From the Mathematical Impossibility Results of the High School Curriculum to Theoretical Computer Science

The academic results that students of computer science degrees obtain in their learning of subjects of theoretical computer science are traditionally low, as a consequence of the difficulties students experience due to their little theoretical background. In order to reverse this problematic situation in theoretical computing education, it is essential that students acquire an intuitive and progressive knowledge of the main theoretical computing concepts and their associated skills and abilities, even before they finish secondary school. To achieve this goal, in this paper we offer a novel methodology to systematically introduce questions of computability and algorithmic complexity in the curriculum of the final years of high school education. We propose to start from those results of impossibility that are already included in the pre-university curriculum of mathematics courses, and around these theorems of impossibility, conveniently adapted and presented to students, identify motivating and interesting theoretical computing questions. To provide evidence of the applicability of the proposed methodology, we analyze the experimental results we have obtained to confirm that the introduction of theoretical computing questions from impossibility results increases secondary school students’ academic grades and motivation beyond traditional programming courses.