Wolfram Mathematica Functional Possibilities for Curved Lines and Surfaces Visualization

The paper states that the current conditions in which the education system is located, and the rapid development of IT require constant improvement of methodological materials, taking into account the full capacity of the current software. Examples of programs necessary for preparation of methodological materials for high-quality classes are given. The purpose of the paper was to identify the Wolfram Mathematica didactic potential when conducting classes in the disciplines of the geometric and graphic profile at a technical high educational institution. In this paper has been performed analysis of literature sources both domestic and foreign ones on the Wolfram Mathematica system application in science and teaching of various disciplines. It has been shown that the program use scope is very wide, in fact, it is comprehensive and requires additional and in-depth study. Examples of Wolfram Mathematica using in mathematics, physics, chemistry, geometry, robotics, virology, and the humanities are given. In the paper have been provided examples for pedagogical design of simulation models for an electronic course on descriptive geometry in the Moodle system. An example of code written in the Wolfram Mathematica is provided. Interactive models developed during the design are presented, which allow the user to change the constructed curves and surfaces’ parameters. Have been defined some functional capabilities of the system, and has been revealed the Wolfram Mathematica didactic potential for teaching geometric and graphic disciplines. Have been considered other authors’ similar models, which can be used in the educational process to increase the clarity of the material presented in the classroom. In conclusion it is pointed out that interactive visualization in the "Descriptive Geometry" discipline, together with classical working practices, significantly enriches the content of geometric education.

Wolfram Mathematica Functional Possibilities for Curved Lines and Surfaces Visualization

The paper states that the current conditions in which the education system is located, and the rapid development of IT require constant improvement of methodological materials, taking into account the full capacity of the current software. Examples of programs necessary for preparation of methodological materials for high-quality classes are given. The purpose of the paper was to identify the Wolfram Mathematica didactic potential when conducting classes in the disciplines of the geometric and graphic profile at a technical high educational institution. In this paper has been performed analysis of literature sources both domestic and foreign ones on the Wolfram Mathematica system application in science and teaching of various disciplines. It has been shown that the program use scope is very wide, in fact, it is comprehensive and requires additional and in-depth study. Examples of Wolfram Mathematica using in mathematics, physics, chemistry, geometry, robotics, virology, and the humanities are given. In the paper have been provided examples for pedagogical design of simulation models for an electronic course on descriptive geometry in the Moodle system. An example of code written in the Wolfram Mathematica is provided. Interactive models developed during the design are presented, which allow the user to change the constructed curves and surfaces’ parameters. Have been defined some functional capabilities of the system, and has been revealed the Wolfram Mathematica didactic potential for teaching geometric and graphic disciplines. Have been considered other authors’ similar models, which can be used in the educational process to increase the clarity of the material presented in the classroom. In conclusion it is pointed out that interactive visualization in the "Descriptive Geometry" discipline, together with classical working practices, significantly enriches the content of geometric education.

Modern Problems of “Applied Geometry and Engineering Graphics” Course Teaching For Exploitative Specialties of an Aviation High Educational Institution

In an aviation high educational institution, when getting students education in exploitative specialties it must be taken into account that it must be conducted in accordance with necessary requirements to the formedness level of professional competences in a specialized area. The planned results of “Applied Geometry and Engineering Graphics” learning include knowledge of methods for applied engineering and geometric problems solving, the ability to use the main elements of applied geometry and engineering graphics in professional activities, and solving of specific applied problems related to geometric modeling. The results of “Applied Geometry and Engineering Graphics” study are to gain experience and skills for solution of cognitive, organizational and other problems by themselves related to students’ future professional activities. In this paper are considered the main problems and tasks to be solved to achieve the necessary level for compliance of a student studying in one of the exploitative specialties at the Ulyanovsk Institute of Civil Aviation named after Chief Marshal of Aviation B.P. Bugaev, with professional competencies and modern educational standards. Issues related to the organization of “Applied Geometry and Engineering Graphics” discipline study, such as computerization of the educational process, use of distance learning technologies in the educational process, formation of students’ cognitive interest and spatial imagination. Has been presented the proposed structure of “Applied Geometry and Engineering Graphics” course for the exploitative specialties of Ulyanovsk Institute of Civil Aviation; the need to develop a task book for classroom and home works, taking into account their applied value for formation of professional competencies, has been justified.

“Applied Geometry” Discipline Adaptation to Undergraduate for Exploitative Specialities of an Aviation High Educational Institution

The problem of teaching and formulating the tasks for the “Applied Geometry” discipline is considered in this paper. Currently, in aviation high educational institutions there is a tendency to reduce the number of hours allocated to graphic disciplines; in addition, “Descriptive Geometry” – the habitual name of the discipline – has been replaced by name “Applied Geometry”. This is certainly connected with the transition to learning on undergraduate programs, that implies a competency-based approach, i.e., training in accordance with the necessary knowledge and methods of activity in a particular area [4; 9; 23; 29; 30; 34]. The planned results of learning in “Applied Geometry” include knowledge of methods for solving applied engineering-geometric problems, as well as the ability to use the basic elements of applied geometry and engineering graphics in professional activities, and to solve specific applied problems of geometric modeling [4; 14; 20; 22; 32]. For these reasons arises the question of the need to adapt “Descriptive Geometry” to the requirements and programs for the training of bachelors, bringing it to conformity with the name “Applied Geometry” of the discipline. According to the results of “Applied Geometry” studying, students ought to gain experience and have the ability to independently solve cognitive, organizational and other problems related to their future professional activities [28–30]. In this paper is proposed a general approach to the formulation of “Applied Geometry” problems for cadets pursuing a bachelor's degree in “Air Navigation” (25.03.03) and “Operation of Airports and Flight Support of Aircraft” (25.03.04). Using rather simple examples, has been considered the possibility to formulate the problem in such a way that instead of the traditional formulation it could be applied for a specific bachelor's degree. As well has been considered a complex applied problem, which is suitable as a task for performing a computational and graphic work, since it integrates several topics of the discipline.

The Development of Innovative Activities in High Edsucation

Changes in modern high education of the Russian Federation have occurred within recent years. They were caused by new demands of the state and society as well as innovations in economy. In modern higher education there is a need for the development of innovation and its continuous improvement. In modern realities, each higher education institution faced a task that is extremely difficult to solve. It consists in the development and implementation of the latest innovative information and educational environment. The electronic environment of a high educational institution expands educational opportunities, raises the level of educational services, therefore today the issue of the development of electronic activities in an educational institution is so urgent. The purpose of the article is to develop a question concerning introduction of e-learning in high education. For this purpose, a model of methodological support of innovation activity in electronic environment was developed. It allows increasing the level of electronic environment development and the quality of students’ education in general. Based on it, we have developed recommendations for the introduction of e-education in high education.Experimental verification of the model methodological support of innovative activities in electronic environment showed that the willingness of teachers to use electronic environment has increased significantly. The research can be used in the further development of higher education electronic environment.

Academic Olympics on Descriptive Geometry As a Catalyst of Heuristic Thinking

Gaspard Monge wrote: "The charm that accompanies science can overcome man's natural aversion to the mind intenseness and make them find pleasure in their mind’s exercise that for most of people seems as tiresome and boring occupation". He had written it including descriptive geometry. To exercise one’s mind — what is this but the brain building, and science is accompanied just by heuristic thinking, so that brings new discoveries for an intellectual. The most difficult in descriptive geometry is the ability to represent a spatial geometric figure or such figures’ combination on two images. It is clear that the usual problems of a course are resolved within the academic discipline, and are typical ones, readily understandable for any student of a technical high educational institution, while the tasks at Academic Olympics, even if these tasks are destined for use inside a high educational institution, are more difficult. If for a solving of problems from an ordinary problem book on descriptive geometry’s course it is enough to know literally a few algorithms, for tasks of increased difficulty that is not enough. The Academic Olympics’ functions reveal such a feature of those on descriptive geometry as their inseparable property to be a catalyst for development of heuristic thinking. Here there is not only the disclosure of students’ abilities to solve ordinary geometric problems, but the ability to solve problems of heuristic direction in general. It is obvious that knowledge of typical problems on the course of descriptive geometry is absolutely insufficiently, as well as it is insufficiently to know school geometry, that currently almost is not teaching in schools — now it is necessary to have not only the spatial perception, but at least the beginnings of heuristic thinking. This, plus the mobilization of all mental resources, contributes both to the solution of given geometric problems, and further solving other problems in the related areas of science and technology.

Kharkov in the formation of N. V. Morozova-Vodyanitskaya as a botanist-algologist

In the work, a number of facts and dates of the Kharkov period of life (1893–1920) of the botanist-algologist Nina Vasilievna Morozova-Vodyanitskaya are given, who graduated from the Kharkov High Women’s Courses, taught at them (as well as in other educational institutions of the city) and studied algae under the guidance of V. M. Arnoldi, Professor of the Departments of Botany of Kharkov University and High Courses. The origin of the rich merchant family allowed N. V. Morozova get both secondary and high education. The Kharkov High Women’s Courses were a huge, rapidly developing non-state high educational institution, similar to the classical university in terms of teaching natural sciences, equipping departments and laboratories, and the number of students. The Department of Botany, where N. V. Morozova studied and worked as a laboratory assistant and then as an assistant, has provided to the students an extensive workshop, participation in excursions outside the city and in expeditions to the basims of Russia. Students of the courses had the opportunity to engage in scientific work in laboratories and at a biological station on the Seversky Donets River. Among the students and junior teachers (colleagues of N. V. Morozova-Vodyanitskaya, who has formed the scientific school of V. M. Arnoldi) there were many well-known botanists, algologists, hydrobiologists who became professors, correspondent members, and so on. It is concluded that the scientific and pedagogical environment surrounding of N. V. Morozov-Vodyanitskaya in Kharkov favored her becoming as a researcher. Only the harsh conditions of the Civil War and devastation delayed the publication of the results of the first work of a young algologist, started in 1913.