Developing students’ creative skills during the process of teaching geometry

This article discusses possible approaches for developing the creative abilities of secondary school students in the process of teaching geometry. The main disadvantages that hinder creative development discovered based on a comparative analysis of geometry textbooks by Russian scientists. These disadvantages are axiomatic methods, excessive theorization, non-systematic set of tasks, complex definitions etc. The author proposes the study of planimetry using the properties of simple geometric shapes without invoking axioms. As a concrete example of that, proof of triangle equality that is based on the property of "corresponding chords of angles" is demonstrated. Furthermore, the equality outcome is used to study the properties and features of other figures. Formulation of parallel postulates is simplified using formulas for the areas of a rectangle and a circle, and the circumference of a circle as the starting axioms. The author suggests a three-level system of tasks for each topic. The first level is designed to test the comprehensibility of the theoretical material. The second level applies the acquired knowledge in practice. The third level of tasks is intended to develop an independent study and critical thinking skills of a student. Additionally, at the end of each chapter, a wide range of extra tasks is given. Preparation for Science Olympiads and science fairs should be systematic. We succeeded at formulating general provisions for the management of scientific projects of schoolchildren in mathematics. The article provides an example of such implementation related to learning a special property of trapezoids.