Geometric Concepts Research Articles

PENGEMBANGAN LEMBAR KERJA PESERTA DIDIK (LKPD) BERBASIS ETNOMATEMATIKA PADA MATERI TRANSFORMASI

This study aims to produce teaching materials in the form of ethnomathematics-based worksheets on Lampung batik motifs in understanding valid and practical geometric transformation concepts. The type of research used is Research and Development (R&D). This research produced a product in the form of ethnomathematics-based worksheets on transformation material at SMP PGRI Kesumadadi. The research procedure used is the Borg and Gall development model which goes through several stages including: potentials and problems, data collection, product design, design validation, design revision, product testing, and product revision. In the product trial stage, a limited trial was carried out involving 15 class IX students at SMP PGRI Kesumadadi. The research instruments used were material expert validation sheets, media expert validation sheets, and student response questionnaires. The results of this development research show that the assessment of the material expert validation obtained an average validation result of 88.12% with the validation criterion of "Very Valid". Furthermore, the results of the validation of media experts obtained an average validation result of 91.66% with the validation criterion of "Very Valid". The results of the analysis of the student response questionnaire at the limited trial stage obtained a percentage of 92.6% with the practicality criterion "Very Practical".

The Effects of Augmented Reality Geometry Learning Applications on Spatial Visualization Ability for Primary School Pupils

Geometry is considered a fundamental component to be mastered in the elementary school mathematics curriculum. Lower primary school pupils frequently experience obstacles because of the abstract nature of geometric concepts and the requirement for spatial visualization skills, which are necessary for strengthening their conceptual understanding. Augmented reality (AR) technology offers a promising solution by providing visual representations of geometric shapes. Thus, this study aimed to investigate the effects of AR technology in primary school education on pupils’ spatial visualization abilities in geometry. Employing a quasiexperimental pre- and post-test research design, this study involved 61 second-grade pupils from two Northern Malaysian primary schools. The selection of schools followed cluster sampling techniques, while intact groups were utilized to select samples. Data were collected from two groups: an experimental group that utilized the LearnGeoAR applications and a control group that employed conventional teaching methods to learn geometric shapes. This study used the spatial visualization ability test (SVAT) instrument, grounded in Van Hiele’s theory of geometric thinking. The findings revealed that the experimental group, which utilized AR applications, exhibited a higher mean score in pupils’ spatial visualization ability in geometry compared to the control group. Additionally, the experiment demonstrated a moderate effect on both groups. This finding highlights the potential of AR technology in enhancing pupils’ spatial visualization skills in geometry instruction, providing valuable insights for instructional methodologies.

Attitude of Mathematics Teachers Towards the Use of Activity Based and Guided Discovery Strategies in Improving Students Understanding of Geometric Concepts

Attitude of Mathematics Teachers Towards the Use of Activity Based and Guided Discovery Strategies in Improving Students Understanding of Geometric Concepts

ГЕОМЕТРИЯ ПРЕДМЕТИН ОКУТУУДА ЖАСАЛМА ИНТЕЛЛЕКТТИН ОКУУЧУЛАРДЫН ЧЫГАРМАЧЫЛЫК ИШМЕРДҮҮЛҮГҮНДӨГҮ ОРДУ

In this paper, the place of artificial intelligence in the creative activity of students in teaching geometry as a subject of research was considered. The aim of the study is to determine how various artificial intelligence tools, such as computer programs, virtual environments, and robotics, can stimulate students' thinking for creative activities when learning geometry. The study used scientific methods such as comparison, analysis, survey and observation. As a result of the research, such advantages were achieved as the use of artificial intelligence to personalize learning, emotional organization, motivate students to creative activities, increase activity levels and improve understanding of geometric concepts. The study concluded that, in general, the use of artificial intelligence in geometry teaching gives students great opportunities to develop creative abilities and optimize the learning process. In the context of studying geometry, a deeper understanding of the impact of artificial intelligence on students' creativity was proposed, as well as suggestions for further improving the educational process using modern artificial intelligence technologies.

Interference of prototypical geometry representations in students’ construction of concepts and development of proofs

ABSTRACT This study investigates the impact of prototypical geometric representations on students’ ability to construct accurate geometric concepts and their subsequent performance in proving tasks related to those concepts. Ninety-one 11th-grade students participated in the study. We intentionally designed and utilized a questionnaire as the primary data-collection tool. We used the questionnaire items and findings as a basis for semi-structured interviews that we conducted with approximately 10% of the study participants. This allowed the integration of the quantitative and qualitative analyses, to provide a comprehensive understanding of the learning processes. Our analysis reveals that many Grade 11 students struggle with geometric concept formation due to an overreliance on prototypical examples, which in turn hinders their ability to construct proofs concerning the attributes of these concepts, highlighting the need for more diverse representations in geometry instruction.

Ethnomathematics Exploration of Multiplying and Measuring Activities on The Dome of The Great Mosque of Baitul Hakim Madiun City

Ethnomathematics is a study that explains the relationship between culture and mathematics. Ethnomathematics is applied as a means to motivate, stimulate, overcome saturation, and give a new feel to mathematical learning. One of the cultures that can be studied with ethnomathematics is the mosque. This study aims to learn mathematical concepts and explore ethnomathematics in the building of the Grand Mosque of Baitul Hakim Kota Madiun, the explored building, namely the dome of the mosque. This qualitative research uses an ethnographic approach with data retrieval using observation, interview, and documentation techniques. The research was conducted at the Grand Mosque of Baitul Hakim City of Madiun with 3 subjects being mosque administrators (secretariat admin, takmir, and marbot). The results of the research were obtained from mathematical concepts and ethnomathematics activities at the Grand Mosque of Baitul Hakim. The mathematical concept obtained is the geometric concept related to the flat construction of isosceles triangles, isosceles trapezoids, ellipses, and limas space structures. The ethnomathematics activity obtained is the activity of measuring and enumerating. Therefore, it can be concluded that there is ethnomathematic activity and there are mathematical concepts in the Grand Mosque of Baitul Hakim Kota Madiun that can be used as a learning resource by educators.

Developable forming of high-strength corrugated sheet metal

The classical theory of folded developables suggests that curved crease folding can be applied to sheet metal of high strength to manufacture parts with complex geometries. However, its application has been limited to sheet metals with low strength and requires grooving or perforation of the material at the fold lines. Applying the geometrical concept otherwise remains unexplored despite its potential in sheet metal-intensive industries like automotive, transportation, and construction. The current study introduces a novel sheet metal forming technique called developable forming. The theory of folded developables is applied to design a die tool for flange drawing a developable-shaped steel sheet. A developable connection is produced from high-strength material without resorting to thickness accommodation techniques. Experimental findings establish that the novel process does not follow the premises of the theory of folded developables. New shape effects are observed and the terms curving and coning are introduced to describe these. Additionally, significant redundant strains are identified in the flange, highlighting the different deformation modes in the developable forming process. A higher formability is achieved for a material with limited uniaxial elongation highlighting the need for further investigation on the mechanisms involved in the novel process.

A Geometric Approach to Textual Augmented Data Filtering

Abstract Data augmentation is necessary if the amount of training data is insufficient for supervised learning. For natural language processing tasks, obtaining good quality augmented data is not easy. This paper introduces GATFilter, a novel method for filtering out inappropriate augmented textual data for text classification (TC). Utilizing geometric concepts, more specifically the principle component and convex hull analyses, this method adeptly preserves the semantic integrity of words within augmented texts. GATFilter is versatile and applicable across various types of textual augmentation methods. Experiments using several datasets and augmentation strategies showed that classifiers trained with GATFilter-filtered augmented data sets showed improvements in key performance metrics, including accuracy, precision, recall, and F1 score. The method’s efficacy is notably influenced by the quality of the underlying augmentation techniques, indicating its potential to complement and refine various text augmentation strategies. Furthermore, our analysis showed that GATFilter is particularly able to amplify the effectiveness of methods that generate good quality augmented data. GATFilter is openly available online on Github1, and as a Python package2.

Enhancing senior high school students' visual imagery creativity in geometry through Geoboard

This study examines innovative learning tools to enhance students' understanding of geometry subjects. The research aims to describe the use of Geoboards in fostering the visual imagery creativity of 12th-grade students in geometry learning. The method used is descriptive qualitative, with subjects consisting of six students selected through purposive sampling. The results show that students with high visual imagery creativity possess good abilities in fluency, diversity, originality, and detail aspects. Students with moderate creativity still require guidance, while students with low creativity experience difficulties and need intensive practice. Using Geoboards has proven effective in enhancing visual imagery creativity, making learning more interesting and meaningful, and facilitating understanding of three-dimensional geometric concepts. The implications of this research suggest that Geoboards can be an effective learning tool in mathematics education.

Cα-CURVES AND THEIR Cα-FRAME IN CONFORMABLE DIFFERENTIAL GEOMETRY

The aim of this study is to redesign the space curve and its Frenet framework, which are extremely important in terms of differential geometry, by using conformable derivative arguments. In this context, conformable counterparts of basic geometric concepts such as angle, vector, line, plane and sphere have been obtained. The advantages of the conformable derivative over the classical (Newton) derivative are mentioned. Finally, new concepts produced by conformable derivative are supported with the help of examples and figures.

Ethnomathematics Study: Geometrical Concept in Kudus Market Snacks

Most students consider mathematics difficult, because it is abstract. To respond to this, teachers can use ethnomathematics in learning mathematics so that mathematics is easy to understand. One of the ethnomathematics objects that can be used is market snacks. Market snacks are traditional foods that are often sold in crowded places such as markets. This study aims to analyze the geometrical concepts that exist in various forms of market snacks in Kudus. This research uses a type of qualitative research with an ethnographic approach. Data collection used semi-structural interviews with 3 market snack sellers, literature studies, and documentation. The results of the study found that there are geometric concepts in market snacks. Triangular, rectangular, and circular shapes are found, while for spatial shapes, rectangular pyramids, blocks, spheres, triangular prisms, and tubes are found. The research results can be used as an alternative source of learning mathematics, especially in geometry material.

Origami: A path to successful teaching and learning of geometric concepts in basic education

The teaching of geometry requires encouraging the student to develop concentration processes. Attention, patience, creativity, among others, so that they learn to think and understand abstract concepts that can have meaning and usefulness within the educational process and daily life, analyzing the origami technique for the successful teaching and learning of geometric concepts.

Applying Hamilton’s vector formula in mathematics education: enhancing student mathematical skills through innovative teaching methods

The relevance of this discussion is driven by the need to improve mathematics teaching methods to enhance students’ mathematical competencies, particularly critical thinking and problem-solving skills. With its broad didactic potential, Hamilton’s vector formula becomes an essential tool in the educational process. The study aims to examine the impact of integrating Hamilton’s vector formula on the development of students’ mathematical competencies. The research methodology includes a literature review, expert evaluations, a pedagogical experiment with control and experimental groups, testing, and student surveys. The study results showed that using Hamilton’s vector formula promotes the development of students’ critical and analytical thinking, increases their confidence in solving complex problems, and improves overall mathematical competencies. The experimental group demonstrated higher test scores and practical task performance than the control group. Students noted that working with Hamilton’s vector formula helped them better understand geometric concepts and see the practical application of theoretical knowledge. The survey showed a positive perception of the new methodology, although some initial difficulties were noted. The practical significance of the results lies in developing recommendations for the effective use of Hamilton’s vector formula in the educational process, which can significantly improve the quality of students’ mathematical training and contribute to their successful learning process in the future.

Exploring Ethnomathematical Geometry in Indonesian Shadow Puppetry Gunungan: Philosophical and Educational Implications

This study delves into the philosophical dimensions of traditional architecture and the ethnomathematical geometry inherent in the mountains of shadow puppets, a significant aspect of Indonesia's cultural heritage. Utilizing a qualitative methodology with an ethnographic design, data were collected through observations and interviews with primary, secondary, and additional informants. The objective of this research is to uncover the mathematical concepts embedded in the mountains of shadow puppets, including geometry, algebra, arithmetic, and statistics, using an ethnographic approach that addresses four principal inquiries: "Where should I begin my investigation?", "How do I proceed with the search?", "How can I identify significant findings?", and "How do I interpret these findings?". The results indicate that among the four mathematical concepts investigated, only geometric concepts are present in the puppet mountains, as validated by a geometer. The geometric sub-concepts identified encompass (1) geometric transformations such as translation and reflection, (2) plane geometry including rhombuses, rectangles, triangles, and circles, and (3) congruence and symmetry. This research holds significant implications for enhancing students' mathematical education by incorporating geometric examples from local cultural contexts. Integrating ethnomathematics into school curricula can expand students' artistic horizons, boost their engagement in learning, and deepen their comprehension of mathematical concepts.

Numerical investigation of the erosion reduction in elbows using separate and helical inner ring

This study presents a comprehensive numerical investigation of erosion in bends equipped with inner rings as a novel geometric concept for erosion control. The research aims to assess the effectiveness of these innovative configurations in reducing erosion through rigorous computational fluid dynamics (CFD) simulations. Numerical modeling for the gas-solid two-phase flow has been carried out based on one-way coupling using an Eulerian-Lagrangian approach. The CFD model employed in this work incorporates the RNG k-ε turbulence model for flow solution, the Oka model for simulating surface erosion, and the Grant and Tabakoff model to account for particle-wall collisions. The primary focus of the investigation is to evaluate the erosion reduction capabilities of different inner ring configurations. By systematically varying the number of inner rings, the study elucidates the influence of this parameter on erosion mitigation. The obtained numerical results are analyzed in terms of erosion patterns, erosion reduction percentages, and the integral erosion surface criterion. The findings reveal the elbow with two separate inner rings as the most effective configuration, exhibiting a remarkable decrease in erosion of up to 43 % compared to the standard elbow. Moreover, based on the integral erosion surface criterion, the elbow with five separate inner rings emerges as a more desirable alternative to the standard elbow. In addition, the study investigates the impact of an elbow with helical inner rings configuration on erosion. It is observed that this configuration intensifies flow velocity, thereby accelerating particle motion and leading to increased erosion along the outer wall.

Supporting Young Learners in Learning Geometric Area Concepts Through Static Versus Dynamic Representation and Imagination Strategies

Supporting Young Learners in Learning Geometric Area Concepts Through Static Versus Dynamic Representation and Imagination Strategies

Pattern recognition among primary school students: The relationship with mathematical problem-solving

This paper explores the relationship between primary school students’ pattern recognition and mathematical problem-solving. A mixed-method research approach combining worksheets and interviews is used to identify patterns in students’ responses, with a focus on spatial, repeating, and growing patterns. The results of preliminary experiments with four Greek students aged eight to 11 years old, suggest a preference for geometric concepts and real-world examples. The findings could contribute to the discussions on customized pedagogical strategies in mathematics education, highlighting the importance of individualized approaches for optimal learning outcomes. The study advocates for the inclusion of visual and applied elements to cultivate critical thinking and problem-solving skills in early education.

Analysıs Of Students' Problem-Solvıng Abılıtıes On Hıgher Order Thınkıng Skıll (Hots) Geometry Problems In Terms Of Spatıal Reasonıng

Geometric concepts in mathematics possess abstract properties that require a spatial reasoning process. Evaluating problem-solving abilities through HOTS (Higher-Order Thinking Skills) questions focusing on spatial reasoning is crucial for enhancing students' skills. The aims of this research are: (1) To understand the process of students' problem-solving skills in geometry HOTS based on spatial reasoning; (2) To analyze and pinpoint the challenges faced by students in solving geometry problems through HOTS questions that involve spatial reasoning. This study employs a qualitative approach with data analysis following the Miles and Huberman model, comprising data collection, data reduction, data presentation, and conclusion. The data gathered includes test outcomes, interviews, and documentation. The participants consist of 2 fifth-grade teachers and 3 students from SD N Lulut 05 and SD N Lulut 03. The findings indicate the necessity of regular training for students to effectively tackle HOTS questions and avoid difficulties. The test results showed that the spatial reasoning of the two schools reached 32% in the high category, while the HOTS geometry problem solving reached 30% in the high category. Students with strong spatial reasoning skills excel in solving HOTS problems, whereas those with moderate to low abilities encounter challenges in geometry problem-solving. Therefore, the spatial reasoning skills of students with different proficiency levels vary in addressing geometric problems compared to those with high mathematical abilities. A tailored learning strategy is essential to cater to the diverse needs of these students.

Exploration of mathematical concepts in prayer and Mushofahah movements

Knowledge of integration between mathematics and religion is necessary to increase a Muslim's mastery of scientific treasures. This article describes several mathematical concepts contained in prayer movements and Mushofahah. This research is a qualitative descriptive research type of literature review. Data/information collection methods are carried out by observation and documentation. These two methods are used to collect information about mathematical concepts contained in prayer movements and Mushofahah, obtained from several primary and secondary sources in the form of the al-Qur’an, al-Hadith, books, and scientific journals as well as documentation of prayer movements and Mushofahah (shaking hands). The data analysis technique used is content analysis. The research results showed many daily life activities, including prayer and Mushofahah, concrete examples of the integration of mathematics and Islamic religion. These concepts include: In the prayer movement, there were number concepts, which included the addition and multiplication of integers, algebraic concepts in the form of sets, arithmetic sequences, and geometric concepts in the form of lines and angles. Meanwhile, in Mushofahah, there were factorial concepts, permutation concepts, and opportunities.

Ethnomathematics Exploration of Islamic Ornaments of the Mataram State Islamic University Building

The aim of this research is to determine the ethnomathematics elements in the Islamic ornament design of building B FTK UIN Mataram. This research is a type of qualitative descriptive research. Data on ethnomathematics elements in the Islamic ornament design of building B FTK UIN Mataram was taken using observation and documentation techniques. The object in this research is the Islamic ornaments of building B FTK UIN Mataram. All data were analyzed using qualitative descriptive with the Miles and Huberman model. The results of the research are that there are ethnomathematics aspects in the Islamic ornaments of building B, Faculty of Tarbiah and Teacher Training, Mataram State Islamic University. This can be seen from the geometric concepts of flat shapes and spatial shapes such as rectangles, hexagons, hexagrams, blocks and tubes. Then there are the concepts of transformation geometry such as translation, reflection and rotation