Geometry Textbooks Research Articles

Geometry Textbook Development Based on Gorontalo Local Wisdom for Elementary School Students

The current use of geometry textbooks in elementary schools still focuses on abstract theories and concepts, adhering to national standards that do not always align with local cultural characteristics. The development of a geometry teaching material based on the local wisdom of Gorontalo was chosen as one of the solutions to this issue. This research and development utilized the ADDIE model, which consists of five stages: Analysis, Design, Development, Implementation, and Evaluation. The subjects of the study were fourth, fifth, and sixth-grade students and teachers at MIT Al-Ishlah and SDN 3 Bulango Ulu. Data were collected through evaluation tests, expert validation questionnaires, and questionnaires for teachers and students. The results of the validation by content experts, language experts, and media experts were 78.4%, 83.33%, and 94.64%, respectively, all categorized as "valid." The responses from teachers and students during the trial phase were 83.33% and 81.71%, respectively, both categorized as "very practical." Thus, the Geometry Textbook Based on Local Wisdom of Gorontalo: Plane Figures and Solid Figures for 4th, 5th, and 6th Grade Students can be declared valid and practical for use in teaching.

Gender-related differences and social entanglements in mathematics education during 19th century: The subject of geometry

This paper examines mathematics teaching and learning, specifically of Geometry, in Greek girls’ schools in the 19th century. It explores how educational laws and school practice defined its teaching. Research has proved that female students received only the basics in Geometry, substantially less than what was offered to male students in all-boys’ schools. Also, the Geometry textbooks designed for girls are discussed. The problems considered in the article are at the intersection of economic, political and ideological issues. The study draws on a wide range of primary sources such as school archives and records as well as government gazettes. In particular, the school archives of the Philekpedeutiki Etaireia provide this research with a rich source of information regarding female schooling in 19th century.

Visualisation of educational material in geometry using digital technologies on the Unity 3D platform

Relevance. Digital technologies are progressively being incorporated into the educational framework. Training with the use of digital technologies corresponds to the modern way of life, which is inextricably linked with access to, receipt, and use of information. This entails the modernization of not only the content of education, but also the forms, methods, and means of teaching. Purpose. This study aims to investigate the impact of augmented reality on the spatial abilities and academic performance of students. It involves the development and testing of an educational application for geometry classes to provide interactive material and improve learning efficiency. Methodology. The study used pedagogical experiments, observations, and assessments. The Geometria mobile application with augmented reality for visualizing spatial geometry problems was developed for a tenth-grade geometry textbook. Results. The study involved 40 tenth-graders studying the section "Parallelism in Space". Following the experiment, all participants except for four demonstrated improvements in their prior test outcomes, with ten out of nineteen participants achieving outstanding grades. According to the study results, teachers and students noted the originality of this product and the fact that its use increased the visibility and understanding of the geometric material. Conclusions. A positive experience of using augmented reality technology in the study of stereometry has been obtained. The study highlights the effectiveness of augmented reality in enhancing students' spatial abilities and academic performance in geometry. The results suggest that incorporating digital technologies like augmented reality can significantly improve learning outcomes and engagement in educational settings. Keywords: secondary education system; geometry; spatial thinking; stereometry

The Journey Continues: Mathematics Curriculum Analysis from the Official Curriculum to the Intended Curriculum

In this paper, we share major lessons we have learned in our curriculum analysis explorations and provide suggestions for future mathematics curriculum research. Specifically, we will discuss the successes and challenges of using comparative methods and developing analytical frameworks. Using an old Chinese saying, follow the vine to get the melon (顺藤摸瓜), our journey starts with getting a holistic picture of standards and moves to identifying a specific topic in the textbooks. We first conducted a study to compare the geometry standards of the Common Core State Standards for Mathematics (CCSSM) and the Chinese Compulsory Education Mathematics Curriculum Standards (CMCS); then we analyzed the presentation of a specific topic, triangle congruence, in multiple geometry textbooks. For each comparative study we conducted, developing the analytical framework that can be used to guide future investigations constituted a critical step in the research methodology. We have learned lessons from adapting the well-known van Hiele model, which was created for the development of geometric reasoning, into a lens for a detailed curriculum analysis. We have also learned lessons from elaborating on the key constructs from the “Mathematics Curriculum as Story” framework for coding and analysis. These lessons as well as our future directions serve as the primary focus of this paper.

Formation and development of mathematical literacy in the context of evaluative – Study tasks of PISA

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.

The Practicality of Plane and Space Geometry Textbook as Teaching Materials in Mathematics Education Department of UMRAH

This study aims to produce teaching materials in the Geometry of Plane and Space course integrated with the maritime context of the Riau Islands. This research is a solution to problems arising from a need for teaching materials to the characteristics of students in the Mathematics Education Department of UMRAH. The 4D model (Define, Design, Development, and Disseminate) is used as the research development model. The research has reached the final activity of the Development stage, namely the practicality test of textbooks produced. The instrument used in the practicality test is a practicality questionnaire with a Likert scale. The evaluation results show that the textbooks produced through this development research have met the applicable criteria for use as teaching materials, with an achievement level of 72,85%. Thus, the textbook produced with the title Plane and Space Geometry Textbook has met the practical to use as teaching material in the Geometry of Plane and Space course. Integrating the maritime context of the Riau Islands helps students connect the content of teaching materials with their daily life. It helps them more easily understand the new knowledge.

Formation of students' mental activity by improving the applied focus of learning a geometric

Prerequisites for the study the problems of implementing the applied direction of teaching the topic of geometric construction in the geometry course of secondary school are most relevant, since there are no clear basic methods for the formation of students' thinking activities in this direction. This article discusses the results of a scientific study aimed at obtaining theoretical knowledge in any section of school geometry, which aims to give the student the skills to use the means of drawing the properties of geometric shapes and relationships. For this purpose, students were given a review of the literature on the implementation of the applied direction of geometry, focusing on mathematical statements in order to improve the applied direction of geometry. In the framework of the topic, the analysis was carried out in the course of improving this topic, due to the fact that mathematics teachers did not pay enough attention to the problems of construction in the geometry course of secondary school due to lack of time, students did not develop skills in solving problems of the applied direction of geometry. As a result of research, geometric construction problems are an important element of the mathematical preparation of schoolchildren. Using the problems of geometric construction, its application points were determined. The ways of implementing the applied direction in teaching geometry to students are described. Also, when teaching the geometry course, problems of the applied direction were collected in the school's geometry textbooks, ways to solve them were considered, and plot geometric tasks were prepared in order to increase the creativity of students. The stages of solving the practice-oriented geometric construction problem and the principles of implementing the applied direction of teaching mathematics, defined as a special type of plot problem, reflecting the use of geometric means in practical situations, are also studied. In the future, it can be used as a methodological tool for mathematics teachers in teaching construction problems.

A quantitative study of French 19th century geometry textbooks

A quantitative study of French 19th century geometry textbooks

Experimental Geometry, Pythagorean Theorem and Montessori

Background: Some 19th and 20th-century geometry textbooks show methodological innovations in relation to the traditional books that followed Euclid's logical-deductive proposal. Objective: To analyse in the book Psico Geometria: el estúdio de la geometria basado en la psicologia infantil by Maria Montessori (1934) as the didactic approach of the Pythagorean theorem, proposed by her, fits into an experimental geometry perspective. Design: Using documentary analysis, we analysed the books of the following authors: Hoüel (1867), Méray (1874), Laisant (1898, 1906), Calkins (1861), Bert (1886), Prestes (1895), Lyra da Silva (1923), Wentworth and Hill (1901) and Montessori (1916, 1934) to understand the approach to teaching geometry.Environment and participants:The research sources collected in the National Library of France (BNF) and in the Universidade Federal de Santa Catarina (UFSC) Digital Repository refer to the geographic environment of authors from four countries Data collection and analysis: The selected and analysed documents can be found at BNF – Gallica in a digitized version, as well as at the UFSC Digital Repository. Based on the documentary analysis of these books, we found that the methodological proposals seek to escape from a deductive presentation of elementary geometry and include in their texts experiences for the introduction of concepts and visual demonstrations of elementary geometry. Results: The authors of the analysed works, from different countries, criticized the elementary teaching of geometry, especially the authors of textbooks, for the fact that they approach deductive geometry in the initial classes, favouring a deductive presentation of mathematics. Montessori's book shows an experimental geometry proposal for the Pythagorean theorem. Conclusion: We found that Montessori's proposal, besides presenting characteristics of an experimental geometry, also inserts some deductive reasoning.

ГЕОМЕТРИЯЛЫҚ ЕСЕПТЕРДІ ШЕШУДІҢ ОҢТАЙЛЫТӘСІЛДЕРІН ІЗДЕУ

Currently, we are observing a lot of new phenomena occurringin the environment around us. These phenomena require any person to havenew qualities. First of all, society needs people who think outside the box,make decisions based on their own thinking and offer new initiatives. Suchqualities can be formed in math lessons or in extracurricular time, solvingproblems. In a geometry textbook, the solution of geometric problems is oftenbased on a standard algorithm. This algorithm can be difficult for students.Therefore, it is necessary to find the optimal method in search of other differentways to solve geometric problems. In this article, we will find the optimalmethod by describing several methods for solving a single geometric problem.Solving a geometric problem by various methods deepens students'mathematical knowledge and develops creative abilities.

ГЕОМЕТРИЯЛЫҚ ЕСЕПТЕРДІ ШЕШУДІҢ ОҢТАЙЛЫ ТӘСІЛДЕРІН ІЗДЕУ

Currently, we are observing a lot of new phenomena occurring in the environment around us. These phenomena require any person to have new qualities. First of all, society needs people who think outside the box, make decisions based on their own thinking and offer new initiatives. Such qualities can be formed in math lessons or in extracurricular time, solvingproblems. In a geometry textbook, the solution of geometric problems is often based on a standard algorithm. This algorithm can be difficult for students.Therefore, it is necessary to find the optimal method in search of other different ways to solve geometric problems. In this article, we will find the optimalmethod by describing several methods for solving a single geometric problem. Solving a geometric problem by various methods deepens students' mathematical knowledge and develops creative abilities.

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.

High school geometry textbooks’ proving opportunities of Common Core theorems

AbstractThe Common Core State Standards for Mathematics (CCSSM) explicitly states many specific theorems for students to prove across multiple domains (i.e., congruence, similarity, circles, and coordinates) in high school geometry. This study examined five high school geometry textbooks for how they approached proof of 17 theorems stated in the congruence domain focused on lines and angles, triangles, and parallelograms. Results showed that although textbooks provided 75 student opportunities to prove these theorems, no textbook provided student opportunities to prove all 17. Textbooks rarely had students write proofs from general conditional statements, and instead typically provided consistent hard scaffolding including the given, what to prove, and a diagram for all proof opportunities. Some of the textbooks used novel scaffolding such as partially completed proofs, flowchart proofs, second proofs, and hints in the back of the book. Textbooks need to continue shifting more responsibility to students proving the CCSSM theorems by incorporating more diverse scaffolding along with a process for removing the scaffolding as student learning progresses.

The influence of multimodal textualization in the conversion of semiotic representations in Italian primary school geometry textbooks

Abstract Starting from the corpus of the Swiss National Science Foundation (FNS) project Italmatica. Understanding Mathematics at school, between common language and specialized language (Italmatica. Comprendere la matematica a scuola, fra lingua comune e linguaggio specialistico), an analysis of some examples taken from geometry textbooks used in the Italian primary school is presented. The analysis is based on the application of two intertwined theoretical frameworks: Duval’s semio-cognitive approach, which addresses problems related to mathematics education, and a linguistic approach to multimodal discourse analysis inspired by Bateman. The analysis shows how certain semiotic resources used as rhetorical devices for paraphrastic reformulation (restatement) can support or hinder the semiotic conversion of representations associated with two different semiotic registers (figural and natural language) in print documents with a strong multimodality component.

Constructivist Approach in Ottoman Mathematics Education: Salih Zeki

In this study, it is aimed to determine whether the mathematics education approach of Salih Zeki, one of the late Ottoman mathematicians, has a constructivist character. For this purpose, 6 geometry textbooks written by Salih Zeki at middle school level were examined. Document analysis method was used in the research. In order to determine whether the textbooks have a constructivist character, 11 criteria have been determined and books have been analyzed based on these criteria. According to the results obtained, 6 geometry textbooks written by Salih Zeki have a constructivist character.

Конструирование задач инженерной направленности при реализации внеурочной деятельности

The article examines the content of state-level documents related to the need to train highly qualified engineering personnel for modern Russia, on the need for early career guidance at school. The integration of government documents and documents of the Ministry of Education and Science on the organization of extracurricular activities (2011, 2017) in the context of the Federal State Educational Standard, allowed the author of the article to identify and justify the possibility of orienting students to the choice of engineering professions through the organization of extracurricular activities in a primary school.
 To solve the problem of organizing extracurricular activities focused on students choosing engineering professions, the article proposes a system of authoring work programs for extracurricular activities for a primary school. A systematic approach to the design of integrated work programs (mathematics + physics + engineering) was considered at two stages: the propaedeutic stage (grades 5–7) and the pre-profile stage (grades 8–9). The main difficulty in the implementation of work programs by teachers is the selection and design of engineering tasks.
 The author of the article has developed three approaches to constructing problems of engineering orientation of mathematical content. The first approach is considered in detail: a contextual (engineering) presentation of a well-known educational task given in a textbook, didactic materials, and other teaching aids. The design and solution of the system of additional tasks to the problem from the geometry textbook for grade 8, where the cross section of the road in the form of an isosceles trapezoid is considered, made it possible to organize a research project for the construction of the highway. The students got acquainted with the types of engineering professions in the construction of the road, learned the incorrectness of some data in the contents of the textbook task and replacing them with possible numerical data in the construction of roads of different types.
 Creating a holistic image of the studied task situation in the context of engineering, we develop the creative abilities of students that are necessary both in educational and professional engineering activities of any direction.

Constructivist Learning and the Law of Sines in Advanced 10th Grade Geometry Textbooks in Vietnam

The law of Sines is the law that appears much in mathematics in particular and in science in general. The law of Sines allows us to calculate the length of the remaining sides and angles when we know three of the six elements of the side or angle of a triangle. This law, along with the law of Cosines, are the first two laws, the most important when one wants to build a trigonometric system. In Vietnam, they teach the law of Sines in Geometry 10 program, including the Basic and Advanced sections. Constructivist learning is one of the theories of the teaching process based on Piaget's psychology generating awareness and Vygotsky's operation theory. There are many different views on constructivist learning. All of these points of view agree that this is a positive teaching method, promoting the internal strengths of learners. In other words, this is a learner-centered teaching method. Although the law of the Sines function is important, there are not many documents that mention how to teach the law of Sines effectively. The paper examines the combination of the constructivist learning method and the law of Sines as well as the relationship between mathematics and other fields expressed through this law. https://doi.org/10.26803/ijlter.19.1.3

Принципи добору системи вправ до підручника з геометрії для ліцею

Принципи добору системи вправ до підручника з геометрії для ліцею

Visual Arts in U.S. Geometry Textbooks Aligned with the Common Core Standards

This study investigates visual arts references in five U.S. high school geometry textbooks aligned with the Common Core State Standards for Mathematics. In all of the textbooks, architecture is the most commonly used context. More than half of the visual arts references are in the exercises. Congruence is the domain most often used, followed by Similarity, Right Triangles & Trigonometry. The visual arts references support the four traditional arguments justifying the geometry course but mostly support the goal of teaching geometry in ways that allow students to draw upon their intuition.

Analyzing The Presentation Of Geometry Material Based On Bruner's Theory In Mathematics Textbook

This research aims to know the conformity of presentation based on Bruner’s theory on fourth-grade mathematics textbook. This is qualitative research. The object of research is the material presentation of a fourth-grade mathematics textbook. Based on the analysis of theorem of presentation by Bruner, the facets chapter obtains a percentage of 56% which belongs to the appropriate category. The circumference and width chapter obtains a percentage of 92% which belongs to the appropriate category. The line connection chapter obtains a percentage of 50% which belongs to the appropriate category. The angle measuring chapter obtains a percentage of 56% which belongs to the appropriate category. The overall percentage of the geometry textbook is 64% which belongs to the appropriate category. The percentage of enactive aspects implemented in the presentation of geometry in mathematics textbook is 28%., the percentage of iconic aspects implemented in the presentation of geometry in mathematics textbook is 73%, and the percentage of the symbolic aspect is 56%.