School Geometry Research Articles

The use of augmented reality (AR) in education has shown potential to improve primary school students' numeracy skills. However, AR research for elementary school geometry is still rare. This study aims to develop augmented reality (AR)-based interactive learning media using the assembler edu platform to improve students' numeracy literacy in geometry subjects. The development method uses ADDIE, the research stages include needs analysis, design, development, implementation, and evaluation. The needs analysis identified problems such as the lack of interactive learning materials and students' difficulties in understanding geometry material. At the design stage, the storyboard and flowchart are made using assembler applications. Media development is done by combining components such as materials, geometry images, animations, and music. Implementation is done through trials by material experts, media experts, and field practitioners, as well as small group and large group trials. The evaluation results show that the developed media has high validity with a percentage of 92% from material experts and 88% from media experts, as well as a significant increase in student numeracy literacy with the percentage of completeness increasing from 6.15% (pre-test) to 79.8% (post-test). With an N-Gain Score of 0.52, this media is proven effective and feasible to use as an additional learning resource.. Recommendations for future research include developing content for other topics, testing in different conditions, and improving interactive features.

Constructivism is a learning theory perspective that strongly influences how mathematics is learned. Since secondary school students are just beginning to recognize and understand abstract thought processes, it is not appropriate to educate them through meaningless memorization, especially in mathematics which is full of abstract symbols. The writing of this article aims to find out the research trends regarding the constructivism approach and to find out the research themes that have the opportunity to be used as research in the future. The method in this research is using bibliometric analysis. Research data obtained through Harzing's Publish or Perish software with Google scholar database, keywords constructivism and junior high school geometry and the result of the maximum number "1000", the article obtained as many as 996 articles with a period of 2017-2023. Then limited to accredited journals sinta 2 obtained 50 articles. The results showed that the publication trend with the research theme of the constructivism approach experienced the highest increase between 2017 - 2020. In addition, the theme of research on the constructivism approach that has the opportunity to be used as research in the future there are four keywords, namely constructivism and Realistic Mathematics Education (RME).

The lack of contextualization and innovation in developing learning materials for 2nd-grade elementary school geometry has become a major issue leading to students' difficulty in understanding concepts. This research aims to develop an Electronic Student Worksheets Based on Ethnomathematics Upakara Bali in Geometry for 2nd-Grade Elementary School. Trial subjects in this study include two material experts, two media experts, one 2nd-grade teacher, 6 individual trial students, and 10 small group trial students. This research utilizes the ADDIE model (analyze, design, development, implementation, evaluation). Data collection methods used were questionnaires, interviews, and observations. Data analysis techniques involved quantitative and qualitative descriptive analyses. The results of this developmental research are the Electronic Student Worksheets product, covering: (a) the design and development of an ethnomathematics-based Electronic Student Worksheets on Upakara Bali for 2nd-grade Elementary School Geometry, including analysis, design, and development stages; (b) validity test results gain criteria of excellent qualification; (c) effectiveness test belongs to teacher response, individual trial score, small group trial score belongs to excellent qualification. Hence, it can be concluded that this Electronic Student Worksheets is suitable for use in the learning process. The implication of this research is the existence of a valid and suitable Electronic Student Worksheets to enhance 2nd-grade Elementary School geometry learning within the local cultural context.

The mathematical connection abilities of middle school children are the primary subject of this study, which aims to understand how means-end analysis (MEA) policies and procedures might assist. Students need to build mathematical connection abilities that enable them to comprehend and associate various mathematical concepts to improve their ability to comprehend and apply mathematics in real-world contexts. This is an essential component of the learning process. The research uses a quasi-experimental methodology by administering tests to the control and experimental groups before and after the intervention. One group utilised the MEA tactics in the mathematics lesson, while the other group remained committed to the tried-and-true method. Data was collected through mathematical connection tests, and then statistical analysis was performed on it to determine whether or not the intervention was effective. According to the findings, students whose courses contained MEA strategies showed a considerable improvement in their mathematical connection abilities compared to the control group. This study validates that incorporating MEA approaches into the mathematics curriculum is a viable alternative for increasing students' mathematical literacy and competence. The findings of this study provide more evidence to support this idea.

Science challenges the relevance of school geometry in its treatment of space. Therefore, the research discusses the incorporation of non-Euclidean geometries in the initial and continuing education of mathematics teachers. Hence, this literature review aims to synthesize and describe, in a broad and current range, the recent state of research in educational mathematics on these geometries in teacher education. To do this, we configured a method in three moments: the search, evaluation, selection, and organization of the sources found and reading, analyzing, and writing results. The results highlight a regional and temporal interest that prioritizes teaching practice. Furthermore, a deficit and prescriptive perspective of teachers' knowledge and a minority perspective of the teacher as a subject of knowledge are recognized. We conclude with the need for research on various phenomena, including Euclidean generalizations.

Abstract For years, school geometry has faced with many issues including losing its strong position in school mathematics and earning the reputation of being the “problem child” of mathematics teaching. These issues stem from the problems in the intended curriculum. The goal of this paper is to shed light on the two intended curricula for primary mathematics education in Croatia in terms of the diversity and coherence of geometry topics through the lens of fundamental ideas of geometry. Additionally, the analysis is associated with previous results on the attained and potentially implemented curriculum regarding textbook tasks and primary school students’ images of geometry. Even though the new curriculum reflects more diversity regarding the fundamental ideas of geometry compared to the old curriculum, there is clear evidence that they still do not offer the learning opportunities in line with modern geometry education. Based on the data, the results are discussed with regard to their theoretical and practical implications with the goal of providing suggestions on how to improve the position of school geometry in mathematics education in Croatia conducive to modern geometry education, as emphasised in the literature.Keywords: fundamental ideas; geometry education; primary education; tripartite model of curriculum.---SažetakŠkolska geometrija tijekom godina suočavala se s mnogim problemima, u što ulazi i gubitak nekad snažne pozicije unutar školske matematike te dobivanje reputacije „problematičnog djeteta” nastave Matematike. Ovi problemi proizlaze iz planiranog kurikula. Cilj ovoga rada je analiza dvaju planiranih kurikula za razrednu nastavu Matematike u Hrvatskoj s fokusom na raznolikost i koherentnost geometrijskih sadržaja i kroz objektiv fundamentalnih ideja geometrije. Uz to, rezultati su povezani s prethodnim nalazima o postignutom (slike učenika o geometriji) i potencijalno primijenjenom kurikulu (udžbenički zadatci). Iako novi kurikul odražava više raznolikosti u pogledu fundamentalnih ideja geometrije u odnosu na stari, rezultati pokazuju da ti kurikuli još uvijek ne nude značajke suvremene metodike geometrije u punom potencijalu. Na temelju dobivenih rezultata provedena je rasprava s prijedlozima kako poboljšati položaj školske geometrije u matematičkom obrazovanju u Hrvatskoj prema preporukama iz literature.Ključne riječi: fundamentalne ideje; nastava geometrije; razredna nastava; trodijelni model kurikula.

Mathematics is considered a difficult subject. So in the learning process teachers need teaching materials to help students with difficulties in understanding abstract material. The aim of this research is to create an interactive e-module based on ethnomathematics in mathematics subjects with valid and practical geometry material. The type of research used is development research with the ADDIE model. The test subjects in this research were two material expert lecturers, two media expert lecturers, a class II teacher and 10 students. The data collection method is a questionnaire in the form of a rating scale. The data analysis method uses qualitative and quantitative analysis. Based on the analysis results, it was found that the validity test results according to media experts obtained a score percentage of 99% with very good qualifications. The test results from the teacher's responses obtained a score percentage of 98% with very good qualifications. The test results from individual student trials obtained a score percentage of 99% with very good qualifications. The test results from a small group of students obtained a score percentage of 98% with very good qualifications. Based on this, the e-module developed is valid and suitable for use in learning activities. The implication of this research is that teachers can use e-modules based on Balinese upakara ethnomathematics as a reference or special learning tool for grade 2 elementary school geometry material. Through the use of this e-module, students will gain new learning experiences. Apart from that, the use of technological developments and attractive visual, audio and video displays will accommodate students' learning styles, both auditory and visual learning styles.

The article provides two approaches for the implementation of the inference search procedure in the ontological base. One is based on the SWRL-rules, the other is a system with the natural language processing elements. The procedures have been established as a part of the recommendation system, which is developed at the Faculty of Informatics at National University of Kyiv-Mohyla Academy.We also add a description of the created approaches with their fragments of the taxonomic hierarchy for the planimetry ontology. For the performance examples, simple open-type problems with a short answer taken from the school geometry textbooks are used. The features of the approaches, how they work, as well as the capabilities they have are reviewed.The approach with natural language processing capabilities has a module for preprocessing raw Ukrainian text using the UDPipe 2.12 model, a module for rechecking the lemmas by using VESUM dictionary, a module with a described planimetry ontology, and a module for creating an illustration of the figures (triangles).To better illustrate the capabilities of the approaches on equal terms, we tried to use the same geometric problem. English translation of the problem: «Perimeter of an isosceles triangle = 40 cm and base = 10 cm. Find the legs of the triangle.». To solve this problem, systems should have a rule that subtracts the base from the perimeter, divides it by two, and sets the result to the correct variables (in our case, the legs of the triangle). We demonstrated that both approaches solved the problem successfully. But in order to achieve it, minor changes were added. Therefore, the more complete the ontology is, the greater the number of problem types the systems are able to cover.Having analyzed the results of the study, we can conclude that the systems are effective for solving geometric problems. The next step may be to combine the capabilities of the approaches to form a more complete knowledge base.

artifacts, and so on. However, there still needs to be more emphasis on the connection between traditional boat building and mathematics. Therefore, this article aims to characterize the ethnomathematics connections built from the traditional Indramayu boat shape. Theoretically, this research is based on ethnomathematics, ethnomathematics connections, and Universal Activity. The research approach used is qualitative by using an ethnographic design. This article's research object is the form of traditional boats in Indramayu—the research data obtained from preliminary studies, observations, interviews, and documentation. Interviews were conducted with three people, namely two builders and crew members (Ship's Crew). Based on the results of the study, it was found that the ethnomathematics connection to traditional boats can be seen in the forms of boat buildings and the accessories that complement them, such as the lunas, haluan, lambung, kemudi, hatch, and storage area. Institutionalizing the parts of the boat can represent the concepts of plane and spatial geometry. Therefore, the implications of this article can enrich students' starting points for learning mathematics and facilitate students' understanding of abstract mathematics using the context of society's culture.

The article describes the main methodological features of teaching “vector methods” in a school geometry course. In order to increase the efficiency of teaching students the vector method, the connections between the vector method and coordinate methods are analyzed. Examples of solving algebraic and geometric problems using the vector method were shown, showing the scope of vector studies covered in the school course. A brief overview of the history of the development of the vector method is given. The article is recommended for students, school teachers, methodologists and all interested parties.

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.

Abstract The present work establishes a study within the scope of a broader project on the relationships between the History of school geometry and the Modern Mathematics Movement (MMM). We analyzed how a particular knowledge – geometric transformations (GT) – circulated in the Brazilian context during the mentioned period. From a historical perspective, we investigated four textbooks produced between the 1960s and 1970s by MMM leaders. The guided questions of this study were the following: what are the similarities and differences in the approaches to GT between the different books? How did the articulation between GT and Euclidean Geometry (EG) happen? The process of insertion of GT through textbooks was diverse, highlighting the complexity of the dialogue and the prediction of reconciling demands arising from specific cultures: the academic one, as a representative of scientific production, and the school one, representing experiences of professional practices.

The aim of this study is to analyses the reasoning, awareness, and metacognitive thinking skills of middle school geometry teachers from Generations X and Y in transferring mathematics to Generation Z. The study is designed as a case study, and the content is analyzed using the content analysis method. 40 middle school teachers from Generation X, 52 middle school teachers from Generation Y, 92 teachers in total (51 females, 41 males), participated in the study. The study results show that the reasoning skills of middle school teachers differ among the generations. Another result of the study is that the awareness of teachers of the difference between the concepts of geometric shapes and objects as well as the awareness of the number of edges required when drawing geometric shapes differ from generation to generation. In addition, while the metacognitive skills of teachers were similar in some points according to the generations, the metacognitive skills of teachers differed in some points.

The study explored gender and school location-related differences with respect to difficulties in geometry among students. The study is an analytic survey research design, because, it attempted to compare the statuses of two groups of subjects in a given tribute. The effect or observation investigated in this study was students’ areas of difficulties in geometry. Three research questions and two hypotheses guided the study. The population of the study was 9,200 senior secondary school three students from Obollo and Nsukka Education zones of Enugu state, Nigeria. The sample of the study, using cluster proportionate random sampling technique was 1,000 students made up of 492 boys and 508 girls, clustered as 515 urban and 485 rural students from the two education zones. The instrument for data collection was Test on Secondary School Geometry (TOSSG) developed by the researchers, using Test Blue Print to ensure content validity. The 30-multiple choice test instrument was validated by two experts from the department of Science Education, University of Nigeria, Nsukka and trial tested on 20 students from a co-educational school in Enugu education zone of the state. The reliability coefficient of the instrument was 0.91, Using Kuder-Richardson 20 (KR-20). Data were analyzed using mean and standard deviation to answer research questions, while the null hypotheses were tested at 0.05 level of significance, using the Z-test statistic. The result of the study indicated differences in achievement with respect to gender and school location. Boys experienced less difficulty than girls, while urban students experienced less difficulty than their rural counterparts. It was recommended that teachers should adopt a variety of pedagogical strategies that are gender and culture-sensitive, capable of securing girl-child education and addressing different learning styles within instructional environments.

In theory and practice, we repeatedly come across ideas that for some reason are considered unconditionally true, like the axioms of school geometry. Over time, they are often refuted or forgotten, but others come in their place, in the same capacity. In this regard, the theory of knowledge based on axiomatics, the creator of which is R. Descartes, is of interest. The article shows the breadth of Descartes’ views, in particular the presence of an empirical component in his rationalistic version of cognition. An attempt is made to compare the versions of knowledge of R. Descartes and F. Bacon, revealing the possibility of their synthesis.

Mathematics is still seen as a non-cultural subject. Mathematics and culture are two aspects that have a strong relationship. Culture provides a natural means for students to access a framework for conceptual understanding in mathematics. One of the important cultural objects in Indonesia is the Phinisi. The phinisi is a traditional wooden ship originating from Bulukumba Regency, South Sulawesi province which is recorded as a world cultural heritage. This study explores the concept of ethnomathematics geometry on phinisi ships. The method used in this research is an exploratory-descriptive method through an ethnographic approach to explain and analyze the ethnomathematical concepts of geometry on the components of the phinisi. Research data were collected through a literature review, direct observation of the shape and process of making phinisi, and interviews with expert phinisi shipbuilders. The results showed that there are geometric ethnomathematical concepts in the form of flat shapes and spatial shapes on several phinisi components. This ethnomathematical concept is relevant to the formal mathematical concepts learned in school so it has the potential to be a source of learning mathematics.

Traditional games are rooted in a regional culture with educational values that are important for future generations. These educational values, among others, contain various mathematical concepts (geometry). This study aims to improve students' Spatial Nets ability through the outdoor learning-based traditional game 'Baju Simi.' The type of research used is classroom action research. The research subjects were 20 students of class VI Sekolah Dasar Negeri 98 Kaur, Bengkulu. The study was conducted in the Even Semester 2022/2023. The instrument used is a test on 'Spatial Nets' with as many as ten essay questions. In addition, it also uses questionnaire instruments, observation guidelines, and interview guidelines. Data were analyzed qualitatively. The results obtained are as follows: (1) In Cycle 1, there was an increase in the ability of 'spatial nets' by 0.21 with low pre-test and post-test scores of 45 and 56.5, respectively; and (2) In Cycle 2, there was an increase in the ability of 'spatial nets' by 0.36 with an average pre-test and post-test score of 53 and 70.25 respectively. As many as 92% of students can understand the meaning of space-building nets correctly. 87% and 82% of students can precisely define the webs of cubes and blocks. This study implies that traditional games can be used as a medium and source of learning mathematics (geometry) in elementary schools so that students are highly motivated (4.2 on a scale of 5) in learning mathematics (geometry).

Proof, as a central and integral part of mathematics, is an essential component of mathematical education and is considered as the basic procedure for revealing the truth of mathematical propositions and for teaching productive reasoning as part of human civilization. Is there therefore room for conjectures in mathematics? In this paper after discussing at a theoretical level the concepts of proof and conjecture, both in a paper-and-pencil environment and in a dynamic geometry environment (DGE) as well as how school practice affects them, we fully explain a task involving various mathematical disciplines, which we tackle using elementary mathematics, in a mathematics education context. On the occasion of the Greek educational system we refer to some parameters of the teaching of geometry in school and we propose an activity, within a DGE, that could enable students to be guided in the formulation and exploration of conjectures. Finally, we discuss the teaching implications of this activity and make some suggestions.

To identify the level of education of schoolchildren in different countries of the world, the OECD conducts international studies in the field of education. Comparative results of these studies make it possible to determine the effectiveness of national educational systems contributing to adapting programs for modernization and reform of educational systems. This study aims to develop mathematical literacy among 15-year-old students of the Republic of Kazakhstan by developing the basic skills of the 21st century in solving practice-oriented problems. An experimental study was conducted to determine teachers' attitudes toward the formation of mathematical literacy among schoolchildren. The study involved 32 teachers. The Analysis of the results of the survey revealed that the majority of teachers had a negative attitude towards the formation of mathematical literacy among schoolchildren, substantiating their points of view by the fact that the formation and development of mathematical knowledge and skills by itself contributed to the development of skills in the 21st century. Only 11% of teachers could accurately indicate those tasks, out of the seven tasks presented for consideration, in the solution of which schoolchildren had shown critical, systemic thinking. An analysis of geometry textbooks used in schools of the Republic of Kazakhstan showed that out of the total number of educational tasks studied in geometry lessons, the share of practice-oriented tasks comprised less than 3%. Based on the results of the experimental study, it is concluded that it is necessary to develop appropriate methodological approaches that contribute to the formation of mathematical literacy among schoolchildren using the learning tasks of the school geometry course.

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.