Relevant bibliographies by topics / Geometry – Textbooks

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Geometry – Textbooks'

Author: Grafiati
Published: 4 June 2021
Last updated: 30 July 2024

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Journal articles on the topic "Geometry – Textbooks"

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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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Dissertations / Theses on the topic "Geometry – Textbooks"

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Cannon, Megan N. "Prevalence of Typical Images in High School Geometry Textbooks." Scholar Commons, 2017. http://scholarcommons.usf.edu/etd/6809.

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Visualization in mathematics can be discussed in many ways; it is a broad term that references physical visualization objects as well as the process in which we picture images and manipulate them in our minds. Research suggests that visualization can be a powerful tool in mathematics for intuitive understanding, providing and/or supporting proof and reasoning, and assisting in comprehension. The literature also reveals some difficulties related to the use of visualization, particularly how illustrations can mislead students if they are not comfortable seeing concepts represented in varied ways. However, despite the extensive research on the benefits and challenges of visualization there is little research into what types of figures students are exposed to through their textbooks. This study examines 14 high school geometry textbooks in total, comprised of eight physical textbooks from the top three major textbook publishers in the United States and six FlexBooks created by a non-profit organization developing free and customizable textbooks online. In each textbook the printed images from four topics were classified: Parallel Lines and Transversals, Classifying Triangles, Parallelograms, and Trapezoids. The ‘typical’ images in each of the four topics were defined and the percentages of images that were typical for each textbook in both the lesson and exercise portions were calculated. Results indicate that lesson portions of sections generally contain more typical images than exercise portions and that the total percentage of typical images in an average section varies from 51.9% typical images in the Parallel Lines and Transversals section to 75.2% typical images in the Trapezoid section. Based on these results we list possible avenues for further research in this area.
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Delil, Huseyin. "An Analysis Of Geometry Problems In 6 - 8 Grades Turkish Mathematics Textbooks." Master's thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/3/12607251/index.pdf.

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The purpose of this study was to analyze geometry problems in a widely used sixth-, seventh-, and eighth-grade Turkish elementary mathematics textbooks series based on the cognitive assessment frameworks of the most recent TIMSS, the Trends in International Mathematics and Science Study 2003. To compare geometry problems in the textbooks and TIMSS 1999, in which Turkish students poorly performed, the cognitive behaviors that the problems required were determined and categorized. After the analysis, it was found that the two most frequent behaviors that the problems require are computing and applying with a total percentage of 72, in case of the textbooks. In TIMSS 1999 geometry problems case, however, applying and analyzing are the most frequent cognitive behaviors with a total percentage of 47. It was also found that a great majority of 22 behaviors of the framework were either not represented or underrepresented by the textbooks geometry problems. When we consider the four major categories of behaviors, 86 percent of the textbooks geometry problems required behaviors belong to two cognitive domains: Knowing Facts and Procedures or Solving Routine Problems. TIMSS 1999 geometry problems, however, mostly belong to Solving Routine Problems or Reasoning with a percentage of 65. In both the textbooks and TIMSS 1999 cases, a relatively small part of the problems required behaviors belong to Using Concepts. The results are discussed in the light of Turkey&
#8217
s performance in TIMSS 1999 and some suggestions related to the textbook problems were given.
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ALMEIDA, REGINA DE CASSIA MANSO DE. "PROOFS OF PLANE GEOMETRY FOUND IN BRAZILIAN TEXTBOOKS SINCE THE XIXTH CENTURY." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2008. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=11761@1.

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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
Esta Tese investiga mudanças ocorridas no texto de demonstração em geometria plana elementar, em livros-textos usados no ensino brasileiro a partir do século XIX. O trabalho está organizado em duas partes: a primeira, um estudo histórico de releituras dos Elementos de Euclides que, a partir do século XVI, em cada época influenciaram a constituição da matemática escolar em seu sentido mais amplo e a segunda, as análises das demonstrações. A base documental inclui obras históricas e livros relevantes no ensino-aprendizagem da geometria dedutiva no Brasil. As releituras de Euclides e os livros-texto permitiram estabelecer os parâmetros de análise das demonstrações e de inferências de ordem mais geral. As análises das demonstrações mostram evidências que confirmam mudanças de várias ordens: a redação, o método e a justificativa da prova. Foi possível identificar dois tipos básicos de livros-texto que denominamos elementos de geometria e livros de matemática, e caracterizar a correlação existente entre eles: o estudo dedutivo em geometria, originário no livro tipo elementos de geometria que se estrutura conforme o padrão euclidiano teorema- problema, se altera devido à interação geometria-álgebra- aritmética, a qual caracteriza o livro de matemática desde a sua origem até a atualidade. Foi possível constatar, ainda, que o estudo dedutivo em geometria tende a desaparecer quase totalmente nos textos tipo livro de matemática. O estudo - texto demonstrativo e suas mudanças - mostra uma história dos conteúdos matemáticos, dos livros-texto e da matemática escolar no Brasil.
This thesis studies changes in proofs of elementary geometry theorems found in brazilian textbooks from the XVIIIth century on. The thesis is composed of two parts. The first one contains a historic survey of re-readings of Euclid´s Elements which, from the XVIth century on influenced the constitution of the school mathematics corpus, in its wide sense. The second ´part contains the actual analysis of proofs. We examine both historically important Works and books that were influential in the teaching and learning of deductive geometry in Brazil. The study of Euclid´s Elements and later works enabled us to set up the guidelines for the proofs analysis and all of more general inferences. The proofs analysis shows several types of change: the style, the method and the actual proof. It was possible to identify two basic kinds of text-books, which we call elements of geometry and mathematics books, respectively, and to establish the correlation between the two types: the deductive study of geometry, present in the elements of geometry, that adopted the Euclidean pattern of theorem - problem, changes due to the interaction between geometry, arithmetic and algebra, which characterizes the mathematics book, from their beginnings to the present. It was also possible to establish that the deductive study of geometry almost disappears in the mathematics books. The study of proofs and their changes shows the history of the contents of school mathematics, their text-books and of school mathematics in Brazil.
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Zorin, Barbara. "Geometric Transformations in Middle School Mathematics Textbooks." Scholar Commons, 2011. http://scholarcommons.usf.edu/etd/3421.

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Abstract This study analyzed treatment of geometric transformations in presently available middle grades (6, 7, 8) student mathematics textbooks. Fourteen textbooks from four widely used textbook series were evaluated: two mainline publisher series, Pearson (Prentice Hall) and Glencoe (Math Connects); one National Science Foundation (NSF) funded curriculum project textbook series, Connected Mathematics 2; and one non-NSF funded curriculum project, the University of Chicago School Mathematics Project (UCSMP). A framework was developed to distinguish the characteristics in the treatment of geometric transformations and to determine the potential opportunity to learn transformation concepts as measured by textbook physical characteristics, lesson narratives, and analysis of student exercises with level of cognitive demand. Results indicated no consistency found in order, frequency, or location of transformation topics within textbooks by publisher or grade level. The structure of transformation lessons in three series (Prentice Hall, Glencoe, and UCSMP) was similar, with transformation lesson content at a simplified level and student low level of cognitive demand in transformation tasks. The types of exercises found predominately focused on students applying content studied in the narrative of lessons. The typical problems and issues experienced by students when working with transformations, as identified in the literature, received little support or attention in the lessons. The types of tasks that seem to embody the ideals in the process standards, such as working a problem backwards, were found on few occurrences across all textbooks examined. The level of cognitive demand required for student exercises predominately occurred in the Lower-Level, and Lower-Middle categories. Research indicates approximately the last fourth of textbook pages are not likely to be studied during a school year; hence topics located in the final fourth of textbook pages might not provide students the opportunity to experience geometric transformations in that year. This was found to be the case in some of the textbooks examined, therefore students might not have the opportunity to study geometric transformations during some middle grades, as was the case for the Glencoe (6, 7), and the UCSMP (6) textbooks, or possibly during their entire middle grades career as was found with the Prentice Hall (6, 7, Prealgebra) textbook series.
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Prytz, Johan. "Speaking of Geometry : A study of geometry textbooks and literature on geometry instruction for elementary and lower secondary levels in Sweden, 1905-1962, with a special focus on professional debates." Doctoral thesis, Uppsala : Department of Mathematics, Uppsala university, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-7902.

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Yau, Kiu-chun, and 丘僑春. "An analysis of Hong Kong textbooks: a focus on problem types and ICT in geometry strand." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B48369342.

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This is an analysis on textbooks for elementary secondary levels in Hong Kong, focusing on the type of problem solving and the use of information and communication technology (ICT) in geometry strand. Textbooks can provide different learning opportunities for students. Usage of textbooks is widespread in secondary schools and most mathematics teachers are used to rely on textbooks in classrooms. As such, the differences of textbooks would affect what happens in the lessons. Problems in the textbooks are significant elements of the approach, as they are of any educational process, because problems focus on energy and attention, and conduct the students in the integration, application, and extension of knowledge. A content analysis has been taken in this study, by comparing the distribution patterns of the quantities of problems representing various kinds of applications in the selected textbooks. The framework is the conceptual framework used by Fan and Zhu (2006) which concerns with the definition of the task from the perspective of textbook analysis. According to the quantitative patterns, it hints the frequencies with students exposed to different kinds of the problems and, therefore, has critical influence on student’s learning. The coding results of the study indicated that the majority of the three types of problems were traditional, closed-end, non-application and problems with sufficient data provided. Most of the to-be-solved problems and worked problems were routine ones while half of the problems with use of ICT were of that type.
published_or_final_version
Education
Master
Master of Education
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Kwong, Ka-to, and 鄺嘉圖. "An analysis of geometry in the junior secondary school (grade 7-9) mathematics textbooks from England, Hong Kong and Chinese Taipei." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hdl.handle.net/10722/198864.

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This dissertation is intented to explore the similarities and differences of pedagogical characteristics in geometry though analyzing the contents of the junior Secondary school (grade 7-9) mathematics textbooks of England, Hong Kong and Taipei. By studying the topic of “Relationships for angles at a point, angles on a line, vertically opposite angles, angles associated with a transversal cutting parallel lines and perpendicularity” of the textbooks, the textbooks of the three places have demonstrated how they organize the contents to achieve the various aims with different means and different emphasis. For English textbooks, their contents are characterized by using geometric intuition for verifying the properties of geometric objects and the theorems. On the contrary, for Taipei textbook, their contents are characterized by the extensive use of deductive reasoning and proof for verifying the properties of geometric objects and the theorems. Lastly, for Hong Kong textbooks, their contents are characterized by encouraging conjecturing through various explorative activities. For developing students’ cognitive thinking in geometry, the progress of developing students’ level of sophistication in deductive reasoning is depended upon their age for England while Hong Kong and Taipei do not. Process of visualization is commonly used in the three countries for enhancing the reasoning process and various apprehensions of geometric objects. On the other hand, Hong Kong and Taipei textbooks tend to apply more on the process of reasoning in the teaching activities while English textbooks apply more on the process of construction.
published_or_final_version
Education
Master
Master of Education
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Hatziminadakis, Sofia. "Students’ Opportunity To Learn Surface Area And Volume In Middle Grades Mathematics Textbooks." Scholar Commons, 2018. https://scholarcommons.usf.edu/etd/7516.

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I conducted a content analysis to examine the treatment of the surface area and volume concepts within four published middle-grades mathematics textbook series. In particular, I examined the treatment of the surface area and volume concepts in terms of the location of surface area and volume lessons in the textbook and the number of pages and lessons devoted to these concepts. I also investigated the sequence of the instructional blocks of surface area and volume lessons. In addition, I evaluated the tasks included in these lessons in regards to the performance expectations of students, the types of visual representations of 3D objects, and the level of mathematical complexity. At last, I examined the extent to which the content of surface area and volume lessons address the Common Core Content Standards (CCCS) for 6-8 geometry that are aligned with these topics. I used content analysis to analyze relevant content in a total of twelve middle-grades student edition mathematics textbooks from two popular textbook series, Go Math!(GM) and Glencoe Math (GMC); and two alternative textbook series, Connected Mathematics 3 (CM) and University of Chicago School Project (UCSMP). First, I used Flanders’ (1994) counting method to examine the physical characteristics of textbooks, such as the location of the surface area and volume lessons in the textbook, the number of pages and lessons devoted to these concepts. Second, I analyzed the sequence of the instructional blocks of surface area and volume lessons by using content analysis. Third, I adapted the Trends in International Mathematics and Science Study [TIMSS] (2002) Performance Expectations for Mathematics Framework to examine the performance expectations of students within tasks. Fourth, I developed and used the Visual Representations of 3D Objects Framework to examine the types of visual representations of 3D objects included in the tasks. Fifth, I employed the Mathematics Framework for the 2007 National Assessment of Educational Progress (NAEP) to examine the level of mathematical complexity of tasks. Finally, I created the CCCS for 6-8 Geometry Components guideline to examine to what extend the surface area and volume lessons address the geometry content standards. Results indicated that the majority of textbooks place the concepts of surface area and volume towards the end of the textbook. Small percentages of instructional pages and lessons are devoted to these concepts in all textbooks. Findings also revealed great similarities among the instructional blocks of lessons within three textbook series (GM, GMC, and UCSMP). The majority of tasks within all textbook series contain miniscule amounts of important performance expectations such as justifying and proving and visual representations of 3D objects such as nets and pictures. A significant amount of tasks are of moderate complexity across all textbook series. Analysis also showed that the CM textbook series offers the greatest opportunity for students to generate visual representations of 3D objects and contains the largest amount of high complexity tasks. At last, nearly all lessons address the appropriate geometry content standard among all textbook series. Limitations of the study, implications for mathematics education, as well as recommendations for future research are also presented.
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Larsson, Emma, and Lena Hansemark. "Tvådimensionella figurer i digitala läromedel : En innehållsanalys av digitala läromedel i grundskolans årskurs 1–3 med fokus på tvådimensionella figurer." Thesis, Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-84672.

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Detta arbete berör ämnesområdet matematik med inriktning geometri. Syftet med detta arbete har varit att analysera olika digitala läromedel för grundskolans årskurs 1–3 för att synliggöra hur innehållet kan förstås utifrån olika lärteorier. De vetenskapliga lärteorierna som ligger till grund för detta arbete är Variationsteorin och van Hieles teori för geometriskt tänkande. I analysen har geometriuppgifter gällande tvådimensionella figurer analyserats utifrån variationsteorin, kring variationsmönster och kritiska aspekter. Samma uppgifter analyserades även utifrån van Hieles teori kring nivåer och faser för det geometriska tänkandet. En innehållsanalys gav oss möjlighet att undersöka både hur frekvent en viss aspekt av de olika teorierna förekom men även hur uppgifter i de valda digitala läromedlen kunde förstås enligt de två teorierna. Resultatet av denna innehållsanalys visade att innehållsmässig variation i uppgifter kan bidra till förståelse för tvådimensionella figurer och dess egenskaper. Resultatet visade även att det fanns möjlighet till progression av kunskaper om tvådimensionella figurer och dess egenskaper, detta genom uppgifter med varierande svårighetsgrader som avancerade inom och mellan årskurserna.
This study concerns the subject of mathematics with focus on geometry. The aim of this study has been to analyze different digital textbooks suited for compulsory school years 1-3 to visualize how the content can be understood based on different learning theories. This study is based on the Variation Theory and the van Hiele Model of Geometric Thinking. In this analysis, geometry assignments regarding two-dimensional figures have been analyzed based on patterns of variation and critical aspects of the Variation Theory. The same assignments were also analyzed based on van Hiele’s theory of levels and phases of geometric thinking. A content analysis gave us the opportunity to examine both how frequently a certain aspect of the various theories occurred but also how the assignments could be understood according to the two theories. The results of this study showed that content variation in assignments can contribute to an understanding of two-dimensional figures and their properties. The results also showed that there were opportunities for progression of knowledge about two-dimensional figures and their properties, this through assignments with varying degrees of difficulty that advanced within and between grades.
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Cabral, Raquel Montezuma Pinheiro. "IntroduÃÃo do estudo de vetores no ensino mÃdio: um ganho significativo para o estudo da geometria analÃtica." Universidade Federal do CearÃ, 2014. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=11653.

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O presente trabalho trata de uma proposta para a introduÃÃo do estudo de vetores no plano e no espaÃo, no 3 ano do Ensino MÃdio, com a perspectiva de um ganho para os estudos de geometria analÃtica. No estudo da disciplina de Geometria AnalÃtica, no Curso de Mestrado Profissional de MatemÃtica (PROFMAT), verificou-se que a introduÃÃo do estudo de vetores à de simples compreensÃo e uma ferramenta poderosa para a Geometria AnalÃtica, facilitando a demonstraÃÃo dos conteÃdos, melhorando a visualizaÃÃo da condiÃÃo de alinhamento de trÃs pontos, da equaÃÃo da reta e de seus vetores tangentes e normais, no plano e no espaÃo, alÃm de simplificar a resoluÃÃo de exercÃcios e poder incluir alguns conteÃdos que tambÃm se tornam mais acessÃveis utilizando tal ferramenta. O conteÃdo da referida disciplina à abordado no 3 ano do ensino mÃdio sem o tratamento vetorial, deixando a aprendizagem da geometria analÃtica restrita. Apresenta-se, neste estudo, uma proposta de introduÃÃo do estudo de vetores no ensino mÃdio, mostrando que o tempo gasto com sua introduÃÃo à recompensado com a maior facilidade para a abordagem dos conteÃdos, resoluÃÃo de problemas e ampliaÃÃo dos conteÃdos.
This work is a proposal for the introduction of the study of vectors in the plane and in space, in the 3rd year of high school , with the prospect of a gain for studies of analytical geometry. In the study of the discipline of analytical geometry, the Masters Course Professional Mathematics ( PROFMAT ) it was found that the introduction of the study of vectors is simple understanding and a powerful tool for Analytic Geometry, facilitating the demonstration of contents , improved visualization of the alignment condition of three points of the straight line equation and its tangent and normal in the plane and space vectors, and simplify problem solving and be able to include some content that also become more accessible using such a tool. The content of that discipline is addressed in the 3rd year of high school without the vector treatment, leaving the learning of restricted analytic geometry. We present in this study a proposal to introduce the study of vectors in high school, showing that the time spent with their introduction is rewarded with greater ease to the approach of content, problem solving and expansion of the content.
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Books on the topic "Geometry – Textbooks"

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Nichols, Eugene Douglas. Holt geometry. New York: Holt, Rinehart and Winston, 1986.

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G, Brown Richard, and Jurgensen John W, eds. Geometry. Boston: Houghton Mifflin, 1985.

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D, Pilger Kathy, ed. Geometry. 3rd ed. Greenville, S.C: BJU Press, 2006.

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Kohn, Edward. Geometry. Lincoln, Neb: Cliffs Notes, 1994.

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Jurgensen, Ray C. Geometry: Solution Key. Boston: Houghton Mifflin, 1992.

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Cox, Philip L. Prentice Hall informal geometry. Needham, Mass: Prentice Hall, 1992.

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Keedy, Mervin Laverne. Addison-Wesley informal geometry. Menlo Park, Calif: Addison-Wesley Pub. Co., 1986.

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Anton, Howard. Calculus with analytic geometry. 5th ed. Chichester: Wiley, 1995.

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(Firm), Amazon com. CK-12: Geometry. S.l: CK-12 Foundation, 2010.

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Swokowski, Earl William. Algebra and trigonometry with analytic geometry. Belmont, CA: Thomson Brooks/Cole, 2005.

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Book chapters on the topic "Geometry – Textbooks"

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Jacob, Bill. "Linear Geometry." In Textbooks in Mathematical Sciences, 40–71. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-59277-5_2.

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Pinho, Eliana Manuel, José Carlos Santos, and João Pedro Xavier. "Portuguese Textbooks on Descriptive Geometry." In International Studies in the History of Mathematics and its Teaching, 97–111. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-14808-9_7.

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Jacob, Bill. "More Vector Geometry." In Textbooks in Mathematical Sciences, 188–214. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-59277-5_6.

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Meskens, Ad, and Paul Tytgat. "The Genesis of Geometry." In Compact Textbooks in Mathematics, 11–26. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-42863-5_2.

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Pinkall, Ulrich, and Oliver Gross. "Surfaces and Riemannian Geometry." In Compact Textbooks in Mathematics, 87–103. Cham: Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-39838-4_6.

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AbstractThe most simple quantity of a one-dimensional curve $$\gamma \colon [a,b]\to \mathbb {R}^n$$ γ : [ a , b ] → ℝ n is its speed $$|\gamma '|\colon [a,b]\to \mathbb {R}$$ | γ ′ | : [ a , b ] → ℝ .
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Chruściel, Piotr T. "Introduction to Tensor Calculus and Riemannian Geometry." In Compact Textbooks in Mathematics, 1–35. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-28416-9_1.

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Pinkall, Ulrich, and Oliver Gross. "Curves in $$\mathbb {R}^n$$." In Compact Textbooks in Mathematics, 3–11. Cham: Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-39838-4_1.

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Fleurant, Cyril, and Sandrine Bodin-Fleurant. "Trigonometry, Geometry of Plane and Space." In Springer Textbooks in Earth Sciences, Geography and Environment, 67–96. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-69242-5_3.

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Jaime, Adela. "Use of Language in Elementary Geometry by Students and Textbooks." In Mathematics Education Library, 248–55. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-017-2211-7_16.

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Lorenat, Jemma. "“Je n’ai point ambitionnée d’être neuf”: Modern Geometry in Early Nineteenth-Century French Textbooks." In Interfaces between Mathematical Practices and Mathematical Education, 69–122. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-01617-3_4.

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Conference papers on the topic "Geometry – Textbooks"

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PORT, Sergiu. "Solving contest problems in constructive geometry." In Ştiință și educație: noi abordări și perspective. "Ion Creanga" State Pedagogical University, 2023. http://dx.doi.org/10.46727/c.v3.24-25-03-2023.p288-292.

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Sachan, Mrinmaya, Kumar Dubey, and Eric Xing. "From Textbooks to Knowledge: A Case Study in Harvesting Axiomatic Knowledge from Textbooks to Solve Geometry Problems." In Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing. Stroudsburg, PA, USA: Association for Computational Linguistics, 2017. http://dx.doi.org/10.18653/v1/d17-1081.

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Sachan, Mrinmaya, and Eric Xing. "Learning to Solve Geometry Problems from Natural Language Demonstrations in Textbooks." In Proceedings of the 6th Joint Conference on Lexical and Computational Semantics (*SEM 2017). Stroudsburg, PA, USA: Association for Computational Linguistics, 2017. http://dx.doi.org/10.18653/v1/s17-1029.

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Youayia, Baoyang, and Ariyadi Wijaya. "A comparative analysis of geometry tasks in Laotian and Indonesian lower secondary school mathematics textbooks from the perspective of revised Bloom’s Taxonomy." In PROCEEDINGS OF THE 4TH INTERNATIONAL SEMINAR ON INNOVATION IN MATHEMATICS AND MATHEMATICS EDUCATION (ISIMMED) 2020: Rethinking the role of statistics, mathematics and mathematics education in society 5.0: Theory, research, and practice. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0129885.

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Rencis, Joseph J., and Hartley T. Grandin. "Solving Beam Deflection Problems Using the Traditional Approach to Solve Axial and Torsion Problems." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-13350.

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This paper presents a new approach to solving beam deflection problems. The approach involves the direct application of derived force-deformation formulas, a procedure commonly used with axial and torsion bar problems. This direct application of derived force-deformation formulas, referred to by the authors as Method of Segments, is extended to beam deflection analysis in order to provide a solution procedure for beams that is consistent in philosophy and application with that presented in most mechanics of materials textbooks for axially loaded bars and torsionally loaded shafts. The beam force-deformation formulas, involving slope and displacement, are derived by double integration for a beam of uniform cross-section, material and distributed loading with end shear forces and couples. Application of the formulas is direct and requires no integration or continuity equations. Furthermore, by identifying segments of uniform geometry, material and distributed loading, this approach can easily be applied to beams of discontinuous geometry and material that supports both concentrated and distributed loading.
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Ghosh, Suhash, and Chittaranjan Sahay. "Characterizing Surface Quality Through 3D Parameters: Why 2D Average Roughness Alone Is No Good." In ASME 2017 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/imece2017-72229.

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Typically, the design of machine parts is based on the dimensional and form tolerances and fragmentally on the surface roughness parameters (predominantly roughness average Ra). Despite the range of available 3D surface quality parameters, and the modern equipment to accurately measure them, design and quality professionals continue to specify surface finish based solely on the value of Ra. There are many reasons that contribute to this tendency: average roughness remains so easy to calculate, it is well understood, and vast amount of published literature explains it, and historical part data is based upon it. The same outlook trails in undergraduate education and their textbooks. It has been seen that Ra, typically, proves too general to describe surface’s true functional nature. Additionally, the push for complex geometry, coupled with tight tolerances, has reinforced the need to maintain increased process control along with improved surface finish. In turn, the surface finish over the entire area, not just the 2D parameters, tends to dictate the performance and reliability of the component. This article explores how these multitudes of 2D and 3D surface quality parameters are to be understood in the design and development of high performance surfaces, and the strong need for them to be incorporated into undergraduate engineering curriculum, and be taught as an improved toolkit to the aspiring engineers, process engineers and quality control professionals.
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Reit, Xenia-Rosemarie. "Enhancing understanding of analytic geometry by augmented reality." In Fifth International Conference on Higher Education Advances. Valencia: Universitat Politècnica València, 2019. http://dx.doi.org/10.4995/head19.2019.9561.

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An augmented reality (AR) system is a technology which combines computer-generated representations or information and reality in real-time. Instead of substituting the real situation, as it is possible with dynamic geometry systems (DGS), AR adds virtual objects or information to reality to make the situation experiential. The project MalAR aims at investigating the impact of an augmented reality (AR) learning environment in the subject area of analytic geometry. The focus of the AR learning environment is an AR-App, which supports learners understanding of mathematics situations usually given through textbook tasks. Mathematics situations are implemented in an AR-App such that the situation gets visually and enactively explorable by changing perspectives using the own body movement. The added value of integrating AR in mathematics classes is worked out and based on different learning theories like embodied cognition. The AR-App and first results of the pilot study will be demonstrated and presented. With the findings and results of the study evidence-based didactical insights in the teaching and learning with AR in mathematics instruction may be identified and needs for future AR-supported learning scenarios can be revealed.
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Shagalova, Anastasia Alekseevna, and Tatyana Nikolaevna Tomchinskaya. "Application of augmented reality to study descriptive geometry." In 31th International Conference on Computer Graphics and Vision. Keldysh Institute of Applied Mathematics, 2021. http://dx.doi.org/10.20948/graphicon-2021-1-88-92.

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This article analyzes the problems of the development of spatial thinking of students in the development of the discipline "Descriptive geometry", solving projection problems and proposes their solution using the technology of augmented reality. The concept and technology of augmented reality, tracking technologies are considered. The substantiation of the relevance and timeliness of its use to support educational processes is given. The article explores the use of augmented reality technologies in teaching students' spatial thinking, which saves time on the transfer and assimilation of information received by students within the framework of this discipline. The analysis of existing research in the field of application of augmented reality technology in teaching the discipline "Descriptive geometry" is carried out. The possibility of using augmented reality technology in education for the purpose of visual presentation of educational material is shown. A project for the development of a mobile AR application for visualizing the tasks of a textbook on descriptive geometry based on the Vuforia platform is considered. The proposed software product is implemented on a mobile platform with the Android operating system. When developing software, the C # programming language is used to write scripts to implement the required functionality, in particular, interactive interaction with three-dimensional objects.
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Max, Brooke, and Rachael Welder. "Textbook use of children’s thinking to support prospective elementary teachers’ geometric understanding." In 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. PMENA, 2020. http://dx.doi.org/10.51272/pmena.42.2020-285.

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O’Dowd, Devin O., and Aaron R. Byerley. "Computational Aid to AEDsys for Designing a Variable-Area Gas Turbine Nozzle." In ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/gt2018-77173.

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This paper presents a practical approach to designing a gas turbine nozzle with the help of the Aircraft Engine Design textbook as well as the software program Nozzle, a subprogram within the Aircraft Engine Design System Analysis Software suite AEDsys. The current textbook and software allow for a variable wetted length of the converging and diverging nozzle sections. Critical feedback from industry experts has inspired an attempt to design a nozzle with fixed wetted material lengths. This paper is written to augment classroom treatment, but will also support others who use the Aircraft Engine Design text and software for a preliminary engine design capstone. This approach is further guided by the actual scaling of the Pratt & Whitney F100 variable geometry converging-diverging nozzle, where wetted lengths are fixed. The chief goal is to equip students at the United States Air Force Academy with a refined approach that is more realistic of a manufactured nozzle design, producing a graphical representation of a nozzle schedule at different speed and altitude flight conditions, both with and without afterburner.
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