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Journal articles on the topic 'Geometry – Textbooks'
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1
Amaral, Rúbia Barcelos, and Karen Hollebrands. "analysis of similarity concept presented in textbooks in Brazil and the United States." Educação Matemática Pesquisa Revista do Programa de Estudos Pós-Graduados em Educação Matemática 25, no. 2 (August 20, 2023): 356–93. http://dx.doi.org/10.23925/1983-3156.2023v25i2p356-393.
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This paper is a product of a research that investigates the presence of Geometry in textbooks, that is part of project of a Theorem – Reflection on Geometry and Mathematics Education research group. The focus here is to present results of the international study: how textbooks present the concept of similarity? For this, a qualitative research were developed and textbooks of three collections from Brazil and three from United States were examined. A synthesis of the literature related to the search for textbooks and the teaching and learning of the concept of similarity is presented, and the theoretical framework explores similarity as positioned at the crossroads of geometry and number to describe the ways in which different textbooks approach it. Sequence of topics and tasks presented in each textbook are described and then comparisons are made. There were theorems and problem types that were presented consistently across all textbooks, but differences in expectations related to proof and the use of coordinates and geometric transformations were identified. Only textbooks in the US included the use of transformations and coordinates and placed more emphasis on formal proof. Implications for the teaching and learning of similarity are provided
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Kirova, Gabriela. "COMPARATIVE ANALYSIS OF THE GEOMETRICAL CONTENT IN THE NEW BULGARIAN TEXTBOOKS OF MATHEMATICS FOR THIRD GRADE." Knowledge International Journal 28, no. 3 (December 10, 2018): 991–96. http://dx.doi.org/10.35120/kij2803991g.
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Starting with 2018/2019 school year in Bulgaria, the math education in the third grade is implemented through new training kits. They were developed on the basis of the new third-grade mathematics curriculum, approved by Order No. РД 09-1093 / 25.01.2017 of the Minister of Education and Science, Annex No. 8, supplemented by Order No. РД 09-2555 / 15.06.2018 of the Minister of Education and Science. Training kits are approved by the Ministry of Education and Science and are 7 in total. Geometric learning content in new math textbooks is the second most important element after arithmetic content. It is combined with the arithmetic learning content, and by this the foundation of the successful study of geometry in the next school grades is laid. The new geometry knowledge that is included in the third grade curriculum is the following: straight line, curve, beam, angle, right angle, obtuse angle, acute angle, right triangle, acute triangle, obtuse triangle; naming geometric figures with Latin alphabet letters [11]78. It is important in a modern mathematics textbook to have a rich and varied geometric content. It is important that the new types of geometry tasks are introduced with rich visualization using a specific-inductive approach. The relative number of tasks of a given type is an important prerequisite for the successful formation and improvement of skills for solving geometric problems in pupils at the age of 9-10. This article will present a comparative analysis of the geometric content in the seven approved Bulgarian third-grade mathematics textbooks, which are used in the mass practice of this school year. For the purpose of the study, a classification of all types of tasks and exercises with geometric content has been developed. Then the tasks in the seven textbooks are systematized by the so chosen classification. The data are statistically processed taking into account the relative share of tasks of each type within a textbook, as well as a comparison between the relative shares of the geometric tasks in the different textbooks. The established differences in the number and relative share of different types of geometric tasks make it possible for the analyzed textbooks to be ranked. Such a study has not been published so far. It has a relation to the assessment of the quality of the textbooks offered. The conclusions formulated in this article can help primary teachers in their choice of textbooks to teach to their third grade students.
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Hsu, Hui-Yu, and Edward A. Silver. "Cognitive Complexity of Mathematics Instructional Tasks in a Taiwanese Classroom: An Examination of Task Sources." Journal for Research in Mathematics Education 45, no. 4 (July 2014): 460–96. http://dx.doi.org/10.5951/jresematheduc.45.4.0460.
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We examined geometric calculation with number tasks used within a unit of geometry instruction in a Taiwanese classroom, identifying the source of each task used in classroom instruction and analyzing the cognitive complexity of each task with respect to 2 distinct features: diagram complexity and problem-solving complexity. We found that instructional tasks were drawn from multiple sources, including textbooks, tests, supplemental materials, and the teacher. Our analysis of cognitive complexity indicated that the instructional tasks frequently involved both diagram complexity and problem-solving complexity. Moreover, the geometric calculation with number tasks from nontextbook sources tended to be more cognitively demanding than those found in the textbooks. Implications of task analysis on geometry domain and textbook analysis studies are discussed.
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Ningsih, Yunika Lestaria, Dina Octaria, Tika Dwi Nopriyanti, and Jumroh Jumroh. "Development of a Desmos-Assisted Planar Analytic Geometry Textbook to Support High Order Thinking Skills." JTAM (Jurnal Teori dan Aplikasi Matematika) 8, no. 2 (April 2, 2024): 544. http://dx.doi.org/10.31764/jtam.v8i2.20775.
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The study focuses on improving higher-order thinking skills (HOTS) in mathematics students using a Desmos-assisted planar analytic geometry course. Analytic geometry, which is essential for understanding geometric properties using analytic methods, requires students to develop problem-solving, analysis, assessment, and creativity abilities. However, current educational practices fall short of acquiring these abilities due to insufficient instructional techniques, textbooks, and a lack of integration with information and communication technologies. To address these shortcomings, the study proposes a Desmos-assisted textbook meant to increase students' HOTS through the use of interactive Desmos platform tools such as graphic depiction, experimentation, simulation, and collaborative learning. The textbook development followed the PLOMP model, which included preliminary research, prototyping, and assessment phases, ensuring the textbook's validity and practicality through reiterated evaluations. The findings show that the textbook is highly valid and practical for instructional purposes, improving students' knowledge of mathematical concepts and ability to engage in HOTS processes. Despite some difficulties with HOTS-related practice questions, generally student feedback was positive, emphasizing the textbook's function in supporting a deeper understanding of analytic geometry and encouraging problem-solving skills. The study indicates that integrating technology such as Desmos into mathematics education can greatly contribute to the development of students' HOTS, and recommends its use in teaching techniques as well as additional research on its implementation in educational contexts.
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Yang, Der-Ching. "The Study of Geometry in Elementary Mathematics Textbooks in Finland, Singapore, and Taiwan." Journal of Mathematics Education 5, no. 1 (July 1, 2020): 16–29. http://dx.doi.org/10.31327/jme.v5i1.1148.
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This study examined the differences in the presentation of geometry concepts and characteristics of geometry questions among elementary mathematics textbooks in Finland, Singapore, and Taiwan. Horizontal and vertical analysis methods were used to collect and analyze the data. A popular Mathematics textbook from a dominant publisher in each country were selected: Laskutaito from Finland, My Pals are Here! Maths from Singapore, and Kang Hsuan from Taiwan. The results indicated differences in the presentation of geometry concepts among the three textbook series. In addition, the questions in these textbooks were determined to demonstrate different characteristics. Moreover, these findings highlight the importance of cross-national textbook comparison to enhance the understanding of differences in learning opportunities across different countries.
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Zhang, Qiao-Ping, and Ngai-Ying Wong. "The Learning Trajectories of Similarity in Mathematics Curriculum: An Epistemological Analysis of Hong Kong Secondary Mathematics Textbooks in the Past Half Century." Mathematics 9, no. 18 (September 18, 2021): 2310. http://dx.doi.org/10.3390/math9182310.
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The topic of similarity plays an essential role in developing students’ deductive reasoning. However, knowing how to teach similarity and understanding how to incorporate deductive reasoning and proof along with plane geometry remain a challenge to both school curriculum creators and teachers. This study identified the problems and characteristics regarding how similarity is treated in secondary mathematics textbooks in Hong Kong in the past half century. The content analysis method was used to analyze six secondary mathematics textbook series published in different periods. From the epistemological perspective of the textbook contents, our analysis shows the historical context and learning trajectories of how similarity was treated in school curriculum. The natural axiomatic geometry paradigm is not emphasized too much at different stages and most of the textbooks did not provide formal proofs of similarity. The intuitive idea was gradually consolidated into a formal definition of similarity. Furthermore, the way that rigorous geometric deduction can be performed from intuitive concepts and experimental geometry to the idea of proofs and formal proofs is also discussed.
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Jung, Hye-Yun, Jin-Ho Jung, and Kyeong-Hwa Lee. "Analyzing Tasks in the Geometry Area of 7th Grade of Korean and US Textbooks from the Perspective of Mathematical." Korean School Mathematics Society 23, no. 2 (June 30, 2020): 179–201. http://dx.doi.org/10.30807/ksms.2020.23.2.001.
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The purpose of this study is to analyze tasks reflected in Korean and US textbooks according to the mathematical modeling perspectives, and then to compare the diversity of learning opportunities given to students from both countries. For this, we analyzed mathematical modeling tasks of textbooks based on three aspects: mathematical modeling process, data, and expression. Results are as follows. First, with respect to modeling process, Korean textbook provides a high percentage of the task at all stages of modeling than US textbook. Second, with respect to data, both countries’ textbooks have the highest percentage of matching task. Korean textbooks have a large gap in data characteristics by textbook. Third, with respect to expression, both countries’ textbooks have the highest percentage of text and picture. Korean textbooks have a large gap in the type of expression than US textbooks, and some textbooks have no other expression except for text and picture. Fourth, tasks were analyzed by integrating the three features. The three features were not combined in various ways. It is necessary to diversify the integration of the three features.
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Abdullah, Abdul Halim, and Bomi Shin. "A COMPARATIVE STUDY OF QUADRILATERALS TOPIC CONTENT IN MATHEMATICS TEXTBOOKS BETWEEN MALAYSIA AND SOUTH KOREA." Journal on Mathematics Education 10, no. 3 (August 17, 2019): 315–40. http://dx.doi.org/10.22342/jme.10.3.7572.315-340.
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This study compares Malaysian and Korean geometry content in mathematics textbooks to help explain the differences that have been found consistently between the achievement levels of Malaysian and South Korean students in the Trends in International Mathematics and Science Study (TIMSS). Studies have shown that the use of textbooks can affect students’ mathematics achievements, especially in the field of geometry. Furthermore, to date, there has been no comparison of geometry content in Malaysian and Korean textbooks. Two textbooks used in the lower secondary education system in Malaysia and South Korea were referred. The topic of quadrilaterals was chosen for comparison, and the topic’s chapter in the South Korean textbook has been translated into English. The findings show four main aspects that distinguish how quadrilaterals are taught between the two countries. These aspects include the composition of quadrilaterals topics, the depth of concept exploration activities, the integration of deductive reasoning in the learning content and the difficulty level of mathematics problems given at the end of the chapter. In this regard, we recommend the Division of Curriculum Development of the Malaysian Ministry of Education reviews the geometry content of mathematics textbook used today to suit the curriculum proven to produce students who excel in international assessments.
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Glasnovic Gracin, Dubravka, and Ana Krišto. "Differences in the Requirements of Digital and Printed Mathematics Textbooks: Focus on Geometry Chapters." Center for Educational Policy Studies Journal 12, no. 2 (June 23, 2022): 95–117. http://dx.doi.org/10.26529/cepsj.1285.
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Textbooks have always played an important role in mathematics education. Textbook tasks are widely used by students, so it is important to examine their requirements in order to identify the opportunities students have to learn mathematics. Publishers now produce both printed and digital versions of textbooks. While the requirements of the tasks in printed textbooks have been well examined all over the world, the tasks in digital textbooks are yet to be analysed and systematically developed. The research presented in this paper encompasses the analysis and comparison of the tasks in the printed and digital versions of the same mathematics textbook set. The examined set covers Grades 1 to 4 of primary education in Croatia. The aim was to find what task requirements are predominant in the printed and the digital textbooks, and to determine whether these textbook versions provide a wide variety of task features. In addition, the features and capacities typical of digital tasks, such as interactivity and dynamics, are examined. These task features are particularly important in geometry education for comprehending visual and dynamic geometrical objects and relations. The results show that both the printed and the digital textbook tasks have traditional requirements, with an emphasis on closed answer forms. Moreover, the new opportunities afforded by digital tasks are not realised. These findings reveal the potential of digital tasks as a new area to be explored and developed.
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Powell, Nancy Nore, Mark Anderson, and Stanley Winterroth. "Reflections on Miniature Golf." Mathematics Teacher 87, no. 7 (October 1994): 490–95. http://dx.doi.org/10.5951/mt.87.7.0490.
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To make geometry meaningful, fun, and applicable to the lives of our students, we adapted the game of miniature golf as a way to teach transformatiOnal geometry. Geometry textbooks often feature twodimensional pictures of miniature-golf holes to illustrate transformational geometry. Geometry students in this project actually brought the golf holes out of the textbook by constructing a life-sized miniature golf course.
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Heo, Nam Gu. "Comparative Analysis of ｢Geometry｣ and ｢Earth Science II｣ Textbooks on Ellipse Construction." Korean Association For Learner-Centered Curriculum And Instruction 24, no. 1 (January 15, 2024): 319–35. http://dx.doi.org/10.22251/jlcci.2024.24.1.319.
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Objectives The purpose of this study is to compare and analyze the meaning and method of ellipse construction of the ｢Geometry｣ and ｢Earth ScienceⅡ｣ textbooks of the 2015 revised curriculum.
Methods To do this, an analysis framework for the meaning and method of ellipse construction was developed, and the contents related to ellipse construction of seven ｢Geometry｣ textbooks and four ｢Earth ScienceⅡ｣ text-books were analyzed in accordance with the analysis framework.
Results First, seven ｢Geometry｣ textbooks and four ｢Earth ScienceⅡ｣ textbooks all suggested activities to mean drawing ellipse. Second, five ｢Geometry｣ textbooks presented the activity of constructing an ellipse using ruler and compass. Third, in the case of the ｢Geometry｣ textbooks, four presented a method of drawing using concen-tric circles, four presented a method of using origami, and five presented a method of drawing using pushpin and thread. Fourth, the same ellipse drawing activity was presented in the four ｢Earth Science Ⅱ｣ textbooks. All text-books presented activities to draw the elliptical orbit of Mars based on observation data, and methods of drawing using pushpin and thread.
Conclusions Since the link between science, mathematics, information, and environmental curriculum is em-phasized, it is necessary to conduct a follow-up study on the curriculum linking mathematics and science based on the results obtained in this study. In addition, research on how to use mathematical technologies in science education has recently been conducted, so follow-up research on various teaching and learning method to con-struct an ellipse orbit such as using mathematical technologies, needs to be conducted in the ｢Earth ScienceⅡ｣ textbook.
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Muccillo de Medeiros, Antonio Paulo, and Lícia Giesta Ferreira De Medeiros. "Textbooks as Historical References in Teaching Geometry in Brazil Between 1925-2010." Advances in Social Sciences Research Journal 8, no. 2 (February 16, 2021): 147–69. http://dx.doi.org/10.14738/assrj.82.9634.
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This paper makes a historical overview about how mathematics textbooks influenced geometry’s teaching in Brazil. Initially the study shows the relevance textbooks have as historical reference for a school discipline. Next, it describes how textbooks tend to transmit the same content in each historical period, a phenomenon Chervel called vulgata. From that point a timeline is created, since the first Brazilian mathematics textbook in 1744 until 2010, to understand how those volumes influenced geometry teaching. Four volumes, ranging from 1925 to 2010, are then analyzed. The focal point of this analysis is how triangles similarity is taught in each one of them. The paper also describes how government policies affected textbooks and school life in general since the beginning of mathematics teaching in Brazil.
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Auliya', Khilyatul, and Djamilah Bondan Widjajanti. "Singaporean and Japanese Maths Textbooks: Character, Structure, and Content." Mosharafa: Jurnal Pendidikan Matematika 12, no. 1 (January 31, 2023): 155–68. http://dx.doi.org/10.31980/mosharafa.v12i1.2141.
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AbstrakMeningkatkan pengajaran matematika secara terus menerus merupakan upaya yang harus terus dilakukan. Hal ini dikarenakan matematika tidak hanya dipelajari oleh siswa sepanjang tahun tetapi juga banyak digunakan sebagai indikator kunci keberhasilan individu siswa. Salah satu faktor penting yang mempengaruhi pengajaran matematika adalah buku teks. Artikel ini membahas buku teks matematika dari dua negara, yaitu Singapura dan Jepang. Kajian terhadap kedua buku teks dilakukan terhadap karakter fisik, struktur, dan topik/isi buku teks. Kesimpulan hasil kajian ini sebagai berikut. Secara fisik, Buku teks matematika Singapura lebih sederhana dalam warna, dibandingkan buku teks matematika Jepang. Jumlah halaman Buku teks Singapura lebih banyak dari jumlah halaman Buku teks Jepang. Dari segi struktur buku, pada Buku teks matematika Singapura, terdapat beberapa bab yang dimulai dengan ringkasan materi prasyarat, kemudian diikuti dengan materi dasar, contoh dan penyelesaiannya, dan latihan. Sedangkan pada Buku teks matematika Jepang, sebagian besar diawali dengan ilustrasi mengenai topik yang dibahas, materi prasyarat, pertanyaan mendasar, ringkasan materi, contoh dan penyelesaiannya, pengayaan, dan latihan soal. Pada buku teks sekolah menengah Singapura, lebih ditekan kan pada domain Geometri dan Pengukuran, sedangkan Buku teks sekolah menengah Jepang lebih ditekankan pada domain Relasi dan Aljabar, kemudian urutan selanjutnya domain Geometri dan Pengukuran. AbstractContinuous improvement of mathematics teaching is a continual process. The ground of the improvement is that mathematics is not only studied by students throughout the year but it is also widely used as a key indicator of students’ success. One of the important factors that influence the teaching of mathematics is textbooks. This study discussed mathematics textbooks from two countries, namely Singapore and Japan. The aim was to examine the textbooks’ physical character, structure, and topic/content. The study pointed out several important points. The Singaporean Math Textbook is physically simpler in colour than the Japanese Math Textbook. It also had more pages than the Japanese Textbook. Regarding the book's structure, several chapters in the Singaporean Mathematics Textbook began with a summary of the prerequisite material, followed by key topics, examples and solutions, and exercises. In Japanese Mathematics Textbooks, most chapters started with illustrations on the topics discussed, prerequisite material, essential questions, summaries, examples and solutions, enrichment, and exercises. In the Singaporean secondary school textbooks, it emphasized the Geometry and Measurement domains, while the Japanese secondary school textbooks emphasized the Relation and Algebra domains followed by the Geometry and Measurement domains.
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Auliya’, Khilyatul, and Djamilah Bondan Widjajanti. "Singaporean and Japanese Maths Textbooks: Character, Structure, and Content." Mosharafa: Jurnal Pendidikan Matematika 12, no. 1 (January 31, 2023): 155–68. http://dx.doi.org/10.31980/mosharafa.v12i1.764.
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Meningkatkan pengajaran matematika secara terus menerus merupakan upaya yang harus terus dilakukan. Hal ini dikarenakan matematika tidak hanya dipelajari oleh siswa sepanjang tahun tetapi juga banyak digunakan sebagai indikator kunci keberhasilan individu siswa. Salah satu faktor penting yang mempengaruhi pengajaran matematika adalah buku teks. Artikel ini membahas buku teks matematika dari dua negara, yaitu Singapura dan Jepang. Kajian terhadap kedua buku teks dilakukan terhadap karakter fisik, struktur, dan topik/isi buku teks. Kesimpulan hasil kajian ini sebagai berikut. Secara fisik, Buku teks matematika Singapura lebih sederhana dalam warna, dibandingkan buku teks matematika Jepang. Jumlah halaman Buku teks Singapura lebih banyak dari jumlah halaman Buku teks Jepang. Dari segi struktur buku, pada Buku teks matematika Singapura, terdapat beberapa bab yang dimulai dengan ringkasan materi prasyarat, kemudian diikuti dengan materi dasar, contoh dan penyelesaiannya, dan latihan. Sedangkan pada Buku teks matematika Jepang, sebagian besar diawali dengan ilustrasi mengenai topik yang dibahas, materi prasyarat, pertanyaan mendasar, ringkasan materi, contoh dan penyelesaiannya, pengayaan, dan latihan soal. Pada buku teks sekolah menengah Singapura, lebih ditekan kan pada domain Geometri dan Pengukuran, sedangkan Buku teks sekolah menengah Jepang lebih ditekankan pada domain Relasi dan Aljabar, kemudian urutan selanjutnya domain Geometri dan Pengukuran. Continuous improvement of mathematics teaching is a continual process. The ground of the improvement is that mathematics is not only studied by students throughout the year but it is also widely used as a key indicator of students’ success. One of the important factors that influence the teaching of mathematics is textbooks. This study discussed mathematics textbooks from two countries, namely Singapore and Japan. The aim was to examine the textbooks’ physical character, structure, and topic/content. The study pointed out several important points. The Singaporean Math Textbook is physically simpler in colour than the Japanese Math Textbook. It also had more pages than the Japanese Textbook. Regarding the book's structure, several chapters in the Singaporean Mathematics Textbook began with a summary of the prerequisite material, followed by key topics, examples and solutions, and exercises. In Japanese Mathematics Textbooks, most chapters started with illustrations on the topics discussed, prerequisite material, essential questions, summaries, examples and solutions, enrichment, and exercises. In the Singaporean secondary school textbooks, it emphasized the Geometry and Measurement domains, while the Japanese secondary school textbooks emphasized the Relation and Algebra domains followed by the Geometry and Measurement domains.
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Soares Junior, Jalmir, and Jarbas Sampaio. "The approach to spatial geometry in the mathematics textbook: BNCC in focus." Concilium 23, no. 11 (June 15, 2023): 185–98. http://dx.doi.org/10.53660/clm-1437-23g18a.
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The present work focuses on an analysis of textbooks. This teaching tool was chosen due to its importance in the teaching and learning process in Brazilian schools. The goal is to verify the adequacy of mathematics textbooks to the competencies and abilities presented at BNCC, and it has as central research question: How do the textbooks of Mathematics address the content of Spatial Geometry and how is this content articulated in relation to the BNCC for effective learning in High School? It was sought to evaluate qualitatively, based on learning criteria required by the BNCC, the second-year high school textbook most commonly used by schools in the city of Camacari in Bahia, specifically in the chapters of Space Geometry. The textbook alone will not be able to sufficiently develop in the student all the necessary abilities and competences, much of the methodology used by the teacher.
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Yang, Seong Hyun. "A View on the Deviation of Content Elements of Quadratic Curve in High School Geometry Textbooks." Korean School Mathematics Society 25, no. 1 (March 31, 2022): 61–77. http://dx.doi.org/10.30807/ksms.2022.25.1.004.
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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.
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Oliveira, Marcilio Martins de, and Samuel Edmundo Lopez Bastos. "LIVROS DIDÁTICOS DE MATEMÁTICA: O PONTO, A RETA E O PLANO DA GEOMETRIA EUCLIDIANA E A TRANSPOSIÇÃO DIDÁTICA." Cadernos de Educação Tecnologia e Sociedade 12, no. 2 (August 6, 2019): 127. http://dx.doi.org/10.14571/brajets.v12.n2.127-150.
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This study presents a discussion on the area of plane geometry or non-Euclidean geometry, having as focus the primitive ones of plane geometry: point, line and plane. As the name itself refers to this geometry is from the work of the Greek mathematician Euclid of Alexandria, whose work dates back to approximately 300 BC. As theoretical contribution was the theory of Didactic Transposition the French Yves Chevallard (1991), this theory refers briefly to the changes and transformations that you know suffers from your appearance in the scientific community to your entry in the living room class. A research on textbooks of mathematics 6th grade belonging to several times. On choice of textbooks of mathematics, were taken as the basis year of 1985, the date on which the creation of the National Textbook Program (PNLD) and the year of 1996 date of implementation of the new guidelines and Bases of Brazilian Education (LDB 9394/96). The textbooks of mathematics were chosen because they are one of the means used for the input of knowledge in the classroom. In this research paper was used qualitative research and documentation, the books were analyzed one by one, in order to understand how was the process of addressing the concepts of point, line and plane in math textbooks and the scientific community. The paper presents a theoretical discussion involving the textbooks, the PNLD and the work of Euclid-Elements.
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Flanders, James R. "Textbooks, Teachers, and the SIMS Test." Journal for Research in Mathematics Education 25, no. 3 (May 1994): 260–78. http://dx.doi.org/10.5951/jresematheduc.25.3.0260.
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This article is a report of a study of relationships between intended, implemented, and tested curricula of 84 classes of United States eighth-grade mathematics students in 1981–82. It is based on data from the Second International Mathematics Study (SIMS, Population A) and the SIMS test: 180 multiple-choice questions covering topics in arithmetic, algebra, geometry, measurement, and statistics. The study focused on three areas: (a) coverage of the SIMS test items in six nonalgebra textbooks, (b) teacher reports of whether students had the opportunity to learn the SIMS items, and (c) teacher expectations for student success on the SIMS items. Of special concern was the challenge presented to students as measured by textbook and teacher coverage of new, versus reviewed, mathematics topics.The analysis indicated that the SIMS test for eighth graders was not representative of the curriculum defined by students' texts. The books were heavily biased toward a review of arithmetic and away from algebra or geometry items. Items new to texts were among the least covered. Teacher expectations for student success mirrored the textbook coverage of SIMS items and indicated a high degree of reliance on textbooks for topic sequencing. Teachers using nonbasal texts had higher expectations than teachers of basal texts. Teachers reported that they taught more old items than new items and more arithmetic and algebra items than geometry, measurement, or statistics items.
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Kim, Hangil. "An Investigation of Proving-Related Tasks in Geometry: The Case of Grade 8 Korean Textbooks." Korean Society of Educational Studies in Mathematics - Journal of Educational Research in Mathematics 33, no. 3 (August 31, 2023): 821–35. http://dx.doi.org/10.29275/jerm.2023.33.3.821.
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Proof and reasoning, as one of five process standards, is well recognized as fundamental to student learning of mathematics and important in the field of mathematics as well as school mathematics. Despite calls for proof to play a central role in school mathematics, there have been studies which documented that not much of textbook is devoted to tasks in which students engage proving-related activities. This study was designed to investigate the nature of proving-related tasks in chapters where Euclidian geometry is covered at Grade 8 and examined all of the available textbooks in Korea. Proving-related tasks were examined with respect to how frequently proving-related tasks appear in textbook and what kind of proving-related activity students engage. Results of this study showed that the proportions of proving-related tasks varied greatly across textbooks ranging from 12 percent to 32.9 percent and the most frequent type of proving-related activity was testing the truth of a conjecture. Also, tasks coded for providing a proof were analyzed using the RGCP model and the results revealed that the vast majority of them was at the highest level of the model.
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Sal'kov, N. "The Main Reasons for Poor Assimilation of Descriptive Geometry." Geometry & Graphics 9, no. 2 (November 11, 2021): 3–11. http://dx.doi.org/10.12737/2308-4898-2021-9-2-3-11.
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Descriptive geometry is the most difficult subject studied by first-year students in technical universities. The paper considers the reasons for poor geometric knowledge among university graduates. It is determined that there are three main objective reasons. 1. Poor geometric training in high school, where they study planimetry and stereometry, but not all the knowledge that future students will need at the university is included for passing the Unified State Exam. Also, in high school, students do not develop the habit of thinking analytically, although when proving geometric theorems, this function has developed greatly. 2. Descriptive geometry has a completely different method, which differs from all the methods of disciplines that are studied at school, is the projection method, which develops spatial imagination. Exactly the method that gives any description in the daily activities of any person and in the work of any engineer. 3. Disadvantages of university textbooks on descriptive geometry. Each section of the textbook on descriptive geometry has been based on a particular geometric image since ancient times: a point, a straight line, a plane, etc. As a result, tasks that could be collected in their own section of the textbook (for example, all positional problems or all metric problems) are scattered throughout the entire body of the textbook. And from this there is an opinion that each of the tasks has its own unique solution algorithm. It is shown that with a systematic approach, all positional problems, as well as all metric ones, are solved, in principle, according to a single algorithm.
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Ogbonnaya, Ugorji I. "Opportunity to Learn Euclidean Geometry in Two Mathematics Textbooks of Tenth Grade in South Africa." Edumatika : Jurnal Riset Pendidikan Matematika 4, no. 2 (November 5, 2021): 112–25. http://dx.doi.org/10.32939/ejrpm.v4i2.976.
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Textbooks play a central role in the teaching and learning of mathematics. In some schools, textbooks serve as the only resource material available to teachers and students. Yet, little is known about the learning opportunities in mathematics textbooks in most countries. This study investigated the opportunities to learn Euclidean Geometry in two textbooks of tenth-grade mathematics in South Africa. It examined the content coverage, content organization, and the type of tasks used in teaching the topic in the textbooks. This study followed a case study research design and a qualitative approach. The Curriculum and Assessment Policy Statement's (CAPS) grade 10 Euclidean geometry curriculum and Gracin's mathematical activity types served as frameworks for the analyses. The data were analyzed following the deductive content analysis approach. The result shows that the contents of Euclidean geometry were well covered in both textbooks following the curriculum and the contents were presented in logical and sequential order to enhance learning. In addition, it was found that the tasks in the textbooks were predominantly of argumentation and reasoning type. It was concluded that the textbooks offer sufficient opportunities for learning Euclidean geometry as specified in the curriculum for the grade level. However, the inclusion of a wider range of tasks in the future editions of the textbooks was recommended.
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Ramadhona, Rezky, Nur Asma Riani Siregar, and Okta Alpindo. "The Practicality of Plane and Space Geometry Textbook as Teaching Materials in Mathematics Education Department of UMRAH." Jurnal Gantang 8, no. 1 (July 31, 2023): 65–73. http://dx.doi.org/10.31629/jg.v8i1.5658.
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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.
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Litoldo, Beatriz Fernanda, Rúbia Barcelos Amaral, and Lucas Carato Mazzi. "Contextualisation of Geometry Tasks in High School Mathematics Textbooks." Acta Scientiae 24, no. 8 (March 27, 2023): 69–98. http://dx.doi.org/10.17648/acta.scientiae.7131.
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Background: Geometry is often seen as an area of mathematics that is present in everyone’s daily life. Looking around, we see it in the shapes of objects, in nature, etc. Therefore, it would be natural to expect that its approach in textbooks, for example, would bring different contexts in which it would be present. Objective: To discuss how contexts are introduced in geometry tasks in a collection of mathematics textbooks. Design: We use a qualitative approach of the documentary type as a methodology. Environment and participants: A collection of high school mathematics textbooks approved by the National Textbook and Didactic Material Program – 2018 was selected. Data collection and analysis: Data were produced, organised, and analysed using horizontal and vertical analysis methods in each collection volume, according to the different references of contexts. Results: They concern the different references of contexts involved in the tasks. From the 1,335 tasks analysed, 1,108 were contextualised in purely mathematical situations, while the rest, 227, were in contexts of reality. In this, there are 215 referring to reasonable semi-realities, and, on the other hand, the real context contemplates only three. Finally, nine concern tasks in unreasonable semi-real contexts. Conclusions: The restriction of the different context references that students can experience from this collection is discussed. The contexts presented do not include a broad spectrum based on a diversity of experiences among the different references of contexts.
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Yi, Gyuhee. "Mathematical analysis and textbooks analysis for teaching of 'point' and 'line' corresponding to the Euclid geometry perspective." Korean School Mathematics Society 24, no. 1 (March 31, 2021): 39–57. http://dx.doi.org/10.30807/ksms.2021.24.1.003.
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In this study, mathematical analysis is conducted by focusing to the 'size' of the 'point' and the 'line'. The textbook descriptions of the 'point' and the 'line' in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum and US geometry textbooks were compared and analyzed between. First, as a result of mathematical analysis of' 'the size of a point and a segment', it was found that the mathematical perspectives could be different according to 1) the size of a point is based on the recognition and exclusion of 'infinitesimal', and 2) the size of the segment is based on the 'measure theory' and 'set theory'. Second, as a result of analyzing textbook descriptions of the 'point' and the 'line', 1) in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum, after presenting a learning activity that draws a point with 'physical size' or line, it was developed in a way that describes the 'relationship' between points and lines, but 2) most of the US geometry textbooks introduce points and lines as 'undefined terms' and explicitly states that 'points have no size' and 'lines have no thickness'. Since the description of points and lines in the geometry content area of middle school mathematics 1 by the 2015 revised Korean mathematics curriculum may potentially generate mathematical intuitions that do not correspond to the perspective of Euclid geometry, this study suggest that attention is needed in the learning process about points and lines.
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Həsənov, Abdulla, and Cəmalə Bağırova. "Elementar həndəsədə optimallaşdırma məsələləri və onların funksional metodla araşdırılması." InterConf, no. 43(193) (March 20, 2024): 415–28. http://dx.doi.org/10.51582/interconf.19-20.03.2024.041.
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In the study of extremes in elementary geometry, the functional method is mainly used. To do this, an independent variable (argument) is first selected and the geometric process is described as a function depending on this argument. Then elements of differential calculus are used. Thus, with the help of derivatives, the properties of functions are investigated-their stability, monotonicity, the points of its extremes, the largest and smallest values. Practically, textbooks and textbooks on elementary mathematics pay little attention to these issues. Therefore, in this article, the solution of the problems of extremum geometry was studied using derivatives in theoretical and practical aspects. The article is relevant for specialists, teachers, students and schoolchildren engaged in elementary mathematics.
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Na, Gwi Soo, Hyuksang Kwon, Soyeong Kim, Hyeonmin Choi, and Dong-Won Kim. "Exploring Aspects of Mathematical Reasoning in Elementary School Mathematics Textbook: Focusing on Geometry-related Units for Grades 3-4." Korean Society of Educational Studies in Mathematics - Journal of Educational Research in Mathematics 33, no. 4 (November 30, 2023): 1137–59. http://dx.doi.org/10.29275/jerm.2023.33.4.1137.
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The purpose of this study was to explore how mathematical reasoning, one of the most important topics in school mathematics, is implemented in elementary school mathematics textbook. To this end, this study analyzed the type of reasoning, level of cognitive demands, and structural characteristics of mathematical reasoning tasks provided in the elementary school mathematics textbooks. As a result of this study, it was revealed that the mathematics textbooks had the strength of providing sufficient tasks dealing with pattern recognition type, but were deficient in providing tasks dealing with multiple types of mathematical reasoning, such as making a conjecture, investigating a conjecture, developing a justification, finding a counterexample, and evaluating an argument. Regarding the level of cognitive demands of mathematical reasoning tasks, the mathematics textbooks provided sufficient tasks of procedures with connections, but insufficiently provided tasks of doing mathematics requiring complex thinking. In relation with the structural characteristics of mathematical reasoning, the mathematical reasoning tasks in the mathematics textbooks embodied only the aspects of pattern recognition-making a conjecture and pattern recognition-developing a justification, but were insufficient in embodying the structural flow of mathematical reasoning. In addition, this study suggested that elementary school mathematics textbooks need to provide a wealth of tasks dealing with multiple types of mathematical reasoning, tasks of doing mathematics, and tasks reflecting the structural characteristics of mathematical reasoning.
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Purnomo, Yoppy Wahyu, Masitah Sharill, Olivia Pandansari, Rika Susanti, and Winarni Winarni. "Cognitive demands on geometrical tasks in Indonesian elementary school mathematics textbook." Jurnal Elemen 8, no. 2 (July 1, 2022): 466–79. http://dx.doi.org/10.29408/jel.v8i2.5235.
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Examples and exercises in mathematics textbooks have an essential role in directing teaching and learning to achieve the objectives of the mathematics curriculum. This study examines mathematical tasks, i.e., examples and exercises, for a grade 4 elementary school mathematics textbook published by the Indonesian Government in 2018. We focus on geometry tasks and categorize them based on the dimensions of cognitive processes and knowledge of the revised Bloom’s taxonomy. Textbook research is used to achieve the objectives of this study. The validity of the data was carried out by employing peer debriefing. The findings of this study indicate that only about 30% of the geometry tasks in this mathematics textbook require high-level mathematical thinking skills. This study also shows that procedural knowledge is more dominant and becomes an orientation in presenting geometry tasks. This finding becomes less relevant to the orientation of researchers and policymakers who want the direction of mathematics education to be forming students as problem solvers.
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Келдибекова, Аида, Aida Keldibekova, Нина Селиванова, and Nina Selivanova. "Olympiad tasks on geometry, methodical techniques for their solution." Profession-Oriented School 7, no. 4 (September 24, 2019): 34–37. http://dx.doi.org/10.12737/article_5d6772e7b75a81.22805374.
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The main content of the article is devoted to the geometric problems of mathematical school olympiads. The study revealed the types of operating with spatial images in the process of solving problems, the stages of forming spatial representations of students in the study of geometry and objectives of the course of visual geometry. It was concluded that the formation of spatial, topological, spatial, projective representations goes through successive stages, developing the geometric skills of schoolchildren. Olympiad tasks, designed on the basis of school programs and textbooks on geometry, make it possible to check the formation of the geometric skills of schoolchildren. The article may be of interest to mathematics teachers, students and schoolchildren who are interested in methods of solving olympiad problems in geometry.
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Vladeva, Pavlina. "The Revival Textbooks from the Old-fashioned Collection of the Centre Community "Nadejda-1869"." Cultural and Historical Heritage: Preservation, Representation, Digitalization 5, no. 2 (2019): 208–32. http://dx.doi.org/10.26615/issn.2367-8038.2019_2_019.
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The subject of the study was 45 textbooks, published from 1835 to 1875 were preserved in the old-fashioned collection of the centre community „Nadejda-1869”. Their authors are 17 teachers who wrote, translated and published first Bulgarian textbooks in the XIX-th century. They are journalists writing the first newspapers and magazines. They lead the struggle for new Bulgarian education, church independence and political freedom. They reform the education and the place of the cell, they build the secular. They are innovators, they introduce the study of new school subjects and languages according to the needs of the time. The text presents first textbooks in Bulgarian language, readings and grammar, arithmetics, geometry and physics. They are textbooks on history, geography, textbooks of natural history. Were preserved textbooks of logic, textbooks of moral and textbooks and dictionaries in French and German, sacred Orthodox catechisms. The article presents the history and development of the curriculum in Bulgarian schools in the ХIX c..2 Keywords: Old-fashioned collection, centre community „Nadejda-1869”, teachers, authors, first Bulgarian textbooks in the XIX-th, new Bulgarian secular education, new school subjects and languages, first textbooks in Bulgarian language, readings, grammar, arithmetics, geometry and physics, history textbooks, geography, textbooks and dictionaries in French and German
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Fehr, Howard F. "The Present Year-Long Course in Euclidean Geometry Must Go." Mathematics Teacher 100, no. 3 (October 2006): 165–68. http://dx.doi.org/10.5951/mt.100.3.0165.
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It is assumed that the geometry course refers to one that is commonly taught in the tenth school year. It is traditional Euclidean synthetic geometry, of 2- and 3-space, modified by an introduction of ruler and protractor axioms into the usual synthetic axioms. A unit of coordinate geometry of the plane is usually appended. It is a course that is reflected in textbooks prepared by the School Mathematics Study Group and in most commercial textbooks.
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Fehr, Howard F. "The Present Year-Long Course in Euclidean Geometry Must Go." Mathematics Teacher 100, no. 3 (October 2006): 165–68. http://dx.doi.org/10.5951/mt.100.3.0165.
Full textAbstract:
It is assumed that the geometry course refers to one that is commonly taught in the tenth school year. It is traditional Euclidean synthetic geometry, of 2- and 3-space, modified by an introduction of ruler and protractor axioms into the usual synthetic axioms. A unit of coordinate geometry of the plane is usually appended. It is a course that is reflected in textbooks prepared by the School Mathematics Study Group and in most commercial textbooks.
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Takıcak, Müjdat. "Constructivist Approach in Ottoman Mathematics Education: Salih Zeki." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 1 (February 5, 2021): 378–423. http://dx.doi.org/10.17762/turcomat.v12i1.281.
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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.
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Wong, Wing-Kwong, Sheng-Kai Yin, and Chang-Zhe Yang. "Drawing dynamic geometry figures online with natural language for junior high school geometry." International Review of Research in Open and Distributed Learning 13, no. 5 (November 15, 2012): 126. http://dx.doi.org/10.19173/irrodl.v13i5.1217.
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<p>This paper presents a tool for drawing dynamic geometric figures by understanding the texts of geometry problems. With the tool, teachers and students can construct dynamic geometric figures on a web page by inputting a geometry problem in natural language. First we need to build the knowledge base for understanding geometry problems. With the help of the knowledge base engine InfoMap, geometric concepts are extracted from an input text. The concepts are then used to output a multistep JavaSketchpad script, which constructs the dynamic geometry figure on a web page. Finally, the system outputs the script as an HTML document that can be visualized and read with an internet browser. Furthermore, a preliminary evaluation of the tool showed that it produced correct dynamic geometric figures for over 90% of problems from textbooks. With such high accuracy, the system produced by this study can support distance learning for geometry students as well as distance learning in producing geometry content for instructors.<br /><br /></p>
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Silva, Circe Mary Silva. "Experimental Geometry, Pythagorean Theorem and Montessori." Acta Scientiae 24, no. 8 (March 27, 2023): 376–404. http://dx.doi.org/10.17648/acta.scientiae.7023.
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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.
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OKUYUCU, Mehmet Ata. "Dimensioning of measurement and evaluation tasks in high school education mathematics text-books and examination of cognitive." International Journal of Social Sciences and Education Research 8, no. 4 (October 31, 2022): 390–403. http://dx.doi.org/10.24289/ijsser.1166709.
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The aim of the study is to examine the relationship between the tasks in the high school mathematics textbooks and the information in the textbook and their cognitive levels. For this purpose, it was decided to use the qualitative research method in the research. The data of the research were obtained through document analysis. In the research, the tasks related to the learning fields of “numbers and algebra”, “geometry” and “data, counting and probability” in the high school mathematics textbooks taught in the 2020-2021 academic year were discussed. The analysis of the tasks in the textbooks was carried out at the micro level. In the micro level analysis, tasks were sized as high relatedness, local low relatedness, and global low relatedness. As a result; In terms of the tasks in the 9th, 10th, 11th and 12th grade textbooks, it was determined that the highest relatedness tasks and the least global low relatedness tasks. In addition, when the tasks in the textbooks of all grade levels were analyzed according to the revised Bloom taxonomy, it was determined that the tasks belonging to the application level were the most. For these reasons, the number of local and global low relatedness tasks in the textbooks can be increased and the tasks in the textbooks can be prepared considering metacognitive skills.
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Hidayah, Miftahul, and Helen Forgasz. "A COMPARISON OF MATHEMATICAL TASKS TYPES USED IN INDONESIAN AND AUSTRALIAN TEXTBOOKS BASED ON GEOMETRY CONTENTS." Journal on Mathematics Education 11, no. 3 (September 10, 2020): 385–404. http://dx.doi.org/10.22342/jme.11.3.11754.385-404.
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This study examined the type of mathematical tasks in two Australian and two Indonesian mathematics textbooks for 7th-grade students. The quantitative data were collected from the coding results of the tasks in the textbooks. The tasks were coded based on six categories: the presentation forms, the cognitive requirements, the contextual features, the information provided, the number of steps required, and the numbers of answers. Both the similarities and differences in the mathematical tasks provided in the selected textbooks were analysed. The coding results reveal that the majority of tasks in both the Australian and Indonesian textbooks were presented in verbal and combined forms. Routine and closed tasks were still dominant in the four textbooks. More than 93% of tasks in the four textbooks had sufficient information for students to solve the problem. One of the Australian textbooks had a higher proportion of tasks with real-world contexts than the other textbooks. One of the Indonesian textbooks showed a high proportion of tasks requiring multiple steps or procedures. These results were used to explore the learning opportunities offered by the textbooks, and the possible influence on students’ performances in international assessments. Some recommendations for the refinement of the textbooks and future research are also outlined at the end of the study.
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Dimmel, Justin K., and Patricio G. Herbst. "The Semiotic Structure of Geometry Diagrams: How Textbook Diagrams Convey Meaning." Journal for Research in Mathematics Education 46, no. 2 (March 2015): 147–95. http://dx.doi.org/10.5951/jresematheduc.46.2.0147.
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Geometry diagrams use the visual features of specific drawn objects to convey meaning about generic mathematical entities. We examine the semiotic structure of these visual features in two parts. One, we conduct a semiotic inquiry to conceptualize geometry diagrams as mathematical texts that comprise choices from different semiotic systems. Two, we use the semiotic catalog that results from this inquiry to analyze 2,300 diagrams from 22 high school geometry textbooks in which the dates of publication span the 20th century. In the first part of the article, we identify axes along which the features of geometry diagrams can vary, and in the second part of the article, we show the viability of using the semiotic framework to conduct empirical studies of diagrams in geometry textbooks.
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Almeida, Laura Isabel Marques Vasconcelos de, and Marta Maria Gama. "Os Conceitos Geométricos na Obra de Molina e Rico (1970)." Revista de Ensino, Educação e Ciências Humanas 22, no. 2 (June 23, 2021): 243–53. http://dx.doi.org/10.17921/2447-8733.2021v22n2p243-253.
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ResumoA coletânea “Criança, Geometria, Aritmética” de Molina e Rico, publicada no ano de 1969, foi objeto de estudo da pesquisa de Mestrado em Ensino do Programa de Pós-Graduação da Universidade de Cuiabá (UNIC). O artigo tem como objetivo destacar a análise empreendida nos quatro dos seis livros inventariados no Colégio Liceu Cuiabano, com o intento de compreender como os conteúdos de Geometria foram trabalhados na escola primária de Mato Grosso na década de 1970. Ancorada na dimensão metodológica histórico-cultural, a pesquisa se centra nos fundamentos teóricos de autores que discutem com propriedade os conceitos Matemáticos em destaque nos livros didáticos. O estudo revela que a Geometria se constitui como um saber elaborado ao longo do tempo e destaca os primeiros elementos sistematizados da Geometria em destaque: ponto, reta, plano, polígonos, congruência e ângulos que foram sendo construídos, historicamente, pela cultura escolar e disseminada pela escola primária de Mato Grosso. Palavras-chave: Ensino de Geometria. Cultura Escolar. Livro Didático. AbstractThe collection "Child, Geometry, Arithmetic" by Molina and Rico, published in 1969, was the object of study by the Master's in Education research of the Graduate Program at University of Cuiabá (UNIC). The article aims to highlight the analysis undertaken in four of the six books inventoried at Colégio Liceu Cuiabano, with the intention of understanding how the geometry contents were worked in the primary school of Mato Grosso state in the 1970s. Anchored in the historical-cultural methodological dimension, the research focuses on the theoretical foundations of authors who properly discuss the mathematical concepts highlighted in textbooks. The study reveals that geometry is constituted as knowledge elaborated over time and highlights the first systematized elements of geometry highlighted: point, line, plane, polygons, congruence and angles that have been historically constructed by the school culture and disseminated by the primary school of Mato Grosso state. Keywords: Geometry teaching, School culture, Textbook.
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Semadeni, Zbigniew. "Reformy programów i podręczników szkolnych sprzed pół wieku inspirowane prądami tzw. nowej matematyki." Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia 12 (December 31, 2020): 211–48. http://dx.doi.org/10.24917/20809751.12.10.
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The purpose of this paper is to outline the reforms of mathematics education in the spirit of “New Math” in USA, France and to document their features in Poland. Activities and achievements of Zofia Krygowska are listed. Particular attention is paid to two radical reforms: the 1967 textbook on geometry based on set-theory for grade IX and far-reaching changes in primary math education in the 1970s. Excerpts from articles, curricula and textbooks are included.
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Sal'kov, N. "A Systematic Approach to the Study of Descriptive Geometry." Geometry & Graphics 10, no. 1 (June 20, 2022): 14–23. http://dx.doi.org/10.12737/2308-4898-2022-10-1-14-23.
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The issues of inconsistency of some terms used in descriptive geometry with the rules of GOST R 2.105-2019 ESCD "General Requirements for Text Documents", as well as related to the projection of surfaces, are considered. The structure of descriptive geometry’s textbooks is considered, according to which all textbooks of this discipline have been built up until recently. This structure forms a sequence in the study of descriptive geometry in almost all higher education institutes. Criticism of this structure, which has been using for teaching since time immemorial without significant changes what, in particular, presents significant difficulties in descriptive geometry studying, is given.
In contrast with the existing structure, a new one is proposed (if the structure proposed near 50 years ago can be called new), but this new structure is almost nowhere used for release of information on descriptive geometry. This proposed structure is scientifically justified, practically verified and offered for universal use.
In addition, the classification of positional and metric problems, and use of algorithms common for them is proposed.
The proposed structure contains the following sections: 1. Basic concepts of descriptive geometry. 2. Set up of geometric figures in a drawing. 3. Positional problems. 4. Metric problems. 5. Conversion methods. 6. Involutes.
The sections arranged in the proposed coherent system, considered separately from each other and not subject to mixing, make it possible to systematize and algorithmize the processes of descriptive geometry layout and studying.
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Otten, Samuel, Lorraine M. Males, and Nicholas J. Gilbertson. "The introduction of proof in secondary geometry textbooks." International Journal of Educational Research 64 (2014): 107–18. http://dx.doi.org/10.1016/j.ijer.2013.08.006.
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McKillip, William D., and Cynthia Stinnette Kay. "A Few Problems Involving Scale." Mathematics Teacher 78, no. 7 (October 1985): 544–47. http://dx.doi.org/10.5951/mt.78.7.0544.
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Many mathematics textbooks contain material on scale drawing as applications of ratio and proportion involving geometric figures. This article suggests some applications that students may find interesting. The material might be most useful in seventh- or eighth-grade mathematics or in general mathematics in secondary school. Algebra and deductive geometry are avoided.
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BEBA, D. N., and V. A. GUREEV. "PEDAGOGICAL FEATURES OF A.P. KISELEV'S TEXTBOOKS." Scientific Notes of Orel State University 100, no. 3 (September 26, 2023): 180–83. http://dx.doi.org/10.33979/1998-2720-2023-100-3-180-183.
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The article examines the life and work of mathematician and educator A.P. Kiselev, whose textbooks were used in Russia for more than 50 years. Based on an analysis of Kiselev’s works, the key pedagogical features of his textbooks are identified, including rigorous presentation of material, scientific style, and a variety of practical exercises. Kiselev was among the first to introduce elements of mathematical analysis into secondary school mathematics curriculum. Kiselev’s textbooks defined the structure and content of school courses in arithmetic, algebra and geometry for many decades, and contributed to the systematization and unification of mathematical knowledge in secondary education. The author succeeded in combining fundamental mathematical knowledge with accessible presentation. His books embodied the principles of intra-subject (between arithmetic, algebra and geometry) and inter-subject (between teaching of mathematics, physics and drafting) continuity. A.P. Kiselev’s textbooks were in demand not only in the USSR, but also in other countries.
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Collier, C. Patrick, and Tina Pateracki. "Exchange: Geometry in the Middle School: An Exchange of Ideas and Experiences." Mathematics Teaching in the Middle School 3, no. 6 (March 1998): 412–15. http://dx.doi.org/10.5951/mtms.3.6.0412.
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Geometry and measurement represent two of the nine content strands in the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) and thirteen of the forty-nine objectives for grades 5-8. In addition, several other content strands have explicit connections to geometry. For example, some of the “patterns and functions” deal with geometric patterns, and some of the probability is in geometric settings. The Standards document describes a vision for the role of geometry and measurement that is different from, and larger than, the traditional role. No longer is it to be a “frills” topic relegated to the back of commonly used textbooks nor restricted to identifying figures and reciting a litany of their properties. Instead, geometry should encompass a variety of experiences in which middle schoolers create their own understanding of the relationships in our multidimensional world. Geometric models should be used to analyze, interpret, and solve problems from probability, algebra, and other areas of mathematics. That is, geometry should take a place among the major topics of emphasis in the mathematics study of a middle school student.
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Sal'kov, N., and Nina Kadykova. "The Phenomenon of Descriptive Geometry Existence in Other Student Courses." Geometry & Graphics 8, no. 4 (March 4, 2021): 61–73. http://dx.doi.org/10.12737/2308-4898-2021-8-4-61-73.
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Among specialists prevails the primitive view, according to Prof. G.S. Ivanov, on descriptive geometry only as on a "grammar of a technical language", as it characterized V.I. Kurdyumov in the XIX Century. If in the century before last his definition was actual, although many contemporaries had a different opinion, then a century and a half later this definition became outdated, especially since have been revealed the close relationships of descriptive geometry with related sections: analytical, parametric, differential geometry, etc., and descriptive geometry became an applied mathematical science. In this paper it has been shown that an image is obtained as a result of display (projection). In this connection, according to prof. N.A. Sobolev, "All visual images – documentary, geometrographic, and creative ones – are formed on the projection principle". In other words, they belong, in essence, to descriptive geometry. Thus, all made by hand creative images – drawings, paintings, sculptures – can be attributed with great confidence to descriptive geometry as a theory of images. These creative images, of course, have a non-obvious projection origin, nevertheless, according to Prof. N.A. Sobolev, "They, including the most abstract fantasies, are essentially the projection ones". Further in the paper it has been shown which disciplines apply some or other of graphic models, and has been considered a number of drawings belonging to different textbooks, in which graphic models are present. Thus, clearly, and also referring to the authorities in the area of images and descriptive geometry, it has been proved that each of the mentioned textbooks has a direct or indirect connection with descriptive geometry, and descriptive geometry itself is present in all textbooks, at least, in the technical and medical ones.
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Jayathirtha, Gayithri. "An Analysis of the National Intended Geometry Curriculum." Contemporary Education Dialogue 15, no. 2 (June 28, 2018): 143–63. http://dx.doi.org/10.1177/0973184918783291.
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Geometrical concepts play a crucial role in developing spatial thinking and reasoning. Further, curricular materials play a key role in shaping student-learning experiences in the classroom. The organisation of the content of textbooks plays a decisive role in how and when students are introduced to concepts, especially given the ‘textbook-centric’ teaching practices observed in the Indian classroom. I thus analysed the geometry curriculum from grades one through eight through the lens of the five-level hierarchical van Hiele model of geometrical thinking.1 I organized the analysis to highlight conceptual details at two levels—across a chapter in a particular grade level and across chapters in all the eight grade levels. The analysis has illuminated the affordances of curricular materials to constantly connect students to multiple levels of geometric reasoning, but at the same time it points to the need for reorganizing the curriculum to enable students to systematically progress from visual-based to deduction-based reasoning. The analysis also calls for redesigning certain conceptual representations to promote relational geometrical understanding among students.
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Ismailova, Nelli. "SCIENTIFIC SCHOOL "APPLIED GEOMETRY AND ENGINEERING GRAPHICS NAMES OF ANATOLIY PODKORYTOV"." APPLIED GEOMETRY AND ENGINEERING GRAPHICS, no. 100 (May 24, 2021): 34–36. http://dx.doi.org/10.32347/0131-579x.2021.100.34-36.
Full textAbstract:
The founder of the scientific school of applied geometry in Odessa was Anatoly Podkorytov, academician of the higher school of Ukraine, doctor of technical sciences, professor. During the scientific and pedagogical activity, A. Podkorytov prepared 15 candidates of technical sciences, 3 doctors of technical sciences.
He was awarded the Order of the Badge of Honor, silver and bronze medals for the development of 5 automatic installations that were exhibited at the exhibition of achievements of the national economy, he was also awarded two government awards. A. Podkorytov is the author of 27 copyright certificates for inventions, more than 549 printed scientific and methodological works published in Ukraine and abroad. Among them are several textbooks and textbooks on sketching geometry, computer graphics, several monographs. A. Podkorytov edited inter-university scientific and methodological collections on textual geometry.
Today, the head of the scientific school "Applied Geometry and Engineering Graphics" named after Anatoly Nikolayevich Podkorytov is his student, Academician of the Higher School of Ukraine, Doctor of Technical Sciences, Professor Ismailova Nellya.
The basis of all research areas of the scientific school is applied mechanics, the main areas of scientific research are related to weapons and military equipment. Representatives of the scientific school are engaged in geometric modeling of technical forms and automation of their design process.
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Barrantes, Manuel, Marco López, and Manuel Ángel Fernández. "<p>Análisis de las representaciones geométricas en los libros de texto</p>." PNA. Revista de Investigación en Didáctica de la Matemática 9, no. 2 (January 1, 2015): 107–27. http://dx.doi.org/10.30827/pna.v9i2.6105.
Full textAbstract:
La investigación analiza y clasifica las imágenes gráficas relacionadas con la enseñanza-aprendizaje de la geometría en libros de textos. Se estudian varios aspectos de las representaciones geométricas a lo largo de las unidades de geometría de los libros. Algunos de estos aspectos son la variedad de representaciones al introducir conceptos geométricos, los elementos de las imágenes que puedan derivar en dificultades en el proceso de enseñanza-aprendizaje de la geometría, la representación plana de figuras tridimensionales y las imágenes reales que se utilizan para aludir a elementos geométricos abstractos. Se realiza una categorización que sirve como instrumento de análisis de los textos.Analysis of geometric representations in textbooksIn this research, we analyze and classify the graphical images related to the teaching-learning of geometry appearing in textbooks. It focuses on the study of several aspects of the geometrical representations included in the Geometry units of the books. Some of the these aspects are the variety of representations used when introducing geometrical concepts, the elements of these figures which could lead to difficulties in the Geometry teaching-learning process, the plane representation of tridimensional figures and the real images that are used to refer to abstract geometrical elements. We develop a categorization that serves as an instrument of text analysis.Handle: http://hdl.handle.net/10481/34157WOS-ESCI
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Guillet, Carène. "A quantitative study of French 19th century geometry textbooks." Acta Scientiae 24, no. 8 (March 27, 2023): 163–201. http://dx.doi.org/10.17648/acta.scientiae.7191.
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Hwang, Won Ho, and Minshik Cho. "An analysis and comparison of national standard high school mathematics curriculum for gifted students in Korea and China." Korean Association For Learner-Centered Curriculum And Instruction 24, no. 2 (January 31, 2024): 795–814. http://dx.doi.org/10.22251/jlcci.2024.24.2.795.
Full textAbstract:
Objectives The purpose of this study is to find implications for Korean mathematics education by examining how gifted mathematics education is operated in Korea and China through a comparison and analysis of the basic direc-tions of gifted mathematics education in high schools in both countries.
Methods We analyzed the contents and composition methods for mathematically gifted students in the education curriculum and textbooks in Korea’s 2022 and 2015 curricula and China’s 2017 revised mathematics and curricu-lum contents and textbooks.
Results Korea adheres to standardized processes and contents in each area of algebra, analysis, geometry, proba-bility and statistics, and mathematical history and definitional areas, while China sometimes develops integrated processes that are not restricted to areas by focusing on specific topics. In the geometry area, Korea’s 2015 curric-ulum lacked content for mathematics gifted students compared to China, but this was sufficiently overcome in the advanced geometry newly established in the 2022 curriculum, and the parts that were lacking compared to China, such as mathematical history and definitional areas, were also expanded in mathematics and culture, AI mathe-matics, and other areas of the 2022 curriculum.
Conclusions Both countries have advanced courses and textbooks being used in mathematics gifted education, but Korea is divided into general courses and elective courses and specialized courses used in special purpose high schools such as science high schools according to the content composition elements and difficulty, while China is only divided into required courses and elective courses. However, while Korea’s specialized course textbooks are a single book, China allows publishers to create level-based textbooks based on composition elements and difficulty, resulting in diverse content and levels.