Geometry Course Research Articles

Analysis of Students' Mathematical Reasoning Ability with the Constructivism Approach through Mobile Learning System

Aims: To analyze the mathematical reasoning ability of mathematics education students.
 Study Design: Qualitative research with a descriptive approach.
 Place and Duration of Study: The population of all 3rd-semester mathematics education students at Bung Hatta University who take geometry courses is 25 students.
 Methodology: This research is qualitative research with a descriptive approach. Researchers directly measure the mathematical reasoning ability of students in the mathematics education study program. Judging from the research subjects, the population of all 3rd-semester mathematics education students at Bung Hatta University who took geometry courses was 25 students.
 Results: From the analysis results, it was found that the achievement of mathematical reasoning abilities for indicators of students' ability to present mathematical statements orally, in writing, pictures, and diagrams indicated by question number 1 was 74% (Good Category). The indicators of mathematical manipulation ability shown in questions number 2 and 5 are 41% (Category Enough), and 42% (Category Enough). And the indicators of students' ability to conclude, compile evidence, provide comments, or evidence from several solutions shown by questions number 3 and 4 are 67% (Good Category) and 58% (Enough Category).
 Conclusion: The conclusion of this study is to be able to determine the category of mathematical reasoning of the 3rd-semester students of the Bung Hatta University Mathematics Education Study Program.

ДИАСТАСИС: ВВЕДЕНИЕ В ТЕОРИЮ ДИСТАНЦИИ

The word “distance” itself is ambiguous: it means both the gap between two things, and the very ability of a thing to be at some distance from another, to stand at a distance. In the first case, we are simply talking about the impossibility of things to interact in the usual mode, while in the second about the thing’s own position, its individuation, which does not allow confusions. The superposition of these two meanings is productive for thought: from Plato’s reasoning about the causes of civil disorder through Nietzsche’s melancholic concept of elitism to 20th century theories proceeding from “social distance” (R. Park) as one of the starting points for constructing social reality. Although the translation of this word into different languages is not a problem, since the visual metaphor suggested by the geometry course (segment of a line) is clear, in all cases it is necessary to take into account rather explosive potential of its semantics.

IMPACT OF DESCRIPTIVE GEOMETRY ON THE IMPROVEMENT OF SPATIAL ABILITIES OF ARCHITECTURE STUDENTS

<jats:p>Spatial intelligence is an important skill for students of technical faculties, especially those fields where the capacity for engineering thinking and creative expression is equally valued. The field of Architecture is emphasized here, and the issue of assessing the spatial abilities of architecture students and their improvement has often been observed. This paper will examine the impact of the course of descriptive geometry on the development of their spatial thinking, and whether there is progress between the initial spatial abilities with which students were enrolled and abilities after completing the first semester of study.</jats:p>

An analysis of mathematics understanding of prospective student-teachers of mathematics

This quantitative-qualitative descriptive study aims to reveal the mathematics understanding of prospective student-teachers, describe the types of their mistakes in mathematics understanding, and recommend appropriate teaching of mathematics understanding. The subjects were 34 first-year students taking the Geometry course in the Mathematics Education Study Program, at a State University in Yogyakarta, Indonesia. The test instrument was consisting of four items, two of which were about the problems of procedural instrumental understanding and the other two were about the problems of relational understanding. The data were analyzed through the stages of reducing data, presenting data, and concluding data. The results show that students' mathematical understanding is categorized as good (87.75%). Students' procedural instrumental understanding (87.75%) is better than their relational understanding (77.52%) which is in good and sufficient categories, respectively. Some students made mistakes in representing theorems, performing mathematical procedural using appropriate concepts/theorems, and interpreting conclusions or proofs using appropriate notation and representation. It is recommended that mathematical learning should prioritize relational understanding by exploring a concept with other concepts and using various representations, situations, and contexts. Learning should focus more on relational understanding, namely discussing a concept and its relationship with other concepts with different representations, situations, and contexts.

\u201cAnything taking shape?\u201d Capturing various layers of small group collaborative problem solving in an experiential geometry course in initial teacher education

Collaborative problem solving (CPS) is widely recognized as a prominent 21st-century skill to be mastered. Until recently, research on CPS has often focused on problem solution by the individual; the interest in investigating how the theorized problem-solving constructs function as broader social units, such as pairs or small groups, is relatively recent. Capturing the complexity of CPS processes in group-level interaction is challenging. Therefore, a method of analysis capturing various layers of CPS was developed that aimed for a deeper understanding of CPS as a small-group enactment. In the study, small groups of teacher education students worked on two variations of open-ended CPS tasks—a technology-enhanced task and a task using physical objects. The method, relying on video data, encompassed triangulation of analysis methods and combined the following: (a) directed content analysis of the actualized CPS in groups, (b) process analysis and visualizations, and (c) qualitative cases. Content analysis did not show a large variation in how CPS was actualized in the groups or tasks for either case, whereas process analysis revealed both group- and task-related differences in accordance with the interchange of CPS elements. The qualitative cases exemplified the interaction diversity in the quality of coordination and students’ equal participation in groups. It was concluded that combining different methods gives access to various layers of CPS; moreover, it can contribute to a deeper articulation of the CPS as a group-level construct, providing divergent ways to understand CPS in this context.

INVESTIGATION OF SECONDARY EDUCATION MATHEMATICS CURRICULUM IN THE CONTEXT OF 21ST CENTURY SKILLS

With the transition to the digital age, changes have emerged in the skills expected from the individuals of the 21st century, and accordingly, the preparation of curricula to develop these skills has become the main goal of all countries in the world. In our country, studies have been carried out to develop curricula in this direction, and with this research, it is aimed to examine the secondary education mathematics (2010, 2011, 2013 and 2017) and geometry (2011) teaching programs in the context of 21st century skills. The research is a survey study aimed at examining the secondary school mathematics and geometry course curriculum in terms of 21st century skills. As the data source of the research, secondary school mathematics course and secondary school geometry course curricula shared on the official website of the Ministry of National Education were taken. Document analysis method was used in the collection and analysis of data in the research in which these teaching programs were accepted as documents. Curriculums specified within the scope of document analysis were analyzed with descriptive analysis method based on 21st century skills within the scope of Partnership for 21st Century Learning [P21]. The skills included in the curricula were supported by direct quotations from the curricula. According to the results of this research, it has been determined that the curriculum is not qualified to cover all 21st century skills. The fact that media literacy, leadership and responsibility skills are not included in the curriculum, and that the evaluation elements of the programs are insufficient in the context of 21st century skills are among the remarkable results. The findings obtained at the end of the research were discussed with the support of the literature and suggestions were made for future research.

The Students’ Mathematics Communication Skill Performance After GeoGebra-Assisted EPIC-R Learning Implementation

Mathematical communication is a fundamental skill needed by students. An application of ICT-based learning media, such as GeoGebra, using correct approach may increase mathematic communication. Therefore, this research aimed to analyze the effect of GeoGebra-assisted EPIC-R learning in improving students' mathematical communication skills. The study was sequential and explanatory research consisting of a sample size of 35 students from the Mathematical Education program at UIN Walisongo. The treatment class was treated using GeoGebra-assisted EPIC-R learning in geometry courses. Mathematical knowledge was observed from students’ communication skills while explaining answers to an assignment and formative assessment. The GeoGebra and formative assessment were used as the X1 and X2 variables. Meanwhile, students' answers from the formative assessment worksheet, which consists of their communication level, are used as the Y variable. The results showed that the X1 and X2 variables significantly affected Y by 24%, which means that applying GeoGebra-assisted with EPIC-R learning increases students' understanding of geometry and mathematical communication skills. However, this research is limited by providing significant reasons why students provide incomplete and insufficient answers. Therefore, further studies need to be carried out to understand students' mathematical communication by observing their main problems in explaining solutions.

Analisis Kemampuan Koneksi Matematis Mahasiswa ditinjau dari Self Regulated Learning(SRL) pada Pembelajaran Daring

This study aims to examine the ability of mathematical connections to be viewed from independent learning (SRL) in learning flat geometry courses. One class sample, namely second-semester students, collected 26 people, the mathematics education study program STKIP La Tansa Mashiro Rangkasbitung-Lebak, the 2020/2021 academic year. This type of research is descriptive qualitative chosen because it aims to describe the ability of students to solve math problems independently. The instrument used in this study is 30 questions for high, medium and low-level SRL, aiming to determine student learning independence. In contrast, five questions are given through the WhatsApp class group for the test instrument for mathematical connection abilities used in descriptions. The subjects in this study were selected based on active students and had good grades during bold learning activities. Then the interview test process was carried out six about the explanation between the researcher and the research subject. The results of the analysis of students' mathematical connection abilities, the mean value of the complete subject type SRL group = 96 with a score of 100%, moderate SRL of semi-complete type = 92.67 with a score of 90%, and Low SRL of incomplete type = 91 .67 with a score of 80%. Based on this, it shows that the value of the SRL category (high, medium, low) in the bold learning done after the analysis significantly affects the students' mathematical connection abilities.

Raising the Van Hiele Level of College Students

ABSTRACT This article describes the application of technology to the van Hiele Model for Geometric Thought to increase the van Hiele levels in an undergraduate Euclidean geometry course. Following the model with activities and phase-based instruction, students showed significant gains in the van Hiele levels in five different sections over the course of five semesters. By including the use of the CanFigureIt website, a Desmos activity, the Geometer’s Sketchpad and WebSketchpad during the fifth semester, students showed the largest gains in levels as measured by the van Hiele test.

Norms That Regulate the Theorem Construction Process in an Inquiry Classroom of 3D Geometry: Teacher’s Management to Promote Them

This paper aims to illustrate how a teacher instilled norms that regulate the theorem construction process in a three-dimensional geometry course. The course was part of a preservice mathematics teacher program, and it was characterized by promoting inquiry and argumentation. We analyze class excerpts in which students address tasks that require formulating conjectures, that emerge as a solution to a problem and proving such conjectures, and the teacher leads whole-class activities where students’ productions are exposed. For this, we used elements of the didactical analysis proposed by the onto-semiotic approach and Toulmin’s model for argumentation. The teacher’s professional actions that promoted reiterative actions in students’ mathematical practices were identified; we illustrate how these professional actions impelled students’ actions to become norms concerning issues about the legitimacy of different types of arguments (e.g., analogical and abductive) in the theorem construction process.

Students' Mathematical Critical Thinking Based on Self-Esteem Through Problem Based Learning in Geometry

This study aims to describe and determine mathematical critical thinking skills based on students' self-esteem. This type of research is a mixed method with a sequential explanatory research design. The population in this study were first year mathematics education students who took geometry courses with the sampling technique used purposive sampling. Determination of the subjects grouped based on self-esteem with high, medium, and low categories to be interviewed about students' critical thinking skills. The instruments in this study were tests and interviews. The results showed that description of mathematical critical thinking skills in terms of self-esteem of students varied. Four students indicate this with high self-esteem obtained by mathematical critical thinking skills results in the form of two students in high category and two students in medium category. From 25 students with moderate self-esteem, the results of the mathematical critical thinking skills were obtained in the form of five high category students, 14 moderate category students, and six in the low category students. From three students with low self-esteem, the results of the mathematical critical thinking ability result in the form of one student in the high category and two students in the low category. It can be concluded that there is a not too significant effect on students' critical thinking skills. Meanwhile, there are differences in students' critical thinking skills in terms of self-esteem at high, medium, and low levels.

Butterfly spirals

In this article special sequences involving the Butterfly theorem are defined. The Butterfly theorem states that if M is the midpoint of a chord PQ of a circle, then following some definite instructions, it is possible to get two other points X and Y on PQ, such that M is also the midpoint of the segment XY. The convergence investigation of those sequences reveals bounded piecewise spirals, and is done by using the free dynamic mathematics software GeoGebra. It is also supported with rigorous reasoning concerning the convergence of a special sequence. Moreover, it raises related problems that encourage further investigation. This article suggests a content that can be useful for students at secondary as well as undergraduate levels since it incorporates principles taught to students during their first courses in Algebra, Calculus and Geometry especially those related to convergent sequences, the algebra of complex numbers, plane isometries and basic Euclidean geometry.

Values Conveyed through Distance Education in Geometry Courses during COVID-19

Due to the COVID-19 pandemic, countries have had to change their usual teaching environment, and processes (especially traditional face to face education) with distance education. The purpose of this study was to investigate the Grade 9 mathematics course contents shared on the EBA platform in terms of mathematics values (mathematical values and mathematics educational values). In this sense, this study was a qualitative research based on document review. Data were collected from the Grade 9 mathematics course contents that exist in the EBA affiliated to the Turkish Ministry of National Education and were analysed using semantic content analysis. The results showed that the mathematical values such as objectivism, openness, rationalism, and the mathematics educational values such as formalistic view of mathematics learning, inquiry, instrumental understanding, facts & theories are often emphasized in distance education mathematics courses. The results of the study were also compared in detail with the results of the face-to-face mathematics education studies in the relevant literature (especially in the context of Turkey) and in this context some suggestions were also made for further studies.

Fostering Collaboration in an Asynchronous IBL Modern Geometry Course

The shift of evidence-based, active and inquiry-based pedagogy to online modalities has typically been done with a synchronous model, using video conferencing technology to facilitate interaction and collaboration amongst students. Such an approach can be infeasible for some students and create inequitable situations within a class. This paper details an implementation of using discussion boards to conduct an asynchronous inquiry course in Modern Geometry. Some advantages and drawbacks of this delivery are discussed. Finally, lessons learned from this implementation are laid out, as well as some advice for instructors who wish to implement such a course, or use discussion boards to supplement their current courses.

Analysis of Mathematical Representation Ability Based on Level of Reading Interest in Geometry Course

Reading literacy activities are currently being held by all levels of education. Literacy activities have a positive effect on students in understanding information. The ability to understand information can be realized through mathematical representation, which is one of the main elements in mathematical understanding. This research can help educators in mapping the mathematical representation ability based on the reading interest of students. The purpose of this research is to identify which indicators can be mastered by students who have reading interests at high, medium, and low levels. This research is qualitative. The research subjects were students of the Mathematics Education Department of Ivet University. The data collection procedures used were scale, test, and interview. The instruments of this study were the reading interest scale, mathematical representation ability test, and interview sheets. The data analysis technique of this study adopted data analysis techniques from Miles and Huberman. The conclusions of this study are (1) students with high and medium reading levels have the ability to represent mathematical representations to model and interpret physical, social, and mathematical phenomena; have the ability of mathematical representations to create and use representations to communicate mathematical ideas or concepts; have the ability of mathematical representations in selecting, applying, and translating mathematical representations to solve problems, (2) students with a low reading level have lacked on the ability of mathematical representations to use representations to model and interpret physical, social, and mathematical phenomena, thus it caused them couldn’t mastering the ability of mathematical representations to create and use representations to communicate mathematical ideas or concepts and the ability of mathematical representations to select, apply, and translate mathematical representations to solve problems.
 Keywords: mathematical representation ability, reading interest, 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

Using Creative Thinking in Defining Geometry Concepts via Recognizing Elementary Objects, Drawing, and Writing Process of Concept Image

Mathematics teacher's competences in understanding some properties and relationships between the elements of geometry objects support the students' learning in mastering the geometry contents. This research investigates and describes the creative thinking approach of teacher candidates in defining geometry concepts based on recognizing primitive and elementary objects, drawing, and writing process of concept image. The steps are as follows. Using pre-test, we evaluated the students who had a good basic knowledge of geometry to attend a geometry course. We provided seven geometry definitions to encourage the students to understand. Then, they were tested and ranked by their understandings of the seven definitions with passing grade minimum score sixty of interval 0-100. From the qualified students, they do the task to compose some alternative definitions of these concepts through the creative thinking scheme. We interviewed them to know the understanding process. This research found that students' creativity offers many ideas and ways to construct diverse alternative definitions. It included understanding pre-knowledge, the essential features needed to build the geometry concepts, and structuring definition language. We discovered three group types of creative thinking result in the defining geometry concepts, i.e., productive-creative, constant-creative, and decrease-creative thinking. This research contributes knowledge for students about how geometry definitions are constructed by introducing primitive and elementary objects of geometry, sketching concepts image, and writing practice of the concepts. The creative thinking scheme can guide and lead students to state the geometry definitions in both descriptive and connotative expressions with different sentences.

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.

Evaluation of virtual laboratory media to learning geometry in Universitas Terbuka

The virtual laboratory is developing rapidly at present. The increasing numbers of students of state or private universities who eagerly find references related to practical geometry courses online is one of the development indicators. The invention of virtual laboratories with Virtual Reality based become the entity of concern to add values to lectures. This study applied ADDIE, a R&D model (Analysis, Design, Develop, Implementation and Evaluation). The steps done were implementing and marketing the product in State and Private Universities in the region of Central Java and its surroundings. Based on the findings on the use of virtual geometry lab product, it scores 91 and 94 meaning that the virtual geometry lab product is very suitable to use in teaching. Then more than 90% of lecturers and students at Universitas Terbuka are pleased to use it. Enabling the virtual laboratories with Virtual Reality based, enhanced the teaching and learning process.

Development of a web-based worksheet with a project-based learning model assisted by GeoGebra

Previous studies on the use of GeoGebra in mathematics learning were more focused on implementation and effectiveness in learning outcomes. However, not many studies focus on providing opportunities to students to explore Geo­Gebra to find concepts in plane geometry through developing an application. Therefore, this research and development applied a 4D model to produce a web-based worksheet using project-based learning (PjBL) assisted by GeoGebra that was valid, practical, and effective in the plane geometry course. The web-based worksheet intended to facilitate students to be independent, creative, and able to find the concepts in the plane geometry course through exploration activities using GeoGebra. The results of the data analysis revealed that this research and development produced a web-based worksheet using PjBL assisted by Geo­Gebra that was valid, practical, and effective. The validity of the web-based student worksheet was shown from the validation results explaining that the worksheet was good in terms of content, construction, and language. The prac­ticality of the worksheet was shown from the results of practitioner assessments and student questionnaires, showing that the web-based worksheet was easy to use and attractive. The effectiveness of the worksheet was shown from the formative assessment results with the interpretation that the use of the web-based worksheet could help students understand the content of plane geometry well.