Teaching Of Geometry Research Articles

Incorporation of Indigenous Knowledge in the Mathematical Geometry Discipline at a TVET College

Mathematical geometrical (MG) concept is often perceived as abstract and difficult to understand by students at the TVET College. Students are unable to perform well in Mathematic Assessments Tasks specifically on this concept. Drawing from this is the declining percentages of student enrolments in mathematics at National Qualification Framework (NQF) level 2. The aim of this study was to enhance the teaching and learning of Mathematical Geometry through the integration of indigenous knowledge in the form of a pilot-practical assessment task (PAT). The research team made use of focus group discussions to gather empirical data. Students were given the practical assessment task that incorporated indigenous knowledge to close the gap of students being unable to relate the mathematical geometry taught in the classroom to their everyday lives that seemed to prevail amongst mathematics students at a TVET College. Ten co-researchers were homogeneously selected based on their level of experience in teaching mathematical geometry at a TVET college located in the Afromontane communities of Thabo Mofutsanyane municipality, South Africa. The result indicated that indigenous knowledge can be utilized as an effective way of learning and teaching mathematical geometry at the TVET college.

An Assessment of Pre-Service Mathematics Teachers’ Techno-Pedagogical Content Knowledge regarding Geometry

Despite the significance of incorporating technology into geometry instruction, many teachers still find it difficult to teach geometry using technology. This study employed a techno- pedagogical content knowledge (TPACK) survey of 70 pre-service mathematics teachers (29 males, 41 females) from a public university. The goal was to determine which domains, if any, were open for development so that a course could be designed to meet these needs. The data was analysed thematically according to the TPACK sub-domains. The results showed that the pre-service teachers were confident in the areas of pedagogy knowledge, content knowledge, and pedagogical content knowledge (90% confidence) and open to improvement in the areas of technology, technological content, and technological pedagogy knowledge (70% confidence). As a result, we suggest creating a 14-week course to increase pre-service mathematics teachers' TPACK of these components in the hopes of bridging the knowledge gap identified in this study.

Teaching and learning angles in elementary school: physical versus paper-and-pencil sequences

This paper discusses the relevance of using physical situations to introduce the concept of angles at elementary school. We compare the effectiveness of two geometry teaching sequences. In the first one (physical sequence), the pupils learned the angle concept by experimenting on the playground (i.e. mesospace) and then modelling the situation. In the second one (paper-and-pencil sequence), the pupils worked solely in the space of a sheet of paper (i.e. microspace). In both sequences, pupils compared areas of space delineated by an angle between two directions. Pupils in two Grade 3 classes were exposed to one of the two teaching sequences. The unfolding of these sequences was videotaped and analyzed, and the pupils were tested individually, before and after teaching, to measure each sequence’s effectiveness. Results showed that both sequences are effective to grasp the angle concept: Most pupils overcame the common erroneous conception of comparing angles’ sides’ lengths instead of angle openness. The comparison of areas of space delineated by an angle between two infinite directions, which is the two sequences’ common core, seems to be the key factor underlying angle conceptualization. This paper ends with a discussion of these results’ teaching implications and the merits of each sequence.

Methods of teaching geometry in the framework of the updated curriculum in mainstream education

This study aimed to determine that the area benefiting from the secondary education curriculum published in the 2020–2021 academic year is the training related to geometry lessons. In this direction, the opinions of 35 secondary school geometry students working in 2 different secondary schools and geometry lessons were consulted. To determine what will be done, a study design from qualitative research was used. Training can be obtained from the delivery of this product. It consists of questions from restructuring and explaining the research. After the findings were reached, they were analysed in detail by the content analysis method used in the described method, and the predicted were categorised. It has been reached that it can be applied for geometric use, due to problems related to educational principles, insufficient mathematics education, use of materials and so on. Teaching the new education can be achieved by having too much content for teaching, teaching well and teaching the new education correctly. In the same way, the scanning of the application contents and the resource counting process have not been completed in order for the new ones to work better. The conclusions to be drawn from the results of this research are described.
 Keywords: Secondary education, education, curriculum, geometry, opinion;

Trends in learning and teaching of geometry: The case of the Geometry and its Applications Meeting

We characterize the thematic trends of the Geometry and its Applications Meeting. This meeting is held periodically in Colombia, country in which our study was carried out. We used a taxonomy of key terms specific to mathematics education to code the proceedings of this meeting. The study variables are purpose, educational level, pedagogical notions, and topics. We establish the thematic trends in terms of the values of the variables. We describe their evolution over time and, using a normalization process, we compare the extent to which geometry topics are treated with respect to the other variables. The meeting has disseminated activities and curricular innovations to a lesser extent. The community that attends the meeting is focused on the theoretical development associated with geometry and on higher educational levels. The papers that address pedagogical notions focus on learning and the classroom. The topics with the highest percentage of research are geometry in three dimensions and Euclidean geometry. We suggest that the meeting should promote the dissemination of curricular innovations and give more attention to the notions of teaching, curriculum and assessment in both research and innovations. We perceive the need to address learning and teaching in preschool and primary education.

Three-dimensional geometric perceptions in ENEM: a contribution from GeoGebra for mathematics teachers in Brazil

"This article presents a didactic situation focused on geometric reasoning using 3D GeoGebra, using the concepts Theory of Didactical Situations (TDS). The objective of this work is to bring a didactic proposal for the teaching of Spatial Geometry, working with the students' geometric perception, oriented and elaborated based on the dialectic of TDS - action, formulation, validation, and institutionalization. For its construction, a question from the National High School Examination (ENEM) was used about polyhedra, worked in an intuitive way. Finally, it is pointed out that TDS associated with technology has great potential to leverage the student's geometric reasoning, satisfying what is sought to develop in school curricula. "

Application of GeoGebra in the Teaching of Descriptive Geometry: Sections of Solids

Technologies came to revolutionize the teaching of technical design; they brought resources that enabled 3D and 2D graphic simulation. The objective of this research is to understand how the implementation of the dynamic software GeoGebra on the topic of cylindrical sections can improve 3D spatial visualization in students because of the challenges in understanding the 3D representations and transporting them to the 2D sheet. This is a quasi-experimental case study in a mixed qualitative and quantitative approach which was conducted in a grade 12 class on the subject of descriptive geometry. The instruments used were a pre-test, post-test and Santa Barbara Solids Test. The students of the experimental group used GeoGebra and obtained better results in the post-test than the students in the control group, which suggests an improvement in learning; however, the Santa Barbara Solids Test results showed that the difficulties in visualizing views of the projected solids in a two-dimensional plane persisted. This study is also intended to test software in a classroom with students who have never experienced a 3D technology in their educational practices and direct future research in the complex content of descriptive geometry with the help of software.

Use of GeoGebra to Improve Performance in Geometry

The main purpose of this study was to use GeoGebra in the teaching and learning of Geometry among mathematics education students as well as in-service teachers, using an action research approach. The purposive sampling technique was used to select two public tertiary institutions for the study. The sample size consisted of 150 students comprising 51 from the University of Ghana and 99 from the University of Education, Winneba. Pre- and post- test design, involving teacher-made tests, were used during the experiment to collect data on the samples used. The paired samples t-test and analysis of covariance were used to analyse the scores of tests. The finding showed that there is a statistically significant improvement in the students’ scores and interest in the learning, as well as the teaching of Geometry. Also, the GeoGebra method made the lessons more practical and easier to understand. It is therefore recommended that mathematics teachers should incorporate GeoGebra in the teaching and learning of Geometry.

Investigation of Classroom Practices of Middle School Mathematics Teachers in the Context of Geometric Reasoning Processes

Cognitive processes and cognitive apprehensions known as geometric reasoning processes play a significant role in enabling students to make geometrical deductions and develop their spatial skills, geometrical skills, imaginations, and geometrical intuitions through geometrical properties, to discover the transformations between geometrical models and to establish a bond between the concepts. This study examined classroom practices of middle school mathematics teachers in the context of cognitive processes and cognitive apprehensions in geometry teaching. In this context, using the descriptive survey model, three classroom practices of middle school mathematics teachers with three different levels were examined. The descriptive analysis method was used to analyze these data. According to the findings obtained from the data, it was observed that geometric reasoning processes differed in each teacher’s classroom practices. It has been observed that the most common dimensions of geometric reasoning in courses with geometry content are visualization and reasoning. It was further observed that cognitive apprehensions were involved simultaneously with the cognitive processes. In this respect, it was concluded that the processes are interactive with each other.

İlköğretim Matematik Öğretmenlerinin Geometri Dersinin İşlenişi İle İlgili Görüşleri

Geometri dersi soyut yapısı gereği öğrencilerin bilişsel olarak hem öğrenmekte hem de algılamakta zorluk yaşadığı, öğretmenlerin de öğretme sürecinde problem yaşadığı bir derstir. Bu çalışmanın amacı ilköğretim matematik öğretmenlerinin geometri öğretimiyle ilgili görüşlerini incelemektir. Araştırmanın yöntemi nitel araştırma yöntemlerinden durum çalışması modelidir. Uygun örneklem yöntemi kullanılarak oluşturulan çalışma grubunda yer alan 16 ilköğretim matematik öğretmenine yarı yapılandırılmış görüş formu şeklindeki veri toplama aracı uygulanarak görüş alınmış, toplanan veriler nitel analiz yöntemlerinden içerik analizi yöntemiyle analiz edilmiştir. Sonuçlara bakıldığında öğretmenlerin büyük çoğunluğunun geometri dersinde anlatmakta zorlandığı konular olduğu, teknolojiyi ve somut materyalleri kullanarak çözüm geliştirdikleri ayrıca öğretmenlerin tamamının teknolojiyi ve somut materyalleri kullanmaya olumlu baktıkları ve istekli oldukları ancak bazı öğretmenlerin okulunda teknoloji alt yapı yetersizliği ile materyal eksikliklerinin bulunduğu belirlenmiştir.

Using tactile imagery to teach geometry to students with visual impairments in the United Arab Emirates

Learning geometry is difficult for students with visual impairments (VIs). However, tactile imagery, the process of constructing mental images of physical objects with certain shapes, may help them make sense of geometrical shapes. Thus, discussions have centred on interventions to promote the participation of students with VIs in the learning of shapes. This study explored tactile imagery connecting physical touch to memory as an approach to teaching shapes to students with VIs. Eleven students, five with VIs and six sighted students took part in this experimental design study. A tactile imagery test and intervention lessons were developed for this study. Four tactile imagery domains (tactile discrimination, tactile memory 2D, tactile memory 3D and pattern recall), each made up of 10 tests, guided the design of the tests and training lessons. The students’ scores from the pre-test and post-test were subjected to mean computations, Mann-Whitney U tests and the Wilcoxon signed-rank test. The post-test results revealed that students with VIs performed better than their sighted peers. The study concludes with a discussion of the need for teacher educators to consider using tactile imagery as a way of teaching geometry to students with VIs.

Geometry Teaching in Transition: An Investigation on the Importance of School Geometry in Primary Education

Mathematics instruction in primary school has been influenced by many policy changes and empirical findings in the previous two decades. Geometry lessons, in particular, were re-evaluated due to a paradigm change and, consequently, were attributed a new meaning within the mathematics curriculum worldwide. The present paper focuses on this paradigm shift in the sense of the evaluation to what extent both the didactical potential and the practical value of geometry instruction in elementary education are currently recognised and utilised by primary grade teachers. In total, 120 primary grade teachers participated in the study. The results showed that there had been positive recognition of the didactical potential of school geometry by the teachers over the previous two decades; however, it lacked actual implementation in school practice for different reasons. The results are discussed not only with regard to the latter of these but also with regard to their theoretical and practical implications.

Are 9th Grade Students Ready to Engage in the Theoretical Discursive Process in Geometry?

This study was conducted to examine whether newly enrolled 9th grade students were ready to directly engage in the theoretical discursive process from the perspective of Duval’s Cognitive Model. The sample of the study was comprised of 51 newly-enrolled 9thgrade students between the ages of 14 and 15, who had not received any prior geometry instruction. These 51 students were posed two open-ended questions that would enable them to make a transition between perceptual and discursive apprehension. The qualitative data obtained from the open-ended questions were classified into three categories, and clinical interviews were held with three students from each category. According to the findings obtained from the study, many of the students could not display the necessary behaviors for theoretical discursive process. Students were mostly unsuccessful in converting discursive information into perceptual information, in writing discursive information based on perceptual information, and making inferences based on discursive information. These findings indicate that recent graduates of secondary school are not ready enough to directly engage in theoretical discursive process and, thus, they could experience difficulties in such high order skills as providing proof requiring the theoretical discursive process.

Visual foundations of Euclidean geometry

Geometry defines entities that can be physically realized in space, and our knowledge of abstract geometry may therefore stem from our representations of the physical world. Here, we focus on Euclidean geometry, the geometry historically regarded as “natural”. We examine whether humans possess representations describing visual forms in the same way as Euclidean geometry – i.e., in terms of their shape and size. One hundred and twelve participants from the U.S. (age 3–34 years), and 25 participants from the Amazon (age 5–67 years) were asked to locate geometric deviants in panels of 6 forms of variable orientation. Participants of all ages and from both cultures detected deviant forms defined in terms of shape or size, while only U.S. adults drew distinctions between mirror images (i.e. forms differing in “sense”). Moreover, irrelevant variations of sense did not disrupt the detection of a shape or size deviant, while irrelevant variations of shape or size did. At all ages and in both cultures, participants thus retained the same properties as Euclidean geometry in their analysis of visual forms, even in the absence of formal instruction in geometry. These findings show that representations of planar visual forms provide core intuitions on which humans’ knowledge in Euclidean geometry could possibly be grounded.

Analysis of Graphic Perception Education for Young Children Based on Fuzzy Clustering Analysis.

Geometric ability includes elements of identification, conceptualization, combination, drawing, and reasoning, and graphic perception is an important part of it. Kindergarten science education includes geometry instruction. Children are guided to perceive the relationship between shapes and figures through direct perception, first-hand experience, and practical operation through concentrated educational activities, and form image-concrete thinking over time, enhancing their perception and experience of the relationship between shapes in the objective world, and accumulating certain mathematical perceptual experience. Clustering is a branch of unsupervised pattern recognition that is very useful. Fuzzy clustering, which establishes the uncertainty description of samples to categories and can objectively reflect the real world, has become the mainstream of cluster analysis research. The graphics perception education of children is investigated using fuzzy clustering analysis. The main topic of this paper is how to apply children's graphics to the design of children's educational institutions and open up new creative perspectives for the design of children's educational institutions. The method of graphic perception education: perception education for preschool children is proposed based on the multichannel characteristics of preschool children's aesthetic perception and with reference to the theory of perception. The experimental results show that the improved algorithm reduces segmentation time by 171.48 s when compared to the traditional FCM algorithm for both noisy and high-quality images and that it is significantly faster than the FCM algorithm in terms of segmentation speed. As a result, the model construction of a set of children's graphic perception education for the cognitive characteristics of the age group children can provide corresponding references and references for related topic research.

Methodological Features of Teaching Construction Tasks in the Course of School Geometry

Construction tasks are one of the main materials of the geometry course. Construction tasks in a geometry course are of great importance when teaching theoretical material, as they allow students to better understand the relationship between geometric shapes. The formulation of definitions, the use, if possible, of geometric constructions in proving theorems - increases the activity of the whole class and ensures the awareness and strength of the material. In the process of solving construction problems, students develop spatial representations and constructive skills, that is, the ability to perform mental and constructive operations to construct a given figure, with a detailed discussion of how to construct a geometric figure sought for certain elements. In addition, the solution of each problem, in addition to constructing geometric shapes, plays an important role in the systematization and consolidation of students' knowledge, as it consists of the stages of preliminary analysis, proof of the solution of the problem and research of the solution. However, the need to teach construction tasks when teaching geometry at school and its educational and methodological literature, didactic materials, applied information resources, etc. The presence of contradictions between insufficient support determines the relevance of the problem of teaching geometric construction tasks. This article provides scientific and methodological recommendations for solving problems, identifying problems that arise in the process of teaching construction tasks in the course of planimetry.

The Possibilities of Using New Digital Technologies in Teaching Students the Course of Geometry

This article discusses the possibilities of using digital educational resources, including virtual and augmented reality (VR/AR) technologies in the process of teaching geometry to future mathematics teachers. In the modern education system, in order for students to receive an effective education, they must first arouse their interest in learning new knowledge, and only then will the new material move into long-term memory. And it is impossible to interest the youth of the 21st century with videos, presentations, pictures. Therefore, the use of VR/AR technologies in the learning process is considered promising. The authors of the article analyzed the state programs and concepts on the research topic, analyzed the work of domestic and foreign scientists on the research topic, conducted online surveys and conversations with students, and analyzed the results. . In addition, the article presents a number of tasks performed by the use of technology in augmented reality, and examples of their digital performance in the chapter "Rotating body" in the course of practical training. As part of the math education program, 54 students were surveyed to find out how well students are familiar with VR/AR technologies and how they use them, and the results of the survey are presented in detail. According to the results of the survey, it was found that students do not know the possibilities of applications and programs of VR/AR technology in the course of geometry and need to improve their knowledge in this area from a methodological and psychological-pedagogical point of view. The authors believe that teaching future mathematics teachers to use augmented reality technologies in geometry lessons will stimulate the process of visualization and create a creative, informational and educational environment for students.

Effects of GeoGebra on Students’ Attitudes towards Learning Geometry: A Review of Literature

The rapid growth of technology for teaching and learning of geometry includes the introduction of educational software commonly known as GeoGebra. However, a few studies were found that provide evidence on the effectiveness of this software on students’ attitudes towards geometry. The present study aims to provide a comprehensive view of prior literature related to the effects of GeoGebra in enhancing students’ attitudes towards geometry. The present study employed a systematic review. To collect data, the researcher downloaded journal papers, conference proceedings papers, and theses from different databases such as Google Scholar, Research gate, Academia, Research for life, and Education Resources Information Center (ERIC). Thus, 96 documents were initially obtained. After download, duplicating papers were immediately deleted. Thus, a deep analysis followed and 68 documents were filtered out. Twenty-three documents including 22 journal papers and one thesis remained for analysis. The reviewed literature showed that there are positive effects on students’ attitudes towards geometry in terms of interest, engagement and active learning, self-efficacy and self-regulation, and enhanced positive attitudes. More than a half of authors (12 out of 23) employed quasi-experimental research design to investigate the effects of GeoGebra on students’ attitudes toward geometry. Considering categories of attitudes identified, the majority of authors (8 out of 23) reported that GeoGebra enhanced students’ interest to learn geometry.

SpaceGeo_AR: augmented reality application for teaching and learning spatial geometry by deaf and non-deaf students

Objective: to present the SpaceGeo_AR application with augmented reality resources for teaching and learning spatial geometry aimed at deaf and non-deaf students. Methodology: the Heroku platform was used to program the application, a cloud system that allows the development of mobile applications through numerous resources of web technologies. Results: the application allows the registration of teachers and students, where the former has permissions to create, delete and edit classes and questionnaires, while the student is allowed access to the contents of Position Geometry (a chapter of Spatial Geometry), as well as how to answer questionnaires associated with this theme. Final considerations: applications to improve teaching and learning in the classroom have become a constant in an increasingly technological world, where augmented reality can help in this process, especially when considering Spatial Geometry, a topic strongly related to the three-dimensional. Another trend is the inclusion of people with disabilities in teaching processes, a feature that was also implemented in the application. With this, it is expected that the application can help deaf and non-deaf teachers and students with the learning of Position Geometry through the interactions that augmented reality allows to perform.

Using Xerte Toolkit to Enhance Pre-Service Teachers’ Conceptual Understanding of Coordinate Geometry

This study was to investigate the effect and explore students’ interest in using Xerte Toolkit in teaching and learning of Coordinate Geometry. In all, 50 pre-service teachers were involved in the study. The study adopted a mixed method approach. Semi – structured interviews as well as achievement test were the instruments used for data collection. The items in the achievement test were analyzed using statistical tools such as percentages, mean, standard deviation and t-test from Excel 2016 Analysis Tools. The descriptive statistics indicated that there was a significant difference between pretest and post test scores. The findings in this study posits that students’ interest in using Xerte Toolkits in teaching and learning Coordinate Geometry has increased and are ever ready to use Xerte Toolkit again in their studies.