Computability and Algorithmic Complexity Questions in Secondary Education
Rafael del Vado Vírseda · 2019
Theoretical computing is a difficult area to teach in university courses due to different causes. Many students who begin computing subjects have little mathematical or theoretical background. It is important that students acquire an intuitive knowledge of these theoretical concepts before they finish their secondary education. In this work we describe how to bring computability and complexity questions in secondary education to address classic issues raised in the curriculum about the limits of mathematics and its formal systems, and subsequently, their algorithmic and algebraic complexity. We report a complete educational experience for enhancing the algorithmic curriculum of pre-university computing and mathematics courses to know what computability and algorithmic complexity questions may be introduced into secondary education, how to teach these concepts, and train teachers to do it. The good experimental results obtained are compared with the results in standard high school courses in which these questions about theoretical computing are not addressed. The conclusions obtained are exposed, as well as the pros and cons of the educational experience carried out, so that they can be taken into account in the future design for the curriculum of an official subject in computing on a global scale, or be included in the curriculum of pre-university courses.