Начертальная геометрия и математика


физико-математические науки

В статье освещается о возникновении и становлении предмета «Геометрия». Данная наука помогает учащимся развивать пространственное воображение и логическое мышление.

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Many people think that mathematics is a complex, abstract, boring, useless and far from real life science. Therefore, you will be surprised to learn that geometry — an important branch of mathematics-appeared because of the need to solve certain practical problems. It is believed that it was invented by the Egyptians, who had to periodically mark the land, because the Nile river during floods constantly erased borders. In fact, from the etymological point of view, the word geometry means "measurement of the earth".

Mathematics is so practical that few of those around us can function without it. From banks and shops, stock exchanges and insurance companies to barcodes, listening to CDs and talking on a mobile phone-all this and much more works thanks to processors and mathematical models, whose task is to constantly perform mathematical operations.

A sharp jump in the development of technology and science occurred in a relatively short time. Physics, medicine, chemistry, civil engineering, architecture, electronics and space exploration, as well as many other fields of knowledge that simplify our lives, would be unviable without the methods invented by mathematics, which developed the theoretical models on which their research is based.

The peculiarity of geometry that distinguishes it from other branches of mathematics, and all areas of science in General, is an inseparable, organic connection of living imagination with strict logic. In its essence and the basis of geometry is the spatial imagination, permeated and organized by strict logic. It always contains these two inextricably linked elements: a clear picture and an accurate formulation, a strict logical conclusion. Geometry combines these opposites, they mutually penetrate, organize and direct each other.

One has only to recall the classical works of architecture, starting with the ancient pyramids, as soon as it becomes obvious that geometry in some sense refers to art. Art is best perceived directly. This is facilitated by M. K. Escher's engravings, they form a kind of artistic and geometric film, giving the viewer a rare opportunity to see the geometric beginning in many phenomena of nature and beauty-in purely geometric designs.

The subject "Geometry" allows the teacher to develop logical thinking, spatial imagination, teaches children to generalize, organize, see the beauty, but it causes great difficulties in the study. Therefore, the teacher should always, and especially in the first lessons, strive to ensure that the material was available to each student, to present it vividly, colorfully, so that the student, leaving the lesson, wanted to find something new in the additional literature, to learn more of what was set at home.

In the first lessons of the study of a systematic course of geometry laid the foundations of a course of plane geometry: introduces the concepts and properties of simple geometric shapes that allows for the construction of the course. The introduction of the basic properties of geometric shapes is based on the systematization and generalization of students ' knowledge and ideas about geometric shapes, accumulated in the process of studying mathematics in grades 1-6 and life experience. Therefore, in methodological terms, concepts introduced early in the course of plane geometry is quite simple and familiar to students and, therefore, no preparatory work, no significant testing is not required.

The study of the first topics should solve the problem of introducing terminology, development of visual representations and skills of the image of planimetric figures and simple geometric configurations, both in terms of the problem and in the course of solving problems. All this is necessary for further study of the course of geometry, which is why important aspects of the study of a systematic course is to work with drawings and drawings, the use of simple geometric tools (ruler, protractor). When solving problems should primarily rely on visual representations of students. Nevertheless, the solution of problems should be used for the gradual formation of students ' first skills of using the properties of geometric shapes as a support in solving problems.

Here the foundations of the whole course of geometry are laid: the basic concepts and the system of axioms (basic properties) are introduced, which allows for the deductive construction of the course. So, for the first time students meet with a strictly logical presentation of the material, with a new task for them — to justify each statement, each step of solving the problem, based on the definitions and basic properties of simple geometric shapes during the evidentiary reasoning.

Teaching students competent logical reasoning begins with the training of their competent oral and written speech. Most of the tasks and exercises of textbooks, in which there is a consolidation of terminology and the study of the basic properties of geometric shapes, contributes to the formation of students ' skills to accurately formulate thoughts and conduct evidential reasoning. The solutions of some problems given in the text of textbooks serve as examples of such reasoning.

It is advisable that at first the sample answer was given by the teacher himself, offering to repeat it repeatedly in solving similar problems. Each answer of the student must complete the correct and accurate forms of the teacher, without reducing the assessment for the" clumsy language " of the student with the correct understanding: the essence of the theoretical material and the correct solution to the problem.

The main goal is to teach how to think correctly, to prove and defend your point of view. Thus, the study of the first lessons of geometry becomes relevant.

At the beginning of work on the topic put forward the hypothesis that the first lessons of geometry in secondary school due to the insufficient amount of time to the study of geometry, because the literal understanding of teachers a separate study of plane and solid geometry among students is not sufficiently formed spatial representations, they do not master the basic methods of reasoning, are unable to absorb the aspen geometric concepts.