Teaching Of Geometry Research Articles

Effectiveness of Paper Folding and GeoGebra on Students’ Geometric Thinking and Visualization

Finding teaching methods that foster students' development of geometric thinking and visualization skills is still a current challenge. This study analyses the effects of the combined use of paper folding and dynamic geometry on high school students’ geometric thinking and visualization skills. A quasi-experimental study pre-test/post-test design was conducted in distance learning in Italy. The instruments employed were van Hiele Geometry Test (VHGT) and the Visual Test (VT) before and after the treatment. The data were analysed using statistical tests according their nature. The results revealed that both groups have improved in the post-tests compared to their respective pre-tests. However, the students in the experimental group achieved better geometric thinking scores and performed better in three out of four sections of the visual test compared to the students in the control group. Thus, the proposed combination of instruments may be suggested in high school to make geometry teaching more effective, even with distance learning.

Culturally responsive pedagogy for the promotion of understanding Mathematics: The case of rural situated primary schools in Post-apartheid South Africa

The language of instruction, awareness, and creativity are at the centre of the realities faced by both mathematics teachers and learners, shaped by a socio-political history whose impact and legacy transcend generations in South Africa. Consequently, the dire state of mathematics education in South Africa remains a cause for concern. Recognising the need to conceptualise and develop culturally responsive pedagogy, this paper presents the results from the third phase of a three-year longitudinal study focused on teachers' journeys in infusing indigenous knowledge when teaching geometry to senior primary learners in rural schools. This qualitative study, which followed a case study design, explored several approaches to discussing, teaching, and considering an immediate, perpetual, operative, and discursive approach as culturally disruptive pedagogy used as an indigenous way to promote geometric understanding. Observations and semi-structured interviews were conducted with two purposefully selected participants after their lesson presentations to allow them to clarify, elaborate, and introduce more detail, enriching their explanations of the artefacts used. Results indicated that teachers’ references to several artefacts and indigenous activities, such as using straws, wool, and staplers, promoted the understanding of the construction of prisms and pyramids. Recommendations include training mathematics teachers to prepare lessons that incorporate indigenous knowledge and to explore ethnomathematics as a culturally responsive teaching strategy, particularly in contextualising mathematical geometry learning, so that this concept can have relevance and meaning for rural students.

Developing the Competence of Using Tools and Materials in Learning Mathematics for 4th-Grade Students in Geometry and Measurement Content

In Vietnam's general education program, Mathematics is a significant tool for many other subjects. Mathematics originates from practicality and serves as the "key" in most human activities, as well as in learning other subjects. In teaching Mathematics, teachers not only guide students to acquire knowledge but also form and develop students' abilities and intellectual qualities, training their critical thinking and creativity. The ability to use tools and learning materials for Mathematics is one of the five components of mathematical competence in the 2018 Mathematics curriculum for general education. This article focuses on proposing some basic measures to develop and nurture the ability of using tools and materials in learning Mathematics for fourth-grade students through teaching Geometry and Measurement content.

Teacher: Where are You? About a Scenario for Permanent Teacher Training in Which the Teaching of Geometry is Invited to Think Professionally

In this article we share the story of a proposal for permanent training for mathematics teachers who are in charge of the training of students between 12 and 18 years old. We present a task and the fundamentals that lead us to develop it in this training scenario, for the collective construction of specialized knowledge of those who teach topics related to metric geometry and its relationship with optical illusions. We comment on the planning of the scenario and the results achieved from the perspective of the Mathematics Teacher's Specialized Knowledge Model (MTSK Model), which we relate to studies on the use of technologies in mathematics classrooms. We conclude with an analysis of the strengths and weaknesses, opportunities and threats that may arise in scenarios such as the one described for the permanent training of teachers considered teaching professionals.

Determining the needs of teachers for teaching geometry education activities to children with visual impairments in early childhood using digital learning tools

The purpose of this research is to determine the needs of teachers for teaching geometry education activities to early childhood children with visual impairments using digital learning tools. The data for the study was collected during the fall semester of 2024-2025 through need analysis forms filled out by a total of 9 preschool and special education teachers working in state schools for the visually impaired located in Turkey's three largest cities: İzmir, Istanbul, and Ankara. The study is designed as a case study, one of the qualitative research designs. A single embedded case design was used in the study. In a single embedded case design, there are often multiple sub-units or layers within a single case (Yıldırım and Şimşek, 2018). The data collected in this study was analyzed using the content analysis method. When the results obtained from this research are generally examined, it was determined that the needs of teachers regarding the process of teaching and learning geometry to early childhood children with visual impairments are composed of the sub-themes of achievements, activities, and materials under the theme of the geometry teaching and learning process, and the sub-themes of learning and teaching under the theme of difficulties experienced in the geometry teaching and learning process. Additionally, the needs of teachers concerning the use of digital tools and technology in the geometry teaching and learning process were identified under the sub-themes of benefits, in-service training, and recommendations.

Investigation of Gifted Students' Errors Related to Height and Diagonal Concepts in Geometry Teaching

The aim of this study was to examine the errors of gifted students regarding the concepts of height and diagonal in Geometry. Eighteen gifted students studying at a Science and Art Center in central Anatolia participated in the study. A knowledge test consisting of 5 questions was prepared to collect data. The knowledge test was applied to gifted students. Descriptive analysis method was used to analyze the data in the study. The data obtained in line with the responses of the students to the knowledge test used as a data collection tool were classified under categories in line with the purpose of the study by coding the errors in the solutions of the questions. According to the data obtained, it was concluded that the concept of diagonal and height, which constitute the basis of many subjects in geometry education of gifted individuals, should be emphasized more.

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.

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.

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.

МЕКТЕП ГЕОМЕТРИЯСЫНДАГЫ ФИГУРАЛАРДЫН КЛАССИФИКАЦИЯСЫ

This work proposes a classification of geometric figures studied in a systematic course in school geometry. Classification of geometric shapes is said to be an important aspect of teaching geometry to enable students to understand and analyze different shapes; identify similarities and differences between figures; recognize common features and differences between figures belonging to the same class or type; systematize and organize knowledge; reveal patterns and relationships between figures with similar properties, which provides the basis for subsequent discoveries; derive new properties and theorems; solve spatial geometric problems. New areas of spatial perception (virtual space, multidimensional space, digital technologies, including cloud, etc.), technologies and industries are increasingly emerging. In such changes, the relevance of the science of geometry does not disappear, but rather increases. This is due to the fact that geometric knowledge and geometric thinking give a person the basis for solving various problems in theoretical (geometric) and practical (physical) spaces. However, despite this, geometry is considered a difficult subject to perceive and understand.

O SOFTWARE GEOGEBRA COMO FERRAMENTA PARA O ENSINO DA GEOMETRIA ANALÍTICA NA EEMTI LICEU VILA VELHA

This paper aims to present a methodology differentiates teaching of analytic geometry in high school with the help of GeoGebra software. For this sequence of activities developed by the authors that are proposed constructions involving the basic contents of analytic geometry is presented . The paper also presents a historical study of analytic geometry and its importance today. Also made a study of the importance and contribution that Information and Communication Technologies ( ICT ) can make to the teaching of mathematics as well as the guidelines from the National Curricular Parameters ( PCN ) that encourage the use of ICTs . For better development of the work a thorough study of GeoGebra software is performed . Shortly after the proposed activities , a case study conducted with a group of third year of high school at EEMTI(High School) Vila Velha, this study analyzes both the qualitative results as well as the students' opinion on the use of ICTs in the room is shown classroom and more specifically the GeoGebra as a tool for the teaching of analytic geometry . Finally, consideration and positive conclusions are made regarding the completion of the work and also considerations on the difficulties encountered and the prospects for its future applicability.

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.

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.

Pengaruh Pendekatan Kontekstual terhadap Kemampuan Pemecah Masalah Matematika pada Materi Bangun Ruang Sisi Lengkung

<p><em>This research aims to evaluate the effect of a contextual approach on students' mathematical problem solving abilities in curved geometric shapes. The literature review (SLR) study method was used to analyze 6 scientific articles relevant to the research topic. This research identifies themes and patterns that emerge regarding the influence of a contextual approach on students' mathematical problem solving abilities. The results of the analysis show that the application of the contextual approach has a positive influence on students' mathematical problem solving abilities. Comparison table of scores for the experimental group achieved higher achievement than the control group. Data visualization graphs also reinforce these findings. The conclusion of this research confirms that the application of a contextual approach has a positive impact on solving mathematical problems in curved geometric shapes. The implications of these findings can be a guide for educators and researchers to enrich mathematics learning strategies by integrating everyday life contexts into geometry teaching</em></p>

Rethinking the teaching of Euclidean geometry

Rethinking the teaching of Euclidean geometry

A classroom experience for teaching and learning of high school geometry through virtual reality

This study explores the integration of virtual reality (VR) in geometry education and examines the immersive platform’s potential to enhance student engagement and understanding through a case report. While students appreciated the interactive and collaborative aspects of VR, they also faced challenges such as VR sickness and technical issues. Recommendations for future sessions include incorporating breaks and providing additional technological guidance. Future research will focus on addressing these challenges, evaluating long-term educational outcomes, and exploring the integration of other immersive technologies like augmented reality. The study contributes to the wide discussion regarding the importance of balancing technological innovation with pedagogical effectiveness for successful VR integration in educational settings.

The Effect Of Using Aesthetical Approach in Teaching Geometry To Develop The Skills of Visual Thinking And Attiude Towards Mathematics Among Middle School Students

The Effect Of Using Aesthetical Approach in Teaching Geometry To Develop The Skills of Visual Thinking And Attiude Towards Mathematics Among Middle School Students

Validity of PMRI-Based Geometry Teaching Materials for Elementary School Students

Validity of PMRI-Based Geometry Teaching Materials for Elementary School Students

Formation of Schoolchildren Competencies when Teaching Geometry using Geometric Tasks with Life Content

This article discusses the importance of using geometric tasks with life content in the process of teaching geometry in order to develop key competencies of students. The authors note that this approach to teaching not only promotes the acquisition of geometric concepts, but also develops logical thinking, spatial imagination, analytical skills, problem solving skills and informed decision making. Examples of geometric problems with real-life content are provided that demonstrate the application of mathematical knowledge in real-life situations, which makes learning more interesting and practical for students. It also emphasizes the importance of using such tasks in the educational process to successfully prepare students to solve real life problems and adapt to the modern world.

The effect of distance education practices during the COVID-19 pandemic on mathematics and geometry teaching

With the research discussed here I aimed to examine the effect of the COVID-19 pandemic on primary school mathematics teaching processes and specifically the teaching process of 1st-grade geometric shapes. A holistic multiple case study design was used in this qualitative research. The participants were primary school teachers who have taught both processes and geometric shapes in 1st grade primary school and were selected using purposive sampling. Semi-structured interviews based on an interview form developed by me was used as data collection instrument. In this form, questions about the 4 skills in the programme related to geometry were included. Lesson content, materials, and content related to the method of expression related to each skill were examined comparatively during and before the COVID-19 pandemic. Semi structured interviews during which the questions on the form were asked, were conducted with participating teachers. The content analysis technique was used to analyse the obtained data. The results of the analysis show that the transition to online education during the COVID-19 pandemic had serious consequences. Positive and negative effects were found in both primary school mathematics teaching process and the teaching process of geometric shapes in the 1st grade.