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Journal articles on the topic 'Geometric understanding'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Fan, Jianqing, Hui-Nien Hung, and Wing-Hung Wong. "Geometric Understanding of Likelihood Ratio Statistics." Journal of the American Statistical Association 95, no. 451 (September 2000): 836–41. http://dx.doi.org/10.1080/01621459.2000.10474275.

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2

Lei, Na, Dongsheng An, Yang Guo, Kehua Su, Shixia Liu, Zhongxuan Luo, Shing-Tung Yau, and Xianfeng Gu. "A Geometric Understanding of Deep Learning." Engineering 6, no. 3 (March 2020): 361–74. http://dx.doi.org/10.1016/j.eng.2019.09.010.

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3

Elia, Iliada, and Athanasios Gagatsis. "Young children's understanding of geometric shapes: The role of geometric models." European Early Childhood Education Research Journal 11, no. 2 (January 2003): 43–61. http://dx.doi.org/10.1080/13502930385209161.

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4

Hannibal, Mary Anne. "Young Children's Developing Understanding of Geometric Shapes." Teaching Children Mathematics 5, no. 6 (February 1999): 353–57. http://dx.doi.org/10.5951/tcm.5.6.0353.

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How can we improve geometry instruction at the preschool and primary levels? To answer that question, I conducted research to analyze young children's understanding of the geometric concepts of triangle and rectangle and to determine patterns in the development of this understanding from ages 3 through 6. The research suggests that early childhood educators need to rethink the way that basic shapes are introduced to young children. Since a basic understanding of shapes is essential to a future study of geometry, teachers need to focus on how best to help children develop that initial understanding of shape categories. After a brief explanation of the research, specific ways to present developmentally appropriate activities designed to enhance children's understanding of basic shapes are discussed.

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Arthur, John W. "Understanding geometric algebra for electromagnetic theory [Advertisement]." IEEE Antennas and Propagation Magazine 56, no. 1 (February 2014): 292. http://dx.doi.org/10.1109/map.2014.6821800.

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6

Özçakır, Bilal, Ahmet Sami Konca, and Nihat Arıkan. "Children';s Geometric Understanding through Digital Activities: The Case of Basic Geometric Shapes." International Journal of Progressive Education 15, no. 3 (June 3, 2019): 108–22. http://dx.doi.org/10.29329/ijpe.2019.193.8.

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7

Shaw, Jean M., Conn Thomas, Ann Hoffman, and Janis Bulgren. "Using Concept Diagrams to Promote Understanding in Geometry." Teaching Children Mathematics 2, no. 3 (November 1995): 184–89. http://dx.doi.org/10.5951/tcm.2.3.0184.

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The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) and the van Hiele model for geometric thought (Crowley 1987) advocate increasing students' understanding of geometric properties and relationships as they enter the intermediate anil middle grades.

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KAJIYAMA, Kiichiro. "Understanding of Pictortial Drawing with Incorrect Geometric Concept." Journal of Graphic Science of Japan 34, no. 1 (2000): 9–16. http://dx.doi.org/10.5989/jsgs.34.9.

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Soucy McCrone, Sharon M., and Tami S. Martin. "Assessing high school students’ understanding of geometric proof." Canadian Journal of Science, Mathematics and Technology Education 4, no. 2 (April 2004): 223–42. http://dx.doi.org/10.1080/14926150409556607.

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Andrews, Brock, Shane Brown, Devlin Montfort, and Michael P. Dixon. "Student Understanding of Sight Distance in Geometric Design." Transportation Research Record: Journal of the Transportation Research Board 2199, no. 1 (January 2010): 1–8. http://dx.doi.org/10.3141/2199-01.

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Dharmakumar, Rohan, and Graham A. Wright. "Understanding steady-state free precession: A geometric perspective." Concepts in Magnetic Resonance Part A 26A, no. 1 (2005): 1–10. http://dx.doi.org/10.1002/cmr.a.20033.

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Choi, Wongun, Yu-Wei Chao, Caroline Pantofaru, and Silvio Savarese. "Indoor Scene Understanding with Geometric and Semantic Contexts." International Journal of Computer Vision 112, no. 2 (November 12, 2014): 204–20. http://dx.doi.org/10.1007/s11263-014-0779-4.

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13

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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Burgess, Claudia R. "Untangling Geometric Ideas." Teaching Children Mathematics 20, no. 8 (April 2014): 508–15. http://dx.doi.org/10.5951/teacchilmath.20.8.0508.

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This geometry lesson uses the work of abstract artist Wassily Kandinsky as a springboard and is intended to promote the conceptual understanding of mathematics through problem solving, group cooperation, mathematical negotiations, and dialogue.

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15

de la Escalera, Arturo, and Jose Maria Armingol. "Vehicle detection and tracking for visual understanding of road environments." Robotica 28, no. 6 (December 10, 2009): 847–60. http://dx.doi.org/10.1017/s0263574709990695.

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SUMMARYMany of the advanced driver assistance systems have the goal of perceiving the surroundings of a vehicle. One of them, adaptive cruise control, takes charge of searching for other vehicles in order to detect and track them with the aim of maintaining a safe distance and to avoid dangerous maneuvers. In the research described in this article, this task is accomplished using an on board camera. Depending on when the vehicles are detected the system analyzes movement or uses a vehicle geometrical model to perceive them. After, the detected vehicle is tracked and its behavior established. Optical flow is used for movement while the geometric model is associated with a likelihood function that includes information of the shape and symmetry of the vehicle and the shadow it casts. A genetic algorithm finds the optimum parameter values of this function for every image. As the algorithm receives information from a road detection module some geometric restrictions are applied. Additionally, a multiresolution approach is used to speed up the algorithm. Examples of real image sequences under different weather conditions are shown to validate the algorithm.

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16

Bennett, Albert B. "Visualizing the Geometric Series." Mathematics Teacher 82, no. 2 (February 1989): 130–36. http://dx.doi.org/10.5951/mt.82.2.0130.

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FERNÁNDEZ, V. V., A. M. MOYA, and W. A. RODRIGUES. "GEOMETRIC ALGEBRAS AND EXTENSORS." International Journal of Geometric Methods in Modern Physics 04, no. 06 (September 2007): 927–64. http://dx.doi.org/10.1142/s0219887807002387.

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This is the first paper in a series (of four) designed to show how to use geometric algebras of multivectors and extensors to a novel presentation of some topics of differential geometry which are important for a deeper understanding of geometrical theories of the gravitational field. In this first paper we introduce the key algebraic tools for the development of our program, namely the euclidean geometrical algebra of multivectors [Formula: see text] and the theory of its deformations leading to metric geometric algebras [Formula: see text] and some special types of extensors. Those tools permit obtaining, the remarkable golden formula relating calculations in [Formula: see text] with easier ones in [Formula: see text] (e.g. a noticeable relation between the Hodge star operators associated to G and GE). Several useful examples are worked in details for the purpose of transmitting the "tricks of the trade".

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18

Thompson, Frances M. "Geometric Patterns for Exponents." Mathematics Teacher 85, no. 9 (December 1992): 746–49. http://dx.doi.org/10.5951/mt.85.9.0746.

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NCTM's Professional Standards for Teaching Mathematics suggests that “tasks that require students to reason and to communicate mathematically are more likely to promote their ability to solve problems and to make connections” with other mathematical ideas (1991, 24). Yet too frequently our classroom introductions to mathematics concepts and theorems demand little reasoning from students, leaving them unconvinced or with minimal understanding. Concrete, visual, or geometric models are seldom offered as aids, particularly when studying new numerical relations (Suydam 1984, 27; Bennett 1989, 130), even though many people depend heavily on visual stimuli for their learning, The challenge to the teacher is to select appropriate tasks and materials that will stimulate students to visualize and think about new mathematical concepts, thereby allowing them to develop their own understanding.

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19

Fox, Thomas. "Research, Reflection, Practice: Implications of Research on Children's Understanding of Geometry." Teaching Children Mathematics 6, no. 9 (May 2000): 572–76. http://dx.doi.org/10.5951/tcm.6.9.0572.

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In my mathematics methods course for preservice teachers, I ask my students to assess a group of elementary school students concerning their level of geometric reasoning. To do so, they use tasks that focus on assessing and extending students' geometric understandings. These open-ended tasks, along with a framework developed from research findings involving children's geometric reasoning, are described in this article. An important aspect of these tasks is that they focus on how students communicate their reasoning so that my preservice teachers can make more informed instructional decisions when planning a follow-up geometry lesson. Research on geometric reasoning has shown that a match between students' reasoning level and instructional tasks is crucial if meaningful learning is to occur (Crowley 1987).

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20

Halat, Erdoğan, and Ümmühan Yeşil Dağli. "Preschool Students' Understanding of a Geometric Shape, the Square." Bolema: Boletim de Educação Matemática 30, no. 55 (August 2016): 830–48. http://dx.doi.org/10.1590/1980-4415v30n55a25.

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Abstract The purpose of this study was to explore preschool children's conceptual understanding of geometric shapes, the square in particular. There were a total of 115 children, 61 girls and 54 boys, from state preschool education programs, who participated in the study. The data were collected in two semesters through interviews in a one-on-one setting, where the researchers administered a paper-pencil test to the participants. The test included six questions. One question asked children to draw a square, one question asked to select the square among three other geometric shapes, three questions asked to differentiate the square among five to seven geometric shapes which were printed in rotated directions and in various fonts and sizes and one question asked to identify a picture of a square-like real life object among a selection of pictures. The findings showed that 65% of children were able to draw a square accurately, and 77% of children were able to identify a picture of a square-like object. Approximately 69% were able to differentiate three squares in different sizes among five geometric shapes, while 27% of the remaining were not able to identify the square in smaller sizes. Approximately 79% in one task and 56% in another task were unsuccessful in identifying squares in rotated directions. Moreover, there was no gender difference in the test between boys and girls. Findings were interpreted linking to Duval's theory, van Hiele's theory, Prototype theory and Simon's task design model.

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21

Olive, John. "Logo Programming and Geometric Understanding: An In-Depth Study." Journal for Research in Mathematics Education 22, no. 2 (March 1991): 90–111. http://dx.doi.org/10.5951/jresematheduc.22.2.0090.

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The Logo work of 30 ninth-grade students was analyzed from three theoretical perspectives: the van Hiele levels of thinking, the SOLO taxonomy, and Skemp's model of mathematical understanding. Using computer dribble files of the students' Logo work, summary analyses across four tasks examined the Logo programming aspects and the geometric aspects of the tasks. Relationships among the three theoretical models and between Logo programming and geometric understanding emerged from the summary analyses. SOLO learning cycles in which students achieve relating level responses to a task are more likely to result in relational understanding of the task when students are able to approach the task with at least a transition towards descriptive level thought. Success in Logo programming appears to be necessary but not sufficient for success with the geometric aspects of the tasks. The results suggest the possibility of constructing an integrated model of teaching and learning based on the three theoretical perspectives.

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22

Hersberger, Jim, Gary Talsma, and James P. Herrmann. "Sharing Teaching Ideas: Improving Students' Understanding of Geometric Definitions." Mathematics Teacher 84, no. 3 (March 1991): 192–95. http://dx.doi.org/10.5951/mt.84.3.0192.

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As middle school mathematics teachers work to restructure a mathematics curriculum that now contains little in the way of new ideas or concepts (Flanders 1987), careful attention must be paid to pedagogical ideas that enhance and facilitate the attainment of newly developed curricular goals. In particular, even as a greater amount of class time is spent considering geometric topics, care must be taken to employ activities that help students attain higher levels of geometric understanding (Crowley 1987; Talsma and Hersberger 1990).

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23

Olive, John. "Logo Programming and Geometric Understanding: An In-Depth Study." Journal for Research in Mathematics Education 22, no. 2 (March 1991): 90. http://dx.doi.org/10.2307/749587.

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24

Sanders, Cathleen V. "Sharing Teaching Ideas: Geometric Constructions: Visualizing and Understanding Geometry." Mathematics Teacher 91, no. 7 (October 1998): 554–56. http://dx.doi.org/10.5951/mt.91.7.0554.

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Geometric constructions can enrich students’ visualization and comprehension of geometry, lay a foundation for analysis and deductive proof, provide opportunities for teachers to address multiple intelligences, and allow students to apply their creativity to mathematics.

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25

Weile, Daniel S. "Understanding Geometric Algebra for Electromagnetic Theory [Reviews and Abstracts]." IEEE Antennas and Propagation Magazine 55, no. 1 (February 2013): 149–52. http://dx.doi.org/10.1109/map.2013.6474507.

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26

Yanik, Huseyin Bahadir, and Alfinio Flores. "Understanding rigid geometric transformations: Jeff's learning path for translation." Journal of Mathematical Behavior 28, no. 1 (March 2009): 41–57. http://dx.doi.org/10.1016/j.jmathb.2009.04.003.

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27

Uwamahoro, Jean, Kizito Ndihokubwayo, Michael Ralph, and Irénée Ndayambaje. "Physics Students’ Conceptual Understanding of Geometric Optics: Revisited Analysis." Journal of Science Education and Technology 30, no. 5 (March 21, 2021): 706–18. http://dx.doi.org/10.1007/s10956-021-09913-4.

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28

Yao, Xiangquan, and Azita Manouchehri. "Teacher Interventions for Advancing Students’ Mathematical Understanding." Education Sciences 10, no. 6 (June 18, 2020): 164. http://dx.doi.org/10.3390/educsci10060164.

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The relationship between teacher interventions and students’ mathematical thinking has been the subject of inquiry for quite some time. Using the Pirie–Kieren theory for dynamic growth in mathematical understanding, this study documents teacher interventions that support students’ growth toward developing a general understanding of a mathematical idea in a designed learning environment. By studying the interactions of seven middle school students and the teacher-researcher working on a two-week unit on geometric transformations within a dynamic geometry environment, this study identified nine major categories of teacher interventions that support and extend students’ investigations of mathematical ideas around geometric transformations. The typology of teacher interventions reported in this study provides a cognition-based framework for teacher moves that extend and advance students’ mathematical understanding.

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29

Maarif, Samsul, Fitri Alyani, and Trisna Roy Pradipta. "The implementation of self-explanation strategy to develop understanding proof in geometry." JRAMathEdu (Journal of Research and Advances in Mathematics Education) 5, no. 3 (July 17, 2020): 262–75. http://dx.doi.org/10.23917/jramathedu.v5i3.9910.

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Proof is a key indicator for a student in developing mathematical maturity. However, in the process of learning proof, students have the difficulty of being able to explain the proof that has been compiled using good arguments. So we need a strategy that can put students in the process of clarifying proof better. One strategy that can explore student thought processes in explaining geometric proof is self-explanation strategy. This research aimed to analyze the ability to understand the geometric proof of prospective teacher students by implementing a self-explanation strategy in basic geometry classes. This study used a quasi-experimental research type of nonequivalent control group design. The participants of this research were 75 students of mathematics education study programs at one private university in Semarang. This research used four instrument tests of geometric proof. Before being used for research, the instruments were tested for validity and reliability using product-moment and Cronbach's alpha. Data analysis in this study used a two-way ANOVA test. The results showed that: the increased ability to understand the geometric proof of students who used self-explanation strategy was better than those who obtained direct learning; there was a significant difference between the increase of students’ mathematical proof ability in a group of students with a high and moderate level of initial mathematical ability; the initial ability (high, medium, low) of mathematics did not directly influence the learning process to improve the ability to understand the geometric proof. Hence, it can be concluded that the self-explanation strategy is effective to be used to improve the understanding of the geometric proof.

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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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Forni, D. M., M. S. Iriondo, C. N. Kozameh, and M. F. Parisi. "Understanding singularities in Cartan’s and null surface formulation geometric structures." Journal of Mathematical Physics 43, no. 3 (March 2002): 1584–97. http://dx.doi.org/10.1063/1.1408282.

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Ramdas, Aaditya, and Javier Peña. "Towards a deeper geometric, analytic and algorithmic understanding of margins." Optimization Methods and Software 31, no. 2 (November 13, 2015): 377–91. http://dx.doi.org/10.1080/10556788.2015.1099652.

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Wanko, Jeffrey J., and Jennifer V. Nickell. "Reinforcing Geometric Properties with Shapedoku Puzzles." Mathematics Teacher 107, no. 3 (October 2013): 188–94. http://dx.doi.org/10.5951/mathteacher.107.3.0188.

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Leonard, Alison E., and Nicole A. Bannister. "Dancing Our Way to Geometric Transformations." Mathematics Teaching in the Middle School 23, no. 5 (March 2018): 258–67. http://dx.doi.org/10.5951/mathteacmiddscho.23.5.0258.

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35

Gan, Wenbin, Xinguo Yu, and Mingshu Wang. "Automatic Understanding and Formalization of Plane Geometry Proving Problems in Natural Language: A Supervised Approach." International Journal on Artificial Intelligence Tools 28, no. 04 (June 2019): 1940003. http://dx.doi.org/10.1142/s0218213019400037.

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Automatically understanding natural language problems is a long-standing challenging research problem in automatic solving. This paper models the understanding of geometry problems as a problem of relation extraction, instead of as the problem of semantic understanding of natural language. Then it further proposes a supervised machine learning method to extract geometric relations, targeting to produce a group of relations to represent the given geometry problem. This method identifies the actual geometric relations from the relation candidates using a classifier trained from the labelled examples. The formalized geometric relations can then be transformed into the target system-native representations for manipulation in various tasks. Experiments conducted on the test problem dataset show that the proposed method can extract geometric relations at high F1 scores. The comparisons also demonstrate that the proposed method can achieve good performance against the baseline methods. Integrating the automatic understanding method with different geometry systems will greatly enhance the efficiency and intelligence in geometry tutoring.

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Friel, Susan N., and Kimberly A. Markworth. "A Framework for Analyzing Geometric Pattern Tasks." Mathematics Teaching in the Middle School 15, no. 1 (August 2009): 24–33. http://dx.doi.org/10.5951/mtms.15.1.0024.

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Lelinge, Balli, and Christina Svensson. "TEACHERS’ AWARENESS AND UNDERSTANDING OF STUDENTS’ CONTENT KNOWLEDGE OF GEOMETRIC SHAPES." Problems of Education in the 21st Century 78, no. 5 (October 5, 2020): 777–98. http://dx.doi.org/10.33225/pec/20.78.777.

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Few research studies have been conducted in a primary school in early mathematical education about the teaching of geometry. This research aims to contribute with knowledge of how teachers’ awareness and understanding of necessary conditions to enhance students’ abilities to discern two- and three-dimensional shapes develop. In this research, qualitative methods were used to analyse data from a lesson study in grade 4 in the subject of mathematics. Data were primarily collected through audio-recorded conversations with teachers before and after the lesson, and the results of students’ pre- and post-test. The results of this research showed increased awareness of using collaboration opportunities to apply professional classroom instructions and activities to enhance students’ knowledge of two- and three-dimensional shapes. This research elucidates how the practice-based professional development approach emphasised the teachers’ teaching targets for understanding students’ content knowledge of geometric shapes. Additionally, the result highlighted teachers’ awareness and understanding of the challenges students face in learning about three-dimensional shapes from two-dimensional representations. Future research should develop a more iterative and revised research lesson design to develop more powerful content knowledge and classroom activity in this topic area. Keywords: early mathematics education, geometric shapes, practice-based professional development, lesson study

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Strutchens, Marilyn E., Kimberly A. Harris, and W. GARY Martin. "Take Time for Action: Assessing Geometric and Measurement Understanding Using Manipulatives." Mathematics Teaching in the Middle School 6, no. 7 (March 2001): 402–5. http://dx.doi.org/10.5951/mtms.6.7.0402.

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Studying geometry benefits students in a number of ways. Geometry enables students to represent and make sense of the world, analyze and solve problems, and represent abstract symbols pictorially to facilitate understanding (NCTM 2000). Similarly, measurement establishes important connections between school mathematics and everyday life. However, students often have very little understanding of geometry and measurement concepts (Martin and Strutchens, in press). More often than not, students are asked to memorize geometric properties rather than to experience geometry through nature walks or worthwhile tasks that involve hands-on explorations. Further, students learn measurement through memorizing formulas rather than exploring the underlying concepts.

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Lejeune, Emma, Ali Javili, and Christian Linder. "Understanding geometric instabilities in thin films via a multi-layer model." Soft Matter 12, no. 3 (2016): 806–16. http://dx.doi.org/10.1039/c5sm02082d.

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In thin films, the contribution of inhomogeneities due to interfacial regions with finite thickness cannot be ignored. We introduce a multi-layer model for wrinkling initiation in thin films adhered to compliant substrates as an analytical solution verified by numerical results.

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Hedrick, Brandon P., and Peter Dodson. "Lujiatun Psittacosaurids: Understanding Individual and Taphonomic Variation Using 3D Geometric Morphometrics." PLoS ONE 8, no. 8 (August 9, 2013): e69265. http://dx.doi.org/10.1371/journal.pone.0069265.

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41

Mason, Marguerite M. "The Vanx Hiele Model of Geometric Understanding and Mathematically Talented Students." Journal for the Education of the Gifted 21, no. 1 (October 1997): 38–53. http://dx.doi.org/10.1177/016235329702100103.

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Mathematically talented students typically begin the traditional precalculus sequence by completing Algebra I in seventh grade or earlier. Consequently, they enroll in geometry early based on their successful completion of Algebra I. Little or no attention is paid to their readiness for geometry as indicated by such measures as their van Hiele level of geometric understanding. Logical reasoning ability is a characteristic often used to identify mathematically talented students, but how it applies to reasoning about geometry is unknown. This study investigated the geometric understanding and reasoning about geometry of mathematically talented students in the sixth through eighth grades prior to a formal course in geometry. This paper describes and analyzes the responses from 120 students who completed the van Hiele Geometry Test, developed by the Cognitive Development and Achievement in Secondary School Geometry Project (Usiskin, 1982), and 64 students who participated in 30–45 minute individual interviews, using an abbreviated version of Mayberry's van Hiele protocols.

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42

Skordialos, Emmanouil, and Georgios Baralis. "A teaching approach of geometric shapes’ properties with the use of online educational tools in Greek primary school." New Trends and Issues Proceedings on Humanities and Social Sciences 4, no. 9 (January 11, 2018): 101–9. http://dx.doi.org/10.18844/prosoc.v4i9.3044.

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A number of researchers have shown concern at the difficulties that primary school pupils cope with in learning geometry, and have tried to explain why this happens and what can be done to make the subject more understandable to young learners. Van Hiele’s theoretical model postulates five levels of geometric thinking as visualisation, analysis, abstraction, formal deduction and rigour. Each level uses its own language and symbols. Pupils pass through the levels ‘step by step’. This hierarchical order helps them to achieve better understanding and results. In this research the teacher taught geometry in the 2nd class in a primary Greek school with the use of information and communication technologies. The aim is to find out the level of geometrical thought of the pupils and how geometrical activities – based on online tools – concerning the geometrical shapes and their properties, help students improve their mathematical knowledge in the class. Keywords: Geometric thinking, online tools, shapes, geometrical activities

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43

Sari, Puspita. "GeoGebra as a Means for Understanding Limit Concepts." Southeast Asian Mathematics Education Journal 7, no. 2 (December 29, 2017): 71–84. http://dx.doi.org/10.46517/seamej.v7i2.55.

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Limit is a major concept in calculus that underpins the concepts of derivatives and integrals. The common misconception about limits is that students treat the value of a limit of a function as the value of a function at a point. This happens because usually the teaching of limit only leads to a procedural understanding (Skemp, 1976) without a proper conceptual understanding. Some researchers suggest the importance of geometrical representations to a meaningful conceptual understanding of calculus concepts. In this research, GeoGebra as a dynamic software is used to support students’ understanding of limit concepts by bridging students' algebraic and geometrical thinking. In addition to this, realistic mathematicseducation (RME) is used as a domain theory to develop an instructional design regarding how GeoGebra could be used to illustrate and explore the limit concept of so that students will have a meaningful understanding both algebraically and geometrically. Therefore, this research aims to explore the hypothetical learning trajectory in order to develop students’ understanding of limit concepts by means of GeoGebra and an approach based on RME.The results show that students are able to solve limit problems and at the same time they try to make sense of the problem by providing geometrical representations of it. Thus, the use of geometric representations by GeoGebra and RME approach could provide a more complete understanding of the concepts of limit. While the results are interesting and encouraging and provide some promising directions, they are not a proof and a much larger study would be needed to determine if the results are due to this approach or due to the teachers’ enthusiasm, the novelty effect or what is known as the Hawthorne Effect.

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Pezzulla, Matteo, Steven A. Shillig, Paola Nardinocchi, and Douglas P. Holmes. "Morphing of geometric composites via residual swelling." Soft Matter 11, no. 29 (2015): 5812–20. http://dx.doi.org/10.1039/c5sm00863h.

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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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Jiang, Sen, Hua Ji, Tianhao Wang, Donglin Feng, and Qian Li. "Enhanced understanding of leakage in mechanical seals with elliptical dimples based on CFD simulation." Industrial Lubrication and Tribology 72, no. 1 (August 22, 2019): 24–30. http://dx.doi.org/10.1108/ilt-03-2019-0087.

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Purpose The shapes of surface textures have been designed to control the leakage of mechanical seals in recent years. The purpose of this paper is to demonstrate the influence of geometric properties of elliptical dimples on the leakage rate. Design/methodology/approach A new geometric feature point is expressed using an analytical solution to locate the high-pressure zones. Furthermore, a numerical model of the three-dimensional flow field for the mechanical seal with elliptical dimples is developed using ANSYS Fluent to demonstrate the influencing mechanism. Findings The location of the proposed geometric converging point coincides with the maximum pressure point under different orientation angles. An inward flow on the leakage section observed from the simulation results is responsible for decreasing the leakage rate. Originality/value The influencing mechanism of the elliptical dimple on the leakage rate is demonstrated, which can facilitate the design of surface textures.

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(Chris) Renne, Christine G. "Is a Rectangle a Square? Developing Mathematical Vocabulary and Conceptual Understanding." Teaching Children Mathematics 10, no. 5 (January 2004): 258–63. http://dx.doi.org/10.5951/tcm.10.5.0258.

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Desiring to better encourage students' thinking and conceptual development, a fourth-grade teacher examines classroom discourse and written work during her students' analysis and description of basic geometric shapes.

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Baldwin, Elizabeth, and Paul Klemperer. "Understanding Preferences: “Demand Types”, and the Existence of Equilibrium With Indivisibilities." Econometrica 87, no. 3 (2019): 867–932. http://dx.doi.org/10.3982/ecta13693.

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An Equivalence Theorem between geometric structures and utility functions allows new methods for understanding preferences. Our classification of valuations into “Demand Types” incorporates existing definitions (substitutes, complements, “strong substitutes,” etc.) and permits new ones. Our Unimodularity Theorem generalizes previous results about when competitive equilibrium exists for any set of agents whose valuations are all of a “demand type.” Contrary to popular belief, equilibrium is guaranteed for more classes of purely‐complements than of purely‐substitutes, preferences. Our Intersection Count Theorem checks equilibrium existence for combinations of agents with specific valuations by counting the intersection points of geometric objects. Applications include matching and coalition‐formation, and the “Product‐Mix Auction” introduced by the Bank of England in response to the financial crisis.

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Rodríguez, Claudia Orozco, Erla M. Morales Morgado, and Filomena Gonçalves da Silva Cordeir Moita. "Learning Objects and Geometric Representation for Teaching “Definition and Applications of Geometric Vector”." Journal of Cases on Information Technology 17, no. 1 (January 2015): 13–30. http://dx.doi.org/10.4018/jcit.2015010102.

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Often during the teaching of mathematics, students have difficulties to understand some abstract concepts. That's why it is necessary to show the student the concepts as clearly and definitely as possible. The proposal of this project is a teaching strategy. It is the use of Geometric Representation integrated Learning Objects for the internalization of concepts. The research process involves the design, development, and evaluation of Learning Objects and how it promotes understanding of the contents of the topic “Real Geometric Vectors and their application”. At the beginning of this article are the context and the latest research concerning to this project. Then an overview of the theoretical framework that supports this work is shown. Finally, the paper describes the methodology used in the project, results of data, expected contributions and conclusions.

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Liu, Qing Tang, Huan Huang, and Lin Jing Wu. "Using Restricted Natural Language for Geometric Construction." Applied Mechanics and Materials 145 (December 2011): 465–69. http://dx.doi.org/10.4028/www.scientific.net/amm.145.465.

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Human-Computer Interaction is crucial for Instructional Software. It is significant to make Geometry Instructional Software understand geometric proposition described by natural language and construct geometric figure automatically. However, it is difficult for computer to accurately understand the flexible and variable geometric proposition because of the immaturity of Natural Language Processing Technology. This paper defines a restricted geometric proposition, presents a corresponding comprehension model based on ontology, and designs a matching algorithm for geometric relation pattern, finally transforms the restricted geometric proposition to geometric construction command sequence. The experiment results suggest that the average accuracy of understanding clauses of geometric proposition is almost to 88.9%, and the percentage of constructing correct geometric figure is to 82.5%.

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