A Theoretical Analysis Method of Spatial Analytic Geometry and Mathematics under Digital Twins

In recent years, online education in China has made considerable achievements. But there are also some problems: the teaching quality of online education is unsatisfactory; students’ online learning effects are frustrating, and students’ autonomous learning ability is poor. Based on analysis, teachers’ literacy and Internet technology are important factors restricting the online teaching reform, and online teaching easily falls into the dilemma of “shallow learning.” Digital twins can effectively realize the intelligent interconnection and interaction of the physical world and the information world, optimize the remote teaching process, and provide high-quality remote learning experience for learners. Based on this, the technology is used to the teaching of space geometry to help students understand it and improve their performance. First, the principle and advantages of digital twins are expounded. Second, the platform system based on digital twins is constructed. Then, the corresponding digital model is drawn by using the drawing function of MATLAB software, and the system based on virtual reality (VR) is established. Finally, the students of four classes of the same major are selected as the research subjects to test the teaching effect of advanced mathematics on the digital platform. The results show that students’ scores in the traditional classrooms are form 2.5 to 5.5 and their average score is 4.049, while the scores of the students in the digital twin classrooms are between 5.5 and 9.5 and their average score goes up to 7.986. This shows that students’ performance in the digital twin classrooms is 97.2%, higher than that in the traditional classrooms. A fully digitized spatial geometric model is implemented by using digital twins, and it can help students understand the mathematical theory of spatial analytic geometry, and their learning effect is greatly improved. This study provides a new direction for the application of new technologies in mathematics teaching.

On the Implicit Equation of Conics and Quadrics Offsets

A new determinantal representation for the implicit equation of offsets to conics and quadrics is derived. It is simple, free of extraneous components and provides a very compact expanded form, these representations being very useful when dealing with geometric queries about offsets such as point positioning or solving intersection purposes. It is based on several classical results in “A Treatise on the Analytic Geometry of Three Dimensions” by G. Salmon for offsets to non-degenerate conics and central quadrics.

ANALISIS KESALAHAN FAKTA DAN KESALAHAN KONSEP MAHASISWA DALAM MENYELESAIKAN SOAL GEOMETRI ANALITIK RUANG

This study aims to describe both fact and concept error of students in solving space analytic geometry problems. The subjects of this research are two students of Mathematics Department of Universitas Negeri Makassar. Each of them represents for each error (fact and concept errors). The collecting data were employed by using space analytic geometric tests and depth-interview. Interview guidelines and researcher were as research instruments. Data were qualitatively analyzed, using three stages of analysis: data reduction, data display and concluding. The main findings of this research are (1) the subject of fact error made mistakes in writing vector symbols, (2) the subjects of concept error made mistakes in identifying an equation (plane equation or line equation), since his focus was only in the number of variables of the equation.Keywords: fact error, concept error, space analytic geometry

WHAT ARE THE TYPE OF LEARNING MEDIA INNOVATION NEEDED TO SUPPORT DISTANCE LEARNING?

This exploratory qualitative article with an inductive approach aims to analyze the needs of students of the mathematics education study program at one of the leading universities in Surakarta City regarding learning media that can facilitate the implementation of distance learning during the Coronavirus pandemic. Data were obtained through distributing questionnaires using Google Form to 63 students who had taken the analytic geometry course at the beginning of the Coronavirus pandemic, interviews with 2 lecturers, and 3 students selected through snowball sampling technique. The results of the analysis showed that students need interactive audio-visual teaching materials that can be accessed easily without any internet network constraints. It is evidenced by the results of the survey which show that 70% of students need audio-video-based learning media. The results of this study become the basis for developing learning media that supports the implementation of distance learning

ANALISIS KEBUTUHAN MAHASISWA CALON GURU MATEMATIKA TERHADAP APLIKASI GEOGEBRA PADA PEMBELAJARAN GEOMETRI ANALITIK

The purpose of this study was to analyze the needs of the GeoGebra application in mathematics learning, especially the learning of analytic geometry for prospective mathematics teacher students. This research is descriptive quantitative research with a survey method. Participants in this study were prospective teacher students who had taken a course in analytic geometry at a university in Bandung, Indonesia. The sample of this research is student-teacher candidates in the sixth, fourth and second semesters. The total sample was 72 students with 20 males and 52 females. The data collection instruments used questionnaires and interviews. Based on the results of the study, it is known that when learning analytical geometry, most students have difficulty visualizing geometric shapes so that students feel they need GeoGebra as a learning medium in lectures on analytic geometry.

Competency approach to the study of the second-order surface interface as the geometric location of points in space

The necessity of the formation of students' functional literacy as a competency approach to the training of future Mathematics teachers is substantiated on the example of studying of one of the topics of analytical geometry. It has been established that a prerequisite for the development of any competency prescribed in the standards of secondary education is the initial existence of a sufficiently new concept of functional literacy for a student of a certain level. The basic literacy comes down to the ability to read, write and express of one's thoughts correctly. Let us consider the issue of functional literacy from the point of view of the pedagogic specialty. Acquaintance with the well-known textbooks of analytic geometry allows us to say that 2nd order algebraic surfaces in Euclidean space are determined in most cases algebraically by means of equations. A constructive approach is also of use – surfaces are obtained by rotating 2nd degree curves around their symmetry axes and by deformation of the resulting surfaces by compression. The metric approach, as it used for 2nd order curves, is restricted only by the formulation of problems to find the certain locus of points in space. The exception is the article Dmitriy Perepyolkin which was published in 1936. In this paper the locus of points in space with the following characteristic property is studied – the ratio of the distance to a given point to the distance to a given straight line is constant. The strait line is assumed not to contain the point. The study is held out in pure geometrical manner – it is done using the method of sections and known loci of points on the surface. In the present article we study the locus of points in space defined by metric relation to a certain set of pairs of points, lines and planes. It is shown that any non-degenerate 2nd order surface can be considered as a certain locus of points of space and this interpretation is not unique.

Álgebra Lineal y Geometría Analítica en carreras de Ingeniería: reporte de investigaciones

In this paper, 168 researches on Linear Algebra (LA) and Analytic Geometry (AG) at the university are analyzed, with the objective of knowing if these researches deal with the phenomenon of the split between this knowledge and to investigate about the main topics that guide the research on these subjects. An analysis is made using qualitative techniques obtaining a categorization in an inductive way. The results allow us to conclude that the split between LA and AG that operates in the study programs is not addressed by the researchers. Most focus on describing and analyzing students' difficulties with this knowledge, and among the proposals for teaching, the incorporation of software stands out. Only a minority consider, from an epistemological point of view, the benefits of a hybrid teaching between LA and AG.