МЕТОДИЧНІ АСПЕКТИ ВИКОРИСТАННЯ SAGEMATH CLOUD У НАВЧАННІ АЛГЕБРИ І ПОЧАТКІВ АНАЛІЗУ
DOI:
https://doi.org/10.14308/ite000488Ключові слова:
хмарні технології, хмарні обчислення, СКМ, Web-СКМ, SageMath CloudАнотація
Якість математичної освіти багато в чому залежить від якості освіти в цілому.Основну ідею, можна резюмувати наступним чином: для того, щоб виховувати молоде покоління людей, щоб мати можливість гідно зустріти вимоги часу, необхідно створити умови для утворення високоякісної математики. Підвищення якості математичної освіти учнів в середній школі є однією з найбільш актуальних проблем.
Зміст шкільного курсу математики і її методу навчання завжди був предметом дослідження, а іноді бурхливих наукових суперечок. Є спеціальні методи навчання алгебри та аналізу у вищій школі. Проте в навчальному процесі алгебраїчні поняття та принципи аналізу наведені в такій абстрактній і узагальненій формі, що студент може має значні труднощі для зіставлення цих загальних абстрактних понять з певними конкретними образами.
Поліпшення показників якості освіти може бути досягнуто за допомогою відповідного комп'ютерних технологій.
Статтю присвячено проблемам використання хмаро орієнтованих систем комп’ютерної математики (СКМ). Розглянуто перспективи розвитку Web-СКМ в аспекті хмаро орієнтованого середовища. Виявлено педагогічні особливості застосування SageMath Cloud як засобу навчання математичних дисциплін. Розкрито методичні аспекти навчання алгебри і початків аналізу у старшій профільній школі за допомогою хмаро орієнтованої СКМ SageMath Cloud.
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Посилання
<uk>
1. Bondarenko T. V. Informatsiyni tekhnolohiyi na urotsi matematyky [Information technology in math class] / T. V. Bondarenko, I. I. Dmitrenco // Theory and methods of teaching mathematics, physics, computer science: Collection of scientific works: in 3 vols. – Kryvyi Rig: Publishing Department KDPU, 2001. – Vol 1: Theory and methods of teaching mathematics. – P. 29-31 (in Ukrainian).
2. Kobylnyk T. P. Rozvyazuvannya zadach z parametramy z vykorystannyam kompyutera [Solving problems with parameters using a computer] / T. P. Kobylnyk // Teoriya ta metodyka navchannya matematyky, fizyky, informatyky: Zbirnyk naukovykh prats. Vypusk V: V 3-kh tomah. – Kryvyy Rih: Vydavnychyy viddil NMetAU, 2005. – T. 1: Teoriya ta metodyka navchannya matematyky. – P. 134-139 (in Ukrainian).
3. Merzlyak A. G Alhebra. 11 klas: pidruch. dlya zahalnoosvit. navch. zakladiv : akadem. riven, prof. riven [Algebra. 11 class: textbook for secondary schools: academic level, profile level] / A. G. Merzlyak, D. A. Nomirovskyy, V. B. Polonsky, M. S. Yakir – H.: Gymnasium, 2011. – 431 p. (in Ukrainian).
4. Popel M. V. Prohramni zasoby navchalnoho modelyuvannya [Educational software simulation] / M. V. Popel, S. V. Shokalyuk // Innovative information and communication technology education in mathematics, physics, computer science in secondary and higher education: a collection of research papers on the materials of Ukrainian of scientific-methodical conference of Young Scientists, 17-18 February 2011 – Kryvyi Rig: Kryvyi Rig State Pedagogical University, 2011. – P. 364-367 (in Ukrainian).
5. Rashevska N. V. Mobilni informatsiyno-komunikatsiyni tekhnolohiyi navchannya vyshchoyi matematyky studentiv vyshchykh tekhnichnykh navchalnykh zakladiv: dys. … k. ped. nauk: 13.00.10 [Mobile Information and Communication Technology Learning of Mathematics students of technical schools: dis. k ... ped. sciences: 13.00.10] / Natalya Vasylivna Rashevska; Institute of Information Technologies and Learning Tools of the National Academy of Pedagogical Sciences of Ukraine. – K., 2011. – 244 p. (in Ukrainian)
6. Semerikov S. O. Teoriya i metodyka zastosuvannya mobilnyh matematychnyh seredovyshch u protsesi navchannya vyshchoyi matematyky studentiv ekonomichnyh spetsialnostey [Theory and methods of use of mobile media in the mathematical study of higher mathematics students of economic specialties] / S. O. Semerikov, K. I. Slovak // Information technology and learning tools – 2011. – № 1 (21). – Available from: http://journal.iitta.gov.ua/index.php/itlt/article/view/413/369#.UvtgYIX... (in Ukrainian).
7. Slovak K. I. ICT intensification of teaching and learning of students [Information and communication technologies intensify teaching and learning of students] / Kateryna Ivanivna Slovak // Electronic scientific specialized edition of "Scientific Bulletin of Donbass". – 2011. – №3 (15). – Available from: http://nvd.luguniv.edu.ua/archiv/NN15/11skinds.pdf (in Ukrainian).
8. Slovak K. I. Lecture demonstration course in higher mathematics [Lecture demonstration course in higher mathematics] / K. I. Slovak, M. V. Popiel // The latest computer technology materials VIII International Scientific Conference: Kyiv, Sevastopol, 14-17 September 2010 – Kyiv: Ministry of Regional development and Construction of Ukraine, 2010. – P. 142-144 (in Ukrainian).
9. Slovak K. I. Metodyka vykorystannya mobilʹnykh matematychnykh seredovyshch u protsesi navchannya vyshchoyi matematyky studentiv ekonomichnykh spetsialnostey: dys. … k. ped. nauk: 13.00.10 [Methods of mathematical use of mobile media in teaching higher mathematics students of economic specialties: dis. k ... ped. sciences: 13.00.10] / Kateryna Ivanivna Slovak; Institute of Information Technologies and Learning Tools of the National Academy of Pedagogical Sciences of Ukraine. – K., 2010. – 290 p. (in Ukrainian)
10. Shyshkina M. P. Khmaro oriyentovane seredovyshche navchalnoho zakladu: suchasnyy stan i perspektyvy rozvytku doslidzhen [Cloud based learning environment of educational institutions: the current state and research prospects] / M. P. Shyshkina, M. V. Popel // Informatsiyni tekhnolohiyi i zasoby navchannya [Elektronnyy resurs]. – 5(37). – 2013. Available from: http://journal.iitta.gov.ua/index.php/itlt/article/view/903/676 (in Ukrainian)
</uk>
<en>
1. Bondarenko T. V. Informatsiyni tekhnolohiyi na urotsi matematyky [Information technology in math class] / T. V. Bondarenko, I. I. Dmitrenco // Theory and methods of teaching mathematics, physics, computer science: Collection of scientific works: in 3 vols. – Kryvyi Rig: Publishing Department KDPU, 2001. – Vol 1: Theory and methods of teaching mathematics. – P. 29-31 (in Ukrainian).
2. Kobylnyk T. P. Rozvyazuvannya zadach z parametramy z vykorystannyam kompyutera [Solving problems with parameters using a computer] / T. P. Kobylnyk // Teoriya ta metodyka navchannya matematyky, fizyky, informatyky: Zbirnyk naukovykh prats. Vypusk V: V 3-kh tomah. – Kryvyy Rih: Vydavnychyy viddil NMetAU, 2005. – T. 1: Teoriya ta metodyka navchannya matematyky. – P. 134-139 (in Ukrainian).
3. Merzlyak A. G Alhebra. 11 klas: pidruch. dlya zahalnoosvit. navch. zakladiv : akadem. riven, prof. riven [Algebra. 11 class: textbook for secondary schools: academic level, profile level] / A. G. Merzlyak, D. A. Nomirovskyy, V. B. Polonsky, M. S. Yakir – H.: Gymnasium, 2011. – 431 p. (in Ukrainian).
4. Popel M. V. Prohramni zasoby navchalnoho modelyuvannya [Educational software simulation] / M. V. Popel, S. V. Shokalyuk // Innovative information and communication technology education in mathematics, physics, computer science in secondary and higher education: a collection of research papers on the materials of Ukrainian of scientific-methodical conference of Young Scientists, 17-18 February 2011 – Kryvyi Rig: Kryvyi Rig State Pedagogical University, 2011. – P. 364-367 (in Ukrainian).
5. Rashevska N. V. Mobilni informatsiyno-komunikatsiyni tekhnolohiyi navchannya vyshchoyi matematyky studentiv vyshchykh tekhnichnykh navchalnykh zakladiv: dys. … k. ped. nauk: 13.00.10 [Mobile Information and Communication Technology Learning of Mathematics students of technical schools: dis. k ... ped. sciences: 13.00.10] / Natalya Vasylivna Rashevska; Institute of Information Technologies and Learning Tools of the National Academy of Pedagogical Sciences of Ukraine. – K., 2011. – 244 p. (in Ukrainian)
6. Semerikov S. O. Teoriya i metodyka zastosuvannya mobilnyh matematychnyh seredovyshch u protsesi navchannya vyshchoyi matematyky studentiv ekonomichnyh spetsialnostey [Theory and methods of use of mobile media in the mathematical study of higher mathematics students of economic specialties] / S. O. Semerikov, K. I. Slovak // Information technology and learning tools – 2011. – № 1 (21). – Available from: http://journal.iitta.gov.ua/index.php/itlt/article/view/413/369#.UvtgYIX... (in Ukrainian).
7. Slovak K. I. ICT intensification of teaching and learning of students [Information and communication technologies intensify teaching and learning of students] / Kateryna Ivanivna Slovak // Electronic scientific specialized edition of "Scientific Bulletin of Donbass". – 2011. – №3 (15). – Available from: http://nvd.luguniv.edu.ua/archiv/NN15/11skinds.pdf (in Ukrainian).
8. Slovak K. I. Lecture demonstration course in higher mathematics [Lecture demonstration course in higher mathematics] / K. I. Slovak, M. V. Popiel // The latest computer technology materials VIII International Scientific Conference: Kyiv, Sevastopol, 14-17 September 2010 – Kyiv: Ministry of Regional development and Construction of Ukraine, 2010. – P. 142-144 (in Ukrainian).
9. Slovak K. I. Metodyka vykorystannya mobilʹnykh matematychnykh seredovyshch u protsesi navchannya vyshchoyi matematyky studentiv ekonomichnykh spetsialnostey: dys. … k. ped. nauk: 13.00.10 [Methods of mathematical use of mobile media in teaching higher mathematics students of economic specialties: dis. k ... ped. sciences: 13.00.10] / Kateryna Ivanivna Slovak; Institute of Information Technologies and Learning Tools of the National Academy of Pedagogical Sciences of Ukraine. – K., 2010. – 290 p. (in Ukrainian)
10. Shyshkina M. P. Khmaro oriyentovane seredovyshche navchalnoho zakladu: suchasnyy stan i perspektyvy rozvytku doslidzhen [Cloud based learning environment of educational institutions: the current state and research prospects] / M. P. Shyshkina, M. V. Popel // Informatsiyni tekhnolohiyi i zasoby navchannya [Elektronnyy resurs]. – 5(37). – 2013. Available from: http://journal.iitta.gov.ua/index.php/itlt/article/view/903/676 (in Ukrainian)
</en>
1. Bondarenko T. V. Informatsiyni tekhnolohiyi na urotsi matematyky [Information technology in math class] / T. V. Bondarenko, I. I. Dmitrenco // Theory and methods of teaching mathematics, physics, computer science: Collection of scientific works: in 3 vols. – Kryvyi Rig: Publishing Department KDPU, 2001. – Vol 1: Theory and methods of teaching mathematics. – P. 29-31 (in Ukrainian).
2. Kobylnyk T. P. Rozvyazuvannya zadach z parametramy z vykorystannyam kompyutera [Solving problems with parameters using a computer] / T. P. Kobylnyk // Teoriya ta metodyka navchannya matematyky, fizyky, informatyky: Zbirnyk naukovykh prats. Vypusk V: V 3-kh tomah. – Kryvyy Rih: Vydavnychyy viddil NMetAU, 2005. – T. 1: Teoriya ta metodyka navchannya matematyky. – P. 134-139 (in Ukrainian).
3. Merzlyak A. G Alhebra. 11 klas: pidruch. dlya zahalnoosvit. navch. zakladiv : akadem. riven, prof. riven [Algebra. 11 class: textbook for secondary schools: academic level, profile level] / A. G. Merzlyak, D. A. Nomirovskyy, V. B. Polonsky, M. S. Yakir – H.: Gymnasium, 2011. – 431 p. (in Ukrainian).
4. Popel M. V. Prohramni zasoby navchalnoho modelyuvannya [Educational software simulation] / M. V. Popel, S. V. Shokalyuk // Innovative information and communication technology education in mathematics, physics, computer science in secondary and higher education: a collection of research papers on the materials of Ukrainian of scientific-methodical conference of Young Scientists, 17-18 February 2011 – Kryvyi Rig: Kryvyi Rig State Pedagogical University, 2011. – P. 364-367 (in Ukrainian).
5. Rashevska N. V. Mobilni informatsiyno-komunikatsiyni tekhnolohiyi navchannya vyshchoyi matematyky studentiv vyshchykh tekhnichnykh navchalnykh zakladiv: dys. … k. ped. nauk: 13.00.10 [Mobile Information and Communication Technology Learning of Mathematics students of technical schools: dis. k ... ped. sciences: 13.00.10] / Natalya Vasylivna Rashevska; Institute of Information Technologies and Learning Tools of the National Academy of Pedagogical Sciences of Ukraine. – K., 2011. – 244 p. (in Ukrainian)
6. Semerikov S. O. Teoriya i metodyka zastosuvannya mobilnyh matematychnyh seredovyshch u protsesi navchannya vyshchoyi matematyky studentiv ekonomichnyh spetsialnostey [Theory and methods of use of mobile media in the mathematical study of higher mathematics students of economic specialties] / S. O. Semerikov, K. I. Slovak // Information technology and learning tools – 2011. – № 1 (21). – Available from: http://journal.iitta.gov.ua/index.php/itlt/article/view/413/369#.UvtgYIX... (in Ukrainian).
7. Slovak K. I. ICT intensification of teaching and learning of students [Information and communication technologies intensify teaching and learning of students] / Kateryna Ivanivna Slovak // Electronic scientific specialized edition of "Scientific Bulletin of Donbass". – 2011. – №3 (15). – Available from: http://nvd.luguniv.edu.ua/archiv/NN15/11skinds.pdf (in Ukrainian).
8. Slovak K. I. Lecture demonstration course in higher mathematics [Lecture demonstration course in higher mathematics] / K. I. Slovak, M. V. Popiel // The latest computer technology materials VIII International Scientific Conference: Kyiv, Sevastopol, 14-17 September 2010 – Kyiv: Ministry of Regional development and Construction of Ukraine, 2010. – P. 142-144 (in Ukrainian).
9. Slovak K. I. Metodyka vykorystannya mobilʹnykh matematychnykh seredovyshch u protsesi navchannya vyshchoyi matematyky studentiv ekonomichnykh spetsialnostey: dys. … k. ped. nauk: 13.00.10 [Methods of mathematical use of mobile media in teaching higher mathematics students of economic specialties: dis. k ... ped. sciences: 13.00.10] / Kateryna Ivanivna Slovak; Institute of Information Technologies and Learning Tools of the National Academy of Pedagogical Sciences of Ukraine. – K., 2010. – 290 p. (in Ukrainian)
10. Shyshkina M. P. Khmaro oriyentovane seredovyshche navchalnoho zakladu: suchasnyy stan i perspektyvy rozvytku doslidzhen [Cloud based learning environment of educational institutions: the current state and research prospects] / M. P. Shyshkina, M. V. Popel // Informatsiyni tekhnolohiyi i zasoby navchannya [Elektronnyy resurs]. – 5(37). – 2013. Available from: http://journal.iitta.gov.ua/index.php/itlt/article/view/903/676 (in Ukrainian)
</uk>
<en>
1. Bondarenko T. V. Informatsiyni tekhnolohiyi na urotsi matematyky [Information technology in math class] / T. V. Bondarenko, I. I. Dmitrenco // Theory and methods of teaching mathematics, physics, computer science: Collection of scientific works: in 3 vols. – Kryvyi Rig: Publishing Department KDPU, 2001. – Vol 1: Theory and methods of teaching mathematics. – P. 29-31 (in Ukrainian).
2. Kobylnyk T. P. Rozvyazuvannya zadach z parametramy z vykorystannyam kompyutera [Solving problems with parameters using a computer] / T. P. Kobylnyk // Teoriya ta metodyka navchannya matematyky, fizyky, informatyky: Zbirnyk naukovykh prats. Vypusk V: V 3-kh tomah. – Kryvyy Rih: Vydavnychyy viddil NMetAU, 2005. – T. 1: Teoriya ta metodyka navchannya matematyky. – P. 134-139 (in Ukrainian).
3. Merzlyak A. G Alhebra. 11 klas: pidruch. dlya zahalnoosvit. navch. zakladiv : akadem. riven, prof. riven [Algebra. 11 class: textbook for secondary schools: academic level, profile level] / A. G. Merzlyak, D. A. Nomirovskyy, V. B. Polonsky, M. S. Yakir – H.: Gymnasium, 2011. – 431 p. (in Ukrainian).
4. Popel M. V. Prohramni zasoby navchalnoho modelyuvannya [Educational software simulation] / M. V. Popel, S. V. Shokalyuk // Innovative information and communication technology education in mathematics, physics, computer science in secondary and higher education: a collection of research papers on the materials of Ukrainian of scientific-methodical conference of Young Scientists, 17-18 February 2011 – Kryvyi Rig: Kryvyi Rig State Pedagogical University, 2011. – P. 364-367 (in Ukrainian).
5. Rashevska N. V. Mobilni informatsiyno-komunikatsiyni tekhnolohiyi navchannya vyshchoyi matematyky studentiv vyshchykh tekhnichnykh navchalnykh zakladiv: dys. … k. ped. nauk: 13.00.10 [Mobile Information and Communication Technology Learning of Mathematics students of technical schools: dis. k ... ped. sciences: 13.00.10] / Natalya Vasylivna Rashevska; Institute of Information Technologies and Learning Tools of the National Academy of Pedagogical Sciences of Ukraine. – K., 2011. – 244 p. (in Ukrainian)
6. Semerikov S. O. Teoriya i metodyka zastosuvannya mobilnyh matematychnyh seredovyshch u protsesi navchannya vyshchoyi matematyky studentiv ekonomichnyh spetsialnostey [Theory and methods of use of mobile media in the mathematical study of higher mathematics students of economic specialties] / S. O. Semerikov, K. I. Slovak // Information technology and learning tools – 2011. – № 1 (21). – Available from: http://journal.iitta.gov.ua/index.php/itlt/article/view/413/369#.UvtgYIX... (in Ukrainian).
7. Slovak K. I. ICT intensification of teaching and learning of students [Information and communication technologies intensify teaching and learning of students] / Kateryna Ivanivna Slovak // Electronic scientific specialized edition of "Scientific Bulletin of Donbass". – 2011. – №3 (15). – Available from: http://nvd.luguniv.edu.ua/archiv/NN15/11skinds.pdf (in Ukrainian).
8. Slovak K. I. Lecture demonstration course in higher mathematics [Lecture demonstration course in higher mathematics] / K. I. Slovak, M. V. Popiel // The latest computer technology materials VIII International Scientific Conference: Kyiv, Sevastopol, 14-17 September 2010 – Kyiv: Ministry of Regional development and Construction of Ukraine, 2010. – P. 142-144 (in Ukrainian).
9. Slovak K. I. Metodyka vykorystannya mobilʹnykh matematychnykh seredovyshch u protsesi navchannya vyshchoyi matematyky studentiv ekonomichnykh spetsialnostey: dys. … k. ped. nauk: 13.00.10 [Methods of mathematical use of mobile media in teaching higher mathematics students of economic specialties: dis. k ... ped. sciences: 13.00.10] / Kateryna Ivanivna Slovak; Institute of Information Technologies and Learning Tools of the National Academy of Pedagogical Sciences of Ukraine. – K., 2010. – 290 p. (in Ukrainian)
10. Shyshkina M. P. Khmaro oriyentovane seredovyshche navchalnoho zakladu: suchasnyy stan i perspektyvy rozvytku doslidzhen [Cloud based learning environment of educational institutions: the current state and research prospects] / M. P. Shyshkina, M. V. Popel // Informatsiyni tekhnolohiyi i zasoby navchannya [Elektronnyy resurs]. – 5(37). – 2013. Available from: http://journal.iitta.gov.ua/index.php/itlt/article/view/903/676 (in Ukrainian)
</en>
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2015-03-06
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Попель M. (2015). МЕТОДИЧНІ АСПЕКТИ ВИКОРИСТАННЯ SAGEMATH CLOUD У НАВЧАННІ АЛГЕБРИ І ПОЧАТКІВ АНАЛІЗУ. Збірник наукових праць "Information Technologies in Education" (ITE), (19), 093–100. https://doi.org/10.14308/ite000488
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