Elements of Algorithmic Thinking in the Teaching of School Geometry through the Application of Geometric Problems

Abstract

Algorithmic thinking and the creation of algorithms have traditionally been associated with mathematics. It is based on the general perception of an algorithm as a logically unambiguous and precise prescription for performing a certain set of operations, through which we reach a result in real time in a finite number of steps. There are well-known examples from history, such as the division algorithm used by ancient Babylonian mathematicians, Eratosthenes algorithm for finding prime numbers, Euclid’s algorithm for finding the greatest common divisor of two numbers, and cryptographic algorithm for coding and breaking, invented by Arabic mathematicians in the 9th century. Although the usage of algorithms and the development of algorithmic thinking currently fall within the domain of computer science, algorithms still play a role in mathematics and its teaching today. Contemporary mathematics, and especially its teaching in schools of all grades, prefers specific algorithms in arithmetic, algebra, and calculus. For example, operations with numbers, modifications of algebraic expressions, and derivation of functions. Teaching geometry in schools involves solving a variety of problems, many of which are presented as word problems. Algorithmization of school geometric tasks is therefore hardly visible and possible at first glance. However, there are ways to solve examples of a certain kind and to establish a characteristic and common algorithmic procedure for them. Algorithmic thinking in geometry and the application of algorithms in the teaching of thematic parts of school geometry are specific issue that we deal with in this study. We will focus on a detailed analysis of the possibilities of developing algorithmic thinking in school geometry and the algorithmization of geometric tasks.