VISUALIZATION OF SOLVING PROBLEMS WITH NUMBERS: STATISTICAL COMPARISON TWO METHODS
Sažetak
The XXI century has brought the growing use of information and communication technologies in many spheres of human life. In the learning process, students are increasingly focused on the use of modern technologies. Exploring the quality of maths teaching in primary school, we found students' knowledge of using modern technologies but also the lack of visual-logical approach in solving mathematical problems. In this paper, we show how the establishment of figurative numbers and selected examples that demonstrate the observation of legality, can direct students to a visual-logical approach to solving tasks with sets of numbers. We organized a three-hour exercise in experimental and control group, during which the experimental group was working with figurative numbers and the control group with selected examples. On the pre-test both groups showed a low degree of ability to observe legality among the numbers. On the post-test, both groups achieved progress compared to the pre-test, although the experimental group achieved greater progress.
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Reference
Allegra, M., Chifari, A., & Ottaviano, S. (2001). ICT to train students towards creative thinking. Educational Technology & Society, 4(2), 48-53.
Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational studies in mathematics, 52(3), 215-241.
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.
Bennett, M. A. (1997). Effective measures of irrationality for certain algebraic numbers. Journal of the Australian Mathematical Society, 62(3), 329-344.
Bozkurt, G., & Ruthven, K. (2017). Classroom-based professional expertise: A mathematics teacher’s practice with technology. Educational Studies in Mathematics, 94(3), 309-328.
Brindza, B., Pintér, Á., & Turjányi, S. (1998). On equal values of pyramidal and polygonal numbers. Indagationes Mathematicae, 9(2), 183-185.
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. sg/ictconnection/slot/u2 00/mp3/monographs/advancing% 20collaborative, 2.
Deza, M.M., & Deza, E. (2012). Figurate numbers. World Scientific.
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.
Dooly, M. (Ed.). (2008). Telecollaborative language learning: A guidebook to moderating intercultural collaboration online. Peter Lang
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.
Duval, R. (1999). Representation, Vision and Visualization: Cognitive Functions in Mathematical Thinking. Basic Issues for Learning.
Garcia, I., & Pacheco, C. (2013). A constructivist computational platform to support mathematics education in elementary school. Computers & Education, 66, 25-39.
Ghyka, M., (1971). Philosophie et mystikue du nombre, Ed. Payot, Paris.
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.
Hajdu, L., Pintér, Á., Tengely, S., & Varga, N. (2014). Equal values of figurate numbers. Journal of Number Theory, 137, 130-141.
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.
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.
Iran-Nejad, A. (1995). Constructivism as substitute for memorization in learning: Meaning is created by learner. EDUCATION-INDIANAPOLIS-, 116, 16-16.
Kagan, S. (1994). Cooperative learning, San Clemente, CA: Resources for Teachers, Inc..
Kim, C. Y. (2002). Teachers in digital knowledge-based society: new roles and vision. Asia Pacific Education Review, 3(2), 144-148.
King, B. (2007). Max Wertheimer & Gestalt theory, Somerset, Transaction Publishers.
Laal, M., & Ghodsi, S. M. (2012). Benefits of collaborative learning. Procedia-social and behavioral sciences, 31, 486-490.
Lavicza, Z., & Papp‐Varga, Z. (2010). Integrating GeoGebra into IWB‐equipped teaching environments: preliminary results. Technology, Pedagogy and Education, 19(2),245-252.
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).
McPhail, G. (2016). The fault lines of recontextualisation: The limits of constructivism in education. British Educational Research Journal, 42(2), 294-313.
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).
Mihajlov-Carević, M., Petrović, M. & Denić, N. (2019). Figurative numbers contribution in perceiving the legality in numerous strings tasks and long-term memory of numerous data, EURASIA J.Math., Sci Tech. Ed 2019;15(4):em1692. https://doi.org/10.29333/ejmste/103387.
Oh, B. K., & Sun, Z. W. (2009). Mixed sums of squares and triangular numbers (III). Journal of Number
Theory, 129(4), 964-969.
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.
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.
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.
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.
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.
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.
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.
Tabach, M. (2012). A mathematcs teacher΄s practice in a tehnological environment: A case study analysis using two complementary theories, Tehnology, Knowledge and Learning, 16(3), 247-265.
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.
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.
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).
Walny, J., Carpendale, S., Riche, N. H., Venolia, G., & Fawcett, P. (2011). Visual thinking in action: Visualizations as used on whiteboards. IEEE Transactions on Visualization and Computer Graphics, 17(12), 2508-2517.
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.
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.
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