Secondly, a software tool is proposed - AlSort - based on gamification and story-telling as a learning strategy of sorting algorithms. The tool is implemented for the gymnasium and high-school level and it is under development for the university. It covers the first four levels from Bloom’ Taxonomy.