School Geometry Research Articles

USE OF AUGMENTED REALITY MEANS IN THE PROCESS OF STUDYING PLANIMETRY IN INSTITUTIONS OF SECONDARY EDUCATION

Visualization of educational material in secondary education institutions is one of the successful components of qualitative learning of this material and its further application in the learning process. In a special need of visualization are the school subjects that are difficult to understand and, essentially, do not have a wide practical application at the beginning of the study, that is, subjects of the mathematical cycle. This is why the aim of this study is to analyze the mobile tools that can be used to visualize educational material when studying a geometry course in high school. The study used such research methods as analysis and justification of the choice of mobile augmented reality tools for studying mathematics. As a result of this analysis, two augmented reality tools, Arloon Geometry and Geometry AR, were identified as ones that can be used to visualize educational material and create a problematic situation in order to gain new knowledge in high school geometry lessons. The analysis of these tools made it possible to say that the use of augmented reality tools in geometry lessons creates the conditions for positive emotional interaction between the student and the teacher. Firstly, students understand that a mobile device can be used to organize the learning process, to intensify it and to build a personal learning trajectory. Secondly, the emotional component of learning creates conditions for better memorization of educational material, promotes their mathematical interest, actualizes their creative potential, introduces conditions for finding different ways to solve geometric problems. Thirdly, the ability to find solutions of simple geometric problems with the help of augmented reality instills into the student a positive attitude towards success, and the solution of more complex problems becomes faster and more intense.

Materialist epistemology lends design wings: educational design as an embodied process

Materialist design is presented as an embodied perspective on educational design that can be applied to redesign of classroom-based learning environments. Materialist design is informed by a framework of materialist epistemology, which positions material innovation on equal placement with symbol-based formal theory. Historical examples of Einstein’s conceptual reliance on trains for his Theory of Relativity and the Wright brothers’ use of wind tunnels in aeronautics illustrate how materialist design drives progress on complex design problems. A key aspect is the application of scale-down methodology, where complex systems are reconceptualized as interactions among nearly decomposable subsystems that can be redesigned and integrated back into the entire system. The application of materialist design is illustrated with the redesign of an embodied video game that uses real-time motion capture technology to promote high school geometry reasoning and proof, following its use in an ethnically and linguistically diverse classroom. Our embodied perspective offers particular insights for understanding and implementing designs of complex learning environments, and assessing their influences on educational practices and student outcomes.

A variation on an old geometric theme

ABSTRACT The purpose of this note is to introduce two challenging problems in geometry that were inspired by some well-known problems in high school geometry. These problems can be explored in the dynamic geometry environments of computer construction programmes.

Subject Matter Knowledge of Geometry Needed in Tasks of Teaching: Relationship to Prior Geometry Teaching Experience

This study proposestask of teachingas an organizer of dimensionality in teachers’ subject matter knowledge for teaching (SMK) and investigates it in the context of measuring SMK for teaching high school geometry (SMK-G). We hypothesize that teachers use different SMK-G in different aspects of their teaching work and that such differences can be scaled and associated with key elements of instruction. Analyses of 602 high school teachers’ responses to two sets of items designed to measure the SMK-G used in two particular tasks of teaching—understanding students’ work (USW) and choosing givens for a problem (CGP)—suggested the two scales of SMK-G to be distinguishable and differently related to experience in teaching high school geometry.

Educational construction of geometry and the use of concrete materials as a learning process

The research stood out for a didactic reflection that meets the need for experimental constructions in the classroom, with concrete materials to assist in the process of teaching and learning geometry in elementary school. In this sense of attributing an analysis to this problem, we have as axis, mathematics education, as a way to stimulate students for the development of workshops in which they aimed at the construction of didactic materials as a process of learning mathematics. The process of constructing the concept of geometry that attribute the skills and competencies to be developed in the students at this stage, allowed the same to develop a particular type of thought to understand, describe and represent, in an organized way, the geometric spaces, informing the importance that this content has in their social life as a citizen. Through the construction of geometric figures with manipulated materials, we study all the concepts of the figure, through this tool, thus stimulating the interest and motivation of the students, providing them with geometric and mathematical reasoning. The definitions of geometry can be constructed successively, taking as a basis the previous knowledge of the students or not, in which we highlight that educators should create activities in which students make inquiries of situations related to geometric dimensions, thus having experiences of meaning and direction of themselves and of some figure inserted in the space. However, for the absorption of this teaching and learning process, in addition to presenting theories to the students, it was necessary to show the geometric figures by their physical characteristics, that is, in such a way that nature provides us and not only by its properties and defined concepts. Finally, the research allowed us to analyze the intellectual capacity of each student selected for this purpose.

Factors Affecting Mathematics Achievement In Central Asian Specialized Universities

This study examines variables explaining student’s academic performances in mathematics from specialized engineering institutions. A survey consisting of 42 items was conducted from 127 students and statistical multiple regression was carried out to analyze the data set. Based on Fennema-Sherman Mathematics Attitude Scales followed by the result of stepwise linear regression, found a significant impact of high school geometry grades in mathematics performance. Au-thors suggest that mathematics instructors in higher education should pay attention to improve their student’s confidence, which in turn would decrease the anxiety level towards mathematics. The high school teachers should not advise their students to go to technical sciences in higher education unless the student’s confidence and high school math grade are sufficiently high

지식의 구조로서 변환기하를 다루기 위한 성취기준 방향 탐색

While Korean students learn more about Euclidean geometry earlier than other countries, they learn transformation geometry less. Therefore, in this study, we proposed a way to find consistency and systematicness of the geometric curriculum in Korea, focusing on transformation geometry. For this reason, the importance of transformation geometry was discussed in terms of the structure of knowledge. Also, we analyzed the transformation-based perspective expressed in the curriculum standards of the Common Core State Standards for Mathematics(CCSSM) and the Korean 2015 revised mathematics curriculum in terms of curriculum articulation. As a result, the topics of transformation geometry that can be dealt with in school geometry were “congruent transformation”, “symmetry”, “similar transformation”, and “analytic approach to transformation”. In the case of CCSSM, the standards for each topic were structured to have a curriculum articulation, but in the case of Korea, the curriculum articulation of each topic was insufficient. Among the topics of transformation, 'similar transformation' was selected, which is important but not emphasized in Korea, and suggested what can be changed when the relevant standards are systemized into a transformation-based perspective.

METHODS OF FORMING STUDENTS' CREATIVE ACTIVITY DURING THE COURSE OF GEOMETRY

The article describes some problems of the theory and methodology of teaching geometry in the secondary school, which are performed with the active use of independent work. Here you can find examples of how planimetry and stereometry are considered and how they are compared in elective classes. When studying the systematic course of geometry, the methods of mastering new concepts, patterns, and dependencies that form the creative activity of students are considered. The article shows that comparative training based on questions and advices is carried out at the stages of "acceptance" of the problem, search for solutions, reflexive processing of the obtained solution, as well as further generalization and development of the original problem situation.

Effects of VH-iSTEM Learning Strategy on Basic Secondary School Students' Degree of Acquisition of van Hiele Levels of Thinking in Sokoto State, Nigeria

Learning school geometry and development of geometric thinking skills required a careful selection of strategy, that provides collaborative learning behaviors, use of appropriate tasks, and materials. Thus, teaching and learning should be meaningful not just merely transmission and absorption. Hence opportunities should be given for students to experiment and discover learning experience by themselves. This study investigated the effect of instructional strategy (VH-iSTEM) designed to help in solving the problems of learning school geometry and develop students' geometric thinking skills. The strategy emphasized the learning of geometry based on the connections of the iSTEM (engineering design phase) with the van Hiele phase. A quasi-experimental, design was used in this study with a sample of 89 students divided into two experimental groups of 30 each (VH-iSTEM, and VH); and 29 students in the control group. Additionally, three students were randomly selected from each group for an interview. The qualitative results obtained revealed that the majority of the students at pre-interview were able to achieve complete acquisition of level one of thinking and that, six students achieve low acquisition of level two, with no acquisition of level three among three independent groups. Thus, after the intervention, only students in the VH-iSTEM learning strategy group achieved the complete acquisition of level one to level three of van Hiele levels. Two students achieved a lower acquisition of level three and that one student achieved the high acquisition of level two and level three in the VH group. No students achieved level three in the control group. This demonstrates that VH-iSTEM learning strategy can be applied in classroom instruction to help students achieve a higher level of geometric thinking.

GEOMETRIA NA FORMAÇÃO DAS NORMALISTAS DO INSTITUTO SANTA MARTA NO MUNICÍPIO DE BARRA DO GARÇAS (1960 - 1980)

Este artigo é parte da Pesquisa de Mestrado do Programa de Pós-Graduação da Universidade de Cuiabá e tem como objeto de estudo o ensino de geometria na formação de professoras normaliatas do ensino primário em Barra do Garças/MT. Ancorada na abordagem histórico-cultural, o estudo fundamentou-se nos aportes teóricos de Chervel (1990), De Certeau (1982), Julia (2001), Pinto (2014) e Silva; Valente (2014). Teve como objetivo analisar a presença da geometria na formação das normalistas que cursaram o magistério e lecionaram no Instituto Santa Marta no período delimitado da pesquisa. As fontes foram constituídas pelos depoimentos e diários de classe com ênfase no ensino da geometria na escola primária. Os dados revelam a presença da geometria indicando como as normalistas aprendiam e ensinavam os conceitos geométricos em sala de aula, possibilitando novas indagações e reflexões frente ao descaso das escolas pela disciplina.

The Challenges of South African Teachers in Teaching Euclidean Geometry

The current study identifies challenges confronting teachers in the teaching of Euclidean geometry in schools. This qualitative case study purposefully selected ten schools situated in the Motheo District of Education, Free State, South Africa. Data was generated using classroom observations and focus group interviews. The findings revealed that the majority of the teachers lacked mathematical subject content knowledge as well as pedagogical content knowledge to teach geometry effectively. In many cases, redeployment of teachers led to teachers being ill-equipped to teach specific subjects, such as mathematics. Recommendations have been made to enhance effective teaching and learning of mathematics (geometry in this case) in schools. https://doi.org/10.26803/ijlter.19.8.16

Proof transcription in high school geometry: a study of what teachers recognize as normative when students present proofs at the board

We investigated how US secondary mathematics teachers expect students to present geometric proofs at the board. We analyzed video records of geometry classrooms and found students to be engaged in a practice that we call proof transcription—i.e., mark-for-mark reproductions of previously completed proofs that were not reasoned reconstructions of arguments. To investigate whether or not US secondary mathematics teachers recognize transcriptions as routine occurrences when students presented proofs, we conducted a survey experiment. Participants (n = 60) viewed episodes of instruction and answered questions that elicited their reactions to those episodes. The analysis of open- and closed-ended responses to the survey indicated that participants recognized transcriptions as routine. Our study contributes a fine-grained description of what teachers expect from students when students are called to present their work at the board.

中学校における論証幾何体系化への一つの試み （その 1)

中学校における論証幾何体系化への一つの試み （その 1)

Learning Geometry Online: A Creative Individual Learning Experience

The increasing influence of technology in education has made us want to understand how teachers will view its use when teaching Euclidean geometry. Teachers’ technological knowledge, skills; competence and readiness are crucial, in their preparation to integrate technologies in their future classrooms. This paper is part of a larger study that looked into the experiences of student teachers when using a form of online technology, which utilised meaningful interactions to teach and learn high school geometry. The study was conducted with ten mathematics student teachers at a South African university using a mix methods approach using worksheets, interviews, surveys and observations. This case study sought to capture the students’ knowledge of technologies when teaching circle geometry through a careful implementation of Geometric Habits of Mind and an Instructional Design model. The intention of the support programme was that students will reproduce their learning experience, during this study, in their classrooms. According to results the perceptions of technology can be categorised as: Knowing the essentials, A tool in learning geometry and A catalyst to learning geometry. It can be clearly stated that all of students liked the readily available learning tool online.

Exploring a Learning Management System as a Way to Improve Students’ Understanding of Geometry in Secondary Schools

The adoption of the learning management system (LMS) in secondary schools is scaling up around the globe. Many educational institutions use the LMS to mainstream teaching and learning. This study examined the effectiveness of the Moodle LMS in teaching and learning geometry in secondary schools. A quasi- experimental design was employed to generate data from two groups of students: the control group and the treatment group. The treatment groups learned geometry using the developed Moodle LMS while the control group learned geometry using the traditional chalk and talk method. Both the treatment and control groups did pre-test and post-test to track the impact of the intervention. The analysis of covariance (ANCOVA) test was employed to compare the pre-test and post-test scores and to make statistical analysis. The analysis revealed that the students who were taught geometry through the Moodle LMS outperformed those taught geometry through the traditional chalk and talk method. It is established in the study that for students to learn geometry better through the Moodle LMS, the system should be used to start teaching from the first topics of Form I to upper topics. Also, students should be given enough time to access the Moodle LMS to learn mathematics. The study concludes that the integration of the LMS in teaching and learning mathematics is a means by which failure in mathematics can be minimised.

Development Of Augmented Reality Application As A Mathematics Learning Media In Elementary School Geometry Materials

The problem of this research is the lack of interactive learning media on elementary school geometry which makes it difficult for students to understand the explanation that conveyed by the teacher. This research aims to design geometrical mathematics learning media especially cubes and blocks based on Augmented Reality technology for fifth-grade elementary school students and to know the level of product worthiness from the subject and validator. The development process of this research consists of five steps like Analysis, Design, Development, Implementation, and Evaluation. The data collection method used was a closed questionnaire. The results of the research questionnaire were analyzed using a Likert scale analysis, so the following results are obtained: The results trial of the material expert validator showed a percentage of 92.50% which is included in the excellent category with very decent information. Media design expert validator with a percentage of 93.00% which is included in the excellent category with very decent information. Product response of three elementary school teachers with a percentage score of 89.33% included in the very good category. Product responses of fifteen elementary school students with a percentage score of 83.73% with a very good category. It was concluded that the application of elementary geometrical mathematics learning media based on Augmented Reality technology can be used in elementary schools as a medium for learning mathematics.

Elementary students’ perceptions of 3Dmetric: A cross-sectional study

Rapid changes in the 21st century demand the use of technology in learning geometry in elementary schools. One such technology is augmented reality (AR). 3Dmetric (3D and Geometric) is a geometry learning medium on AR-based 3D space material. Students' perceptions, which refer to their interpretation, are a key factor in studying the changes in their interpretations of a particular phenomenon. The purpose of the current study was to investigate the perceptions of elementary school students after using 3Dmetric to learn geometric shapes. The differences and the relationship between the students’ level of perception and level of spatial ability were also investigated. This study applied a cross-sectional approach with quantitative and qualitative designs. A total of 36 students in one elementary school in Indonesia participated in this study. The instruments used were the Perception Scale for Using 3Dmetric in Geometry Teaching, Spatial Ability Scale, and In-Depth Interview Form. Results showed that the positive perception of elementary school students regarding the use of 3Dmetric does not depend on the level of their spatial ability. Moreover, the difference in their perceptions is not caused by the level of their spatial ability. The positive findings in this cross-sectional study can contribute to the success of AR-based learning and teaching in the 21st century, especially with regard to learning materials for 3D geometry. They can also lead to the formation of the spatial abilities and improvement in the academic performance of elementary school students.

Malind-Papua Ethnomathematics: Kandara Musical Instrument as Learning Media for Geometry Concepts in Elementary School

Each regions has a local culture that is the identity of the area. The Malind (Anim Ha) tribe as the original tribe of Merauke has a musical instrument that has a copyright kandara. Kandara was used as a musical accompaniment of dances and songs at traditional ceremonies. Kandara can be used as a learning media for the concept of geometry in elementary schools. This article aimed to describe the instrument of the musical instrument as an ethnomatematics of the Malind-Papua tribe that can be used as a learning medium for geometrical concepts in elementary schools. It was qualitative research using the ethnographic approach. Sampling using a cluster random sampling technique. The results showed that, the first ethnomatematics were found in parts of the kandara such as the handle or hands of the kandara, head, bodyor middle part and the tail of the kandara. Secondly, the musical instrument of kandara can be used as a learning medium to explain the concepts of geometry in elementary school in the form of the concept of angles, flat shapes (triangles, rectangles and circles) and building spaces (incised cones and tubes). Thirdly, ethnomatematics can be a learning material in elementary schools based on local culture, not only can help students understand mathematical concepts well but also maintain and respect the cultures of local communities (Malind tribe as an indigenous of Merauke).
 Keywords: Ethnomathematics, Kandara, Learning Media, Geometry Concepts

The use of ICT in teaching geometry in primary school

The purpose of this study is to investigate if information and communications technology (ICT) helps improve students’ achievement in geometry regarding solids’ nets. Our research compares the achievement of the students in the experimental group taught using our ICT intervention to students in the control group taught by traditional teaching methodology. In particular, we designed a teaching intervention with educational activities, in which we incorporated Augmented Reality (AR) technology to test whether geometry teaching is enhanced. The study dealt with primary school students of fourth grade, who were divided into two groups (experimental and control). Students in both groups were pre-tested and post-tested for their achievement in geometry. The results of the study indicated that teaching and learning through ICT is an interactive process for students at primary school and has a positive effect on learning geometry as compared to the traditional teaching method.

USING GEOGEBRA IN TEACHING PLANE VECTOR

The study of geometry knowledge is an important component of high school mathematics. Plane geometry is the main thread that runs through high school geometry knowledge. Vector learning is the focus and difficulty of plane geometry. When students encounter a new knowledge, it will be difficult to overcome it, and it is difficult to form a new logical system in their minds. Therefore, when students learn the content of vectors, they will have cognitive conflicts at different levels of thinking. The calculation from planar geometry to directed line segments needs a transition. It is difficult to understand the concept and nature of vectors without the help of teachers. This study attempts to guide the application of Geogebra software in teaching plane vector by using Van Hill Theory to intuitively display abstract geometric knowledge, and guide students to perform dynamic operations and deductive reasoning , Gradually help students transition from point to surface to vector operation, improve classroom teaching efficiency, and thereby optimize geometry teaching, in order to provide some reference for front-line teachers.