Computer visuality in mathematics teaching

Laxmi Rathour; Dragan Obradovic; Lakshmi Narayan Mishra; Vishnu Narayan Mishra

doi:10.59400/jam.v2i2.391

Computer visuality in mathematics teaching

Laxmi Rathour Department of Mathematics, National Institute of Technology, Chaltlang, Aizawl 796012, India
Dragan Obradovic Department of Mathematics and Informatics, Agricultural High School, 12000 Pozarevac, Serbia
Lakshmi Narayan Mishra Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, India
Vishnu Narayan Mishra Department of Mathematics, Faculty of Science, Indira Gandhi National Tribal University, Lalpur, Amarkantak 484887, India

Article ID: 391

924 Views

DOI: https://doi.org/10.59400/jam.v2i2.391

Keywords: mathematics; visualization; computers; tools for mathematics education; visual representation in mathematics

Abstract

The purpose of this study is to look at the changes that computers have made in mathematics itself and in the mathematics curriculum. The aim of the study is to investigate the various applications of computers in education in general, especially in mathematics education, and their application in the mathematics curriculum and in the teaching and learning of mathematics. The primary use of educational tools for mathematical purposes is the quality verification of results. There are various tools for developing student logic based on interactivity. Mathematics education tools are designed for innovative, interactive, and dynamic learning in different areas of mathematics. It is undeniable that the use of computers and mathematical software has great benefits that have been proven and presented in their works by numerous researchers of effective learning. It is also indisputable that one of the main tasks of teaching mathematics is the development of students’ constructive thinking. This work aims to describe the application of educational tools with which it can develop interactivity and help pupils and students to better and more clearly understand mathematics and to understand that it is all around us, that it is our everyday life.

References

[1]Carden J, Cline T. Problem solving in mathematics: the significance of visualisation and related working memory. Educational Psychology in Practice. 2015; 31(3): 235-246. doi: 10.1080/02667363.2015.1051660

[2]Wikipedia. Visualization (graphics). Available online: https://en.wikipedia.org/wiki/Visualization_(graphics) (accessed on 2 March 2024).

[3]Sean Whiteley. Using Visualization for Learning—by Sean Whiteley. Available online: https://trans4mind.com/counterpoint/index-creativitycareer/whiteley.shtml (accessed on 22 January 2019).

[4]Zhang D, Ding Y, Stegall J, et al. The Effect of Visual‐Chunking‐Representation Accommodation on Geometry Testing for Students with Math Disabilities. Learning Disabilities Research & Practice. 2012; 27(4): 167-177. doi: 10.1111/j.1540-5826.2012.00364.x

[5]Hatfield E. The Dangers of Intimacy. In: Derlega VJ (editors). Communication, Intimacy, and Close Relationships, 1st ed. Academic Pr; 1984. pp. 207-220. doi: 10.1016/b978-0-12-210840-2.50013-8

[6]Blok H, Oostdam R, Otter ME, et al. Computer-Assisted Instruction in Support of Beginning Reading Instruction: A Review. Review of Educational Research. 2002; 72(1): 101-130. doi: 10.3102/00346543072001101

[7]McWhaw K, Abrami PC. Student Goal Orientation and Interest: Effects on Students’ Use of Self-Regulated Learning Strategies. Contemporary Educational Psychology. 2001; 26(3): 311-329. doi: 10.1006/ceps.2000.1054

[8]Fuchs K. Computer Algebra—New Perspectives in Mathematics Education (German). University of Salzburg; 1998.

[9]Dundar S, Gokkurt B, Soylu Y. Mathematical Modelling at a Glance: A Theoretical Study. Procedia - Social and Behavioral Sciences. 2012; 46: 3465-3470. doi: 10.1016/j.sbspro.2012.06.086

[10]Doerr HM, Pratt D. The Learning of Mathematics and mathematical modeling. In: Heid MK, Blume GW (editors). Research on Technology in the Teaching and Learning of Mathematics: Syntheses, Cases, and Perspectives. Information Age Publishing; 2008. pp. 259-285.

[11]Gavrilovic J, Kovačevic IK, Savic A. Application of mathematical educational tools in the teaching process. In: Proceedings of the XI International Scientific-Professional Symposium Infotech-Jahorina 2012; 21-23 March 2012; Bosnia and Herzegovina.

[12]Smith B. Integrating Desmos Graphing Calculator into Middle School Mathematics Instruction. Journal of Computers in Mathematics and Science Teaching. 2017; 36(3): 221-234.

[13]Haugan M, Otting H. Using PhET Interactive Simulations in teaching probability in upper secondary school. International Journal of Mathematical Education in Science and Technology. 2016; 47(5): 697-709.

[14]Gikas J, Grant MM. Mobile computing devices in higher education: Student perspectives on learning with cellphones, smartphones & social media. The Internet and Higher Education. 2013; 19: 18-26. doi: 10.1016/j.iheduc.2013.06.002

[15]Mann S, Jai M, Jain S. Integrating Augmented Reality with Mathematics Education. International Journal of Interactive Mobile Technologies. 2019; 13(10): 50-61.

[16]Kaput JJ, Hegedus S. From Manipulative Materials to Inscriptions: Learning about Change in the Digital Age. In: Kelly AE, Lesh RA (editors). Handbook of Research Design in Mathematics and Science Education. Routledge; 2018. pp. 383-429.

[17]Eremin VV, Kuzmenko NE. ONICS 21st century, Peace and Education. Publishing House “Exam”; 2006.

[18]Mordkovitskh AG. Algebra 9th Section: Textbook, 4th ed. Institute for Facultative Education; 2002. p.192.

[19]Franzblau LE, Chung KC. Graphs, Tables, and Figures in Scientific Publications: The Good, the Bad, and How Not to Be the Latter. The Journal of Hand Surgery. 2012; 37(3): 591-596. doi: 10.1016/j.jhsa.2011.12.041

Published

2024-04-30

How to Cite

Rathour, L., Obradovic, D., Mishra, L. N., & Mishra, V. N. (2024). Computer visuality in mathematics teaching. Journal of AppliedMath, 2(2), 391. https://doi.org/10.59400/jam.v2i2.391

Download Citation

Issue

Vol. 2 No. 2 (2024)

Section

Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

Editor-in-Chief

Assoc. Prof. Ahmad Zeeshan

International Islamic University, Pakistan

eISSN

2972-4805

Publication Frequency

Bi-monthly

About the Publisher

Academic Publishing insists on taking academic exchange and publication as the main line, carrying out comprehensive management based on science and technology, and fully exploring excellent international publishing resources. Within 5 years, it will form a strategic framework and scale with science (S), technology (T), medicine (M), education (E), and humanities and arts (H) as the main publishing fields. Academic Publishing is headquartered in Singapore and based in Malaysia, with the United States and China providing the main scientific and academic resources. At the same time, it has established long-term good cooperative relations with other publishing companies, scientific research communities, and academic organizations in more than a dozen countries and regions. Academic Publishing uses English and Chinese as its main publishing languages, mainly publishing books, journals, and conference papers in print and online. The vast majority of publications follow the international open access policy, providing stable and long-term quality and professional publications. With the joint efforts of the expert team and our professional editorial team, our publications will gradually be indexed by international databases in stages to provide convenient and professional retrieval for various scholars. At the same time, manuscripts we accept will be subject to the peer review principle, and cutting-edge and innovative research articles will be preferentially accepted for peer reference and discussion. All kinds of our publications are welcome for peer to contribute, access, and download.

more

Volume Arrangement

2024

2023

Featured Articles

Octagonal-square tessellation model for masting GSM network: A case study of MTN Kumasi-East, Ghana

Masting in GSM network design is one of the most challenging problems in cell planning. The effect of uniform design pattern has been proven geographically to be hexagonal using uniform cell range. In this paper, we present a new uniform greedy semi-regular tessellation model called the octagonal square tessellation model (OSTM) to address the problem of global minimum overlap difference and area. Data from MTN Kumasi-East Ghana was collected and analyzed using the developed model. The original layout for the 0.6 km cell range accounted for an overlap difference of 937.66 m and a total area of 21.41 km² for 50 GSM mosts whereas the OSTM model accounted for an overlap difference of 1316.95 m with an area of 34.23 km². This is a 59.87% reduction of the original total area. Our solution is shown to be optimal in overlap difference and area for non-uniform cell range.

Computation of topological indices of linear chains of perylene and coronene using M-polynomial

The M-polynomial yields degree based topological indices that anticipate different physical and chemical properties of material being scrutinized. In this work, M- polynomial of linear chains of perylene and coronene are acquired. From M-polynomial, some degree based topological dicriptors are determined. Some topological indices of these compounds are compared by plotting graphs.

H∞ hybrid control and MRD in a steel frame building subjected to excessivevibrations caused by the dynamic action of wind and earthquake

The dynamic loads from earthquakes and winds can destroy lives, cause collapse in civil structures, and interrupt basic services provided to the population. In this scenario, structural designs must be developed to decrease the damage induced by these actions. The objective of this work is to design a hybrid controller based on the H∞ optimization via state feedback and the magneto-rheological damper (MRD) to mitigate the excessive vibrations of a three-story steel frame building, represented through the shear building model, subjected to the simultaneous dynamic action of wind and earthquake. All research is based on computational simulation, experimental research and results will not be addressed. In the numerical analysis, digital computer and MATLAB® software are used, and implemented codes generate the expected results based on the mathematical modeling. With the application of the H∞ control technique via state feedback, the displacements were reduced by 77%. With MRD this reduction was 79%. With the hybrid controller, this reduction was 100%. Thus, the verifications in relation to maximum displacements were met for NBR 15421:2006, NBR 8800:2008 and NBR 6118:2014. From the results, it is concluded that the hybrid controller proved to be more efficient and achieved the proposed objective. The exogenous inputs had zero influence on the behavior of the system output.

Topological analysis of multiple tables

The paper proposes a topological approach in order to explore several data tables simultaneously. These data tables of quantitative and/or qualitative variables measured on different homogeneous themes, collected from the same individuals. This approach, called topological analysis of multiple tables (TAMT), is based on the notion of neighborhood graphs in the context of a joint analysis of several data tables. It allows the simultaneous study of possible links between several thematic tables. The structure of the correlations or associations of the variables in each thematic table is analyzed according to quantitative, qualitative or mixed variables considered. Like the multiple factorial analysis (MFA), the TAMT allows several tables of variables to be analyzed simultaneously, and to obtain results, in particular graphical representations, which make it possible to study the relationship between individuals, variables and tables of data. These can also be tables of temporal data, collected at different times on the same individuals. The proposed TAMT approach is illustrated using real data associated with several and different homogeneous themes. Its results are compared to those from the MFA method.

Development of a stacked hybrid Decision Tree model leveraging the NSL-KDD dataset

Intrusion detection in information technology as well as operational technology networks is highly required in modern day systems due to the increased spate of cyber-attacks in both number and complexity. Anomaly-based intrusion detection systems which have the capacity to detect novel or zero-day attacks are highly employed in this regard. One important component of anomaly-based intrusion detection systems which ensures their behaviour is artificial intelligence in general and machine learning in particular. The burden in modern day cybersecurity research is to investigate and develop models that can outperform existing ones. This paper is aimed at developing a hybrid decision tree model using the stacking ensemble approach. Performances were measured on the basis of recall, precision, accuracy, F1-score, receiver operating characteristics and confusion matrices. The hybrid model presented a precision of 97%, accuracy of 81%, F1-score of 80% and AUC score of 0.96, respectively.