GeoGebra Program Research Articles

PENGGUNAAN MEDIA SOFTWARE GEOGEBRA UNTUK MENINGKATKAN KEMAMPUAN REPRESENTASI MATEMATIS SISWA SMA

Mathematical representation ability is an important ability in understanding mathematical concepts as an effort to obtain clarity of meaning and understanding in solving problems. Technology-based learning media can simplify the learning process thereby helping students in representing mathematical problems. This research aims to determine the increase in students' mathematical representation abilities using Geogebra software. This research is quantitative research with a quasi-experimental type. The population is students of class XI MIPA at SMA Negeri 1 Lhoong Aceh Besar for the 2023/2024 academic year consisting of 2 classes totaling 60 people. There are 30 people in Class XI MIPA 1 as an experimental class with the Geogebra software learning media, and 30 people in XI MIPA 2 as a control class without the Geogebra program learning media. The data collection technique in this research is using Pretest and Posttest. Meanwhile, the data analysis techniques used in this research are descriptive statistical analysis and inferential statistical analysis. The results of the research showed that there was an increase in students' mathematical representation abilities who were taught using Geogebra software media in class XI MIPA students at SMA Negeri 1 Lhoong. Most students answered the questions according to indicators of mathematical representation ability in the form of visual, symbolic and verbal representations.

USING INNOVATIVE TECHNOLOGIES IN MATHEMATICS LESSONS (A CASE STUDY OF THE GEOGEBRA)

This article shows the advantages of using the GeoGebra program for mathematics teachers in addressing subject-related problems, as well as the issues of the feasibility of integrating this dynamic software into modern education.

THE DEVELOPMENT OF MATHEMATICS LEARNING ACHIEVEMENT ON THE TOPIC OF SOLVING QUADRATIC FUNCTION GRAPHS OF MATHAYOM 3 STUDENTS BY USING THE GEOGEBRA PROGRAM TOGETHER WITH POLYA'S PROBLEM SOLVING PROCESS

This research used GeoGebra program and organized learning management activities in accordance with Polya’s problem-solving process to develop mathematical learning achievement by solving problems in quadratic function graphs. With the help of GeoGebra program and step-by-step practice of problem-solving techniques using Polya’s problem-solving process, the aforementioned learning management system increases students' enthusiasm and interest in learning about graphs. Consequently, it encourages students to comprehend the knowledge of quadratic function graphs in mathematics efficiently, gain a more thorough comprehension of them, and develop their skills in solving problems. The target group used in the research is 14 Mathayom 3 students studying in the first semester of the academic year 2023 at Chumchonyodkaengsongkhro School, Namon District, Kalasin Province, which obtained purposive random sampling. The tools used in the research were lesson plans using GeoGebra with Polya’s problem-solving process, learning achievement tests, and a satisfaction questionnaire. The statistics used in the data analysis include mean (x̄), standard deviation (SD), percentage, and t-test statistics. The results of the research found that: 1) the results of the efficiency of the lesson plans using GeoGebra program with Polya’s problem solving process are equal to 73.75/74.64, which is higher than with the specified criteria, 2) The post-test scores’ learning achievement using GeoGebra with Polya's problem-solving process was higher than the pre-test scores using GeoGebra with Polya's problem-solving process, with statistical significance at the .05 level, and 3) the satisfaction of students with learning management using GeoGebra program with Polya’s problem-solving process is at a high level with an average of 4.31 and a standard deviation of 0.81.

Use of GeoGebra for teaching quadratic equation

The present study was carried out to massify the use of the GeoGebra program in high school mathematics teachers. A pretest was carried out, after the training an evaluation was used, and then a satisfaction survey with all the teachers, with the dependent variable being the learning of quadratic equations and the use of GeoGebra as an independent variable. The methodology consisted of using this software to motivate students in the teaching-learning process of mathematics. The main results show that the traditional teaching of mathematics can be complex for today's students, however, the use of technological tools such as GeoGebra is attractive to them, which causes motivation and consequently achieves more effective learning.

Association of two square difference identity to regular polygons and circles

GeoGebra is a dynamic software that is frequently used and of increasing importance in mathematics teaching processes in our digital age. Accordingly, in this study a new perspective has been brought to the proofs of the “two square difference identity” expressed for the square, which is a flat polygon, made with different approaches. With side lengths a, b, and a>b, it has been shown that the identity given by the equation (difference of area) a<sup>2</sup>-b<sup>2</sup>=(a-b)(a+b) is true for other regular polygons as well. In the study, direct proof method was used within the framework of the principle of conservation of measure, which is one of the basic principles of geometry teaching. GeoGebra program, which is a dynamic geometry software, was preferred for drawing geometric shapes used in proofs. In order to generalize the number n, a different fragmentation technique was preferred to the proofs made using different drawings for equilateral triangle and square, which are the simplest regular polygons. It has also been shown that this identity is true for circles viewed as polygons with an infinite number of sides.

Synthesis of the contour and dimensions of the guiding channel of an elliptical drum according to the operation conditions and kinematic regimes

The article is devoted to the synthesis of the mechanism of an elliptical drum of a vertically spindle drum, which increases the completeness of the collection and the quality of the harvested raw cotton. In particular, it developed a methodology for substantiating the profile and dimensions of the guide track, which ensures the movement of the spindles along an elliptical trajectory. At the same time, the profile and dimensions of the guide track are considered as a function of the trajectory and kinematic modes of the spindle. It is shown that the trajectory of movement and kinematic modes of the center of the guide roller can be the basis for choosing the profile and basic geometric dimensions of the guide track. The trajectory of the center of the guide roller at its different positions relative to the center of the spindle, moving along an elliptical trajectory, is determined using the GeoGebra program, which is popular in the mathematical modeling environment, and its kinematic parameters are determined by constructing hodographs of the speed of the center of the guide roller.

Some geometric properties of the Padovan vectors in Euclidean 3-space

Padovan numbers were defined by Stewart (1996) in honor of the modern architect Richard Padovan (1935) and were first discovered in 1924 by Gerard Cordonnier. Padovan numbers are a special status of Tribonacci numbers with initial conditions and general terms. The ratio between Padovan numbers is one of the important algebraic numbers because it produces plastic numbers. Up to now, various studies have been conducted on Padovan numbers and Padovan polynomial sequences. In this study, Padovan vectors are defined for the first time by using the Padovan Binet-like formula and reduction relation. Then, geometric properties of Padovan vectors such as inner product, norm, and vector products are analyzed. In the last part of the study, Padovan vectors were calculated with Binet formulas in the Geogebra program. In addition, the first ten Padovan numbers and Padovan vectors were calculated using the Binet formulas and shown as points and vectors in three-dimensional space. According to the Padovan vectors found, the Padovan curve was drawn in space for the first time by using the curve fitting feature of the Geogebra program. Thus, with our study, a geometric approach to Padovan number sequences was brought for the first time.

فاعلية برنامج GeoGebra في تحصيل مادة الرياضيات لدى طالبات الصف الأول المتوسط

The current research aims to identify the effectiveness of the GeoGebra program in the achievement of mathematics among middle first graders. For the purpose of verifying the objective of the research, the following null hypothesis was formulated: There is no statistically significant difference at the level of (0.05) between the average scores of the female students of the experimental group studying using the geogra program and the average scores of the female students of the control group studying in the usual way in the achievement test. The researcher used experimental design with partial control for the two equal groups,which includes two groups. The research sample consisted of (80) female students who were distributed equally between the two groups. The two groups were rewarded in variables (chronological age, intelligence, previous achievement). The researcher also adjusted extraneous variables such as the confidentiality of the experiment and processes related to maturity and experimental extinction. The researcher identified the scientific material represented in chapters (5 , 6) of the mathematics textbook for the first intermediate grade (I 3 of 2018 ) The researcher formulated behavioral goals for the scientific material, which reached (116) behavioral goals. She also prepared a teaching plan for the experimental group and a teaching plan for the control group. With regard to research tools, the researcher has prepared a post-acquisition test where (25) items were drafted for the achievement test (MCQ) for middle first grade students, and they were Answering the test according to four alternatives ( one true and three false ) , and the face validity of it was calculated by presenting it to a group of experienced and competent arbitrators. Reliability was calculated using the Kuder-Regardson equation (20) and calculating the coefficient of difficulty and its discernment and the effectiveness of the wrong alternatives for all items . The experiment was applied in the second course of the academic year (2022-2023) to the research sample of middle first grade students, where the researcher taught the two research groups, and after the end of the experiment, the results were analyzed statistically using the T-test for two independent samples. The results outperformed the experimental group taught using Geogbra software on control group students who studied in the normal way on the achievement test. Keywords: GeoGebra, achievement , Mathematics

فاعلية برنامج GeoGebra في تحصيل مادة الرياضيات لدى طالبات الصف الأول المتوسط

The current research aims to identify the effectiveness of the GeoGebra program in the achievement of mathematics among middle first graders. For the purpose of verifying the objective of the research, the following null hypothesis was formulated: There is no statistically significant difference at the level of (0.05) between the average scores of the female students of the experimental group studying using the geogra program and the average scores of the female students of the control group studying in the usual way in the achievement test. The researcher used experimental design with partial control for the two equal groups,which includes two groups. The research sample consisted of (80) female students who were distributed equally between the two groups. The two groups were rewarded in variables (chronological age, intelligence, previous achievement). The researcher also adjusted extraneous variables such as the confidentiality of the experiment and processes related to maturity and experimental extinction. The researcher identified the scientific material represented in chapters (5 , 6) of the mathematics textbook for the first intermediate grade (I 3 of 2018 ) The researcher formulated behavioral goals for the scientific material, which reached (116) behavioral goals. She also prepared a teaching plan for the experimental group and a teaching plan for the control group. With regard to research tools, the researcher has prepared a post-acquisition test where (25) items were drafted for the achievement test (MCQ) for middle first grade students, and they were Answering the test according to four alternatives ( one true and three false ) , and the face validity of it was calculated by presenting it to a group of experienced and competent arbitrators. Reliability was calculated using the Kuder-Regardson equation (20) and calculating the coefficient of difficulty and its discernment and the effectiveness of the wrong alternatives for all items . The experiment was applied in the second course of the academic year (2022-2023) to the research sample of middle first grade students, where the researcher taught the two research groups, and after the end of the experiment, the results were analyzed statistically using the T-test for two independent samples. The results outperformed the experimental group taught using Geogbra software on control group students who studied in the normal way on the achievement test. Keywords: GeoGebra, achievement , Mathematics

Assessing damage and predicting future risks: A study of the Schilling Titan 4 manipulator on work class ROVs in offshore oil and gas industry

This article undertakes a comprehensive investigation of the damage incurred by the Schilling-manufactured Titan 4 seven-function manipulator during the period of 2017–2022. This particular manipulator stands as the most widely employed equipment on work class remotely operated vehicles (ROVs) globally. The article delves into a detailed discussion of ROVs in general, with a specific focus on those belonging to the work class category. Furthermore, the manipulator is dissected into its constituent elements, as delineated by the manufacturer, and each individual component is subjected to separate evaluation. The damages that were encountered are described in detail, along with the corresponding repair processes.To quantify the likelihood of future damage to the various manipulator elements over the subsequent five-year period, the obtained damage results are inputted into the Geogebra program. This enables the calculation of the probability of damage occurrence for each individual component.The research findings are ultimately summarized and juxtaposed with the real-life experiences of ROV operators, which are captured through a meticulously designed questionnaire. The questionnaire is carefully constructed to elicit valuable insights from the operators regarding the most common faults or defects observed in the Titan 4 manipulator.It is important to note that this manipulator-focused investigation is based on the author's first-hand experience as a ROV Supervisor in the offshore oil and gas industry. The combination of practical expertise and the empirical data gathered from the questionnaire responses ensures a comprehensive and well-rounded examination of the Titan 4 manipulator and its associated operational challenges.

Pelatihan Penggunaan Aplikasi Geogebra sebagai Media Pembelajaran Inovatif pada Calon Guru Sekolah Dasar

Innovative learning media is a form of developing learning media designed to provide a more interesting and interactive learning experience for students. Due to the importance of using innovative learning media, prospective elementary school teacher students must be equipped with various technology mastery skills to develop their abilities so that they can present a meaningful teaching and learning process. Meaningful learning certainly requires interactive media to support the implementation of classroom learning. One program that can be used is the GeoGebra program. The GeoGebra program is a computer or smartphone program that can visualize abstract mathematical material. The GeoGebra application shows that this program can be used as a bridge in delivering mathematics material so as to make it easier for educators in the teaching and learning process. The purpose of this training is to increase the knowledge and abilities of prospective elementary school teachers in designing and using GeoGebra in learning mathematics. In this service, an example of the material practised during the training is. The results of this service can be said to be successful, as seen from the enthusiasm of the participants in participating in the training. This is also marked from the results of the posttest questionnaire that 100% of participants are ready to use the GeoGebra application in developing learning media.

Ways to form practical skills in students using the «Geogebra» program in teaching algebra

Training through special computer resources as ways to form practical skills in students based on the use of the «Geogebra» program in teaching algebra is an urgent problem of our time. The article showed the results of research work on the use of the geogebra program in mastering the topic of quadratic functions in the discipline algebra of the 8th grade in the intensive implementation of the work on constructing graphs of the sought-after functions using a special graphical environment. Scientific research was carried out on the basis of school-gymnasium No.1 in Kentau. In the course of conducting a scientific study within the framework of the topic, a pedagogical experiment was organized among 8th grade students, control research methods were used, and students were surveyed. In the school mathematics course, students practical skills were formed using digital technologies. During the lesson, the Geogebra program was used. The result of scientific research can be used in teaching a course of Mathematics at school as a methodological guide for mathematics teachers or as an additional material for students. With the help of this instruction, you can quickly achieve results during the course of the lesson. Using the search experience, methodological kits for use in mathematics lessons and auxiliary materials for teachers related to the Geogebra program were developed. Within the framework of the «Geogebra» program, using the control method during the lesson, a control and an experiment on the release of reports were carried out.

Využitie programu GeoGebra v intenciách primárneho matematického vzdelávania

According to the results of the nationwide testing of fifth-grade students (T5), Slovak students have a problem with the problems from the thematic unit Geometry and measurement. One of the reasons may be the lack of visualization and manipulative activities during mathematics teaching. Visualization can be improved by using various computer programs focused on planar geometry. GeoGebra is one of these programs. The contribution offers the possibility of using the GeoGebra program to improve the mathematical concepts of primary education pupils.

The Effectiveness of a Training Program Based on GeoGebra Program in Developing Mathematical Generalizations Teaching Skills among Female Student - Teachers at the Islamic University of Gaza

The research aims to design a training program based on GoeGebra program and to explore its effectiveness in developing the teaching skills of mathematical generalizations among the Islamic University in Gaza female students who practice teaching. The research adopted the constructive approach in order to design the intended training program based on interactive programs and the one-group quasi-experimental approach to reveal effectiveness of the designed training program. The sample of the research consisted of (22) randomly selected female students who study mathematics and are enrolled in the module of Field Training. The researchers prepared a note card consisting of (36) items divided into three fields (planning skills, implementation skills, and assessment skills) to evaluate performance of the female students in the teaching skills of mathematical generalizations using the GeoGebra program. The research results showed the effectiveness of the proposed training program based on the GeoGebra program in developing the skills of teaching mathematical generalizations among the female student- teachers. The research recommended the need to train students at faculties of education who practice teaching on the use of GeoGebra program in the teaching of mathematics subjects especially mathematical generalizations.

The Effectiveness of a Training Program Based on GeoGebra Program in Developing Mathematical Generalizations Teaching Skills among Female Student - Teachers at the Islamic University of Gaza

The research aims to design a training program based on GoeGebra program and to explore its effectiveness in developing the teaching skills of mathematical generalizations among the Islamic University in Gaza female students who practice teaching. The research adopted the constructive approach in order to design the intended training program based on interactive programs and the one-group quasi-experimental approach to reveal effectiveness of the designed training program. The sample of the research consisted of (22) randomly selected female students who study mathematics and are enrolled in the module of Field Training. The researchers prepared a note card consisting of (36) items divided into three fields (planning skills, implementation skills, and assessment skills) to evaluate performance of the female students in the teaching skills of mathematical generalizations using the GeoGebra program. The research results showed the effectiveness of the proposed training program based on the GeoGebra program in developing the skills of teaching mathematical generalizations among the female student- teachers. The research recommended the need to train students at faculties of education who practice teaching on the use of GeoGebra program in the teaching of mathematics subjects especially mathematical generalizations.

Penggunaan Geogebra dalam Geometri Ruang

The rapid development of technology opens up new opportunities and ways in doing many things, including to develop the world of education. One of the learning media that is currently developing so rapidly is a computer with various relevant programs. One of the computer programs that can be used as a medium for learning mathematics is the Geogebra program. The purpose of this community service is to find out the use of Geogabra in geometric geometry at Sei Putih High School, Kampar Riau Regency. The methods that will be used in this activity are direct observation, interviews, presentations, and questions and answers. The results of this service activity received a positive response from the partner schools and the teachers participating in the workshop. This can be seen from the enthusiasm of the training participants and the seriousness of the participants during the activity. The participants hoped for further training so that the competence of the Sei Putih High School mathematics teacher in learning using Geogebra would increase.

Conic curves in jungle river metric

In this article, we refer to different way of measuring distances than commonly used Euclidean metric. It is shown how some objects of two-dimensional geometry look like in the jungle river metric. Some examples of the objects are presented in pictures made in the free available Geogebra program, the conditions of occurrence of this objects are exactly described. Reading the text, one may learn that a sphere need not be round and a parabola may not be a bounded curve. Some task for the reader are included.

SOME APPLICATIONS OF EXPONENTIAL AND LOGISTIC GROWTH MODELS IN BUSINESS AND ECONOMICS

The use of mathematics for predicting and analyzing the future has long been a subject of study due to the fact that it is a measurable source. Correct estimation is vital for the business world and its economic society. In this study, by employing the exponential growth model and the logistic and generalized logistic models, we estimate the size of the population of Turkey, the international investment position and the level of the national income per person in 2025. Furthermore, we examine the changes in sales of houses and the number of mobile phone subscribers in Turkey. We use GeoGebra program to determine the constants and use the computer algebraic system Maple 15 for other computations and graphs

ВИЗУАЛИЗАЦИЯ КРИВЫХ ВТОРОГО ПОРЯДКА В СРЕДЕ GEOGEBRA ПРИ ОБУЧЕНИИ МАТЕМАТИКЕ СТУДЕНТОВ КОЛЛЕДЖА

Problem statement. This article is devoted to such a topical issue as the use of the dynamic mathematics system (DMS) GeoGebra in teaching mathematics. DMSs are gradually being introduced into mathematics education, but the question is raised about the effectiveness of their application. The purpose of the article is to study the influence of GeoGebra on the quality of the solving of tasks on the topic «Second order curves» by 2nd year students studying in the specialty “Applied Informatics (by branches)” at NovosibirskProfessional and Pedagogical Vocational Education Institution. The research methodology consisted in the analysis and synthesis of scientific literature on the chosen topic, pedagogical experiment, mathematical methods of processing the results of this experiment and observation of the participants in the pedagogical process.The obtained results of the research indicate that the use of the GeoGebra program has a positive effect on the academic performance of students. Statistical processing of the obtained data shows that there are no differences in the selected criteria between the group that worked in the GeoGebra and the group that worked without computer programs. However, the use of DMSmakes it possible to visually demonstrate the material, draw the attention of students to the academic discipline, promotes the development of creative thinking, and allows students to experiment with mathematical objects on their own. Conclusion. Due to the widespread use of dynamic systems in mathematics education, the study of their influence on the development of various cognitive abilities and personal qualities of students is of practical and scientific interest. The materials of the work can be used in the educational process when teaching and learning the course EN.01 Mathematics at the level of secondary vocational education and distributed to various topics and sections of mathematical disciplines at other levels of education.

Application of the Geogebra Program in the Learning of Geometry in Students of 4th grade of High School N° 86620 Santa Fe de Tumpa -Yungay, 2018 [Aplicación del Programa Geogebra en el Aprendizaje de la Geometría en Alumnos de 4to año de educación secundaria de la I.E. N° 86620 Santa Fe de Tumpa -Yungay, 2018

The objective of the research is to determine the influence of the Application of the Geogebra Program in the Learning of Geometry in students of 4th grade of High school N° 86620 Santa Fe de Tumpa - Yungay, 2018. The research is cross-sectional experimental type, quantitative method and pre-experimental design. Two instruments were applied: an entrance exam and an exit exam, to a population sample of 22 students from the 4th grade of High school N° 86620 Santa Fe de Tumpa. The results were analyzed after applying the Geogebra program to the single study group. It was found that there is a highly significant influence (p = 0.00001 <0.05) of the Application of the Geogebra program in the Learning of geometry course in High school 4th grade students. The verification of the hypothesis was done by applying the t-student.