RESEARCH PAPER
Figurative Numbers Contribution in Perceiving the Legality in Numerous Strings Tasks and Long-term Memory of Numerous Data
 
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Faculty of Mathematics and Computer Science, Alfa BK University, Belgrade, SERBIA
 
2
Faculty of Science and Mathematics, University of Priština, Kosovska Mitrovica, SERBIA
 
 
Online publication date: 2019-01-27
 
 
Publication date: 2019-01-27
 
 
EURASIA J. Math., Sci Tech. Ed 2019;15(4):em1692
 
KEYWORDS
ABSTRACT
Contemporary mathematics teaching is mostly reduced to the application of algebraic formulas and algebraic procedures. The visual-logical approach in solving mathematical tasks is very little represented in teaching mathematics. Such practice should be changed since visualization is of great importance in the process of learning and understanding mathematics as well as in solving mathematical tasks. This paper suggests the possibility of developing students’ ability to perceive lawfulness among numbers by introducing figurative numbers in mathematics teaching. Considering the visual presentation of figurate numbers and obvious rules among their members, students find them interesting and easy for understanding. They can also be a very good paradigms for many tasks with numerous arrays. The research carried out in this paper has shown that figurative numbers contribute to a visual-logical approach in solving tasks with numerous arrays and provide long-term storage of numerous data.
 
REFERENCES (47)
1.
Allegra, M., Chifari, A., & Ottaviano, S. (2001). ICT to train students towards creative thinking. Educational Technology & Society, 4(2), 48-53.
 
2.
Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational studies in mathematics, 52(3), 215-241. https://doi.org/10.1023/A:1024....
 
3.
Bakar, K. A., Ayub, A. F. M., & Tarmizi, R. A. (2010). Utilization of computer technology in learning transformation. International Journal of Education and Information Technologies, 4(2), 91-99.
 
4.
Beery, J. L. (2009). Formulating figurate numbers. BSHM Bulletin: Journal of the British Society for the History of Mathematics, 24(2), 78-91. https://doi.org/10.1080/174984....
 
5.
Bennett, M. A. (1997). Effective measures of irrationality for certain algebraic numbers. Journal of the Australian Mathematical Society, 62(3), 329-344. https://doi.org/10.1017/S14467....
 
6.
Bozkurt, G., & Ruthven, K. (2017). Classroom-based professional expertise: A mathematics teacher’s practice with technology. Educational Studies in Mathematics, 94(3), 309-328. https://doi.org/10.1007/s10649....
 
7.
Braza, P. A., & Tong, J. (2001). 85.25 Square–triangular numbers, revisited. The Mathematical Gazette, 85(503), 270-273. https://doi.org/10.2307/362201....
 
8.
Brindza, B., Pintér, Á., & Turjányi, S. (1998). On equal values of pyramidal and polygonal numbers. Indagationes Mathematicae, 9(2), 183-185. https://doi.org/10.1016/S0019-....
 
9.
Caglayan, G. (2014). Visualizing number sequences: Secondary preservice mathematics teachers’ constructions of figurate numbers using magnetic color cubes. The Journal of Mathematical Behavior, 35, 110-128. https://doi.org/10.1016/j.jmat....
 
10.
Chai, C. S., Lim, W. Y., So, H. J., & Cheah, H. M. (2011). Advancing collaborative learning with ICT: Conception, cases and design. Retrieved from http://ictconnection.edumall.s....
 
11.
monographs/advancing%20collaborative,2.
 
12.
da Silva Figueira-Sampaio, A., dos Santos, E. E. F., & Carrijo, G. A. (2009). A constructivist computational tool to assist in learning primary school mathematical equations. Computers & Education, 53(2), 484-492. https://doi.org/10.1016/j.comp....
 
13.
Deza, M. M., & Deza, E. (2012). Figurate numbers. World Scientific. https://doi.org/10.1142/8188.
 
14.
Dickson, L. E. (2013). History of the theory of numbers: Diophantine Analysis (Vol. 2). Courier Corporation.
 
15.
Dogru, M., & Kalender, S. (2007). Applying the Subject” Cell” through Constructivist Approach during Science Lessons and the Teacher’s View. Online Submission, 2(1), 3-13.
 
16.
Dooly, M. (Ed.). (2008). Telecollaborative language learning: A guidebook to moderating intercultural collaboration online. Peter Lang.
 
17.
Doruk, B. K., Aktümen, M., & Aytekin, C. (2013). Pre-service elementary mathematics teachers’ opinions about using GeoGebra in mathematics education with reference to ‘teaching practices’. Teaching Mathematics and its Applications: An International Journal of the IMA, 32(3), 140-157. https://doi.org/10.1093/teamat....
 
18.
Duval, R. (1999). Representation, Vision and Visualization: Cognitive Functions in Mathematical Thinking. Basic Issues for Learning.
 
19.
Finkelstein, R., & London, H. (1972). On triangular numbers which are sums of consecutive squares. Journal of Number Theory, 4(5), 455-462. https://doi.org/10.1016/0022-3....
 
20.
Garcia, I., & Pacheco, C. (2013). A constructivist computational platform to support mathematics education in elementary school. Computers & Education, 66, 25-39. https://doi.org/10.1016/j.comp....
 
21.
Gomez, E. A., Wu, D., & Passerini, K. (2010). Computer-supported team-based learning: The impact of motivation, enjoyment and team contributions on learning outcomes. Computers & Education, 55(1), 378-390. https://doi.org/10.1016/j.comp....
 
22.
Hajdu, L., Pintér, Á., Tengely, S., & Varga, N. (2014). Equal values of figurate numbers. Journal of Number Theory, 137, 130-141. https://doi.org/10.1016/j.jnt.....
 
23.
Hogben, L. (1954). Figurate Series and Factorial Notation. Human Heredity, 5(2), 115-133. https://doi.org/10.1159/000150....
 
24.
Hohenwarter, J., Hohenwarter, M., & Lavicza, Z. (2009). Introducing dynamic mathematics software to secondary school teachers: The case of GeoGebra. Journal of Computers in Mathematics and Science Teaching, 28(2), 135-146.
 
25.
Hohenwarter, M., & Fuchs, K. (2004, July). Combination of dynamic geometry, algebra and calculus in the software system GeoGebra. In Computer algebra systems and dynamic geometry systems in mathematics teaching conference.
 
26.
Iran-Nejad, A. (1995). Constructivism as substitute for memorization in learning: Meaning is created by learner. EDUCATION-INDIANAPOLIS-, 116, 16-16.
 
27.
Kagan, S. (1994). Cooperative learning. San Clemente, CA: Resources for Teachers, Inc..
 
28.
Kim, C. Y. (2002). Teachers in digital knowledge-based society: new roles and vision. Asia Pacific Education Review, 3(2), 144-148. https://doi.org/10.1007/BF0302....
 
29.
Laal, M., & Ghodsi, S. M. (2012). Benefits of collaborative learning. Procedia-social and behavioral sciences, 31, 486-490. https://doi.org/10.1016/j.sbsp....
 
30.
Lavicza, Z., & Papp‐Varga, Z. (2010). Integrating GeoGebra into IWB‐equipped teaching environments: preliminary results. Technology, Pedagogy and Education, 19(2),245-252. https://doi.org/10.1080/147593....
 
31.
Maněnová, M., Skutil, M., & Zikl, P. A. V. E. L. (2010). Taking advantage of ITC by teachers at the primary school. In Proc. of the 6th Educational technologies (EDUTE’10): WSEAS/IASME international conference. Athens: WSEAS (pp. 48-52).
 
32.
McPhail, G. (2016). The fault lines of recontextualisation: The limits of constructivism in education. British Educational Research Journal, 42(2), 294-313. https://doi.org/10.1002/berj.3....
 
33.
Mihajlov-Carević, M., Kopanja, L., & Denić, N. (2017). Figurative numbers as a tool for presentation paradigms and development constructive opinions. A collection of papers from the National Conference with international participation, Čačak: ITOP (pp.217-224).
 
34.
Oh, B. K., & Sun, Z. W. (2009). Mixed sums of squares and triangular numbers (III). Journal of Number Theory, 129(4), 964-969. https://doi.org/10.1016/j.jnt.....
 
35.
Ono, K., Robins, S., & Wahl, P. T. (1995). On the representation of integers as sums of triangular numbers. In Aggregating clones, colors, equations, iterates, numbers, and tiles (pp.73-94). Birkhäuser Basel. https://doi.org/10.1007/978-3-....
 
36.
Pengelley, D. (2013). Figurate numbers and sums of numerical powers: Fermat, Pascal, Bernoulli. Convergence, Mathematical Association of America. https://doi.org/10.4169/loci00....
 
37.
Petrović M. & Kontrec, N. (2017). Possibilities for applying team teaching system in order to improve the efficiency of math teaching, A collection of papers from the National Conference with international participation, Leposavić: Innovation in education-digitalization,innovation models and programs.
 
38.
Ruthven, K. (2009). Towards a naturalistic conceptualisation of technology integration in classroom practice: The example of school mathematics. Éducation et didactique, 3(1), 131-159. https://doi.org/10.4000/educat....
 
39.
Ruthven, K., Hennessy, S., & Deaney, R. (2008). Constructions of dynamic geometry: A study of the interpretative flexibility of educational software in classroom practice. Computers & Education, 51(1), 297-317. https://doi.org/10.1016/j.comp....
 
40.
Saha, R. A., Ayub, A. F. M., & Tarmizi, R. A. (2010). The effects of GeoGebra on mathematics achievement: enlightening coordinate geometry learning. Procedia-Social and Behavioral Sciences, 8, 686-693. https://doi.org/10.1016/j.sbsp....
 
41.
Schcolnik, M., Kol, S., & Abarbanel, J. (2016). Constructivism in theory and in practice. In English teaching forum (Vol. 44, No. 4, pp. 12-20). US Department of State. Bureau of Educational and Cultural Affairs, Office of English Language Programs, SA-5, 2200 C Street NW 4th Floor, Washington, DC 20037.
 
42.
Tabach, M. (2012). A mathematcs teacher΄s practice in a tehnological environment: A case study analysis using two complementary theories. Technology, Knowledge and Learning, 16(3), 247-265.
 
43.
Takači, D., Stankov, G., & Milanovic, I. (2015). Efficiency of learning environment using GeoGebra when calculus contents are learned in collaborative groups. Computers & Education, 82, 421-431. https://doi.org/10.1016/j.comp....
 
44.
Toh, P. C. (2013). On representations by figurate numbers: a uniform approach to the conjectures of Melham. International Journal of Number Theory, 9(04), 1055-1071. https://doi.org/10.1142/S17930....
 
45.
Viamonte, A. J. (2010). The computer in the teaching of mathematics. In Proceeding of advanced educational technologies. 6th WSEAS/IASME international conference on educational technology (EDUTE’10) (pp. 24-29).
 
46.
Wang, M., Wu, B., Chen, N. S., & Spector, J. M. (2013). Connecting problem-solving and knowledge-construction processes in a visualization-based learning environment. Computers & Education, 68, 293-306. https://doi.org/10.1016/j.comp....
 
47.
Zengin, Y., Furkan, H., & Kutluca, T. (2012). The effect of dynamic mathematics software geogebra on student achievement in teaching of trigonometry. Procedia-Social and Behavioral Sciences, 31, 183-187. https://doi.org/10.1016/j.sbsp....
 
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