Terekhova, N., Zubova, E. / Volume 9 - Issue 27: 560-569 / March, 2020 560
DOI: http://dx.doi.org/10.34069/AI/2020.27.03.60
Information and Communication Technologies of Teaching Higher Mathematics To Students of Engineering Specialties At Technical Universities
Информационно-Коммуникационные Технологии Обучения Высшей Математике Студентов Инженерных Специальностей Технических Вузов
Received: January 25, 2020 Accepted: February 29, 2020
Written by: Natalya Vladimirovna Terekhova213 ORCID : 0000-0003-4570-6261 https://elibrary.ru/author_items.asp?authorid=796649 Elena Aleksandrovna Zubova214 ORCID: 0000-0001-5666-2634 https://elibrary.ru/author_items.asp?authorid=802624
Abstract Аннотация
Excessive anthropogenic pressure on land Высшие технические учебные заведения развитых resources in Ukraine leads to a deterioration of стран имеют значительные педагогические their quality, and consequently they lose their достижения и развитую систему подготовки специалистов инженерных направлений на основе potential. Human impact on the change of land системного использования средств ИКТ. В quality can be direct (by involving land lots in глобализированном пространстве высшего use, carrying out economic activities) and образования проблему повышения качества indirect (as a result of such activity, enhancing подготовки специалистов в отечественных вузах the natural degradation of soils). The tendency целесообразно решать посредством творческого of deterioration of the state of land resources использование опыта передовых вузов инженерного requires the subordination of land relations to the профиля. main goal – to ensure comprehensive protection Цель исследования заключается в осуществлении of this major national wealth of Ukraine. анализа процесса развития информационно- коммуникационных технологий (ИКТ) обучения Legal support for the protection of agricultural высшей математике студентов инженерных land is considered as a single complex of специальностей технических вузов. interdependent elements: legal standards for the В статье отмечена актуальность фундаментальной protection of land, soil, agricultural landscapes, математической подготовки будущих специалистов and the mechanism for their implementation – технического профиля. На основании экспертного legally significant measures: economic, опроса проведен анализ инструментов ИКТ для organizational, scientific and technical. At the совместной работы над проектами при изучении same time, it was concluded that the system of высшей математики, дана характеристика систем legal regulation of the use of agricultural land is компьютерной математики (СКМ) и Web-СКМ и определены методы, формы и средства обучения в not sufficiently saturated with mechanisms for соответствии с разделами высшей математики, regulating agricultural activity. которые изучаются студентами инженерных специальностей в технических вузах. Keywords: Ukraine, land protection, agricultural lands, soil, land plots, agriculture. Ключевые слова: информационно- коммуникационные технологии, высшее учебное заведение, студенты инженерных специальностей, система компьютерной математики, мобильные математические среды, онлайн-консультация.
213 Industrial University of Tyumen, Tyumen, Russia 214 Industrial University of Tyumen, Tyumen, Russia
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Introduction
At the present stage of the development of the and methods of using ICT in education are information society, the use of information and traditionally in the purview of Russian and communication technology (ICT) tools foreign scientists. contributes to the globalization of education, development of the international labor market, Researchers (Martens et al., 2011) determine the and growth of various types of an individual’s following characteristics of teaching technology: mobility (Ushatikova et al., 2018). The growth of 1) teaching is an observable process and its academic mobility, as well as the introduction of results are measurable; 2) the process of international norms and standards, based on achieving the desired teaching results is defined which academic qualifications from different in terms of clearly defined operations; 3) these countries can be compared and recognized, lead operations are defined on the basis of evidence. to increased competition between universities It is noted that computer-oriented teaching and improve the quality of higher education technologies most fully implement these (Zhienbayeva et al., 2019; Zholdasbekov et al., characteristics, because 1) monitoring of the 2019). In this context, the globalization of teaching process is mediated and its results are education contributes to the personal and recorded, processed, and generalized using ICT professional development of specialists who are tools, 2) the teaching process is algorithmized involved in the development and introduction of and implemented in a computer program, and 3) new technologies – engineers (Bulgarova et al., actions that manage the teaching process are 2018; Sergeeva et al., 2018). selected in accordance with the teaching results. Thus, the choice of ICT tools for the One of the components of a professional implementation of teaching technology is engineer’s training system is fundamental appropriate. training, the main task of which is to improve the professional training and all-around development The theory and methods of using ICT in teaching of a student as a person. This includes: mastering higher mathematics were developed in the works research methods for solving production tasks; of such Russian researchers as V.A. Krasilnikova development of rationalization suggestions and (2012), V.P. Diakonov (2010), V.F. Ochkov participation in inventive work; knowledge of (2013), L.V. Sardak (2016), and others. technology and equipment from the field of one’s specialization (specialty) and mastering various E.S. Polat (2010) defines ICT as a set of methods, forms of self-education, which is impossible means, and techniques used to collect, organize, without fundamental knowledge of higher store, process, transmit, and present various mathematics, and skills to put the acquired messages and data. I.N. Semenova and A.A. knowledge into practice and apply it in Slepukhin (2013) define ICT as information professional activity. technologies based on personal computers, computer networks, and communications, which The use of ICT in the process of teaching higher are characterized by a user-friendly environment. mathematics to students of engineering According to C. Blurton (1999), ICT are specialties creates the conditions for student’s different technological tools and resources that self-realization. They help to increase their are used for communication and for the creation, learning activity, develop critical thinking, form distribution, storage, and management of data. students' skills in organizing independent work, According to researchers, the use of ICT- develop creative abilities and leadership teaching supports traditional education and helps qualities, increase responsibility for the results of people cope with learning throughout their lives their work, as well as improve the learning because it makes the learning process easy, process and its quality. motivated, individual, and flexible (Leach, 2005). Therefore, there is a need to study the possibilities of using ICT tools for teaching Among works of foreign scientists, the following higher mathematics to students of engineering works are important for the research: specialties at technical universities. − Birch (2009), R.M. Hernandez (2017), Literature review G. Douglas (2001), N. Selwyn (2007) (the works are devoted to the history The analysis of scientific literature showed that and current state of the use of ICT in the the problems of the development of the theory teaching process);
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− M. Goyal (2009), M. Sandi (2009), E.R. in the educational practice of technical Krueger (2010) (the works are devoted universities; to the use of ICT in the training of − analysis, synthesis, and theoretical students of engineering specialties); generalization of experience in the use − L. Bazzini (2003), R. Wood (2008), P. of ICT in the process of teaching higher Drijvers (2010) (the works are devoted mathematics; to the use of ICT in the process of − expert survey of teachers in order to studying mathematical disciplines). reveal tools, methods, forms, and means of teaching mathematical disciplines J. Engelbrecht and A. Harding (2005) note that that are used with the help of ICT at Internet education in mathematics is developing technical universities. as a new teaching method with its own characteristics and capabilities that differ from Thirty-five experts, teachers and employees of traditional teaching methods. the departments of higher and applied mathematics of Russian technical universities The research hypothesis: The emergence of new took part in the discussion and comparison, as ICT leads to changes in the theory and methods well as in the expert survey. of teaching higher mathematics, which leads to the emergence of new goals, means, forms, and Algorithm methods of organizing the teaching process. At the first stage of the study, an analysis of Proposed Methodology scientific literature on the problem of using ICT for teaching higher mathematics to students of General description engineering specialties at technical universities The specificity and purpose of the work was conducted. determine the choice of a set of scientific research methods: At the second stage of the study, methods, forms, and means of teaching mathematical disciplines − analysis of scientific and pedagogical, using ICT at technical universities were as well as methodological literature in determined. the field of education, in order to reveal the state of implementation of ICT tools
Analysis of scientific literature
Using ICT in teaching higher mathematics to students of engineering specialties at technical universities
Expert survey
General characteristics of Methods, forms, and teaching computer mathematics means in accordance with the Tools for joint work on systems and web computer sections of higher projects mathematics systems mathematics
Figure 1. Flow chart of methodology
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Results and discussion − tools for joint work on projects; − means for supporting domain-specific An expert survey showed that a large number of practice. various means of supporting mathematical educational activities have been developed and Using tools for joint work on projects, teachers implemented in the teaching process now, among can support the learning process at a distance, which are the following: outside the auditorium (Table 1).
Table 1. Tools for joint work on projects
% of № Tool Capabilities mentions creating various documents, working with them together with students and saving documents and other files online, Google 1 providing access to these documents to others; the ability to 91,4% GoogleDocs access one’s documents and files from any computer, if it is connected to the Internet. viewing and sharing files regardless of user’s location; the Microsoft Office ability to work simultaneously with other people on 2 85,7% Web Apps documents on different platforms, devices and in different versions of Office; saving documents online for sharing. the ability to store data on cloud-based servers and share it Cloud data 3 with other users on the Internet. The work is based on data 85,7% storage DropBox synchronization. Using these resources, one can organize webinars (web Platforms for conferences) online or record them. Published courses in any online teaching format in a library can be shared in a virtual classroom or and web distributed to students. The most often used file types are 4 80% conferences: available for download: PDF, Word, PowerPoint, Excel, Elluminate, video and audio files. One has access to the board and iLinc, WiZiQ download training materials before or during class. Uploaded files are hosted in the cloud. platforms Piazza, support of interactive extracurricular interaction between 77,1% Skype, Google+ teachers and students.
Computer support for subject-oriented practical packages (MATLAB, Mathematica, Mathcad, activity consists in providing the user (student or Maple, Statistica, etc.) allows the teacher to teacher) with a set of means and tools that choose a convenient, accessible, and automate and allow seeing the process of solving understandable resource for them, taking into a practical problem. Such a system should be account the indicated advantages and provided with a full set of methodological disadvantages of this software. support. For higher mathematics, there is a textbook, problem book, reference book, student According to the analysis of the educational workbook, collection of tests, methodological practice of technical universities in the USA and recommendations of the teacher, etc. the expert survey, the most popular CMS used in teaching higher mathematics in the USA are When conducting complex calculations of an Mathematica, MATLAB, Maple, GAUSS, intermediate nature, the solution of which takes a Scilab, Mathcad, Maxima, and Sage. large amount of time, according to the experts, it is advisable to use computer mathematics In Table 2, the general characteristic of some systems (CMS). At the same time, the existence CMS used in US universities in teaching higher of a large number of available mathematical mathematics is presented.
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Table 2. General characteristic of CMS used in teaching higher mathematics in the US
General characteristics Name Developer advantages disadvantages - universal CMS for fast and accurate numerical calculations in various subject - lack of support for solving areas; inequalities and recurrence MATLAB - openness and scalability; relations in the core; The MathWorks R2013b - support of 3D graphics; - exactingness to the - compatibility with various operating hardware resources of the platforms; information system. - supports work with databases. - built-in support of parallel computing; - statistical analysis of models; - uniqueness of 3D-graphics; - syntax complexity; - compatibility with various operating - the idea of data as a platforms; Mathematica combination of individual Wolfram Research - high speed of performing mathematical 9.0.1 expressions, which reduces operations and calculations; the performance of solving - has a developed graphical interface, which complex problems. makes it possible to work with many documents; - supports work with databases. - best symbolic core; - high accuracy of calculations; - introduction of mathematical expressions in natural mathematical notation; - inconvenience when - structured document; working with a large amount - intuitive interface; of numerical data; Waterloo Maple - has a developed graphical interface, which - the idea of data as a Maple 17 Inc. makes it possible to work with many combination of individual documents; expressions, which reduces - in the latest versions there is a panel for the performance of solving recognizing characters entered by hand, for complex problems. quick search of a desired command or character; - interaction with CAD. - free; - plenary power for statistical analyzes, including linear and non-linear regression, - classical statistical tests, analysis of time series, cluster analysis, etc.; - can be used for matrix calculations; - the ability to connect the code written in C, C ++ or Fortran; - contains tools for visualizing the results of Ross Ihaka, - command interpreter is R 3.0.2 calculations (2-dimensional, 3-dimensional Robert Gentleman used for work. graphs, charts, histograms, Gantt charts (schemes), etc.); - Sweave function that allows to create dynamic reports; - users can expand the functionality by writing new functions; - provides the ability to create high-quality graphics with various attributes, including mathematical formulas and symbols. - provides an opportunity to solve problems Computational in algebra, numbers theory, geometry and Algebra Group, combinatorics; - lack of support for School of - works on Unix-like and Linux operating integration, solving MAGMA Mathematics and systems, and also Windows; inequalities, differential V2.19-10 Statistics, - has a developed graphical interface that equations, recurrence University of provides the ability to work with many relations in the core. Sydney documents; - supports work with databases.
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According to the experts, mobile mathematical 2) presentation of the calculation results in environments are a new promising direction for a form convenient for perception and the development of CMS. At the same time, construction of two- and three- CMS is integrated into one single network dimensional graphs of curves and environment, i.e. transfer of application software surfaces, histograms and any other (even “desktops”) to the web environment. It is images (including animated ones); important that the use of mobile web 3) combination of calculations, text, and environments in the educational process allows graphics on worksheets with the possibility of printing, publishing on the network and joint work with them; integrating classroom and extracurricular work in 4) creation using built-in programming a continuous educational process. languages of models for the implementation of educational research. The experts point to the following abilities of web CMS: The main areas of application of web CMS in the process of teaching higher mathematics, 1) performance of any calculations, both according to the experts, include graphical analytical (actions with algebraic interpretation of mathematical models and expressions, solving equations, theoretical concepts, automation of routine differentiation, integration) and computing, support of independent work, and numerical (exact – with any digit organization of mathematical research (Table 3). capacity, approximate – with any predetermined accuracy);
Table 3. General characteristic of web CMS
№ Web CMS Characteristic % of mentions mobile mathematical environment that acts as an 1 Sage integrator of various mathematical packages with a 85,7% joint Web interface. contains a large number of demonstrations in higher Wolfram mathematics and has an open access code. In 2 Demonstrations 74,3% demonstrations, one can provide different measures to Project parameters and conduct object research An easy to use applet can be used directly in a Web browser or downloaded to a computer. Users are provided with empty two-dimensional planes on which they can make constructions and perform manipulations with. In an open field, users can set 3 GeoGebra 71,4% equations. It is a universal tool for studying a wide range of topics of two-dimensional plane geometry. During higher mathematics classes it is convenient to illustrate the basic mathematical concepts and constructions and calculate.
Based on the analysis of the expert survey and studied by students of engineering specialties at expert suggestions, the methods, forms, and technical universities (Table 4). teaching means were regulated in accordance with the sections of higher mathematics that are
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Table 4. Methods, forms, and teaching means were regulated in accordance with the sections of higher mathematics that are studied by students of engineering specialties at technical universities
№ Sections Forms Methods Means Lecture; computer-oriented practical lessons; 1. Linear algebra Problem method Sage, MathCad implementation of individual tasks; online consultations Lecture; practical lesson; GeoGebra, Information- implementation of individual Wolfram 2. Vector algebra receptive method. tasks; control activity; online Demonstrations Graphic work consultations Project Lecture; computer-oriented Information- practical lessons; independent Analytic receptieve method. Smath Studio, 3. work of students; computer geometry Demonstration Maple, control of the quality of (dynamic) knowledge; online consultations Lecture; practical lesson; Boundary Partially searching Maple, MathCad, 4. implementation of individual conditions method (heuristic) FooPlot tasks; online consultations Differential Lecture; computer-oriented Information- Maple, Wolfram calculus of a practical lessons; independent receptieve method. 5. Demonstrations one-variable work of students; online Demonstration Project, FooPlot function consultations (dynamic) Lecture; practical lesson; implementation of individual Indefinite and Searching method 6. tasks; computer control of the Sage, MathCad definite integrals (experimental) quality of knowledge; online consultations Lecture; computer-oriented Information- Functions of practical lessons; control receptive method 7. Maple, GeoGebra several variables activity; independent work of Demonstration students; online consultations (dynamic) Lecture; computer-oriented Smath Studio, Differential practical lessons; independent Searching method 8. equations work of students; control (experimental) MathCad activity; online consultations Lecture; computer-oriented Multiple practical lessons; control 9. Problem method MathCad integrals activity; independent work of students; online consultations Lecture; practical lesson; implementation of individual Information- 10. Series tasks; computer control of the MathCad receptive method quality of knowledge; online consultations Lecture; practical lesson; control Probability 11. activity; independent work of Problem method MathCad theory students; online consultations Lecture; computer-oriented Fundamentals of practical lessons; practical Partially searching 12. mathematical Statistica training; control activity; online method (heuristic) statistics consultations
According to the experts, the introduction of new teaching higher mathematics, a combination of teaching means inevitably leads to a change in traditional forms of teaching with computer- teaching methods and forms. With the emergence oriented (based on the systematic, consistent, and and introduction of ICT tools in the process of logical use of ICT in the teaching process) occurs.
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As the interviewed experts indicate, in the new − offer students tasks that should be model of combined teaching, the educational solved using CMS; process of higher mathematics contains the main − use CMS in the classroom to conduct traditional forms of organization of the intermediate calculations that take a educational process: lecture, practical lesson, large amount of time; independent work of students, and knowledge − offer students tasks in higher control. In addition, traditional forms are mathematics of a professional supplemented by forms of organizing distance orientation, which should be solved and mobile learning, as well as learning using the using CMS; Internet and multimedia: course materials, online − gradual complication and expansion of communication, individual and group online the use of CMS in the teaching process; projects, virtual classroom, audio and video − develop students' motivation to master lectures, animation and simulation, mobile independently the ability to apply CMS training, etc. in the learning process; − use CMS to visualize the process of At a lecture, the teacher presents the main learning mathematics. educational material of the course. The explanations, which are accompanied by lecture The experts specify that the problem of choosing demonstrations using software tools, contribute CMS and supporting a large installation base is to a better understanding and assimilation of the solved through the use of network technologies, concepts in question. Recorded lectures posted when a user, using specialized client software, on the Internet allow students to refine unclear accesses the server side of CMS, where user’s material. If it is impossible for a teacher to be commands are executed, and the result is present at the lecture or submit the material to an returned to the client software. Such services are independent study, it is advisable, according to provided in particular by MATLAB Web Server, the experts, to replace the traditional lecture with webMathematica, and wxMaxima. Although not a web conference (webinar, video lecture) and every CMS include built-in network tools, for multimedia lectures. those of them, in which the command interface is supported along with the visual one, it is possible During a practical lesson, students solidify their to create a network add-in. knowledge and acquire skills in solving practical problems. The tasks of a practical lesson should According to the experts, one of the forms of be selected according to the direction of student organizing educational activities related to the training, emphasizing the appropriateness of the acquisition by students of practical skills in the studied material in students' future professional corresponding field of knowledge using ICT activity. According to the experts, it is advisable tools is a computer-oriented practical lesson. to post questions and tasks of a practical lesson This lesson, according to one of the experts, “is and examples for independent work on the based on a combination of traditional and Internet in advance. computer forms of training and knowledge control and is focused on solving problems In addition, according to the experts, it is ensuring continuity between practical, advisable to use ICT tools for rapid testing to laboratory, and lecture classes on the basis of determine the level of learned material during a internal and interdisciplinary logical practical lesson. At the same time, for self- connections”. control, students should be provided with clear instructions for working with CMS, which will The experts note that the quality control of allow them to check answers and to form CMS knowledge can be carried out both in the skills for their future professional activity. audience and beyond using the Internet. The use of CMS, test programs, and test modules in The experts specify that when using CMS in the training support systems allows students to process of teaching higher mathematics one conduct self-control and teachers to automate the should consider the following: teaching process.
− provide students with information about According to the experts, the use of ICT tools various available mathematical significantly expands opportunities of a teacher packages and methodological materials through the implementation of online for their use, allowing students to communication with students for the purpose of independently choose a product timely consultation on problematic issues. Such convenient for them; communication is carried out using various ICT
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tools, among which the use of e-mail, platforms in the theory and methodology of teaching higher for interactive communication, and social mathematics, which, in turn, leads to the networks for communication in groups stand out. emergence of new goals, means, forms, and Web-based tools allow teachers to communicate methods of organizing the educational process. with students in one of the following ways: online, solving a problem with quick response to Bibliographic references questions using instant messages, using e-mail to support prolonged dialogs (for example, Bazzini, L., Bartolini Bussi, M.G. (2003). throughout the whole semester or school year), Research, practice and theory in didactics of and conducting virtual discussions in the mathematics: Towards dialogue between classroom using a discussion board or Web different fields. Educational Studies in conferences. Furthermore, with the help of ICT, Mathematics, 54(2), 203-223. a teacher can conduct individual and group Birch, A., Irvine, V. (2009). Preservice teachers’ consultations outside the university. Using video acceptance of ICT integration in the classroom: recordings of classes, a teacher can demonstrate Applying the UTAUT model. Educational Media examples of problem-solving, which will allow International, 46, 295- 315. students to learn the taught material better. Blurton, C. (1999). New directions of ICT-use in Education. Available: The experts emphasize that for a quality training http://www.unesco.org/education/educprog/lwf/ process, it is necessary to choose such teaching dl/edict.pdf tools that will ensure the best integration of Bulgarova, B.A., Bragina, M.A., Novoselova, classroom and extracurricular education. Among N.V., Voronova, A.V., Semanina, A.A., them, paper and e-books and aids, teaching Bondareva, V.V., Levina, V.N. (2018). Teaching materials posted on the Internet, educational the Scientific Style of the Russian Language audio and video materials, support systems for (Mathematics, Chemistry, Physics) to Foreign mathematical activities, test systems, simulators Students at the University. Espacios, 39(49), 26. for developing skills and abilities, digital Diakonov, V.P. (2010). Entsyklopediia libraries, and reference books, etc. stand out. kompiuternoi algebry [Encyclopedia of Computer Algebra]. Moscow, DMK-Press, Summing up the discussion, the experts conclude 1276. that in the process of teaching higher Douglas, G. (2001). ICT, Education, and Visual mathematics to students at technical universities, impairment. British journal of Educational there is a harmonious combination of classroom Technology, 32(3), 353-364. education with virtual, full-time education with Drijvers, P., Kieran, C., Mariotti, M.A. (2010). distance, individual, and group education. At the Integrating technology into mathematics same time, the teacher and students support both education: Theoretical perspectives. synchronous and asynchronous communication. Mathematics education and technology- rethinking the terrain. Berlin: Springer, 89-132. Conclusions Engelbrecht J., Harding A. (2005). Teaching Undergraduate Mathematics on the Internet. The systems of mathematical training of Journal of Online Mathematics and its engineers currently have the following features: Applications, 58(2), 235-276. a high level of mathematization and Goyal, M., Murthy, S. (2009). Student computerization of general engineering and perceptions on the use of new techonologies in special disciplines; the content of mathematical engineering courses recorded lectures on the training is professionally oriented and internet and moodle. International Workshop on differentiated by the levels of initial training of Technology for Education, 36-41. students; ICT tools are widely used in teaching Hernandez, R.M. (2017). Impact of ICT on higher mathematics. Education: Challenges and Perspectives. Propósitos y Representaciones, 5(1), 325-347. The emergence of a new type of hardware or Krasilnikova, V.A. (2012). Ispolzovanie software ICT tools affects the process of informatsyonnykh i komunikatsyonnykh organizing training in higher mathematics at the tekhnologii v obrazovanii: uchebnoe posobie present stage and creates the conditions for the [The Use of Information and Communication implementation of web-based teaching of higher Technologies in Education: A Training Aid]. mathematics. Orenburg, OGU, 291. Krueger, E.R., Kulacki, F.A. (2010). The results of the study confirm the hypothesis International Trends in Engineering Education. that the emergence of new ICT leads to changes
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