High School Geometry Research Articles

Formation of Key Competencies by Organizing Independent Work in Geometry

In the process of learning geometry in high school, students constantly encounter various difficulties both when solving problems and examples, and when studying theoretical material. By teaching these difficulties, skills and abilities of independent work are developed. We will focus only on developing the skills of independent work through tasks with life content.

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.

Geometric Thinking of Prospective Mathematics Teachers: Assessing the Foundation Built by University Undergraduate Education in Ghana

This study investigates the geometric thinking levels of final year prospective mathematics teachers in Ghana, utilizing the van Hiele model to evaluate their proficiency. The main purpose was to assess whether university undergraduate mathematics education provides a sufficiently strong foundation for teaching senior high school geometry. A descriptive survey design was employed, involving 1,255 prospective mathematics teachers from three universities: University of Education Winneba (UEW), University of Cape Coast (UCC), and Akenten Appiah-Menka University of Skills Training and Entrepreneurial Development (AAMUSTED). The van Hiele Geometry Test (VHGT) was administered to measure participants’ levels of geometric thinking. The results revealed that 8.8% of participants attained van Hiele Level 1 (visualization), 30.0% reached Level 2 (analysis), and 32.4% achieved Level 3 (abstraction). However, only 15.9% and 12.9% of prospective teachers reached Levels 4 (deduction) and 5 (rigor), respectively. These findings indicate a significant gap between the current geometric thinking skills of prospective teachers and the expectations of the Ghanaian mathematics curriculum, which anticipates higher-order thinking skills. The study concludes that the current undergraduate mathematics education programs in Ghanaian universities may not be adequately preparing future teachers to teach senior high school geometry effectively. It is recommended that these programs be revised to include more focus on developing higher-order geometric thinking skills, with an emphasis on deductive reasoning, formal proof-based learning and rigor in geometry thinking. Enhancing the curriculum and teaching methods could narrow this gap and improve the overall quality of geometry education in Ghana.

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.

Tinkering and Modeling

In high school Geometry, three dimensional solids are often overlooked and not part of the regular curriculum. The exclusion of three-dimensional (3D) geometry can affect spatial relationships and cause learner anxiety, correlating to a negative relationship with environmental navigation (Lawton, 1994). To mitigate learner anxiety in the introduction and manipulation of spatial figures, Tinkercad was utilized for creative virtual design and papier mâché was used for a hands-on, artistic approach to mathematics.

Building Mathematics Learning through Inquiry Using Student-Generated Data: Lessons Learned from Plan-Do-Study-Act Cycles

This paper describes how plan-do-study-act cycles engaged a classroom mentor teacher and student teacher in a professional collaboration that resulted in two inquiry activities for high-school geometry classes. The PDSA cycles were carried out in four high school geometry classes, each with 30 to 35 students, in a mid-Atlantic urban school district in the U.S. The four geometry classes were co-taught by the second and third authors of this paper. The data consisted of classroom documents (e.g., activity prompts, tasks), classroom observations, student feedback about activities, and monthly PDSA reports. The PDSA cycles had a direct effect on the professional learning of the teachers. The resultant classroom activities used a data collection approach to engaging students in inquiry to learn about trigonometry functions and density. Student learning behaviors were noticeably improved during these activities compared with traditional mathematics instruction. We concluded that the data collection sequence provided an accessible entry point for students to begin scientific inquiry in mathematics. The process opened the conceptual space for students to develop curiosity about mathematical phenomena and to explore their own research questions. The use of culturally relevant topics was especially compelling to students, and the open-ended nature of these exploratory activities allowed students to see mathematics through their own cultural lenses.

GrafEq 소프트웨어를 활용한 고등학교 수학 수업의 학습 산출물 분석

Purpose: The purpose of this study is to analyze and explore the learning outcomes in which high school classes using GraphEq software are helpful to students who have difficulty in geometry classes. Methods: A case study was conducted to analyze the impact of high school students' learning outcomes using GrafEq on their cognitive and emotional domains in a geometry class at J high school located in a rural area. Results: First, it was found that participating students were more interested in using GrafEq and more easily understood concepts and problems in the area of functions, equations, and graphs. Second, it seems that the students naturally understood and learned the relationship between functions by using the inequality area to color the inner area of various figures. Discussion and Conclusion: In a high school geometry class using GrafEq, students experienced various problem-solving processes through trial and error in the process of conceiving and drawing mathematical images, and it was found that they improved their competencies to achieve designing various figures by themselves while communicating with their friends.

Comparative Study of Traditional Face-to-Face and E-Learning Modes of Teaching Senior High School Geometry

This study compared the traditional face-to-face and e-learning modes of teaching Senior High School geometry and students’ geometry performance. The study used a quantitative strategy which adopted a quasi-experimental design with pre-test and post-test non- equivalent control groups. Pre-test, post-test and retention test were used for the data collection. A total number of 52 second-year Senior High School students from two public schools in the Suame Municipality of the Ashanti Region of Ghana participated in the study. Students’ Geometry Achievement Test (SGAT) was used as pre-test, post-test and retention test instruments. The data was analysed using descriptive statistics and a t-test tested at a 0.05 significance level. The findings of the study revealed no significant difference in the post-test mean scores of students taught face-to-face and those taught using the e-learning mode even though there was a significant improvement in the performance of students after the intervention. Again, there was no significant difference in the retention test mean scores of the students taught using the face-to-face mode and those taught using the e-learning mode. The study, therefore, recommended that; policy makers in general, and mathematics curriculum developers in particular, plan and implement electronic learning modules to facilitate and enhance the teaching and learning of mathematics. It was again recommended that teachers take advantage of the new technology-driven world to blend the traditional face-to-face and e-learning modes of teaching to facilitate and enhance the teaching and learning of mathematics.

Comparative Study of Traditional Face-to-Face and E-Learning Modes of Teaching Senior High School Geometry

This study compared the traditional face-to-face and e-learning modes of teaching Senior High School geometry and students’ geometry performance. The study used a quantitative strategy which adopted a quasi-experimental design with pre-test and post-test non- equivalent control groups. Pre-test, post-test and retention test were used for the data collection. A total number of 52 second-year Senior High School students from two public schools in the Suame Municipality of the Ashanti Region of Ghana participated in the study. Students’ Geometry Achievement Test (SGAT) was used as pre-test, post-test and retention test instruments. The data was analysed using descriptive statistics and a t-test tested at a 0.05 significance level. The findings of the study revealed no significant difference in the post-test mean scores of students taught face-to-face and those taught using the e-learning mode even though there was a significant improvement in the performance of students after the intervention. Again, there was no significant difference in the retention test mean scores of the students taught using the face-to-face mode and those taught using the e-learning mode. The study, therefore, recommended that; policy makers in general, and mathematics curriculum developers in particular, plan and implement electronic learning modules to facilitate and enhance the teaching and learning of mathematics. It was again recommended that teachers take advantage of the new technology-driven world to blend the traditional face-to-face and e-learning modes of teaching to facilitate and enhance the teaching and learning of mathematics.

DEVELOPMENT OF MICROLEARNING OBJECT ON HIGH SCHOOL GEOMETRY MATERIALS

The implementation of this research has the aim of seeing of microlearning material for high school geometry material, to see the location of the microlearning object for high school geometry material. Media Microlearning Object developed using Podcast, Power Point, Poster and Google Form applications that are loaded on the Google site. This study uses the ADDIE development model (Analysis, Design, Develop, Implement, and Evaluate). This research was conducted at SMA Negeri 1 Stabat. The subjects in this study were students of class XI SMA Negeri 1 Stabat and the object of the research was microlearning objects on geometry material. The results of this study obtained a valid and effective object Microlearning product. Where in the aspect of the relevance of the material obtained an average of 3.5 which is included in the valid category and in the media aspect an average of 3.45 is obtained which is included in the valid category. Furthermore, the teacher's response obtained an average of 4.1 and from the student response data obtained a value of 88.5%. This means that the learning media for microlearning objects in high school geometry material gets a positive response. and is said to be effective.

Life Tasks as a Means of Studying New Material When Teaching Geometry in Secondary School

The article reveals the role of life tasks in teaching geometry in high school. The teaching of mathematics in a general education school, in addition to equipping students with certain knowledge, skills and abilities necessary to prepare them for life activities in the conditions of modern production, also pursues the goal of achieving such a level of their mathematical development that they need to study other school subjects at a high level, to continue their education in higher education. And also, for the formation of key and subject competencies in mathematics. The article deals with life tasks as a means of learning new material when teaching geometry in high school. Examples from the production industry are given. And also, the article presents the requirements and goals of studying mathematics, geometry in high school. The content of the textbooks proposed by the Ministry of Education, respectively, for general education and subject state standards in mathematics, contains many examples related to life tasks. The above conclusions define the main problem of the study: to study the role and place of tasks with vital content in revealing the content-applied significance of the school geometry course and in solving general educational problems facing the school. Develop a methodology for teaching problem solving. In the school teaching of geometry, the connection of the studied material with life, with practice, is often not yet rationally realized. Students have poorly developed skills and abilities to apply the acquired knowledge in practice. The goals and requirements of education standards for student-centered learning, i. e. to connect the teaching of mathematics, geometry with life, the passion for studying the basics of production, to form the key and subject competencies of students.

Gumpang Temple as a source of ethnomathematics learning

This study aims to explore the Gumpang Temple as a source of learning mathematics for geometry in junior high school. The form of learning that comes from nature is ethnomathematics. The researcher describes how the Gumpang Temple will be a fun and exciting source of learning. This study uses a qualitative approach. Data collection was obtained by observation and literature sources. The data findings were analyzed using qualitative data analysis with descriptive methods. The results of this study indicate that the wealth of ethnomatematic literature using Gumpang Temple is quite a lot. Various approaches and formulas can be applied to the teaching of geometry. These findings lead researchers to conduct further research to explore the manufacture of teaching materials using different research approaches.

MATHEMATICS LEARNING BASED ON BATIK PANDEGLANG ETNOMATICS TOWARDS GEOMETRY TRANSFORMATION LEARNING MATERIALS

Mathematics as a branch of science that cannot be separated from its existence in everyday life. The existence of mathematics as a science is timeless. The concept of mathematics is contained in the culture that develops in society. The mathematical concepts contained in this culture are called ethnomathematics. Ethnomathematics is a link between culture, mathematics, and education. The purpose of this study was to determine the practice of ethnomathematics in the manufacture of Pandeglang batik and the integration of Pandeglang batik as a learning resource for high school geometry transformation mathematics. This study uses qualitative research with an ethnographic approach. The instrument in this study is the researcher himself and cannot be replaced by someone else. Data collection was done by interview, observation, and documentation. Data analysis techniques used are data reduction, data presentation, and drawing conclusions. The results of this study are basic mathematical activities carried out when making batik pandeglang and mathematical concepts contained in the batik pandeglang motif such as translation, reflection, rotation and dilation. Batik motifs that contain mathematical concepts are integrated into high school mathematics problems so that they can become new sources of learning that are more interesting

EKSPLORASI KONSEP GEOMETRI JENJANG SMP PADA MOTIF SARUNG SAMARINDA

Samarinda sarong is a masterpiece or specal craft that lived in Samarinda city and one of the most icon from this city. This culture should be able to give attention to the people of Samarinda, because through education based on local wisdom it is able to grow the love of students to preserve the culture in which they live. This research purposed to find out junior high school geometry concept that found from activitiy crafter Samarinda sarong. The method that used in this research is qualitative research method with an ethnographic approach. Research data were collected using documentation techniques in one of the most procduction Cahaya Samarinda in RT.07 Tenun Village with research subject is Samarinda sarong and research object is geometry concept form junior high school. Data analysis was carried out by data collection, data reducting, presenting data after have reducted, making conclusions, and then presented in detail by linking supporting theories. Form explore result have found geometry concepts junior high school as lines, geometry shapes, symmetry, congruence, and similarity.

SOME METHODOLOGICAL FEATURES OF TEACHING SCHOOLCHILDREN TO SOLVE STEREOMETRIC PROBLEMS

The article deals with some methodological aspects of teaching school students to solve stereometric problems related to geometric bodies. Stereometric problems on polyhedra and bodies of rotation are studied in the last sections of the high school geometry program and are considered one of the most important topics for students of the natural-mathematical direction and specialized classes. The article is an introduction to the methodological foundations of a number of features for studying the subject of geometry at the level of students in grades 10-11. The article deals with the issues that lead to the inability to solve stereometric problems at the UNT (weakness of theoretical knowledge, the frequency of similar problems in a school textbook) and cause difficulties (weak ability to represent in space). Among the students, a survey was conducted on which tasks they first pay attention to during the UNT in the section of stereometry and in solving other problems. When analyzing the answers in the questionnaire, it was found that during the UNT, little or no time is allocated when solving problems of stereometry. The use of visual aids, multimedia technologies in the classroom for teaching the solution of stereometric problems, improving spatial imagination and self-education and the development of problem-solving skills, as well as the consideration of various methods of problem solving, showed a general positive perception of the problem in an easy and effective way.

Comparison of At-risk Students’ Mathematical Commognition in Geometry based on their Personal Attributes

Students’ academic performance in Mathematics has a significant impact on their success on large scale standardized assessments as well as their eventual job choices. This study determined the level of at-risk students’ mathematical commognition in high school geometry and makes comparisons when grouped according to their family environment, language proficiency, learning style, and attitude towards learning mathematics. This study employed a mixed method research design and was conducted for select Grade 10 at-risk students of Cagayan de Oro City National Junior High School. The data gathered on students’ level of commognition was analyzed using frequency, percentage, mean and standard deviation. Correlation analysis was used to establish the association between students’ mathematical commognition and the perceived variables. The comparison of students’ level of mathematical commognition was analyzed using non-parametric tests such as Kruskall-Wallis and Mann Whitney U tests. Results reveal no significant difference of at-risk students’ level of mathematical commognition based on their personal attributes. Hence, it is recommended that further explorations of other factors that might affect students’ level of mathematical commognition. Students only have a basic level of mathematical commognition and therefore another study can be pursued on employing effective teaching methods on improving students’ mathematical commognition not only in Geometry but also in other mathematics courses across all levels.

고등학교 기하 교과서 이차곡선 내용 요소 편차에 대한 소고(小考)

This study looked at the deviation of each textbook, focusing on the detailed learning content related to the quadratic curve properties contained in high school geometry textbooks. Rather than criticizing the diversity of content elements covered in high school geometry textbooks and suggesting alternatives, it focused on analyzing the actual conditions of content element diversity. The curriculum specifies that the practical application of the quadratic curve should be emphasized so that student could recognize the usefulness and value. However, as a result of the analysis, it was confirmed that the purpose of the curriculum and the structure of the textbook did not match somewhat, the deviation of content elements for each textbook was quite large. In terms of acknowledging the diversity of teaching and learning, the diversity of each textbook on the methods of the introduction and the natures related to the quadratic curve can be fully recognized. But in our educational reality, which is aiming for the university entrance examination system through national evaluation such as CSAT, the results are too sensitive in society as a whole, so the diversity of expressions in mathematics textbooks is sometimes interpreted as a disadvantage of evaluation. It is time to reconsider the composition of textbooks that recognizes the diversity of content elements in textbook teaching and learning and at the same time reflects the aspect of equality in evaluation.

Information Communication Technology (ICT)-Based Instructional Software and Its Effectiveness in Teaching High School Geometry

The study aimed at developing and testing an ICT-based instructional software called UBDGEOMESYS, to facilitate students’ learning of selected topics in Mathematics. It is a researcher-created program that uses a language known as Microsoft Visual Basic. The respondents of the study included 2 groups of second-year Special class students of Koronadal National Comprehensive High School (KNCHS). Data for analyses were the scores from tests administered before and after the instruction. Validity and reliability activities were done to ensure the quality of the tool. The evaluation showed that the ICT-based material was of good quality along with its content, technical and instructional value. The analysis also indicated that the learning achievement of students exposed to the instructional software (R2 = 0.284) was reasonably higher than those who utilized the traditional way (R2=0.05).

Investigating Students’ Proof Reasoning: Analyzing Students’ Oral Proof Explanations and their Written Proofs in High School Geometry

Constructing formal geometry proofs in is an important topic in the mathematics curriculum. But students’ difficulties with proof are well documented. This article focuses on proofs that use triangle congruence postulates in US high school geometry. Examining students’ proof reasoning in one-on-one task-based interviews, we analyzed students’ oral planning/explanations and two-column written proofs. We found that much of the reasoning students conveyed in their oral planning/explanations was not incorporated into their written proofs, resulting in formalization and fatal logical reasoning gaps. We found that the majority of the students utilized sound reasoning in their oral explanations, but struggled to capture that reasoning in their written two-column proofs. We link our findings to learning progression research, further elaborating the van Hiele levels. Our research contributes to understanding the learning and teaching of proof and to the ongoing controversy over the use of two-column proofs in the high school geometry curriculum.

Framework for Articulating Relation between Teachers' Practices and Students' Self-efficacy in Teaching and Learning Euclidian Geometry in High School

The aim of this paper is to explore a framework for articulating the relationship between teachers' practices and students' self-efficacy in teaching and learning of Euclidean Geometry (RTP&SS-EG) in high school. The effective learning of Mathematics, especially Euclidean Geometry by students, is directly influenced by teachers' confidence and competence. The RTP&SS-EG framework was developed based on the gap in literature revealed through international studies, indicating a direct relationship between teachers with a higher level of self-efficacy, and students' achievement. However, the researchers did not come across national studies promoting the relationship between the teachers' practices and students' self-efficacy on the learning of Euclidean Geometry in high school. The question asked was: To what extent is the relationship between the teachers' practices and the students' self-efficacy in teaching and learning of Euclidean Geometry in High school? Geometry Students Self-Efficacy (SGS-EQ) and Geometry Teacher Self-Efficacy questionnaire (GTS-EQ) were utilized. The participants were 81 Mathematics teachers, and 390 Grade 10-12 students from the Mpumalanga and North West provinces in South Africa. Reliability for the entire scale of both instruments computed in terms of the internal consistency was found to be .83. To establish the content validity of the scores from both instruments, the exploratory factor analysis was computed using varimax rotation. The four-factor solution accounting for 43.03% of the total variance was obtained from 36 items of the GTS-EQ. A five-factor solution for 45.37% of the total explained variance was obtained from the 46 items of the SGS-EQ. In RTP&SS-EG, three education theories, constructivism, social constructivism and social cognitivism, policies, as well as teacher and student self-efficacy principles enjoin the practice enacted from the relation between the teachers' practices and the students' self-efficacy in the learning of Euclidean Geometry. The findings revealed that the learning value associated with the relationship between teachers' practices and students' self-efficacy may be integrated into the everyday preparations of teaching-learning plans in Euclidean Geometry. It is critical that policymakers, curriculum developers, teachers and students make use of this model to ensure that self-efficacy of both teachers and students is taken into consideration in Euclidean Geometry.