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Journal articles on the topic 'Visual algebra'

Author: Grafiati

Published: 4 June 2021

Last updated: 2 February 2022

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1

Iurato, Giuseppe. "Eye Movement Pre-Algebra and Visual Semantic Algebra." International Journal of Cognitive Informatics and Natural Intelligence 13, no. 1 (2019): 62–72. http://dx.doi.org/10.4018/ijcini.2019010105.

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This article proposes a new denotational mathematics entity, i.e., the eye movement pre-algebra (EMpA), which may be considered as a pre-algebraic structure in a certain sense generating, according to universal algebra, Husserlian phenomenological theory and structuralism, another basic algebraic structure of denotational mathematics, said to be visual semantic algebra (VSA).

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Wang, Yingxu. "On Visual Semantic Algebra (VSA)." International Journal of Software Science and Computational Intelligence 1, no. 4 (2009): 1–16. http://dx.doi.org/10.4018/jssci.2009062501.

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A new form of denotational mathematics known as Visual Semantic Algebra (VSA) is presented for abstract visual object and architecture manipulations. A set of cognitive theories for pattern recognition is explored such as cognitive principles of visual perception and basic mechanisms of object and pattern recognition. The cognitive process of pattern recognition is rigorously modeled using VSA and Real-Time Process Algebra (RTPA), which reveals the fundamental mechanisms of natural pattern recognition by the brain. Case studies on VSA in pattern recognition are presented to demonstrate VAS’ ex

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Kirshner, David. "The Visual Syntax of Algebra." Journal for Research in Mathematics Education 20, no. 3 (1989): 274–87. http://dx.doi.org/10.5951/jresematheduc.20.3.0274.

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A structured system of visual features can be seen to parallel the propositional hierarchy of operations usually associated with the parsing of algebraic expressions. Some students (proportionately more women than men) were found to depend on these visual cues in their syntactic decision making. Others were found to have access to sound propositional rules. Possible causes and consequences of these different syntactic representation styles are discussed.

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Kirshner, David. "The Visual Syntax of Algebra." Journal for Research in Mathematics Education 20, no. 3 (1989): 274. http://dx.doi.org/10.2307/749516.

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5

Huen, Y. K. "Visual algebra and its applications." International Journal of Mathematical Education in Science and Technology 28, no. 3 (1997): 333–44. http://dx.doi.org/10.1080/0020739970280303.

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6

Jackson, Tess, and Ron Goolsby. "VISUAL JUSTIFICATION OF ALGEBRA CONCEPTS." PRIMUS 6, no. 3 (1996): 209–20. http://dx.doi.org/10.1080/10511979608965824.

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7

Morelli, Lynn. "A Visual Approach to Algebra Concepts." Mathematics Teacher 85, no. 6 (1992): 434–37. http://dx.doi.org/10.5951/mt.85.6.0434.

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8

Shaverdian, Anna A., Hao Zhou, George Michailidis, and Hosagrahar V. Jagadish. "A Graph Algebra for Scalable Visual Analytics." IEEE Computer Graphics and Applications 32, no. 4 (2012): 26–33. http://dx.doi.org/10.1109/mcg.2012.62.

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9

Liao, Liang, and Stephen John Maybank. "Generalized Visual Information Analysis Via Tensorial Algebra." Journal of Mathematical Imaging and Vision 62, no. 4 (2020): 560–84. http://dx.doi.org/10.1007/s10851-020-00946-9.

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10

MIRAH MARIATI, NI PUTU AYU, NI LUH PUTU SUCIPTAWATI, and KARTIKA SARI. "ANALISIS PERCOBAAN FAKTORIAL UNTUK MELIHAT PENGARUH PENGGUNAAN ALAT PERAGA BLOK ALJABAR TERHADAP PRESTASI BELAJAR ALJABAR SISWA." E-Jurnal Matematika 2, no. 2 (2013): 1. http://dx.doi.org/10.24843/mtk.2013.v02.i02.p030.

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The experimental design was applied in research in many different fields of science, such as in education, as used in this study. Block algebra visual aids is a visual aids in the form of the geometry model used to concretize understanding the variables and constants in the algebra which is an abstract concept. This visual aids are used as a basis for factoring algebraic forms. In connection with this, the aims of this research is to determine the effect of the application of algebra block in student academic achievement in class VII in the field of algebra in schools categorized as private, S

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11

Peng Chen, Liang Zhou, Yingxue Yao, and Shengdong Gao. "A Visual Glove Based on Conformal Geometric Algebra." International Journal of Advancements in Computing Technology 4, no. 23 (2012): 499–506. http://dx.doi.org/10.4156/ijact.vol4.issue23.59.

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Honrales, Cynthia C. "Audio-Visual Approach to Remedial Instruction in Algebra." Journal of Social Sciences (COES&RJ-JSS) 6, no. 2S (2017): 1–7. http://dx.doi.org/10.25255/jss.2017.6.2s.1.7.

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13

Shen, Gang, Feng Liu, Zhengxin Fu, and Bin Yu. "Visual cryptograms of random grids via linear algebra." Multimedia Tools and Applications 77, no. 10 (2017): 12871–99. http://dx.doi.org/10.1007/s11042-017-4921-5.

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14

Velleman, Daniel J. "The Fundamental Theorem of Algebra: A Visual Approach." Mathematical Intelligencer 37, no. 4 (2015): 12–21. http://dx.doi.org/10.1007/s00283-015-9572-7.

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15

Darley, Joy W. "Traveling from Arithmetic to Algebra." Mathematics Teaching in the Middle School 14, no. 8 (2009): 458–64. http://dx.doi.org/10.5951/mtms.14.8.0458.

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16

Wu, Keqin, Liang Sun, Carl Schmidt, and Jian Chen. "Graph query algebra and visual proximity rules for biological pathway exploration." Information Visualization 16, no. 3 (2016): 217–31. http://dx.doi.org/10.1177/1473871616666394.

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We present the design and validation of an example-based pathway graph query algebra and visual proximity rules to address challenging large biological pathway exploration tasks. Our pathway graph query algebra interprets relationship queries given by selected examples to find a match for, extract identical parts between, or trace a path from any pathway components. To support the relationship query, users can composite pathway visualizations through visual proximity rules that use proximity to infer users’ intentions in the exploration process. By allowing selection of one or more objects fro

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17

Landy, David, David Brookes, and Ryan Smout. "Abstract numeric relations and the visual structure of algebra." Journal of Experimental Psychology: Learning, Memory, and Cognition 40, no. 5 (2014): 1404–18. http://dx.doi.org/10.1037/a0036823.

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18

López-Franco, Carlos, Nancy Arana-Daniel, and Alma Y. Alanis. "Visual Servoing on the Sphere Using Conformal Geometric Algebra." Advances in Applied Clifford Algebras 23, no. 1 (2012): 125–41. http://dx.doi.org/10.1007/s00006-012-0342-8.

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19

David, Maria Manuela, Vanessa Sena Tomaz, and Maria Cristina Costa Ferreira. "How visual representations participate in algebra classes’ mathematical activity." ZDM 46, no. 1 (2013): 95–107. http://dx.doi.org/10.1007/s11858-013-0550-2.

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20

Lee, Sang-Gu, Ji-Eun Jang, and Kyung-Won Kim. "Visualization of Linear Algebra concepts with Sage and GeoGebra." Communications of Mathematical Education 27, no. 1 (2013): 1–17. http://dx.doi.org/10.7468/jksmee.2013.27.1.001.

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21

Lin, Xiaoyu, and Yingxu Wang. "Simulation and Visualization of Concept Algebra in MATLAB." International Journal of Software Science and Computational Intelligence 6, no. 1 (2014): 30–55. http://dx.doi.org/10.4018/ijssci.2014010103.

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Concept algebra (CA) is a denotational mathematics for formal knowledge manipulation and natural language processing. In order to explicitly demonstrate the mathematical models of formal concepts and their algebraic operations in CA, a simulation and visualization software is developed in the MATLAB environment known as the Visual Simulator of Concept Algebra (VSCA). This paper presents the design and implementation of VSCA and the theories underpinning its development. Visual simulations for the sets of reproductive and compositional operations of CA are demonstrated by real-world examples th

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22

López-Franco, C., and E. Bayro-Corrochano. "Omnidirectional vision and conformal geometric algebra for visual landmark identification." Robotica 26, no. 5 (2008): 559–69. http://dx.doi.org/10.1017/s0263574707003967.

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SUMMARYThe automatic landmark identification is very important in autonomous robot navigation tasks. In this paper, we use a monocular omnidirectional vision system to extract the image features and the conformal geometric algebra to compute the projective invariants from such features. We show how these features can be used to compute projective and permutationp2-invariantsfrom any kind of omnidirectional vision system. Thep2-invariantsrepresent scene sublandmarks, and a set of them characterize a landmark. The advantage of this representation is that the landmarks are more robust than the si

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23

Bouck, Emily C., and Pei-Lin Weng. "Hearing Math: Algebra Supported eText for Students With Visual Impairments." Assistive Technology 26, no. 3 (2014): 131–39. http://dx.doi.org/10.1080/10400435.2013.870939.

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24

Shen, Gang, Feng Liu, Zhengxin Fu, and Bin Yu. "Perfect contrast XOR-based visual cryptography schemes via linear algebra." Designs, Codes and Cryptography 85, no. 1 (2016): 15–37. http://dx.doi.org/10.1007/s10623-016-0285-5.

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25

Apsari, Ratih Ayu, Sariyasa, R. I. I. Putri, S. Rejeki, and U. Lu’luilmaknun. "Same pattern, different visualization: visual support does matter in pre-algebra." Journal of Physics: Conference Series 1776, no. 1 (2021): 012026. http://dx.doi.org/10.1088/1742-6596/1776/1/012026.

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26

Abdelmajead, Ahmed S. "The Effect of Using Mathematical Correlations and Some Visual Teaching Strategies on the Levels of Information Processing and Self Evaluation of the Written Mathematical Knowledge Patterns of the First year Preparatory Students." Journal of Educational and Psychological Studies [JEPS] 7, no. 2 (2013): 167. http://dx.doi.org/10.24200/jeps.vol7iss2pp167-185.

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This research aimed at identifying the effect of using mathematical correlations and some visual teaching strategies on the levels of information processing and self-evaluation of the written mathematical knowledge patterns of the first year preparatory students. To achieve this aim, three groups were selected: two of them were experimental, and the third was a control one. An Algebra unit was taught to the experimental group (39 students) according to the mathematical correlations; and the second experimental group (38 students) studied the same content, according to some visual teaching stra

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27

Beigie, Darin. "Solving Optimization Problems with Spreadsheets." Mathematics Teacher 111, no. 1 (2017): 26–33. http://dx.doi.org/10.5951/mathteacher.111.1.0026.

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28

Sholihah, Ummu, and Maryono Maryono. "Students’ visual thinking ability in solving the integral problem." JRAMathEdu (Journal of Research and Advances in Mathematics Education) 5, no. 2 (2020): 175–86. http://dx.doi.org/10.23917/jramathedu.v5i2.10286.

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Visual thinking plays an essential role in solving problems and in learning mathematics. Many students do not understand how to graphically or geometrically represent problems and solve algebra problems. Visual thinking is the ability, process, and results of creating, interpreting, using, and imagining images and diagrams on paper or with technological tools, describing and communicating information and ideas, developing ideas, and understanding improvement. This research describes students’ visual thinking ability to solve integral problems. The approach used in this study was descriptive qu

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29

S., L. L., Andrew Blake, and Andrew Zisserman. "Visual Reconstruction." Mathematics of Computation 53, no. 188 (1989): 772. http://dx.doi.org/10.2307/2008745.

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30

Bennett, Albert B., and Eugene Maier. "A Visual Approach to Solving Mixture Problems." Mathematics Teacher 89, no. 2 (1996): 108–11. http://dx.doi.org/10.5951/mt.89.2.0108.

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In the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989), the 9–12 standards call for a shift from a curriculum dominated by memorization of isolated facts and procedures to one that emphasizes conceptual understandings, multiple representations and connections, mathematical modeling, and mathematical problem solving. One approach that affords opportunities for achieving these objectives is the use of diagrams and drawings. The familiar saying “A picture is worth a thousand words” could well be modified for mathematics to “A picture is worth a thousand numbers.” As an exam

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31

Burkhardt, Paula, Alice Zhuo-Yu Chan, Gabriel Currier, Stephan Ramon Garcia, Florian Luca, and Hong Suh. "Visual properties of generalized Kloosterman sums." Journal of Number Theory 160 (March 2016): 237–53. http://dx.doi.org/10.1016/j.jnt.2015.08.019.

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32

McGlaughlin, Sean M., Andrew J. Knoop, and Gregory A. Holliday. "Differentiating Students with Mathematics Difficulty in College: Mathematics Disabilities vs. No Diagnosis." Learning Disability Quarterly 28, no. 3 (2005): 223–32. http://dx.doi.org/10.2307/1593660.

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Difficulties with college algebra can be the gatekeeper for earning a degree. Students struggle with algebra for many reasons. The focus of study was to examine students struggling with entry-level algebra courses and differentiate between those who were identified as having a mathematics disability and those who were not. Variables related to working memory, math fluency, nonverbal/visual reasoning, attention, and reading were analyzed using a MANOVA and separate ANOVAs. Significant differences were found on all but attention, supporting the findings of research on students in elementary and

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33

GONZÁLEZ-JIMÉNEZ, LUIS ENRIQUE, ALEXANDER G. LOUKIANOV, and EDUARDO JOSE BAYRO-CORROCHANO. "DISCRETE INTEGRAL SLIDING MODE CONTROL IN VISUAL OBJECT TRACKING." International Journal of Humanoid Robotics 07, no. 03 (2010): 491–509. http://dx.doi.org/10.1142/s0219843610002167.

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Object tracking is an important process for many applications in computer vision. This process must be implemented in a discrete manner because the images are available only at certain periods. A discrete integral sliding mode algorithm is proposed to control a stereo vision system and perform the aforementioned second task. The kinematic model of the structure is obtained using geometric algebra. The performance of the controller is compared with proportional-integral-derivative control via simulation. The implementation for a pan tilt unit is presented in real time. The algorithm presents a

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34

WANG, YINGXU. "ON FORMAL AND COGNITIVE SEMANTICS FOR SEMANTIC COMPUTING." International Journal of Semantic Computing 04, no. 02 (2010): 203–37. http://dx.doi.org/10.1142/s1793351x10000833.

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Semantics is the meaning of symbols, notations, concepts, functions, and behaviors, as well as their relations that can be deduced onto a set of predefined entities and/or known concepts. Semantic computing is an emerging computational methodology that models and implements computational structures and behaviors at semantic or knowledge level beyond that of symbolic data. In semantic computing, formal semantics can be classified into the categories of to be, to have, and to do semantics. This paper presents a comprehensive survey of formal and cognitive semantics for semantic computing in the

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35

Marchetti, Elena, and Luisa Rossi Costa. "Reconstruction of Forms by Linear Algebra." Nexus Network Journal 7, no. 1 (2005): 58–68. http://dx.doi.org/10.1007/s00004-005-0006-2.

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36

Kreknin, V. A., and M. S. Lvov. "The Usage of Programming Software “The Library of Electronic Visual Aids “Algebra 7-9” During Algebra Learning in 7-9 Forms." Information Technologies in Education, no. 1 (April 12, 2008): 78–87. http://dx.doi.org/10.14308/ite000011.

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37

Flores, Alfinio. "Explorations with 142857: Connecting the Elementary with the Advanced." Mathematics Teacher 101, no. 6 (2008): 418–21. http://dx.doi.org/10.5951/mt.101.6.0418.

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Explorations with the cyclic number for students and teachers help connect the mathematics taught in school with algebra and number theory concepts learned in college. Additional ways to manipulate sequential numbers and how they relate create new sequences as well as graphical and visual representations are given.

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38

Booze, David A. "Delving Deeper: Visualizing Pythagorean Triples and Beyond." Mathematics Teacher 104, no. 5 (2010): 393–98. http://dx.doi.org/10.5951/mt.104.5.0393.

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Exploring the algebraic properties that form the framework for analytical generation of Pythagorean triples and quadruples is a challenging topic for high school algebra students. I have had considerable success in motivating my students to explore these properties by using a visual method. Students can use this visual method to find Pythagorean triples and quadruples easily and can capably and colorfully supply as many integer solutions as they desire to these well-known equations. Here I will present a visual method for producing integer solutions to the equations a2 + b2 = c2 and a2 + b2 +

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39

Booze, David A. "Delving Deeper: Visualizing Pythagorean Triples and Beyond." Mathematics Teacher 104, no. 5 (2010): 393–98. http://dx.doi.org/10.5951/mt.104.5.0393.

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Exploring the algebraic properties that form the framework for analytical generation of Pythagorean triples and quadruples is a challenging topic for high school algebra students. I have had considerable success in motivating my students to explore these properties by using a visual method. Students can use this visual method to find Pythagorean triples and quadruples easily and can capably and colorfully supply as many integer solutions as they desire to these well-known equations. Here I will present a visual method for producing integer solutions to the equations a2 + b2 = c2 and a2 + b2 +

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40

Munifah, Munifah, Annisa Nurhuda Romadhona, Ilma Ridhona, Rahmi Ramadhani, Rofiqul Umam, and Hasan Said Tortop. "How to Manage Numerical Abilities in Algebra Material?" Al-Jabar : Jurnal Pendidikan Matematika 10, no. 2 (2019): 223–32. http://dx.doi.org/10.24042/ajpm.v10i2.5325.

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Numerical ability is very help students understand the material, analyze any problems, and apply math concepts in daily life so that numerical abilities of students is a factor that can affect learning outcomes. Determine the effect of learning model Scramble and learning model with SAVI (Somatic, Auditory, Visual, and Intellegence) on the ability of numerical be the purpose of this article. The design of the research used Quasy Experimental Design, with the instrument used for the study in the form of test numerical ability. Data analysis used the T-test. Based on the results of the research

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41

Cairó, Osvaldo, and Karen Poblete. "KAMET II Conceptual Modeling Language, a Visual and Consistent Language Proved using Concept Algebra." Procedia Computer Science 60 (2015): 45–54. http://dx.doi.org/10.1016/j.procs.2015.08.103.

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42

Bouck, Emily C., Pei-Lin Weng, and Rajiv Satsangi. "Digital versus Traditional: Secondary Students with Visual Impairments’ Perceptions of a Digital Algebra Textbook." Journal of Visual Impairment & Blindness 110, no. 1 (2016): 41–52. http://dx.doi.org/10.1177/0145482x1611000105.

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43

Huo, Xinming, Tao Sun, Yimin Song, Yang Qi, and Panfeng Wang. "An analytical approach to determine motions/constraints of serial kinematic chains based on Clifford algebra." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 7 (2016): 1324–38. http://dx.doi.org/10.1177/0954406216643561.

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Determining the motions and constraints of serial kinematic chains in a concise and visual way is an inevitable step in the analysis and design of both serial and parallel mechanisms. The now most used method is the numerical approach which resorts to solving linear equations. By introducing Clifford algebra, this paper intends to propose an analytical approach to determine the unknown 6- n ( n < 6) constraints (motions) from the known n motions (constraints) of serial kinematic chains in different configurations only by drawing some auxiliary points, lines, and planes. The axes and action

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44

Hutchinson, Nancy L. "Effects of Cognitive Strategy Instruction on Algebra Problem Solving of Adolescents with Learning Disabilities." Learning Disability Quarterly 16, no. 1 (1993): 34–63. http://dx.doi.org/10.2307/1511158.

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This study investigated the effects of a two-phase cognitive strategy on algebra problem solving of adolescents with learning disabilities. The strategy was designed to enable students to represent and solve three types of word problems. The study used a modified multiple baseline with 11 replications as well as a two-group design. Conditions of the multiple-baseline design included baseline, instruction to mastery, transfer, and maintenance. Visual analysis of the single-subject data showed the strategy to be an effective intervention for this sample of students with deficits in algebra probl

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45

Abdulhamid, Mohanad, and Lwanga Wanjira. "Image Processing Techniques Based Crowd Size Estimation." Radioelectronics. Nanosystems. Information Technologies 12, no. 3 (2020): 407–14. http://dx.doi.org/10.17725/rensit.2020.12.407.

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Image processing algorithms are the basis for image computer analysis and machine Vision. Employing a theoretical foundation, image algebra, and powerful development tools, Visual C++, Visual Fortran, Visual Basic, and Visual Java, high-level and efficient computer vision techniques have been developed. This paper analyzes different image processing algorithms by classifying them in logical groups. In addition, specific methods are presented illustrating the application of such techniques to the real world images. In most cases more than one method is used. This allows a basis for comparison o

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46

On, Jin-Ho, Jung-Rhan Choi, and Moon-Kun Lee. "Visual Representation of Temporal Properties in Formal Specification and Analysis using a Spatial Process Algebra." KIPS Transactions:PartD 16D, no. 3 (2009): 339–52. http://dx.doi.org/10.3745/kipstd.2009.16-d.3.339.

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47

Bouck, Emily C., Nancy K. Meyer, Gauri S. Joshi, and Dave Schleppenbach. "Accessing Algebra via MathSpeak™: Understanding the Potential and Pitfalls for Students with Visual Impairments." Journal of Special Education Technology 28, no. 1 (2013): 49–63. http://dx.doi.org/10.1177/016264341302800105.

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48

Flores, Alfinio. "Delving Deeper: The Babylonian Method for Approximating Square Roots: Why Is It So Efficient?" Mathematics Teacher 108, no. 3 (2014): 230–35. http://dx.doi.org/10.5951/mathteacher.108.3.0230.

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Mathematicians from the Old Babylonian period (2000–1600 BC) knew a method for using a first approximation to the square root of a number to obtain a second, much better approximation. This article will show that their method is remarkably efficient. We use geometric algebra, much like the Babylonians might have done, to give a visual rationale for the method and its efficiency.

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Effendi, Leo Adhar, and Sindi Amelia. "Students’ Achievement Levels, Gender, and Learning Styles on Abstract Algebra: A Profile of Evidence Developing Ability." Mathematics Research and Education Journal 4, no. 1 (2020): 7–16. http://dx.doi.org/10.25299/mrej.2020.vol4(1).2776.

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Mathematics education students’ ability on developing evidence needs to be reviewed by lecturers. 50% of the subjects in the mathematics education departement require students' accuracy in analyzing mathematical statements. This is increasingly important because the Indonesian National Qualifications Framework (KKNI) for the Bachelor level requires graduates to become technicians / analysts. The diversity of levels of students’ ability, gender, and learning styles are assumsed to be the discrepancy abilities to develop evidence. This study aims to describe the evidence developing ability based

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50

Praveen, Kanakkath, Madathil Sethumadhavan, and Ramakrishnan Krishnan. "Visual cryptographic schemes using combined Boolean operations." Journal of Discrete Mathematical Sciences and Cryptography 20, no. 2 (2017): 413–37. http://dx.doi.org/10.1080/09720529.2015.1086067.

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