CAS MAXIMA AS A TOOL FOR FORMING RESEARCH SKILLS IN THE PROCESS OF PRE-SERVICE INFORMATICS TEACHERS TRAINING
The article looks at the means of forming the research skills of students of pedagogical universities. Considerable attention is paid to the formation of students' creative thinking in the process of solving problems with parameters. A large number of applied problems, economic, physical, chemical, biological, technical, medical, etc., involve solving problems with parameters (within the framework of the constructed mathematical model). Tasks with parameters require more general research than ordinary equations, inequalities and their systems. In the article, solving problems with parameters is accompanied by graphical visualization followed by the use of the analytical method. CAS Maxima is used for graphical visualization (animation). The choice of tasks with parameters is due to the fact that mathematical, logical thinking and the ability to analyze, compare, synthesize, develop research skills evolve in the course of their solution. All this should lead to the search and introduction of new forms of pedagogy and technologies in education. The main component of the methodology here is computer-oriented, namely the use of a computer mathematics system. Using systems of computer mathematics, the student can improve the programming technique and ability to focus on the analysis of methods, immerse in the features of such concepts as the conditionality of the problem, the stability of the method, evaluation of the results of calculations. In this paper, we used the CAS Maxima animation tools with the wxMaxima graphical shell to investigate the problems with the parameters. The choice of the Maxima system is due to the following reasons: it is a freely distributed system, distributed under the GNU/GPL license; there are implementations under various operating systems, including Windows, Linux, MacOS; it offers intuitive interface and is easy and reliable in operation. The results of the study show that training of modern specialists, the development of their professional potential can only be effective provided that students are involved in research activities throughout their course of study.
. A.V. Pruss, and V.O. Shvets, "Tasks with Parameters in a School Mathematics Course." Zhytomyr, Ukraine: Ruta Publishing House, 2016. (in Ukrainian)
. O.O. Hrybiuk, and V.L. Yunchyk, "Features of Using the System Geogebra in Teaching Course "Mathematical Foundations of Informatics," Mathematics. Information Technology. Education 1(4), pp.35-49, 2017. (in Ukrainian)
. S. Ursini, and M.Trigueros, "How Do High School Students Interpret Parameters in Algebra?", In M. J. Hoines & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, pp. 361-368, Bergen University College, 2004. (in English)
. V. Bykov, and M.Shyshkina, "The Conceptual Basis of the University Cloud-based Learning and Research Environment Formation and Development in View of the Open Science Priorities," Information Technologies and Learning Tools, Vol.68(6), pp.1-19, 2018. doi: https://doi.org/10.33407/itlt.v68i6.2609.(in English)
. M. Marienko, Yu. Nosenko, F. Sukhikh, V. Tataurov, and M. Shyshkina, "Personalization of Learning Through Adaptive Technologies in the Context of Sustainable Development of Teachers’ Education," E3S Web of Conferences, Vol. 166, 2020. doi: https://doi.org/10.1051/e3sconf/202016610015 (in English)
. S.Abramovich, and A.Ehrlich, "Computer as a Medium for Overcoming Misconceptions in Solving Inequalities," Journal of Computers in Mathematics and Science Teaching, 26(3), pp.181-196, 2007. (in English)
. A. Kumar, and S. Kumareson, "Use of Mathematical Software for Teaching and Learning," Proceedings of 11th International Congress on Math Education (ICME), July, 6-13, Mexico, pp.373-388, 2008. (in English)
. F. Botana, M. Abánades, and J. Escribano. "Using a Free Open Source Software to Teach Mathematics," Computer Applications in Engineering Education, 22 (4), pp. 728-735, 2014, doi.org/10.1002/cae.21565(in English)
. T. V. Pidgorna, "Theoretical and Methodological Bases of Preparation of Future Teachers of Natural and Mathematical Disciplines for Professional Activity in the Conditions of Informatized Educational Process," Doctor’s dissertation. National Pedagogical Dragomanov University. Kyiv, Ukraine, 2018. (in Ukrainian)
. M.I. Zhaldak, Yu.V. Goroshko, Ye.F. Vinnichenko, and G.Yu. Tsybko, "Mathematics with a Computer (with GRAN1)," the Teacher’s Guide, Third Edition, supplemented. Kyiv, Ukraine: National Dragomanov Pedagogical University, 305 p., 2016. (in Ukrainian)
. N.O. Bugayets, " Development of Educational and Research Skills of Students of Physical and Mathematical Specialties in the Process of Teaching Mathematical Informatics," Ph.D. thesis, National Pedagogical Dragomanov University, Kviv, Ukraine, 2016. (in Ukrainian)
. K. Fuchs, "Teaching Meaningful Mathematics with the Computer Algebra System Maxima Using the Example of Inequalities," Teaching Mathematics and Computer Science, pp. 53-65, 2013, doi: 10.5485/tmcs.2013.0331(in English)
. N.O. Bugayets, "Modeling of Animation Visuals by Means of the Maxima Program Graphic Environment," Information Technologies and Learning Tools, Vol. 47, №3, pp.67-79, 2015. doi: https://doi.org/10.33407/itlt.v47i3.1244 (in Ukrainian)
. O.O. Hrybiuk, and V.L. Yunchyk, "Using Computer Algebra Systems in the Context of a Blended Learning Model," Mathematics. Information Technology. Education: [Coll. articles], Lesya Ukrainka SNU, Lutsk, pp. 52-71. 2015. (in Ukrainian)
. V.M. Rakuta, "GeoGebra Dynamic Mathematics System as an Innovative Tool for the Study of Mathematics," Information Technologies and Learning Tools, №4 (30). 2012. https://doi.org/10.33407/itlt.v30i4.700. (in Ukrainian)
. B.-S. Ilany, and D. Hassidov, "Solving Equations with Parameters," Creative Education, 5, pp.963- 968.2014, doi: 10.4236/ce.2014.511110. (in English)
. S. Abramovich, and A. Norton. "Equations with Parameters: a Locus Approach," Journal of Computers in Mathematics and Science Teaching 25(1), pp. 5-28, 2006.
. S. Goncharenko, "Ukrainian Pedagogical Dictionary," S. Golovko and S. Caverin, Eds., Kyiv: Lybid, 1997. (in Ukrainian)
. I.Ya. Lerner, "Didactic Foundations of Teaching Methods," M .: Pedagogy, 1981. (in Russian)
. V.N. Litovchenko, "Formation of Research Skills of Students of Pedagogical Specialties of the University by Means of NIR," Ph.D. dissertation, Minsk, 1990. (in Russian)
. Ye. I. Mashbits, "Psychological Bases of Management of Educational Activity," Kyiv: Higher school, 1987. (in Russian)
. M.I. Zhaldak, "Informatics Is a Fundamental Scientific Discipline. She Must Study the Laws of Nature, Information Processes and Related Technologies (continued)," Computer in School and Family, № 3, pp. 7-11, 2010. (in Ukrainian)
. Ye.F. Vinnichenko, "Development of Creative Abilities of High School Students in the Process of Learning Information Technologies for Solving Mathematical Problems," Ph.D. dissertation, National Pedagogical Dragomanov University. Kyiv, Ukraine, 2006. (in Ukrainian)
. E.V. Mayevsky, and P.V.Yagodovsky, "Computer Mathematics. Higher Mathematics at CAS Maxima: A Tutorial," Moscow: Financial University, 196 p., 2014. (in Russian)
. P.I. Gornstein, V.B. Polonsky, and M.S. Yakir, "Tasks with Parameters," Kyiv: RIA “Text”; MP "OKO", Kiev, Ukraine, 290 p., 1992. (in Russian)
Copyright (c) 2020 Uliana P. Kohut
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Authors who publish in this journal agree to the following terms:
- Authors hold copyright immediately after publication of their works and retain publishing rights without any restrictions.
- The copyright commencement date complies the publication date of the issue, where the article is included in.
- Authors grant the journal a right of the first publication of the work under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License (CC BY-NC-SA 4.0) that allows others freely to read, download, copy and print submissions, search content and link to published articles, disseminate their full text and use them for any legitimate non-commercial purposes (i.e. educational or scientific) with the mandatory reference to the article’s authors and initial publication in this journal.
- Original published articles cannot be used by users (exept authors) for commercial purposes or distributed by third-party intermediary organizations for a fee.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) during the editorial process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (see this journal’s registered deposit policy at Sherpa/Romeo directory).
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Post-print (post-refereeing manuscript version) and publisher's PDF-version self-archiving is allowed.
- Archiving the pre-print (pre-refereeing manuscript version) not allowed.