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Journal articles on the topic 'Geometry Mathematics'
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1
Murtianto, Yanuar Hery, Sutrisno Sutrisno, Nizaruddin Nizaruddin, and Muhtarom Muhtarom. "EFFECT OF LEARNING USING MATHEMATICA SOFTWARE TOWARD MATHEMATICAL ABSTRACTION ABILITY, MOTIVATION, AND INDEPENDENCE OF STUDENTS IN ANALYTIC GEOMETRY." Infinity Journal 8, no. 2 (September 30, 2019): 219. http://dx.doi.org/10.22460/infinity.v8i2.p219-228.
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Rapid development of technology for the past two decades has greatly influenced mathematic learning system. Mathematica software is one of the most advanced technology that helps learn math especially in Geometry. Therefore this research aims at investigating the effectiveness of analytic geometry learning by using Mathematica software on the mathematical abstraction ability, motivation, and independence of students. This research is a quantitative research with quasi-experimental method. The independent variable is learning media, meanwhile the dependent variables are students’ mathematical abstraction ability, motivation, and independence in learning. The population in this research was the third semester students of mathematics education program and the sample was selected using cluster random sampling. The samples of this research consisted of two distinct classes, with one class as the experimental class was treated using Mathematica software and the other is the control class was treated without using it. Data analyzed using multivariate, particularly Hotelling’s T2 test. The research findings indicated that learning using Mathematica software resulted in better mathematical abstraction ability, motivation, and independence of students, than that conventional learning in analytic geometry subject.
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Manouchehri, Azita, Mary C. Enderson, and Lyle A. Pugnucco. "Exploring Geometry with Technology." Mathematics Teaching in the Middle School 3, no. 6 (March 1998): 436–42. http://dx.doi.org/10.5951/mtms.3.6.0436.
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The study of geometry in grades 5-8 should incorporate opportunities for students to engage in exploring and analyzing geometric shapes to conjecture about geometric relationships through data collection and model construction, according to the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989). In this fashion, students will develop an intuitive understanding of geometric concepts and learn to reason formally and informally. Moreover, it is hoped that through such processes, students will formulate relevant definitions and theorems. The Standards document also encourages the use of computer technologies in middle school mathematics instruction. This suggestion was based on the assumption that interactive environments provided by appropriate geometry software have the potential to foster students' movement from concrete expetiences with mathematics to more formal levels of abstractions, nurture students' conjectuting spirit, and improve their mathematical thinking. Although the NCTM's visions for the geometry curriculum and for methods of teaching geometry in the middle levels are certainly attractive, many teachers are concerned about what software is useful for the middle school population, how such software can be used in instruction. what issues are associated with their use, and what the consequences are of learning and teaching mathematics within such environments.
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Robichaux, Rebecca R., and Paulette R. Rodrigue. "Using Origami to Promote Geometric Communication." Mathematics Teaching in the Middle School 9, no. 4 (December 2003): 222–29. http://dx.doi.org/10.5951/mtms.9.4.0222.
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Rigami has been used frequently in teaching geometry to promote the development of spatial sense; to make multicultural connections with mathematical ideas; and to provide students with a visual representation of such geometric concepts as shape, properties of shapes, congruence, similarity, and symmetry. Such activities meet the Geometry Standard (NCTM 2000), which states that students should be engaged in activities that allow them to “analyze characteristics and properties of twoand three-dimensional geometric shapes and develop mathematical arguments about geometric relationships” and to “use visualization, spatial reasoning, and geometric modeling to solve problems” (p. 41). This article begins with an explanation of the importance of communication in the mathematics classroom and then describes a middle school mathematics lesson that uses origami to meet both the Geometry Standard as well as the Communication Standard.
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Huse, Vanessa Evans, Nancy Larson Bluemel, and Rhonda Harris Taylor. "Making Connections: From Paper to Pop-Up Books." Teaching Children Mathematics 1, no. 1 (September 1994): 14–17. http://dx.doi.org/10.5951/tcm.1.1.0014.
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The goal of the elementary mathematics program is to create an environment that supports the active exploration of mathematical ideas while demonstrating the connections between mathematics and everyday life. Many elementary students have limited instruction in geometry, even though this subject is an essential element in the mathematics curriculum. Students with a background in geometry may be able to rec ite geometric facts but often cannot employ the information to visualize practical solutions to problems. The ideas that foiJow describe geometry-related activities that use an inexpensive manipulative, paper, to create a pop-up card.
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Lin, Qin, and Yumei Chen. "Deepening the Understanding of Mathematics with Geometric Intuition." Journal of Contemporary Educational Research 5, no. 6 (June 30, 2021): 36–40. http://dx.doi.org/10.26689/jcer.v5i6.2214.
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Geometric intuition is one of the core concepts introduced by the new mathematical curriculum standards. It aims to use intuition and intuitive materials to deepen the understanding of mathematics in mathematical cognition activities. It does not only play a role in the learning of “graphics and geometry,’ but its’ irreplaceable role also involves the whole process of mathematics education. Therefore, if teachers can skillfully use geometric intuition in the teaching process, classroom efficiency will be greatly improved.
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Bright, George W. "Teaching Mathematics with Technology: Logo and Geometry." Arithmetic Teacher 36, no. 5 (January 1989): 32–34. http://dx.doi.org/10.5951/at.36.5.0032.
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Interest in teaching geometry through Logo graphics is increasing. It seems reasonable to expect that geometry understandings will improve through exposure to such a visual environment, but the research has not given clear-cut evidence that the improvement is automatic. However, in two recent studies (Kelly, Kelly, and Miller 1986–87; Noss 1987) Logo showed a possible advantage in improving students' understanding of selected geometric concepts. This month's activities illustrate a way that teachers can give students explicit help in focusing on important geometric ideas.
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Carroll, William M. "Polygon Capture: A Geometry Game." Mathematics Teaching in the Middle School 4, no. 2 (October 1998): 90–94. http://dx.doi.org/10.5951/mtms.4.2.0090.
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The curriculum and evaluation standards for School Mathematics (NCTM 1989) calls for an increased role for geometry in the primary and middle school curricula. An important mathematical strand in its own right, geometry also provides opportunities to promote and assess mathematical communication, reasoning, and problem-solving skills. Unfortunately, many students lack the vocabulary and the conceptual understanding needed to desctibe geometric relationships. This atiicle describes a game, Capture the Polygons, that I have designed to help middle school students think about geometric properties and the relationships among them. A version of the game has been tested in firth- and sixth-grade classes as part of the field test of Fifth Grade Everyday Mathematics (Bell et al. 1995). Observations of classes playing the game, as well as feedback from their teachers, indicate that students find the game challenging but fun. Depending on the background of the students, it can be played at different levels of difficulty.
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Robertson, Stuart P. "Getting Students Actively Involved in Geometry." Teaching Children Mathematics 5, no. 9 (May 1999): 526–29. http://dx.doi.org/10.5951/tcm.5.9.0526.
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For the past three years, I have begun my school year by having students write a “mathematical autobiography.” We talk about what an autobiography is and what a mathematical autobiography might be like. The students write about their interactions with mathematics, how they feel about it, and what they have done in mathematics. Their writings often reveal that students view mathematics as computation. They write about addition, subtraction, multiplication, and division; which operations they like to do and which ones they do not like. One activity that I use to address their one-sided view of mathematics is a geometry unit, which gives another view of mathematics and highlights how geometry surrounds students every day.
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McClintock, Ruth. "Animating Geometry with Flexigons." Mathematics Teacher 87, no. 8 (November 1994): 602–6. http://dx.doi.org/10.5951/mt.87.8.0602.
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Viewing mathematics as communication is the second standard listed for all grade levels in the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). This emphasis underscores the need for nurturing language skills that enable children to translate nonverbal awareness into words. One way to initiate discussion about mathematical concepts is to use physical models and manipulatives. Standard 4 of the Professional Standards for Teaching Mathematics (NCTM 1991) addresses the need for tools to enhance discourse. The flexigon is a simple and inexpensive conversation piece that helps students make geometric discoveries and find language to share their ideas.
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Hangül, Tuğba, and Ozlem Cezikturk. "A practice for using Geogebra of pre-service mathematics teachers’ mathematical thinking process." New Trends and Issues Proceedings on Humanities and Social Sciences 7, no. 1 (July 2, 2020): 102–16. http://dx.doi.org/10.18844/prosoc.v7i1.4872.
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We aim to examine the pre-service mathematics teachers' mathematical problem-solving processes by using dynamic geometry software and to determine their evaluations based on experiences in this process. The design is document analysis, one of the qualitative research approaches. In the fall semester of the 2019–2020 academic year, a three-problem task was carried out in a classroom environment where everyone could use geogebra individually. A total of 65 pre-service mathematics teachers enrolled in the course of educational technology. This task includes questions that they would use, their knowledge of basic geometric concepts to construct geometrical relations and evaluations related to this process. Besides the activity papers of the prospective teachers, geogebra files were also examined. The result is pre-service mathematics teachers who are thought to have a certain level of mathematical background are found to have incorrect/incomplete information even in the most basic geometric concepts and difficulties with regard to generalisation.
Keywords: Dynamic geometry, geogebra, instructional technologies, mathematical thinking, teacher education.
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Vinogradova, Natalya. "Quick Reads: Let's Cut a Square." Mathematics Teaching in the Middle School 16, no. 6 (February 2011): 322–24. http://dx.doi.org/10.5951/mtms.16.6.0322.
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Geometry is one of the oldest branches of mathematics. Many important mathematical ideas and theorems are rooted in geometry and can be visualized using geometric interpretations. Students learn about shapes, their properties, and the methods of calculating perimeters and areas of basic shapes early in their school years. Geometry can and should be used to help students visualize and better understand a broad range of mathematical concepts. In the following activity, students use the concepts of area and length to help them understand an important algebraic idea.
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Moyer, Todd O. "Non-Geometry Mathematics and The Geometer's Sketchpad." Mathematics Teacher 99, no. 7 (March 2006): 490–95. http://dx.doi.org/10.5951/mt.99.7.0490.
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The Geometer's Sketchpad (GSP) is a well-known interactive geometry software package. Its usefulness in geometry instruction has been well researched (Choi-Koh 1999; Dixon 1997; Groman 1996; Lester 1996; Moyer 2003; Weaver and Quinn 1999). Finzer and Jackiw (1998) recommend the use of GSP as the dynamic manipulative for geometric concepts. GSP allows students to construct a figure, to perform measurements of lengths and angles, and then to “click and drag” any part or parts of that figure to look for change.
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Morgan, Frank, Edward R. Melnick, and Ramona Nicholson. "Activities: The Soap-Bubble-Geometry Contest." Mathematics Teacher 90, no. 9 (December 1997): 746–50. http://dx.doi.org/10.5951/mt.90.9.0746.
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For many students, playing with soap bubbles is a ritual of childhood. Others observe soap bubbles in action while washing the dishes or the dog. Working with soap bubbles in mathematics class allows students to recognize that mathematics can make common experiences more fascinating. The following soap-bubble-geometry contest allows students to mesh observation and mathematical reasoning and to discover that mathematics is much more than just number crunching. Apparently simple questions expose deep geometric concepts. Students find to their amazement that some simple questions have been answered only recently, by students, and that others remain unanswered today.
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Laing, David R., and Arthur T. White. "Exhibiting Connections between Algebra and Geometry." Mathematics Teacher 84, no. 9 (December 1991): 703–5. http://dx.doi.org/10.5951/mt.84.9.0703.
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NCTM's Curriculum and Evaluation Standards for School Mathematics (1989, 81) encourages the exploration of interconnections among mathematical ideas and the development of an appreciation of “the pervasive use and power of reasoning as a part of mathematics.” This article exhibits some connections between algebra and geometry and presents deductive arguments appropriate for the secondary school mathematics classroom.
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Klepikov, P. N. "Mathematical Modeling in Problems of Homogeneous (Pseudo)Riemaimian Geometry." Izvestiya of Altai State University, no. 1(111) (March 6, 2020): 95–98. http://dx.doi.org/10.14258/izvasu(2020)1-15.
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Currently, mathematical and computer modeling, as well as systems of symbolic calculations, are actively used in many areas of mathematics. Popular computer math systems as Maple, Mathematica, MathCad, MatLab allow not only to perform calculations using symbolic expressions but also solve algebraic and differential equations (numerically and analytically) and visualize the results. Differential geometry, like other areas of modern mathematics, uses new computer technologies to solve its own problems. The applying is not limited only to numerical calculations; more and more often, computer mathematics systems are used for analytical calculations. At the moment, there are many examples that prove the effectiveness of systems of analytical calculations in the proof of theorems of differential geometry.This paper demonstrates how symbolic computation packages can be used to classify neither conformally flat nor Ricci parallel four-dimensional Lie groups with leftinvariant (pseudo)Riemannian metric of the algebraic Ricci soliton with the zero Schouten-Weyl tensor.
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Taback, Stanley F. "Coordinate Geometry: A Powerful Tool for Solving Problems." Mathematics Teacher 83, no. 4 (April 1990): 264–68. http://dx.doi.org/10.5951/mt.83.4.0264.
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In calling for reform in the teaching and learning of mathematics, the Curriculum and Evaluation Standards for School Mathematics (Standards) developed by NCTM (1989) envisions mathematics study in which students reason and communicate about mathematical ideas that emerge from problem situations. A fundamental premise of the Standards, in fact, is the belief that “mathematical problem solving … is nearly synonymous with doing mathematics” (p. 137). And the ability to solve problems, we are told, is facilitated when students have opportunities to explore “connections” among different branches of mathematics.
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Okolica, Steve, and Georgette Macrina. "Integrating Transformation Geometry into Traditional High School Geometry." Mathematics Teacher 85, no. 9 (December 1992): 716–19. http://dx.doi.org/10.5951/mt.85.9.0716.
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The grades 9-12 section of NCTM's Curriculum and Evaluation Standards for School Mathematics defines transformation geometry as “the geometric counterpart of functions” (1989, 161). Further, the Standards document recognizes the importance of this topic to the high school mathematics curriculum by listing it among the “topics to receive increased attention” (p. 126). Also included on this list is the integration of geometry “across topics.”
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Imanah, Ulil Nurul. "KEMAMPUAN MAHASISWA CALON GURU MATEMATIKA DALAM MENYELESAIKAN SOAL OLIMPIADE MATEMATIKA PADA MATERI ALJABAR DAN GEOMETRI." Journal of Mathematics Education and Science 4, no. 1 (April 30, 2021): 37–40. http://dx.doi.org/10.32665/james.v4i1.177.
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This study aims to determine the ability of pre-service mathematics teachers to solve mathematics olympiad questions on algebra and geometry. This research is quantitative descriptive. The research subjects were mathematics education students at the Faculty of Teacher Training and Education at Majapahit Islamic University in semester V of the 2020-2021 academic year who had completed Mathematical Problem-Solving courses. The subjects that study mathematical problem-solving strategies and deepen elementary and secondary mathematics olympiad problems. The research subjects were 14 people. The instrument used was four questions at the high school level mathematics olympiad, consisting of 2 questions about algebra and two questions about geometry. Based on the results of the study, it was concluded that the ability of pre-service mathematics teachers in the Mathematics Education Study Program of the Faculty of Teacher Training and Education, Majapahit Islamic University in solving math Olympiad questions on algebra and geometry was in the sufficient category with an average score of 57.68 Abstrak Penelitian ini bertujuan untuk mengetahui kemampuan mahasiswa calon guru matematika dalam menyelesaikan soal olimpiade matematika pada materi aljabar dan geometri. Penelitian ini merupakan penelitian deskriptif kuantitatif. Subyek penelitian adalah mahasiswa pendidikan matematika Fakultas Keguruan dan Ilmu Pendidikan Universitas Islam Majapahit semester V tahun akademik 2020-2021 yang telah menyelesaikan perkuliahan Pemecahan Masalah Matematika, yaitu mata kuliah yang mempelajari tentang strategi pemecahan masalah matematika dan mendalami soal-soal olimpiade matematika tingkat dasar dan menengah. Subyek penelitian berjumlah 14 orang. Instrumen yang digunakan adalah 4 soal olimpiade matematika tingkat sekolah menengah, yang terdiri dari 2 soal materi aljabar dan 2 soal materi geometri. Berdasarkan hasil penelitian diperoleh simpulan bahwa kemampuan mahasiswa calon guru matematika di Prodi Pendidikan Matematika FKIP Universitas Islam Majapahit dalam menyelesaikan soal olimpiade matematika pada materi aljabar dan geometri berada pada kategori cukup dengan nilai rata-rata 57,68.
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Gunn, Charles. "Geometric Algebras for Euclidean Geometry." Advances in Applied Clifford Algebras 27, no. 1 (February 26, 2016): 185–208. http://dx.doi.org/10.1007/s00006-016-0647-0.
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Erickson, Timothy E. "Connecting Data and Geometry." Mathematics Teacher 94, no. 8 (November 2001): 710–14. http://dx.doi.org/10.5951/mt.94.8.0710.
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Geometrical ideas and representations often help us understand other areas of mathematics. For example, we might use area models for multiplying polynomials, for summing series, or for conditional probability calculations. But we can also use other areas of mathematics to help us understand a geometrical situation. This article describes an activity that was adapted from Erickson (2000, pp. 111–13), in which students use data analysis and mathematical modeling to obtain insight into a geometrical question. This activity explores a simple case of what is called the isoperimetric inequality. A Web search for that term can furnish additional information.
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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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Moyer, Patricia S., and Wei Shen Hsia. "Activities for Students: The Archaeological Dig Site: Using Geometry to Reconstruct the Past." Mathematics Teacher 94, no. 3 (March 2001): 193–201. http://dx.doi.org/10.5951/mt.94.3.0193.
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In secondary mathematics, students often see little connection between geometry and the real-life mathematical situations around them. When asked to describe geometric figures, their descriptions are sometimes no more than an identification of sides and angles. They have not had experience in using more than one property in a mathematical situation or in describing how two geometric properties are related. The van Hiele model of how students learn geometry proposes that students' understandings of geometry move from recognition to description to analysis (Fuys, Geddes, and Tischler 1988). For students to make this transition to analytic thinking, teachers need to create problem situations that enhance development of students' intuitive understandings. These investigations allow students to explore relationships among geometric shapes and to make conjectures about properties. The conjectures can then be stated formally as theorems.
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Ulfa, Maria, Ahmad Lubab, and Yuni Arrifadah. "Melatih Literasi Matematis Siswa dengan Metode Naive Geometry." Jurnal Review Pembelajaran Matematika 2, no. 1 (June 26, 2017): 81–92. http://dx.doi.org/10.15642/jrpm.2017.2.1.81-92.
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The aim of this research is to measure mathematical literacy skills of a student after mathematics learning processes using naive geometry method on the quadratic equation. This research is using quantitative methods. This research was implemented at SMP Ulul Albab. The mathematical literacy skills obtained from observation and mathematics literacy tests which refer to the mathematics literacy indicator. The tests were given after a teaching and learning process using naive geometry while observation was done during the learning process. The results show that 22.73% students have high mathematical literacy skill, 68.18% students have intermediate mathematical literacy, and 9.09% students who have low math skills literacy.
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Berger, Melvyn S. "Book Review: Modern geometry (Sovremennaya geometriya)." Bulletin of the American Mathematical Society 13, no. 1 (July 1, 1985): 62–66. http://dx.doi.org/10.1090/s0273-0979-1985-15366-2.
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Terc, Michael. "Coordinate Geometry—Art and Mathematics." Arithmetic Teacher 33, no. 2 (October 1985): 22–24. http://dx.doi.org/10.5951/at.33.2.0022.
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Our sutudents cry for self-expression, for a chance to see mathematics in action. Frequently, however, the structure of mathematics does not lend itself to individual style or variation. Problem solving can tend to be dull and monotonous rather than exciting and stimulating.
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Zbiek, Rose Mary. "The Pentagon Problem: Geometric Reasoning with Technology." Mathematics Teacher 89, no. 2 (February 1996): 86–90. http://dx.doi.org/10.5951/mt.89.2.0086.
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We value the use of technology in mathematics learning and teaching, and we want students to reason and to explore mathematical ideas in their mathematics courses. In recent years, such computing tools as The Geometer's Sketchpad (1991) and Cabri Geometry II (1994) allow us to devise and operate on geometric figures similarly as symbolic manipulators allow us to work with algebraic expressions. In this article, we call these tools figure manipulators. These tools make it possible for students to explore and connect geometric ideas from synthetic, analytic, and transformational perspectives. Yet we wonder how we can actually get this synthesis to happen in our classrooms. Our doubting colleagues, and we, question the effects of such experiences on our students' understanding of mathematics in general and of geometry in particular.
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Nyangeni, Nosisa P., and Michael J. Glencross. "Sex Differences in Mathematics Achievement and Attitude toward Mathematics." Psychological Reports 80, no. 2 (April 1997): 603–8. http://dx.doi.org/10.2466/pr0.1997.80.2.603.
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In a study of sex differences in mathematics achievement and attitude toward mathematics, a sample of 278 Standard 10 (Grade 12) students (95 boys and 183 girls) from seven senior secondary schools in the Umtata district of Transkei, South Africa, wrote tests in algebra and geometry and completed an attitude questionnaire. Analysis showed no significant difference between the mean scores of boys and girls in algebra but a significant difference between scores in geometry, with the mean score of boys being greater than that of girls. There was no significant difference between the mean scores of boys and girls on the Attitude Toward Mathematics scale, although boys had a significantly more positive Attitude Toward Geometry than girls. Significant low correlations were found between scores on Attitudes Toward Mathematics and scores in mathematics and between scores on Attitudes Toward Geometry and scores in geometry.
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Chazan, Daniel. "Implementing The Standards: Students' Microcomputer-Aided Exploration in Geometry." Mathematics Teacher 83, no. 8 (November 1990): 628–35. http://dx.doi.org/10.5951/mt.83.8.0628.
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Four important themes presented in the K–12 Curriculum and Evaluation Standards for School Mathematics (Standards) (NCTM 1989) are mathematics as problem solving, mathematics as communication, mathematics as reasoning, and mathematical connections. The high school component also stresses mathematical structure. Furthermore, the Standards calls for new roles for teachers and students and suggests that microcomputer technology can help support teachers and students in taking on these new roles.
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Wagner, Roy. "For Some Histories of Greek Mathematics." Science in Context 22, no. 4 (November 9, 2009): 535–65. http://dx.doi.org/10.1017/s0269889709990159.
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ArgumentThis paper argues for the viability of a different philosophical point of view concerning classical Greek geometry. It reviews Reviel Netz's interpretation of classical Greek geometry and offers a Deleuzian, post-structural alternative. Deleuze's notion of haptic vision is imported from its art history context to propose an analysis of Greek geometric practices that serves as counterpoint to their linear modular cognitive narration by Netz. Our interpretation highlights the relation between embodied practices, noisy material constraints, and operational codes. Furthermore, it sheds some new light on the distinctness and clarity of Greek mathematical conceptual divisions.
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Astafieva, Mariіa М., Dmytro M. Bodnenko, and Volodymyr V. Proshkin. "ВИКОРИСТАННЯ КОМП’ЮТЕРНО ОРІЄНТОВАНИХ ЗАСОБІВ ГЕОМЕТРІЇ У ПРОЦЕСІ ФОРМУВАННЯ КРИТИЧНОГО МИСЛЕННЯ МАЙБУТНІХ УЧИТЕЛІВ МАТЕМАТИКИ." Information Technologies and Learning Tools 71, no. 3 (June 29, 2019): 102. http://dx.doi.org/10.33407/itlt.v71i3.2449.
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The article proved that critical thinking is one of the most important and universal competences of a modern teacher of mathematics. It has been established that geometric disciplines, in particular constructive and projective geometries, have the greatest potential for this. The pedagogical technology of critical thinking formation of future teachers of mathematics by means of geometry has been developed. This technology consists of a target, content and legal, and control component. It was found out that the essential element of the technology at all stages (substantive and procedural, control and evaluation etc.) is the purposeful computer support, first of all, the use of computer tools for mathematical activity and communication. The possibilities of information and communication technologies have been disclosed. An expediency of computer support within the process formation of critical thinking of future teachers of mathematics has been proved. There are systems of dynamic geometry and cloud services, which help to make the process of critical thinking formation of future teachers of mathematics more effective by means of geometry. This is the visualization of geometric objects, concepts, connections (in particular, expressed by analytical constructs), statements, proofs; dynamic drawings; computer experiment for research (nomination and hypothesis testing); control of analytical transformations; fast and high-quality execution of necessary images that saves time; interactive tasks generation; providing unlimited communication. The implementation analysis of the developed technology by means of mathematical methods, in particular, on the basis of the theory of fuzzy sets, has been carried out. The effectiveness of computer support of the formation of critical thinking of future mathematics teachers by means of geometry has been revealed.
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Ningsih, Siska Candra, and Palupi Sri Wijayanti. "Efektivitas Penggunaan Bahan Ajar English Mathematics Melalui E-Learning terhadap Pemahaman Geometri Mahasiswa." Journal of Medives : Journal of Mathematics Education IKIP Veteran Semarang 2, no. 1 (January 1, 2018): 57. http://dx.doi.org/10.31331/medives.v2i1.508.
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Tujuan dari penelitian ini adalah untuk mengetahui efektivitas penggunaan bahan ajar English Mathematics melalui e-learning terhadap pemahaman geometri mahasiswa. Penelitian ini merupakan penelitian eksperimen semu (quasi experiment) dengan desain Pre-test and Post-test Group. Populasi dalam penelitian ini adalah seluruh mahasiswa Pendidikan Matematika yang mengambil mata kuliah English Mathematics pada tahun akademik 2016/2017 yang terdiri dari empat kelas. Sampel penelitian adalah salah satu kelasnya yang dipilih dengan teknik cluster random sampling. Pengumpulan data melalui tes pemahaman geometri yang dilakukan sebelum dan sesudah tindakan. Data hasil penelitian dianalisis menggunakan uji t one sample. Banyak kemudahan yang diperoleh dengan menggunakan e-learning diantaranya bahan ajar dapat diunggah sebelum pembelajaran di kelas, diskusi dapat dilakukan tak terbatas waktu dan ruang dan kuis online dapat dilakukan untuk mengetahui pemahaman mahasiswa. Hasil penelitian menunjukkan bahwa bahan ajar English Mathematics materi Geometri melalui e-learning efektif digunakan dalam pembelajaran terhadap pemahaman geometri mahasiswa.
Kata kunci: bahan ajar, English Mathematics, pemahaman geometri
ABSTRACT
This study aims to determine the effectivenes of learning material through e-learning in terms of student’s comprehension of geometry. This study is quasy experimental research with Pre-test and Post-test Group design. The population is all the Mathematics Education students who taked English Mathematics course in academic year 2016/2017. The sample consists of one class that is selected using random sampling. Data is collected by comprehension test of Geometry before and after treatment. Hypothesis test is anylized by t test one sample. There are some conveniences obtained using e-learning such as material learning can be uploaded before learning in the class, discussion can be done not limited by space and time, and online quiz can be done to know the student’s understanding. The result show that learning material of English Mathematics for Geometry theory through e-learning was effective in terms of student’s comprehension of Geometry.
Keywords: material learning, English Mathematics, comprehension of geometry
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Mistretta, Regina M. "Intersecting and Perpendicular Lines: Activities to Prevent Misconception." Mathematics Teaching in the Middle School 9, no. 2 (October 2003): 84–91. http://dx.doi.org/10.5951/mtms.9.2.0084.
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Although geometry is a component of the mathematics curriculum, students are not demonstrating strong conceptual knowledge of this subject. According to the Third International Mathematics and Science Study–Repeat (TIMSS-R) released December 5, 2000, U.S. students scored lower in geometry than they did in other mathematical subjects (Education USA 2000). Studies have shown that many students develop misconceptions and do not move beyond a simple visualization of geometric figures (Carroll 1998). For example, students recognize shapes by appearance rather than by the properties that they possess. Educators advocate a shift in emphasis from a geometry curriculum that is dominated by memorization of isolated facts and procedures to one that emphasizes conceptual understandings, multiple representations, and real-life applications (Reys et al. 2001).
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Crites, Terry W. "Connecting Geometry and Algebra: Geometric Interpretations of Distance." Mathematics Teacher 88, no. 4 (April 1995): 292–97. http://dx.doi.org/10.5951/mt.88.4.0292.
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Activities that demonstrate connections between geometry and algebra should be an Important part of the secondary school curriculum (NCTM 1989). Teachers should design lessons that allow students to investigate, discuss, and strengthen the natural ties that exist between these two areas of mathematics. Exploring topics from both a geometric and an algebraic perspective should be a constant feature of any mathematics curriculum
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Lipka, Jerry, Sandra Wildfeuer, Nastasia Wahlberg, Mary George, and Dafna Ezran. "Elastic Geometry and Storyknifing A Yup'ik Eskimo Example." Teaching Children Mathematics 7, no. 6 (February 2001): 337–43. http://dx.doi.org/10.5951/tcm.7.6.0337.
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Storytelling occurs across cultures but is not generally thought of as having a mathematical component; nor are other everyday activities, such as shopping for groceries, packing for a trip, or making a quilt. Each of these informal activities, however, contains embedded mathematics; in Yup'ik Eskimo storyknifing, the forms etched illustrate a relationship between mathematics and ethnomathematics (see fig. 1). Children usually do not see the relationship between their surroundings and activities and mathematics. Connecting the intuitive, visual, and spatial components of storyknifing, as well as other everyday and ethnomathematical activities, with mathematical reasoning is a way to adapt, enrich, and enlarge the types of problems and processes that elementary school students face when learning mathematics.
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Michasova, Milena. "Regional Implementation Experience of the “Soft” Model of Geometry Teaching Based on the Computer Experiment." Russian Digital Libraries Journal 23, no. 1-2 (March 3, 2020): 99–108. http://dx.doi.org/10.26907/1562-5419-2020-23-1-2-99-108.
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Some results of implementation of the “soft” model of geometry teaching in schools of Nizhny Novgorod region are considered. The realization is based on the ideas of experimental mathematics, according to which the content of educational materials (open problems in geometry) is selected and developed. In addition, it is contributing to the development of students’ intelligence. Thus, student models the geometric situation using open-source software actively, is mobile in the selection of the software, understands geometric facts and regularities, acquires the ability to argue (to analyze, to compare, to generalize, to make conclusions). The experience of the using computer experiments at geometry lessons is examined form psychodidactic approach’s point of view. The advantages of special educational tasks are proved: open problems in geometry, which are based on the “soft” model of teaching geometry using the ideas of experimental mathematics. The peculiarity of the proposed open problems in geometry is that they, being a projection of traditional closed classical problems in geometry, at the same time, firstly, provide the formation of the main components of the mental (cognitive, conceptual, metacognitive, intentional) experience of the student and, secondly, create conditions for the manifestation of individual cognitive styles of students. Enrichment of metacognitive experience is carried out by means of chains of tasks, which create conditions for formation of abilities to plan, predict and control the mathematical activity.
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Carson, Emily. "Kant on Intuition in Geometry." Canadian Journal of Philosophy 27, no. 4 (December 1997): 489–512. http://dx.doi.org/10.1080/00455091.1997.10717483.
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It's well-known that Kant believed that intuition was central to an account of mathematical knowledge. What that role is and how Kant argues for it are, however, still open to debate. There are, broadly speaking, two tendencies in interpreting Kant's account of intuition in mathematics, each emphasizing different aspects of Kant's general doctrine of intuition. On one view, most recently put forward by Michael Friedman, this central role for intuition is a direct result of the limitations of the syllogistic logic available to Kant. On this view, Kant's reasons for introducing intuition are taken to be logical or mathematical, rather than philosophical. The other tendency, which I shall try to develop here, emphasizes an epistemological or phenomenological role for intuition in mathematics arising out of what may loosely be called Kant's ‘antiformalism.’This paper, which focuses specifically on the case of geometry, falls into two parts. First, I consider Kant's discussion of intuition in the Metaphysical Exposition of the concept of space.
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Kurz, Terri L., H. Bahadir Yanik, and Mi Yeon Lee. "The Geometry of Scoliosis." Teaching Children Mathematics 21, no. 6 (February 2015): 372–75. http://dx.doi.org/10.5951/teacchilmath.21.6.0372.
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Scoliosis, the curvature of the spine, is a medical condition that often affects youth. This article provides students with an opportunity to explore the geometry behind the spine's curvature. Students will first develop a method for measuring curvature and then compare their method to the commonly used Cobb method. Contributors to iSTEM: Integrating Science Technology Engineering in Mathematic share ideas and activities that stimulate student interest in the integrated fields of science, technology, engineering, and mathematics (STEM) in K–grade 6 classrooms.
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Libow, Herb. "Explorations in Geometry: The “Art” of Mathematics." Mathematics Teacher 90, no. 5 (May 1997): 340–42. http://dx.doi.org/10.5951/mt.90.5.0340.
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We often pose a mathematical situation, concept, or theorem and do not proceed to explore it fully. We do not experience the thrill of chasing our intuitions, the excitement of meeting the unexpected, the uplift of clarifying ideas, the feeling of enlightenment and pride upon discovering something new to us, and the rush of succinctly capturing the essence of complexity. In short, we miss the artistic experience in one of our great arts—mathematics.
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Tyurin, N. A. "Algebraic Lagrangian geometry: three geometric observations." Izvestiya: Mathematics 69, no. 1 (February 28, 2005): 177–90. http://dx.doi.org/10.1070/im2005v069n01abeh000527.
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Ballmann, Werner. "Book Review: Riemannian Geometry and Geometric Analysis." Bulletin of the American Mathematical Society 37, no. 04 (April 19, 2000): 459–66. http://dx.doi.org/10.1090/s0273-0979-00-00869-7.
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Morrow, Lorna J., and Thomas E. Rowan. "Implementing The Standards: Geometry through the Standards." Arithmetic Teacher 38, no. 8 (April 1991): 21–25. http://dx.doi.org/10.5951/at.38.8.0021.
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An underlying view of mathematics education expressed in the Curriculum and Evaluation Standards (NCTM 1989) is that a student should be actively involved both mentally and physically in constructing his or her own mathematical knowledge: “The K-4 curriculum should actively involve children in doing mathematics. … [They should] explore, justify, represent, solve, construct, discuss, use, investigate, describe, develop, and predict” (NCTM 1989, 17).
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SCHLIMM, DIRK. "PASCH’S PHILOSOPHY OF MATHEMATICS." Review of Symbolic Logic 3, no. 1 (January 25, 2010): 93–118. http://dx.doi.org/10.1017/s1755020309990311.
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Moritz Pasch (1843–1930) gave the first rigorous axiomatization of projective geometry in his Vorlesungen über neuere Geometrie (1882), in which he also clearly formulated the view that deductions must be independent from the meanings of the nonlogical terms involved. Pasch also presented in these lectures the main tenets of his philosophy of mathematics, which he continued to elaborate on throughout the rest of his life. This philosophy is quite unique in combining a deductivist methodology with a radically empiricist epistemology for mathematics. By taking into consideration publications from the entire span of Pasch’s career, the latter decades of which he devoted primarily to careful reflections on the nature of mathematics and of mathematical knowledge, Pasch’s highly original, but virtually unknown, philosophy of mathematics is presented.
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Fitriani, Andhin Dyas. "PENGEMBANGAN MULTIMEDIA INTERAKTIF DALAM PEMBELAJARAN GEOMETRI UNTUK MENINGKATKAN KEMAMPUAN KOMUNIKASI CALON GURU SEKOLAH DASAR." EDUTECH 13, no. 2 (August 12, 2014): 236. http://dx.doi.org/10.17509/edutech.v13i2.3105.
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Abstract. Communication is an essential part of mathematics and mathematics education. Communication is also a way to share ideas and classify understanding. Geometry in elementary school (SD) on the one hand is a very strategic mathematics study to encourage mathematics learning towards appreciation and experience of learning by making the learning meaningful. Van Hiele suggests that there are three main elements in the teaching of geometry, namely time, teaching materials, and teaching methods applied. One of the things that hinder a student's geometric thinking skills is the teaching methods employed by teachers in the classroom. The role of teachers in the 21st century includes "teacher as learners - who always improve and renew their knowledge". Teachers should be able to create an independent learning atmosphere which captivates and attracts students to learn in a pleasant atmosphere. One technology that can be applied is learning multimedia. Multimedia in learning covers several aspects of the synergy between text, graphics, images and animation. The use of multimedia is expected to enhance the learning of mathematics as it allows a wider exploration and can improve the presentation of mathematical ideas.Keywords: Interactive Multimedia, Geometry, Communication CapabilitiesAbstrak, Komunikasi merupakan bagian yang esensial dari matematika dan pendidikan matematika. Komunikasi juga merupakan cara untuk berbagi gagasan dan mengklasifikasikan pemahaman.Geometri di sekolah dasar (SD) di satu pihak merupakan kajian matematika yang sangat strategis untuk mendorong pembelajaran matematika ke arah apresiasi dan pengalaman matematika dengan cara belajar matematika secara bermakna. Van Hiele mengemukakan bahwa terdapat tiga unsur utama dalam pengajaran geometri, yaitu waktu, materi pengajaran, dan metode pengajaran yang diterapkan. Salah satu hal yang menghambat kemampuan berpikir geometri seorang siswa adalah metode pengajaran yang diterapkan oleh guru di kelas. Peran guru pada abad ke-21 diantaranya adalah “teacher as learners – who always improve and renew theri knowledge”. Guru harus dapat menciptakan suatu pembelarajan yang berpotensi menciptakan suasana belajar mandiri, serta mampu memikat dan menarik siswa untuk belajar dalam suasana yang menyenangkan. Salah satu teknologi yang dapat diterapkan dalam pembelajaran adalah penggunaan multimedia dalam pembelajaran. Multimedia dalam pembelajaran mencakup beberapa aspek yang bersinergi antara teks, grafik, gambar dan animasi. Melalui multimedia diharapkan dapat meningkatkan proses belajar matematika karena memungkinkan eksplorasi yang lebih luas dan dapat memperbaiki penyajian ide-ide matematika.Kata Kunci : Multimedia interaktif, Geometri, Kemampuan Komunikasi
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Hamzić, Dina Kamber, and Zenan Šabanac. "Two plane geometry problems approached through analytic geometry." Mathematical Gazette 104, no. 560 (June 18, 2020): 255–61. http://dx.doi.org/10.1017/mag.2020.48.
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Geometry is a very interesting, applicable and beautiful part of mathematics. However, geometry is often difficult for students to understand and demanding for teachers to teach [1]. Constructing proofs in geometric problems turns out to be particularly difficult, even for high attaining students [2]. Sometimes, students do not even know where to start when trying to solve these [3].
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Duncan, Howard. "The Euclidean Tradition and Kant’s Thoughts on Geometry." Canadian Journal of Philosophy 17, no. 1 (March 1987): 23–48. http://dx.doi.org/10.1080/00455091.1987.10715898.
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While not paramount among Kant scholars, issues in the philosophy of mathematics have maintained a position of importance in writings about Kant’s philosophy, and recent years have witnessed a rejuvenation of interest and real progress in interpreting his views on the nature of mathematics. My hope here is to contribute to this recent progress by expanding upon the general tacks taken by Jaakko Hintikka concerning Kant’s writings on geometry.Let me begin by making a vile suggestion: Kant did not have a philosophy of mathematics. When Kant was writing about mathematics, essentially he was reporting the views of others. The texts provide sufficient evidence to make this suggestion plausible. Generally, when Kant writes about mathematics in his mature works, he does so in order to illustrate or argue for a philosophical point. There are important references to mathematical method in the preface to the 1787 edition of Critique of Pure Reason; however, Kant’s purpose is to describe those basic features of a method that he intended to incorporate in his theory of philosophical method: ‘our new method of thought, namely, that we can know a priori of things only what we ourselves put into them.’ Indeed, Kant makes it clear in this preface that he thought there to be no extant problems to be solved in mathematical methodology; such was the state of the science, he thought. It was for this reason that Kant felt some confidence in borrowing from this method to improve the state of metaphysics; it is also for this reason that one should not expect to find Kant engaging in basic research in mathematical methodology. Similarly, the material on syntheticity added to the second edition Introduction to Critique of Pure Reason occurs in the context of a discussion of the syntheticity of metaphysical principles; that the propositions of both disciplines are synthetic a priori lends credence to the extrapolation of some features from the mathematical method for use in developing a metaphysics. Many writers find a philosophy of mathematics in the ‘Transcendental Aesthetic’; it is clear, however, that in this section his concern is to support his theory of the nature of space, time, and sensation. What is said about geometry, for example, is restricted to those of its features relevant to the subjectivity of space. The other major discussion of mathematics and its method is found in the section, ‘Doctrine of Method.’ Here we find Kant’s fullest account of the mathematical method and of constructions. It must be borne in mind, though, that his purpose is to argue against views that the proper methods of mathematics and metaphysics (philosophy generally) are identical, that the disciplines differ in subject matter alone. The result of the discussion is not a theory of mathematical method, but an account of the method proper to the philosopher.2 Kant simply is mentioning certain features of mathematical method sufficient to support the claim that the philosopher cannot incorporate it lock, stock, and barrel.’ In short, we do not find a systematic theory of mathematics or its method described by Kant in the first Critique, nor do we find discussions of mathematics other than in contexts where philosophical positions are being developed. This holds for Kant’s other works, too.
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Tyurin, A. N. "Special Lagrangian geometry as slightly deformed algebraic geometry (geometric quantization and mirror symmetry)." Izvestiya: Mathematics 64, no. 2 (April 30, 2000): 363–437. http://dx.doi.org/10.1070/im2000v064n02abeh000287.
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Stuart, Trevor. "Editorial." Biographical Memoirs of Fellows of the Royal Society 60 (January 2014): 1–4. http://dx.doi.org/10.1098/rsbm.2014.0022.
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As is usual, the volumes of Biographical Memoirs contain much material of interest to the student of the mathematical, physical, engineering, biological and medical sciences. Often a memoir has been written in collaboration with another Academy or Society. In the present volume the memoir of Shiing-Shen Chern is an expanded version of an obituary notice by Nigel Hitchin that appeared in the Bulletin of the London Mathematical Society . Chern was a great geometer, who revolutionized differential geometry and whose mathematical tools are now common currency in geometry, topology and theoretical physics. His proof of the Gauss–Bonnet theorem, which was a pivotal event in the history of differential geometry, led to the importance of the Chern classes. Moreover. S.-S. Chern was extremely influential in the development of mathematics and geometry both in the USA, at the Institute of Advanced Study, Princeton, and Chicago and Berkeley, and in China, in Shanghai and Nankei.
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Ngirishi, Harrison, and Sarah Bansilal. "AN EXPLORATION OF HIGH SCHOOL LEARNERS’ UNDERSTANDING OF GEOMETRIC CONCEPTS." Problems of Education in the 21st Century 77, no. 1 (February 14, 2019): 82–96. http://dx.doi.org/10.33225/pec/19.77.82.
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There is much concern in South Africa about the poor performance of learners in mathematics, particularly in geometry. The aim of this research was to explore the understanding of basic geometry concepts by grade 10 and grade 11 learners in terms of the van Hiele’s levels of geometry thinking. The participants of the research were 147 learners from three high schools in a rural area in the south of KwaZulu Natal, South Africa. The results showed that the learners had difficulties with problems involving definitions of geometric terms, interrelations of properties and shapes, class inclusion and changing semiotic representations. It was also found that most of the learners were operating at the visual and the analysis levels of the van Hiele levels of geometric thinking. It is recommended that teachers should provide learners with tasks that require movements between semiotic representations, and to also focus attention on improving learners’ skills in proving aspects of mathematical relations. Keywords: geometry, high school, van Hiele theory, class inclusion, mathematical proof, necessary and sufficient conditions.
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Gavrilina, Olga V. "Integration of mathematics and informatics by means of geometry in primary school." Science and School, no. 5, 2020 (2020): 142–56. http://dx.doi.org/10.31862/1819-463x-2020-5-142-156.
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The article outlines the relevance of using geometric material as a means of integrating elementary school mathematics and computer science education. Peculiarities of teaching junior schoolchildren elements of geometry are considered. The analysis of mathematics and informatics programs in terms of geometric material content in the elementary mathematics course is carried out. The criteria for selecting the content of geometric material aimed at integrating elementary mathematics and computer science selected in the research process have been illustrated. A set of geometric tasks is presented, aimed at optimising the learning process and improving the quality of knowledge in the subject area of „Mathematics and Computer Science” when integrating primary school mathematics and computer science teaching. The study was based on an analysis of the psychological, pedagogical and methodological literature on the problem under study. The possibility of integrating mathematics and informatics by means of geometry in primary schools to make inter-subject connections was theoretically justified and practically confirmed. The integration of mathematics and computer science contributes to the implementation of inter-subject connections, since the student simultaneously uses knowledge from the field of mathematics, computer science, and computer knowledge. This leads to the formation of a scientific worldview.
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Jelatu, Silfanus, Maria Lim, and Maria Yasinta Ngoe. "Pengenalan Bentuk Geometri bagi Anak Usia Dini dan Sekolah Dasar Kelas Rendah Melalui Origami." Jurnal Pengabdian Pada Masyarakat 4, no. 2 (August 20, 2019): 195–202. http://dx.doi.org/10.30653/002.201942.134.
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INTRODUCTION TO THE GEOMETRY FORM OF EARLY AGE CHILDREN AND LOW-CLASS SCHOOL THROUGH ORIGAMI. Geometry is one of the subjects of mathematics taught from elementary school to the upper secondary level and continued in college. Geometry is also a mathematical subject that has a relationship with the real world or the world that is close to students. Introducing geometry to children is not necessary when children are in formal education, but they can get closer to geometry early. Limitation of geometry that can be given to early childhood is only on form recognition. The process is different, namely by entering the world of children or the world of the play. One that is relevant to accommodating this process is origami. Therefore, the purpose of this community service activity is to introduce geometric forms to early childhood through the game of origami. This activity was carried out in the village of Urang, Kec. Melak Kab. Manggarai NTT. The method used in this PKM activity is training that begins with a presentation. The results obtained from this activity indicate a change in choosing a game, as well as the existence of basic geometric abilities that can recognize geometric shape objects.