The missing mathematics in high school. Theorems, proofs and geometric constructions.

Abstract

In the last 30 years, several reforms have been implemented in the Albanian education system.
They certainly aimed to improve the education system, especially pre-university education, by improving
the school curriculum, teaching and learning methods, infrastructure, teacher training, and the student
assessment system. Many curricula and textbooks have been revised, changed, and added to meet the
challenges of today's society. The advancement of technology has made it possible to create new
materials and interactive teaching methods for a more interesting and attractive school. However, at the
end of the day, beyond the good intentions, discussions, and promises, what matters is what the students
have learned and what they know. What happens to high school students when they reach their first year
of university? What we are witnessing today is that, for quite some time, there has been a growing gap
between the knowledge obtained in high school and the knowledge that students should have in their first
year at Albanian or European universities. In this article, we will discuss some of the most important
elements of mathematics, theorems, and proofs that do not exist anymore in our high school curricula, and
in particular the geometry constructions, as well as the impact on students’ achievement and results in
university.