Geometric Concepts Research Articles

A Survey About Universal Numerical Integrators (UNIs): Part II or Quantitative Approach

AbstractIn Part I, we focused more on the intuitive and geometrical concepts behind Universal Numerical Integrators (UNIs) and their possible classification. This first article worked almost as a categorical analysis for UNIs. In Part I, we also saw an extensive literature review about them. However, in Part II, we examine the mathematics that makes it possible to couple a conventional numerical integrator to some universal approximator of functions. Here, we also present an essential list of the significant mathematical properties related to the design of a UNI. We also hope that the theoretical content in these two articles can help guide researchers aiming to computationally design general problems related to some Universal Numerical Integrator (UNI).

POSSIBILITIES OF USING PROBLEMED LEARNING IN TEACHING GEOMETRIC CONCEPTS IN PRIMARY GRADES

In this article, an idea is given about the possibilities of using problem-based learning in the formation of geometric concepts in elementary school mathematics education. Problematic education includes such categories as problem, learning problem, problem situation, problem, problem question, problem assignment. Teaching concepts like straight-line, straight-line section, broken line, length of broken line, perimeter of a triangle, perimeter of a rectangle, perimeter of a polygon, which are studied in primary grades, using problem-based learning, allows students to quickly and effectively master these concepts, as well as to be able to apply the acquired knowledge in practice gives.

Developing TPACK through task design: exploring the use of multiple modes of representation and the promotion of mathematical processes

ABSTRACT This research considers the need to train teachers who can effectively integrate technology for teaching and learning mathematics. The primary goal of this research is to showcase a successful training experience by identifying and describing some indicators of the technological pedagogical content knowledge acquired by pre-service early childhood education teachers during their participation in this initial training programme. Specifically, we focus on the different ways of representing mathematical concepts and the mathematical processes that can be activated by including such modes of representation. The participants in this research were 28 PECTs, who were organised into groups that planned a set of tasks using technology to teach geometric concepts. The results show that the groups employed a variety of modes of representation, translations and transformations (connections), fostering the emergence of different mathematical processes. Thus, our proposal to integrate technology was satisfactory in this sense, suggesting its potential applicability across diverse subjects, particularly those in which the ways of representing concepts play a relevant role. Also, the analysis conducted may be extrapolated to subjects others than mathematics.

Geometry, anomaly, topology, and transport in Weyl fermions.

Weyl fermions are one of the simplest objects that link ideas in geometry and topology to high-energy physics and condensed matter physics. Although the existence of Weyl fermions as elementary particles remains dubious, there is mounting evidence of their existence as quasiparticles in certain condensed matter systems. Such systems are termed Weyl semimetals (WSMs). Needless to say, WSMs have emerged as a fascinating class of materials with unique electronic properties, offering a rich playground for both fundamental research and potential technological applications. This review examines recent advancements in understanding electron transport in {WSMs}. We begin with a pedagogical introduction to the geometric and topological concepts critical to understanding quantum transport in Weyl fermions. We then explore chiral anomaly (CA), a defining feature of WSMs, and its impact on transport phenomena such as longitudinal magnetoconductance (LMC) and planar Hall effect (PHE). The Maxwell-Boltzmann transport theory extended beyond the standard relaxation-time approximation is then discussed in the context of Weyl fermions, which is used to evaluate various transport properties. Attention is also given to the effects of strain-induced gauge fields and external magnetic fields in both time-reversal broken and inversion asymmetric inhomogeneous WSMs. The review synthesizes theoretical insights, experimental observations, and numerical simulations to provide a comprehensive understanding of the complex transport behaviors in WSMs, aiming to bridge the gap between theoretical predictions and experimental verification.

Augmented Reality for Exploring Solids: A Study on Improving Pre-Service Teachers

Applications of augmented reality are gradually being integrated into teaching at various levels and types of schools. Augmented reality has the potential to transform the training of future teachers in the context of developing their mathematical knowledge, digital skills, and teaching competencies. The paper focuses on researching the impact of augmented reality on the learning of future primary teachers. The aim was to investigate the impact of AR applications on the development of cognitive and psychomotor skills and on students' motivation to learn. The study had a mixed research design. Using a pedagogical experiment, we investigated the effectiveness of an educational intervention based on the use of applications Augmented Reality in combination with hands on activities in the training of future teachers. The educational intervention was a set of activities that were carried out in a mixed reality environment using the 3D solids construction kit, the Polyedres augmentes and GeoGebra applications. The content of the educational intervention was the exploration of significant elements and properties of solids. We tested students' knowledge and abilities in the following areas: identification of simple solids from a picture; identification of significant elements of solids (vertices, edges and faces); identification of the shapes of faces of solids; nets of solids; simple metric tasks with solids. The study was conducted in 2024 with 152 primary education students as part of geometry courses. In line with the results of previous research in this area, we found that AR has the potential to improve understanding of geometric concepts, increase interactivity and student motivation. Augmented reality opens up new possibilities for exploring solids and their properties, as it allows for transfer between planar and spatial representation of solids and helps to develop spatial imagination.

The relationship between peer social support and self-regulated learning in Samarinda Ulu state junior high school students

Purpose: At the age of 2-7 years, based on Piaget's theory, children are in the pre-operational stage. At this stage, children have the ability to understand mathematical concepts concretely through sensory and interactive experiences. Strategies are needed to improve the children's cognitive abilities. This research aims to provide an overview of early childhood cognitive development at the pre-operational stage in the introduction of geometric shapes. Method: Researchers used a descriptive qualitative approach to interpret and explain patterns of behavior of children who are in the pre-operational stage. Data collection techniques included structured interviews and observations with checklists based on Jean Piaget’s cognitive theory. Respondents in this study were selected using a purposive sampling technique. The respondents consisted of five children aged 6-7 years from the Islamic Kindergarten 'Aqila who were not familiar with geometric shapes. Result: The results of this study indicate that children who are the subjects of the study exhibit behavior patterns consistent with Piaget's theory in the pre-operational stage, Children are able to recognize shapes through interactive learning experiences. Conclusion: Based on the results, it is necessary for parents and teachers to pay attention to the child's cognitive development stage when teaching geometric concepts.

Brodsky: The mathematics of poetry

The article examines the use of mathematical terminology in J. Brodsky’s poetry and considers the genesis of geometric and arithmetic concepts in his oeuvre. The author suggests that, having dropped out of school at the age of fifteen and loathing the Soviet secondary school system, Brodsky did, however, absorb a plethora of formulae, concepts, and math-related images, which, in turn, revitalized his poetic vocabulary. Listing Brodsky’s typical ‘mathematical’ motifs and phrases, Artemiev focuses on images that often serve as clues, such as a parallel, a perpendicular, lines, angles, cones, squares, and other geometric shapes; each such item is supplied with several examples and a scholarly commentary. The author characterizes Brodsky’s relationship with mathematics as follows: Stopping short of understanding the subject properly, Brodsky used maths terminology frequently and with ease, if with a somewhat tenuous idea of its meaning, and made it part of his signature poetic style. Mathematics endowed his poetry with a vocabulary that made it truly stand out among predecessors and contemporaries alike.

Indigenous Knowledge Content & Mathematics Curriculum

Cultural practices present opportunities for Mathematics Education to be more relevant, and effective, especially in post-colonial contexts. Despite national policies emphasising integration of Indigenous Knowledge (IK) into school curricula, there has been limited success in incorporating ethnomathematics into Mathematics teaching. We exploredgeometrical concepts inherent in traditional baskets produced by Aawambo women, an ethnic group in northern Namibia. We identified specific geometrical concepts that can be linked to the junior secondary school Mathematics syllabus. We employed ethnographic observations, interviews with local basket makers and focus group discussions with Mathematics junior secondary school teachers for triangulation. Furthermore, we adopted an interpretive paradigmusing a multi-modal method to source empirical data that demonstrated relevance to the curriculum. We explored socio-cultural perspectives of women and artefacts (baskets) to compare the subject matter from literature. The findings revealed common concepts as well as the ethnomathematical content not yet incorporated in the junior secondary school Mathematics curriculum comprising of symmetry (axial symmetry) and geometrical transformation (shear and translation). The study has implications for decolonizing western Mathematical practices through adoption ethnomathematics approaches across Africa.

Design 3D Wallpaper Motifs from Sierpinski Carpet Fractals Using Mathematica Applications

The development of geometric studies is very rapid, including fractal geometry. A fractal is a geometric shape that fulfills the properties of the fractal dimension. If you look at a fractal at first glance, it has an irregular shape, but if you look further, there is a regularity. One of the properties of fractals is self-similarity which occurs when a fractal is enlarged. The fractal form has a pattern obtained from iterating a function with infinite repetition. Among the fractal shapes there is the Sierpinski carpet shape. Fractals in 2D form can be transformed using geometric concepts into 3D fractals. Fractal shapes can be applied for cultural development, namely to form wallpaper motifs. Fractal geometric motifs are obtained from iterating a function with the help of Wolframe Mathematica.

Implementasi Etnomatematika pada Materi Kesebangunan dan Kekongruenan dengan Rumah Adat Karo

This article discusses the Karo traditional house, a review from Etnomathematics. Karo is located in North Sumatra and has high value history, culture and artifacts. One of these artifacts that still survives is the Karo traditional house. This traditional house not only functions as a protector for its residents but also has a deep function and meaning in accordance with the customs and culture of the community. In Karo traditional houses, the form, function and motifs of the aesthetic elements depict the close relationship between humans and their natural environment. Examining the aesthetic elements of Karo traditional houses which contain geometric concepts. Without studying geometric concepts in mathematics, Karo people have applied geometric concepts in everyday life, reflected in creating aesthetic elements in Karo traditional houses. The method used is literature study

The development of geometric concepts through sign language

The development of geometric concepts through sign language

Best approximation theorems via relatively u-continuous and Jaggi nonexpansive mappings

In this paper, we introduced a new type of cyclic (noncyclic) mappings, called Jaggi relatively nonexpansive mappings and use to investigate the existence of best proximity points (pairs) in the framework of reflexive (strictly convex) Banach spaces by using a geometric concept of proximal normal structure. We also present a best proximity version of Schauder’s fixed point problem for non-self mappings. Finally, we prove the existence of a common best proximity point for an arbitrary family of cyclic relatively u-continuous mappings which are compact and then we obtain a generalization of Markov-Kakutani’s theorem.

The Development of Geo-Math Application by Integrating Geo-Gebra Applets to Improve Students’ Spatial Ability

Geometry can be challenging for students due to its abstract nature; The difficulty is often associated with low spatial abilities; to overcome these challenges, educators can employ dynamic and visual learning approaches to help students learn and understand geometric concepts more effectively. This study aimed to develop a Geo Math application by integrating the GeoGebra applets on geometry that fulfill valid, practical, and effective aspects that are expected to improve spatial abilities. This research utilized development research using the ADDIE model, which consists of 5 stages: analysis, design, development, and trial implementation. It went through several trial stages consisting of validation experts, one-to-one trials, and small group trials, and the evaluation stage was carried out through a pre-post-test quasi-experimental study. Based on the results, it can be concluded that the Geo Math application was very feasible to support the implementation of learning mathematics, especially in learning geometric transformations, which could assist students in constructing concepts from various transformations effectively. The interactive and dynamic nature of GeoGebra applets within the application allowed students to visualize and manipulate geometric objects and could make abstract mathematical concepts more concrete and accessible, which could improve students’ spatial abilities.

Implementation of the Realistic Mathematics Education (RME) Approach in Geometry Learning in Secondary Schools

This study aims to analyze the implementation of the Realistic Mathematics Education (RME) approach in geometry learning in secondary schools. Realistic Mathematics Education, which emphasizes mathematics learning through relevant contexts and students' real experiences, aims to improve students' understanding and skills in geometry. This study evaluates the effectiveness of the implementation of RME and identifies various challenges and potential solutions in its implementation. The method used is a literature review that includes studies related to the implementation of RME in geometry learning. The results of the analysis show that RME can improve students' understanding of geometric concepts by linking materials to everyday situations, thereby motivating and involving students more actively in the learning process. This approach helps students link theory to real practice, deepen their understanding, and develop problem-solving skills. There are challenges such as teacher readiness, limited resources, and limited time allocation, recommendations to improve teacher training, develop supportive policies, and provide adequate resources can help overcome these problems. With the right strategy and adequate support, RME has great potential to improve the quality of geometry learning in secondary schools and have a positive impact on student learning outcomes

Students’ Knowledge of Integration of GeoGebra in Mathematics Classes in Uganda

GeoGebra, an open-source Dynamic Mathematics Software (DMS), has emerged as a transformative tool in mathematics education, allowing students and teachers to visualize, explore, and manipulate geometric concepts in dynamic virtual environments. This study investigated the students’ knowledge of integration of GeoGebra in mathematics classes in lower secondary schools in Rwampara District, Southwestern Uganda. The objectives of this study were to identify the most abstract geometrical concepts posing challenges to students, examine the impact of GeoGebra training on the identified abstract concepts, and assess the relationship between students' attitudes and the integration of GeoGebra. This study utilized a quantitative approach, employing quasi-experimental and cross-sectional survey designs. Data were collected from 103 students using questionnaires and pre-and post-tests to evaluate the impact of GeoGebra software intervention. Independent samples t-test, Pearson's linear correlation, and descriptive statistics such as means, standard deviations, and frequencies were employed as data analysis methods. The study found that the students identified rotational transformation as the most abstract geometrical concept. The pre-test results indicated that respondents had similar baseline knowledge of rotational transformation. However, after the GeoGebra intervention, the post-test results showed that the difference in mean scores between the experimental and control groups was statistically significant. Additionally, the experimental group demonstrated a positive attitude towards the software. The study concluded that while rotational transformation posed a significant challenge for students, GeoGebra significantly improved their conceptual understanding and performance in this geometry concept. The study recommended that teachers should strongly consider integrating GeoGebra into their ICT-based teaching and learning resources to help improve students' conceptual understanding, motivation, attitude, and achievement in rotational transformations and other geometric concepts

STUDENTS’ KNOWLEDGE OF INTEGRATION OF GEOGEBRA IN LEARNING MATHEMATICS IN LOWER SECONDARY SCHOOLS IN UGANDA

The use of technology in the pedagogical process is growing at a phenomenal rate and has revolutionized the way students learn. As a result, there is a need for integrating technology into students’ mathematical activities. GeoGebra is a technology software that supports teaching and learning mathematics, especially geometry, algebra, and statistics. This study investigated the students’ knowledge of the integration of GeoGebra in learning mathematics in lower secondary schools in Wakiso District, Uganda. The study utilized quasi-experimental and cross-sectional designs with 42 senior two students in the experimental and 43 in the control group. Data were collected using pre-tests, post-tests, and questionnaires to identify the students’ difficult geometric concepts when learning mathematics, establish the impact of GeoGebra-based training on the students’ learning, and examine the relationship between students’ perceived ease of use of GeoGebra and its integration in learning mathematics. Independent samples t-test, Pearson's linear correlation, and descriptive statistics such as mean, standard deviation, percentages, and frequencies were employed to analyze the data. The study revealed that reflection on the Cartesian plane was the most abstract geometric concept to learn. The results further revealed a statistically significant mean difference between pre-test and post-test scores in favour of the experimental group after the intervention. Furthermore, a moderately significant positive linear correlation existed between students’ perceived ease of use of GeoGebra and its integration in learning reflection on the Cartesian plane. Therefore, the study recommends urgently training students to incorporate this interactive educational software into their mathematics learning.<p> </p><p><strong> Article visualizations:</strong></p><p><img src="/-counters-/soc/0871/a.php" alt="Hit counter" /></p>

Ethno-Science, Technology, Engineering, and Mathematics (EthnoSTEM) Ideas in the Sama Mat-Weaving

Mat weaving has been culturally and economically significant among the Sama ethnolinguistic group since time immemorial. This study sought to find concepts and processes of ethnoscience, ethnotechnology, ethnoengineering, and ethnomathematics (ethnoSTEM) present in weaving tepo, a hand-woven mat of the Sama, made from indigenously processed leaves of pandan or screw pine (Pandanus tectorius). To determine ethnoSTEM ideas, concepts, and processes in tepo weaving, an ethnography was conducted involving five female mat weavers in a coastal village in Tawi-Tawi’s major producer of tepo, the Municipality of Tandubas. Data were gathered primarily through observations during a monthlong community immersion. Results revealed that Ethnotechnology tools were in the form of bolo, pandan-presser, pandan slitter, traditional stove, bamboo scalp scratcher, and other local cooking tools, with each tool exhibiting unique characteristics and functions needed for weaving. Ethnoengineering was evident in preparing pandan strips to create, bleach, and dye pandan strips for weaving and fastening the tepo. Ethnomathematics comprised primitive length measurement, arithmetic calculations, ratio and proportion, linear and quadratic equations, sinusoidal functions, basic geometric concepts, circles, symmetries, and isometries. Ethnoscience was observed in the processes determining the dyeability of pandan strips, as well as in the procedures employed in its softening and bleaching. It is concluded that the concepts and ideas of ethnoSTEM found in Sama weaving of tepo are loaded with scientific affluence that should be preserved to preclude them from fading to oblivion.

Perceived attitude of preservice teachers towards the integration of technology in teaching and learning college geometry: cases of two selected colleges of education in Ghana

Despite growing recognition of the value of using technology in mathematics instruction and learning, preservice teachers consistently performed abysmally in college geometry. This study therefore examined the attitude of preservice teachers towards the integration of technology in the teaching and learning of College Geometry. Quantitative descriptive survey was employed as the design for the study. The study drew on Unified Theory of Acceptance and Use of Technology (UTAUT) as the main theoretical framework. A sample of 185 preservice teacher participants offering college geometry from two Colleges of Education in the Central Region of Ghana were selected using multi-stage sampling technique. Data collected was analysed using mean, standard deviation, independent samples t-test and One-way ANOVA. The study found out that preservice teachers have high positive attitude towards the use of technology in the teaching and learning of college geometry. There was no significant difference between the attitude of male and female preservice teachers towards the use of technology in the teaching and learning of geometric concepts. It was therefore recommended that technology should be used to teach college geometry in Colleges of Education.

EKSPLORASI ETNOMATEMATIKA PADA BENTUK JAJANAN PASAR DI DAERAH JEPARA UNTUK PEMBELAJARAN MATEMATIKA SMP

In the cultural context, traditional market snacks in the Jepara area have the potential to integrate ethnomathematics into mathematics learning. Traditional market snacks in Jepara offer various forms of snacks in which there is a geometric concept. The purpose of this study is to find out the concept of geometry in traditional market snacks in the Jepara area. In this study, qualitative methods are used with an ethnographic approach. The objects studied by the researcher were 5 traditional market snacks, with 3 respondent subjects, namely traditional market snack sellers found in Jepara market, Pecangaan market, and Tegalsambi market. Several techniques for collecting data are used in this study, including observation techniques, interviews, and documentation. Based on the research conducted by the researcher, the results were obtained that there are geometric concepts and cultural elements in 5 traditional market snacks in the Jepara area, including a ball-shaped klepon, a rectangular layer, a ball-shaped onde-onde, a triangular prism-shaped banana bongko, and a solid half-ball shaped kintelan. The results of this research are expected to function as an effective alternative learning resource to introduce geometry concepts to students.

A-priori framework of viscosity and ionic conductivity estimation of ionogel

A-priori framework has been developed to estimate the viscosity and ionic conductivity of ionogel. Six imidazolium-class of ionic liquids (ILs) form ionogels with tetraethyl orthosilicate (TEOS) matrix. Group contribution parameters of TEOS are estimated with the fitting of the density dataset in the predictive Soave−Redlich−Kwong equation of state with the NSM1 alpha function model. Later the parameters are used to estimate the critical property of ILs and TEOS. These facilitate the formulation of the predictive framework of viscosity estimation through the geometric similitude concept with the Valderrama-Patel-Teja cubic equation of state. Later the viscosity of ionogels is estimated through a mixture form of geometric similitude framework as well as the Arrhenius model. Additionally, the estimated viscosities from both frameworks are used to estimate the ionic conductivities of ionogels. The compositional and temperature variance of ionic conductivity reveals the superior ionic conductivity of tetrafluoroborate-based ionogels than the bis(trifluoromethanesulfonyl) imide-based counterparts. Both models estimate the decrease in viscosity as well as incremental trends in ionic conductivity with temperature. However, the concentration of IL rather plays a different trend in the estimation model as well as the class of IL. Such a priori framework shall lead to the design of the ionogels focusing on the physicochemical properties.