Teaching Of Descriptive Geometry Research Articles

Application of GeoGebra in the Teaching of Descriptive Geometry: Sections of Solids

Technologies came to revolutionize the teaching of technical design; they brought resources that enabled 3D and 2D graphic simulation. The objective of this research is to understand how the implementation of the dynamic software GeoGebra on the topic of cylindrical sections can improve 3D spatial visualization in students because of the challenges in understanding the 3D representations and transporting them to the 2D sheet. This is a quasi-experimental case study in a mixed qualitative and quantitative approach which was conducted in a grade 12 class on the subject of descriptive geometry. The instruments used were a pre-test, post-test and Santa Barbara Solids Test. The students of the experimental group used GeoGebra and obtained better results in the post-test than the students in the control group, which suggests an improvement in learning; however, the Santa Barbara Solids Test results showed that the difficulties in visualizing views of the projected solids in a two-dimensional plane persisted. This study is also intended to test software in a classroom with students who have never experienced a 3D technology in their educational practices and direct future research in the complex content of descriptive geometry with the help of software.

The Lost Skills: About the Exclusion of Design and Descriptive Geometry from School Curriculums and Their Consequences

This article seeks to demonstrate how some government decisions dismantled the teaching chain of Drawing, here understood as a support for science and a graphic extension of mathematics in problem solving and in the creation of objects or buildings. Recent researches point to an increasingly complex definition of the act of drawing, but, paradoxically, the teaching of drawing goes in the opposite direction. We begin the article with an examination of what is defined as drawing, followed by a history of drawing education in Brazil, focusing especially on secondary and higher education. Then we address the manual and mental skills obtained from the study of Observation Drawing, Geometric Drawing, Descriptive Geometry, Technical Drawing, which are of great value for personal development and for the advancement of project knowledge, support for the creation of new ones. technologies, objects or buildings. We register the weakening of the design teaching chain and the risk of extinction of the design of the curricula due to mistaken teaching policies. We emphasize the teaching of Descriptive Geometry for being the basis for engineers, architects and designers, a foundation without which there is no possible development and innovation. We also point out the false solutions offered by computer programs that present results, but do not teach the process of reasoning and spatial visualization. The adopted methodology was bibliographical research and critical reflection on the theme, it is, therefore, a descriptive and comparative analytical qualitative study. Evidencing this situation and understanding it is the first step towards a change of attitude.

Web udžbenik za nacrtnu geometriju

In this paper we present educational material which is a basis for a web textbook designed for the lectures on geometric subjects. The textbook is available online for free. It differs from previous textbooks in the application of information technologies in presenting classic contents and introducing 3D modelling in descriptive geometry teaching.

К вопросу о методике использования алгоритмов при решении задач начертательной геометрии

In this paper the urgent problem of the formal approach to the teaching of descriptive geometry (DG) has been formulated. The authors consider the algorithm concept and approaches to formal description of methods (algorithms) for tasks solving. It is emphasized that the known methods for creating and presenting of algorithms for DG tasks solving do not reflect all possibilities of algorithmization as it is. In the third section the authors, in examples, emphasize the complexity of DG tasks solutions algorithmization. The diversity of solutions for one or another DG task is noted depending on location of initial figures that requires a suitable context analysis in solving, and, as a consequence, the algorithm choice. It is pointed out that the reason for this is different ways for expressing of figures’ geometric properties by means of drawing. General algorithms for applying the method of loci and geometric transformations to tasks solving are considered. From the loci position have been considered two basic tasks of DG: plotting a point drawing in the coordinates, and a perpendicular to the plane. The method of loci importance is emphasized in view of algorithms compilation simplicity and wide possibilities for tasks solving. The authors note that algorithmization does not reduce the importance of geometry knowledge or understanding of the tasks geometric content and used methods, but emphasizes the importance of the first stage for tasks solving — the stage of analysis at which basic decisions are made and its method is chosen. In conclusion it is emphasized that in the practice related to solving of DG educational tasks it is optimal to apply the algorithmization in point, as it enables to structure the course, operate with compact algorithms, and introduce automated technologies of constructive geometric modeling.

Role of Descriptive geometry course in development of students’ spatial visualization skills

Spatial ability is of great importance for successful work in various fields such as computer graphics, engineering, architecture and cartography. A number of studies have demonstrated that Descriptive geometry courses have the potential to develop spatial skills. The aim of this study is to investigate the effect of Descriptive geometry course with the current method of teaching on the spatial skills of students at the Faculty of Civil Engineering at the Technical University of Kosice. The study was conducted by a pretest and posttest method. The first grade students studying in the winter term of 2016 to 2017 educational year served as a sample for the study. A significant difference between the pretest and posttest scores was revealed by using the Wilcoxon signed rank test. The findings showed that Descriptive geometry course has a positive impact on development of students’ spatial skills. Although, the Descriptive geometry course provides numerous benefits, it is often regarded by students as one of the most difficult courses. The use of dynamic geometry software with the ability to represent three-dimensional space allows students to overcome the difficulties associated with the plot of this course. The future plans within Descriptive geometry teaching include integration of the dynamic geometry software GeoGebra into the educational process which should lead to the innovation and facilitation of the Descriptive geometry course. Keywords: Spatial ability, mathematics education, engineering education

POINTS ON THE SPHERE SURFACE

Purpose. The extensive use of the computer-aided design system (CAD) in education and industry puts forward new demands on the scope, content and quality of up-to-date descriptive geometry course. The purpose of the work is topicality analysis of traditional descriptive geometry methods for 3D modelling and development of methodological recommendations for its teaching as a subject together with a selected CAD. Methodology. Conclusions about effectiveness and expedience of application of descriptive geometry methods are drawn on the basis of tools analysis and comparison of modern CADs and descriptive geometry for solving problems arising during 3D modelling. Generalization of teaching experience made it possible to give recommendations about optimization of the descriptive geometry course taking into account present-day requirements to professional skills of an engineer. Findings. CADs tools and descriptive geometry methods are compared by way of specific example to give the answer what is more suitable for solving problems arising during 3D modelling. Originality. We presented the methodological recommendations about optimization of descriptive geometry teaching together with a selected CAD. We proposed the conception of a modern textbook on descriptive geometry. First of all, the textbook must describe algorithms for solving problems by means of standard CAD tools exactly in 3D, not on the plane. It is desirable to accompany these algorithms by pictorial images in order to have an opportunity to grasp an idea quickly and implement it through methods of direct modeling in CAD application. We also touched practical problems of students’ motivation to ensure high effectiveness of graphical education. Practical value. This paper may be useful mainly for educators in the field of engineering graphics because it raises a vital question ‘Descriptive Geometry versus CAD’ which now has no definite answer. Topicality and teaching approaches of different solution methods of spatial problems by means of projections is subject of a dispute, taking into account that CAD tools are continuously updated. This paper by way of specific example shows some advantages and limitations of descriptive geometry and CAD, as well as touches the issues of their efficient joint application for teaching.

New educational web resources for the engineering course "descriptive geometry"

A new method of descriptive geometry teaching is proposed in the presented article. The method is based on video, imitating spatial geometric images and their connection with a complex drawing. The method allows to see a geometric image in space and all the constructions in the complex drawing simultaneously. Video is made in the 3ds Max software. The new technique successfully solves the spatial thinking development problem. Based on this course, the authors wrote a digital textbook. Each drawing in this tutorial has a link to the video that illustrates the drawing construction process. Practically, all the videos simulate the thinking process, which should occur in student's mind while solving the problem. The course has been tested for 4 years in the RUDN University. Students have increased their interest in descriptive geometry studying and faster spatial thinking development was noted. Keywords : spatial thinking; geometric forms; complex drawing.

Automation in the Teaching of Descriptive Geometry and CAD. High-Level CAD Templates Using Script Languages

The main purpose of this work is to study improvements to the learning method of technical drawing and descriptive geometry through exercises with traditional techniques that are usually solved manually by applying automated processes assisted by high-level CAD templates (HLCts). Given that an exercise with traditional procedures can be solved, detailed step by step in technical drawing and descriptive geometry manuals, CAD applications allow us to do the same and generalize it later, incorporating references. Traditional teachings have become obsolete and current curricula have been relegated. However, they can be applied in certain automation processes. The use of geometric references (using variables in script languages) and their incorporation into HLCts allows the automation of drawing processes. Instead of repeatedly creating similar exercises or modifying data in the same exercises, users should be able to use HLCts to generate future modifications of these exercises. This paper introduces the automation process when generating exercises based on CAD script files, aided by parametric geometry calculation tools. The proposed method allows us to design new exercises without user intervention. The integration of CAD, mathematics, and descriptive geometry facilitates their joint learning. Automation in the generation of exercises not only saves time but also increases the quality of the statements and reduces the possibility of human error.

Stereo orthogonal axonometric perspective for the teaching of Descriptive Geometry

Purpose – The purpose of this paper is to present the development of a software for stereo visualization of geometric solids, applied to the teaching/learning of Descriptive Geometry. Design/methodology/approach – The paper presents the traditional method commonly used in computer graphic stereoscopic vision (implemented in C language) and the proposed method (implemented in GeoGebra software). The proposed method is a new methodology for stereo spatial visualization. It uses the orthogonal axonometric perspective obtained from the mongean projections of the object, both concepts studied in Descriptive Geometry course. Findings – The use of stereoscopic techniques has great potential for the improvement of spatial visualization ability, because they allow the understanding of spatial situations presented in complex exercises. The students who tested the proposed method said that it offered a superior stereo vision depth in relation to the traditional matrix method. Research limitations/implications – For future work, the paper suggests to carry out a statistical study to evaluate the educational benefit of the tool, and to investigate the proposed method using the conical axonometric perspective. Practical implications – Create a virtual environment to support the process of teaching/learning Descriptive Geometry and contribute to the development of students ' spatial visualization skills. The software will be available on the Internet, in the GeoGebra libraries. The objective is to increase e-learning, where a greater number of students will study. Social implications – The current goal in Brazil universities is to greatly increase the number of poor students entering as a social inclusion strategy. University courses need more efficient teaching techniques to attend the students, so the e-learning techniques are recommended. Originality/value – This paper’s innovative characteristic comes from the implementation of stereoscopic vision from traditional methods used in Descriptive Geometry, so the proposed method improves both the visualization ability and the Descriptive Geometry basic concepts, which points out to its educational role.

CÔNG NGHỆ DẠY HỌC TƯƠNG TÁC ẢO TRONG DẠY HỌC HÌNH HỌC HỌA HÌNH VÀ VẼ KĨ THUẬT

CÔNG NGHỆ DẠY HỌC TƯƠNG TÁC ẢO TRONG DẠY HỌC HÌNH HỌC HỌA HÌNH VÀ VẼ KĨ THUẬT

How to Include Augmented Reality in Descriptive Geometry Teaching

Abstract The geometric representation has always existed, from the antiquity when the man was using it to plan his areas to the present day. For the construction of any object or building the use of geometry is needed since the finish work has to be very precise. Teaching geometry is not easy at all and the new generations every time has more problems for the spatial understanding. With the new digital technologies the young persons are losing increasingly the sense between the royal space and the two-dimensional one, due to the fact that they are immersed on a screen. Therefore, the system of learning as for the spatial representation must change to manage to answer the interest for the use of these technologies. The matter of Descriptive Geometry is directed students of the first and second semester of the careers of Architecture and Industrial Design. Their aim is to develop skills of perception and spatial analysis, under systems of parallel and conical projection in the construction of volumes. The work that is realized in the semester is with instruments to hand, but we see the need to penetrate with the technology on having explaining basic aspects since they are the units, scales and coordinates (length, width and thickness). For what we know that the AR will help to make more understandable the process of modeling of a figure. Later the pupil will be able to be working with hand to learn to project the exposed figure, later it will be possible to work with the software SketchUp. The key point of this process of education is that the pupil learns to project, not to copy, from the work to hand up to the culmination with the software. For it I have to conclude of that the work of the AR does not remove importance to the work that the teacher does since this one is the one that programmes that makes learning understandable.

Modern Educational Instruments And Blended-Learning Technologies In Descriptive Geometry Teaching

AbstractDue to a medium-low level of young students’ technical knowledge from previous school classes the first year of university seems to be very difficult. The complex phenomena and the abstract concepts represent the first lectures avoided by the students if the temporal burden becomes uncomfortable. Therefore the lecture has to be designed in which the prospective engineer clearly recognise their profit. Using the modern educational instruments as DidaTech Platform, CAD or C++ program presentations in higher education for engineering the level of comprehending and interest in the profile subjects should increase.The main concern of this paper is to demonstrate how using electronic methods young engineers learn about the descriptive geometry and improves the student’s intellectual capability of space perception. This will be absolute necessary for the students’ preparation for the Mechanical Drawing and CAD subjects.

Study on the Correlation between Drawing Education and Special Cognitive Ability Evaluation Based on the MCT

Use the international universal theory of evaluation of special cognitive ability with Mental Cutting Test (MCT) to test the students of Science and Technology University. Compare the MCT average scores of fore-and-aft drawing education, it shows that the effect of descriptive geometry teaching is positive correlative with the scores of MCT, the students improved their special cognitive ability from planar drawing to three-dimensional drawing significantly. The students who got lower MCT scores before taking drawing courses improved their MCT scores obviously. The effect of mechanical drawing teaching is feeble correlative with the scores of MCT; it shows feeble improvement in students’ special cognitive ability.

Начертательная геометрия до 1917 года

The paper shows that the descriptive geometry teaching until 1917 was held in real schools, which in soviet period could be assumed to be equivalent to secondary polytechnic school. An album of drawings on descriptive geometry for pupils of the 7th form is cited as an example. A full course of descriptive geometry, which is mandatory for first year students of all technical specialties, is presented in this album.

Конструктивное геометрическое моделировавние как перспектива преподавания графических дисциплин

The questions related to advisability of descriptive geometry teaching in high education institutions are considered. A comparison of descriptive and analytical geometry as well as a comparison of engineering graphics and computer one is given. The necessity of formation in the students’ mind а schematic projection principles is proved.

Организация учебного процесса по начертательной геометрии в Пензенской технологической академии

The problem of «Descriptive geometry» discipline teaching in global computerization conditions of educational process is reflected in this paper. The attention is emphasized on a fact that students’ training according to the proven classical scheme of this discipline teaching is included now into the obvious contradiction with IT technologies, which are strongly taking their place in educational process. The solution of this contradiction, along with providing of well-known conditions, requires development of proved technique related to descriptive geometry teaching with the maximum use of modern CAD systems’ opportunities. The option of organization of standard lecture, practical and laboratory studies related to descriptive geometry and practiced in the Penza State Technological Academy is shown in this paper using the example of one of methodical techniques.

Создание модели пирамиды в компас-3D для решения метрических задач

In modern conditions of young professionals’ preparation the transition to traditional disciplines teaching by the way of assimilation of information technologies and computer aided design systems is on the table. The concrete steps stated in this paper can serve as a basic point to creation of original technique related to descriptive geometry teaching and will be interesting for majority of experts in the area of geometrical and graphic disciplines and computer-aided design systems.

К вопросу организации учебного процесса по графическим дисциплинам в вузах Беларуси

The analysis of the main trends related to descriptive geometry teaching methods in Belarusian engineering education system has been performed in this paper. The traditional structure has been characterized, from whence the need for adjustment the «Descriptive Geometry» section content of «Engineering Graphics» course in accordance with evolving the computer assisted design systems’ trends has been revealed. The organizational and methodological aspects related to descriptive geometry teaching on mechanical engineering faculties with regard to geometric computer simulation as modern design direction have been considered. The curricula change questions are proved, and also the actions for «Descriptive geometry» section teaching technique improvement are offered.

Computer-Aided Descriptive Geometry Teaching

Interactive geometry software brings new opportunities and challenges for how to make the teaching and learning process more effective and simultaneously more interesting. However, the majority of computer-aided activities for geometry courses are oriented especially on basic problems of pre-college mathematics curricula. This article concerns the use of dynamic geometry software in teaching high-level geometry courses for students in mechanical, civil, and other engineering programs at the tertiary level.

La Gournerie versus Monge

Jules de la Gournerie was one of Gaspard Monge’s successors in the teaching of Descriptive geometry and its applications, and both dealt with similar matters. La Gournerie’s writings criticized Monge’s ideas with detailed observations. In this article we go over all the issues on which there was a marked divergence, from the stereotomy of stones to the conical perspective or the organization of teaching. It also show how the constant opposition between the two men, even not explicitly focused on philosophical and political questions, represents two radically different ways to understand the world, each solid by itself.