School Geometry Research Articles

Integration of STEAM in Teaching Modern Geometry through Batik Motifs Creation with Algebraic Surfaces

This paper explains teaching modern geometry for schools using software called Surfer and converting the algebraic surfaces into Batik motifs as one example of teaching mathematics with the integration of STEAM. Typical algebraic surfaces known in schools were, for example, cylinders and spheres which are identified as traditional geometry in this article. On the other hand, other geometrical objects that are not solely identified as traditional ones are called modern geometrical objects. The objects addressed here are governed by multiple algebraic surfaces and existed in the software called Surfer. The software is used for students to learn traditional geometry initially. After knowing how the software Surfer is doing, the software can be used for drawing more complex geometrical objects that are named to be modern geometry. This software is introduced for students in middle schools until students in the university such that technology and art are immersed in learning geometry. In this research, the activity involved creating a Batik piece which was a local textile in Indonesia based on algebraic surfaces created with Surfer. There were two methods of presenting the motif, these are after drawing the algebraic surfaces, students copied the surfaces into textiles using drawing Batik procedures. In the second method, students received some prototypes of algebraic surfaces and converted them into new patterns which were illustrated on a special paper for a copper stamp prototype later on. Using geometry as the routine topic which must be learned by any level of students in learning mathematics, the learning, innovation skills, and technology skills are direct educational values that are targeted by the activities with the approach presented in this article. The educational value is not only for the sake of mathematics and its content but also for integrating mathematics with other fields and exploring mathematical terms such that STEAM is introduced in this sense. The article here has addressed learning geometry by combining technology, art, and creating products to the related geometrical studied objects to develop learning skills, innovative skills, and technology skills that are educational values required skills in 21st-century education.

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.

Integrating Art and Dynamic Geometry Software into the Teaching and Learning of Middle School Geometry

Abstract This study focuses on understanding the ways in which integration of art and dynamic geometry software (DGS) into geometry influenced middle school teachers’ understanding of geometric concepts that are difficult to teach, and their perceptions of teaching these topics. The study indicated that art materials combined with DGS played different roles in teachers’ understanding of geometry: in some cases, they helped acquisition of new knowledge and development of deeper conceptual knowledge while addressing misconceptions; in other cases, they helped the retention of knowledge by association with the activity; and in some cases, they facilitated the transfer of knowledge and development of strategic knowledge. Study results also indicated that integration of art combined with DGS led to a higher level of creative engagement that supported productive struggle and helped teachers appreciate and understand pedagogy differently. Lastly, the teachers made connections from learning mathematics content to the pedagogy of teaching that same content.

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

Development of Augmented Reality Applications-Flat Geometry and Space in Android-Based Primary School

This study aims to design an Android-based Flat and Spatial Geometry Augmented Reality Application in primary school (SD, Sekolah Dasar) that is valid and practical. This application uses the Vuforia library which is capable of playing sound and displaying animated 3D objects, played by the user in a real environment using the help of books and Android-based smartphones. This research is a Research and Development (R&D) study using the ADDIE model (Analysis, Design, Development, Implementation and Evaluation) to develop Flat and Spatial Geometry Augmented Reality Applications in Elementary Schools as a learning medium that is expected to be able to create a fun and effective learning environment to improve students' mathematical literacy ability. The research subjects were 32 students of class VI at SD Negeri 050660 Kwala Bingai Stabat. The research instruments used in this study included validation sheets to obtain an assessment of the validity of the application, and student response questionnaires to determine the practicality of the application. The results of the research and development show that the Application of Augmented Reality Flat and Spatial Geometry is in very good criteria. The results obtained based on the analysis of the black box test obtained a success percentage of 100% and the white box test obtained a success percentage of 100%. While the average validation score is 90.19% of the total interpretation. In the field test, it was obtained an average practicality percentage of 84.5% from 15 assessment items. So that the application of augmented reality flat geometry and space is included in the very good criteria.

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.

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;

From defining as assertion to defining as explaining meaning: teachers' learning through theory-informed lesson study

PurposeThe aim is the introduction of lesson study (LS) in geometry in Malawi secondary schools supported by a teaching framework that includes a focus on language responsive teaching.Design/methodology/approachThe study reports an LS on geometry for professional development (PD) of secondary teachers. Data analysed includes lesson plans, transcripts of lessons, reflective discussions. The analytical approach is qualitative content analysis.FindingsTeachers' lexicalisation of an exterior angle of a triangle evolved as a function of a teaching framework that guided their participation in planning, teaching and reflecting through LS cycle, and that was derived from networking between theories.Research limitations/implicationsThis is both a small-scale study, and a limited content focus in the lesson, a function of LS being a new practice, and teachers simultaneously learning ideas about geometry teaching, those embedded in the framework and doing LS.Practical implicationsThe paper includes a description of how LS might contribute to teachers' learning of language responsive teaching, and so is useful for others working on LS and language practices.Originality/valueThis paper fulfils an identified need to learn more about how networking theories to inform and support LS can create learning opportunities for teachers, particularly about language responsive teaching, an interest and concern worldwide.

A CULTURAL SEMIOTICS STUDY: ETHNOMATHEMATICAL EXPLORATION IN GEOMETRY MATERIALS THROUGH CULTURAL SITE IN ACEH

This study aims to interpret Rumoh Aceh as one of the historical artifacts through an ethnomathematical approach to the focus of the material, namely geometry in elementary school, and to find out the philosophical meaning behind the architecture and ornaments of Rumoh Aceh through a cultural semiotic review which was a type of semiotics from the qualitative content analysis method devoted to the semiotic study in certain cultures. This study referred to secondary sources in journal articles, book and document retrieval through relevant websites to a cultural site in Aceh. Furthermore, the primary sources were obtained from observations about Rumoh Aceh and traditional leaders in Aceh during the archipelago module activities. Determination of the data validity from this study was done by triangulation of sources utilizing cross-check. The results of this study reported that several ethnomathematical concepts in the Rumoh Aceh building could be taught in geometry material in elementary school, including; (1) the concept of the position of an angle concerning a line, (2) the concept of a plane figure (square), (3) the concept of a plane figure (rectangle), (4) the concept of a plane figure (a right triangle) and the Pythagorean principle, (5) the concept of a plane figure (isosceles triangle), (6) the concept of a plane figure (trapezoid), (7) the concept of a flat rhombus, (8) the concept of a spatial figure (tube), and (9) the concept of reflection, tessellation, and translation which might be required to be taught on the introduction of basic concepts at the elementary school level (high grade).

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.

ФОРМИРОВАНИЕ ПРОСТРАНСТВЕННЫХ ПРЕДСТАВЛЕНИЙ У УЧАЩИХСЯ

It is known that the goal set by all subjects studied at school is to give students conscious knowledge and skills, and their successful mastery of the basics of knowledge is impossible without the formation of students' skills of mental work and a culture of thinking. In this regard, the formation and development of the spatial imagination of students are one of the urgent problems of the school geometry course. The article discusses the importance of the formation of the spatial imagination of students and the ways of its development. At the same time, several examples from the mathematics textbook for the 5th grade of secondary school are given in a visual form.

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.

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.

Materiality, Wallcharts, and Educational Change in Sweden from the Mid-nineteenth to the Early Twentieth Century

This article investigates the dissemination of wall charts as an instructional technology in the subjects of history, geography, natural science, and geometry in elementary schools in Sweden, particularly in the Uppsala diocese from 1861 to 1910. Previous research lacks empirical analyses of the charts’ actual dissemination, making this case study of Sweden a valuable contribution to the fields of material culture and the visual aspects of schooling in the history of education. Using school inspector reports, protocols from national inspector meetings, and national and regional pedagogical statistics, the article provides empirical evidence of the active work of school inspectors and state initiatives that contributed to the widespread dissemination and use of wall charts in Swedish elementary schools by 1910.

Correction to: Geometrical Figure Apprehension, Construction of Auxiliary Lines, and Multiple Solutions in Problem Solving: Aspects of Mathematical Creativity in School Geometry

Correction to: Geometrical Figure Apprehension, Construction of Auxiliary Lines, and Multiple Solutions in Problem Solving: Aspects of Mathematical Creativity in School Geometry

우리나라, 일본, IB 중학교 수학 교육과정과 교과서의 증명 내용 분석1)

Korea has not dealt with proof in middle school geometry since the 2009 revision of the curriculum. In this study, we propose to reintroduce proof in the new curriculum in Korea, and examine the contents and methods of proof education in the geometry domain of the Japanese and IB (International Baccalaureate) middle school mathematics curriculum, and based on this, we would like to suggest implications for proof education. To this end, in order to diagnose the current status of proof education in Korea, the introduction period of proof and related terms were analyzed by curriculum period. Next, we looked at the 2017 revised middle school mathematics curriculum in Japan, which has a similar academic system, curriculum, and educational environment to Korea, and the proof of the middle school mathematics textbook first published in 2021 based on this curriculum. In addition, we looked at how proof is handled in the IB (International Baccalaureate) mathematics curriculum and textbook, which is an internationally accredited curriculum. By summarizing these, implications for how to develop proof education in Korea

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.