About Some Methodical Features of the Development of Creative Competence of Students in the Solution of Research Problems in the Process of Differentiated Learning of the Course of Geometry
This article is devoted to the use of tasks for the development of competency in the process of teaching geometry, specific instructions and recommendations are given for the development of students 'thinking on the application of research problems in order to develop students' research skills in solving geometric problems. In the process of developing students' thinking, great opportunities are provided by the following two methods: solving geometric search problems, completing tasks and exercises aimed at one learning goal. The use of these methods is considered on the example of some topics of the geometry course, and the technology of teaching students the skills to generalize is used. As you know, the solution of non-standard problems is a heuristic process, and you will have to move away from logical means. Sometimes a problem can be solved by brute force, so the student’s desire to solve a problem is the basis of her creative activity. With the help of such tasks, students develop the ability to compare, find patterns, observe, put forward hypotheses, substantiate and prove them. On this basis, they have the opportunity to argue, develop companionable abilities, they master the skills to apply knowledge in new situations. The properties of a parallelogram can also be considered with the help of focused tasks and questions: the sum of the distances from the internal point to the lines on which its sides lie is a constant, the line passing through the intersection of the diagonals divides it into two equal triangles, the bisectors of the opposite angles of the parallelogram are parallel, the bisectors of the angles adjacent to one side are perpendicular, a large diagonal lies against a large angle, the angle between the heights drawn from obtuse angles is equal to the acute angle of the parallelogram. When considering the signs of a parallelogram, one can also discuss with students the problems and questions of generalizing the properties of a parallelogram.