Voskoglou M., Salem A.B. [mvoskoglou@gmail.com]
Graduate Technological Educational Institute of Western Greece, Patras, Greece
Download in PDF: http://fmo-journal.fizmatsspu.sumy.ua/journals/2020-v2-24/2020_2-24-Voskoglou-Salem_FMO.pdf


Formulation of the problem. Famous social thinkers of our times are speaking about a forthcoming new industrial revolution that will be characterized by the development of an advanced Internet of things and energy, and by the cyber-physical systems controlled through it. There is no doubt that our students should take full advantage of the potential that the new digital technologies can bring for improving their learning skills.
Materials and methods. This treatise has a review character. The methods of analysis used are based on already reported researches.
Results. The article focuses on the role that the artificial teaching and learning of mathematics could play for education in the forthcoming era of the new industrial revolution Starting with a brief review of the traditional learning theories and methods of teaching mathematics, the article continues by studying the use of computers and of applications of artificial intelligence in mathematics education.
Conclusions. The advantages and disadvantages of artificial with respect to traditional learning are discussed as well as the perspectives for future research on the subject.

Key words: internet of things and energy (IoT & E); learning theories; “5E’s”teaching method; APOS/ACE instructional treatment of mathematics; flipped learning (FL); artificial intelligence (AI); e-learning; machine learning (ML); smart learning system (SLS); ontological engineering; case-based reasoning (CBR); social robots.

Майкл Г. Воскоглу
Вищий технологічний освітній інститут Західної Греції, Греція
Абдел-Баді М. Салем
Аін Шамс Університет, Єгипет

Постановка проблеми. Відомі мислителі нашого часу говорять про майбутню нову індустріальну революцію, яка характеризуватиметься розвиненим Інтернетом речей і енергії та керованими через неї кібер-фізичними системами. Немає сумнівів, що наші студенти повинні вміти використовувати потенціал, який нові цифрові технології можуть принести для вдосконалення їх навичок.
Матеріали та методи.
Дана стаття має оглядовий характер. Використовуються методи аналізу існуючих досліджень з даної проблематики.
Результати. У статті приділяється увага ролі машинного навчання та вивчення математики для освіти в майбутній епосі нової промислової революції. Наведено короткий огляд традиційних теорій та методів навчання математики. Досліджено можливості використання комп'ютерів та додатків штучного інтелекту в навчанні математики.

Висновки. У статті обговорюються переваги та недоліки машинного відносно традиційного навчання, а також перспективи подальших досліджень з цього питання.
Ключові слова: інтернет речей та енергії (IoT & E); теорії навчання; метод навчання "5E"; APOS/ACE навчання математики; перевернуте навчання (FL); штучний інтелект (ШІ); електронне навчання; машинне навчання (ML); розумна система навчання (SLS); онтологічна інженерія; міркування на базі прецедентів (ЦБР); соціальні роботи.


  1. Arnold, L.; Rebecchi, S.; Chevallier, S.; Paugam-Moisy, H. (2011), An introduction to deep learning. In Proceedings of the European Symposium on Artificial Neural Networks, Bruges, Belgium, 27–29 April; pp. 477–488.
  2. Arnon, I.; Cottrill, J.; Dubinsky, E.; Oktac, A.; Roa, S.; Trigueros, M.; Weller, K. (2014), APOS Theory: A Framework for Research and Curriculum Development in Mathematics Education; Springer: Berlin/Heidelberg, Germany.
  3. Bergmann, J.; Sams, A. (2012), Flip Your Classroom: Reach Every Student in Every Class Every Day, 1st ed.; ISTE: Washington, DC, USA; pp. 34–40.
  4. Borji, V.; Voskoglou, M.G. (2016), Applying the APOS theory to study the student understanding of the polar coordinates. Am. J. Educ. Res., 4, 1149–1156.
  5. Breazeal, C. (2002), Designing Sociable Robots; MIT Press: Cambridge, MA, USA.
  6. Cakula, S.; Salem, A.-B.M. (2011), Ontology-Based Collaborative Model for e-Learning. In Proceedings of the Annual International Conference on Virtual and Augmented Reality in Education, Latvia, Valmiera, 18 March; pp. 98–105.
  7. Cherry, K. History and Key Concepts of Behavioral Psychology (2019). Available online: https://www.verywellmind.com/behavioral-psychology-4157183 (accessed on March 18 2020).
  8. Crawford, K. Vygotskian approaches in human development in the information era (1996). Educ. Stud. Math., 31, 43–62.
  9. Das, S.; Day, A.; Pal, A.; Roy, N. (2015), Applications of artificial intelligence in machine learning. Int. J. Comput. Appl., 115, 31–41.
  10. Dneprovskaya, N.V. Knowledge management system as a basis for smart learning (2018). Open Educ., 22, 43–61.
  11. Doabler, T.; Fien, H. (2013), Explicit mathematics instruction: What teachers can do for teaching students with mathematics difficulties. Interv. Sch. Clin., 48, 276–285.
  12. Einhorn, S. Micro-Worlds, Computational Thinking, and 21st Century Learning (2012); Logo Computer Systems Inc., White Paper: Westmount, QC, Canada.
  13. Gallistel, C.R. Mathematical cognition (2005). In The Cambridge Handbook for Thinking and Reasoning; Holyak, K., Morrison, R., (Eds.); Cambridge University Press: Cambridge, UK,; pp. 559–588.
  14. Goyal, S. E-Learning: Future of education (2012). J. Educ. Learn., 6, 239–242.
  15. Hodges, A. (2012), Alan Turing: The Enigma (The Centenary Edition); Princeton University Press: Princeton, NJ, USA.
  16. Jaworski, B. (2006), Theory and practice in mathematics teaching development: Critical inquiry as a mode of learning in teaching. J. Math. Teach. Educ., 9, 187–211.
  17. Kastranis, A. (2019), Artificial Intelligence for People and Business; O’ Reily Media Inc.: Sebastopol, CA, USA.
  18. Kim, T.; Cho, J.Y.; Lee, B.G. (2013), Evolution to smart learning in public education: A case study of Korean public education. In Proceedings of the IFIP Advances in Information and Communication Technology International Conference on Open and Social Technologies for Networked Learning; Ley, T., Ruohonen, M., Laanpere, M., Tatnall, A. (Eds.); Springer: Berlin/Heidelberg, Germany, Volume 395.
  19. Kinard, J.T. (2008), Rigorous Mathematical Thinking: Conceptual Formation in the Mathematics Classroom; Cambridge University Press: Cambridge, UK.
  20. Klir, G.J.; Folger, T.A. (1988), Fuzzy Sets, Uncertainty and Information; Prentice-Hall: London, UK.
  21. Lahdenpera, J.; Postareff, L.; Ramo, J. (2019), Supporting quality of learning in university mathematics: A comparison of two instructional designs. Int. J. Res. Undergrad. Mat. Educ., 5, 75–96.
  22. Lage, M.G.; Platt, G.J.; Tregla, M. (2000), Inverting the classroom: A gateway to create an inclusive learning environment. J. Econ. Educ., 31, 30–43.
  23. Lee, J.; Lim, C.; Kim, H. (2017), Development of an instructional design model for flipped learning in higher education. Educ. Technol. Res. Dev., 65, 427–453.
  24. Martinez-Garcia, M.; Zhang, Y.; Gordon, T. (2016), Modeling lane keeping by a hybrid open-closed loop pulse control scheme. IEEE Trans. Ind. Inform., 12, 2256–2265.
  25. Martinez-Garcia, M.; Gordon, T.; Shu, L. (2017), Extended crossover model for human-control of fractional order plants. IEEE Access, 5, 27622–27635.
  26. Martinez-Garcia, M.; Zhang, Y.; Gordon, T. (2019), Memory pattern identification for feedback tracking control in human-machine systems. Hum. Factors, 0018720819881008, doi:10.1177/0018720819881008.
  27. McKinley, J. (2015), Critical argument and writer identity: Social constructivism as a theoretical framework for EFL academic writing. Crit. Inq. Lang . Stud., 12, 184–207.
  28. Merzon, E.E.; Ibatullin, R.R. (2016), Architecture of smart learning courses in higher education. In Proceedings of the IEEE 10th International Conference on Application of Information and Communication Technologies, Baku, Azerbaijan, 12–14 October; pp. 1–5.
  29. Mitchell, M. (2019), Artificial Intelligence: A Guide for Thinking Humans; Parrar, Straus and Gtraux: New York, NY, USA.
  30. Moor, J. (2006), The Dartmouth college artificial intelligence conference: The next fifty years. AI Mag., 27, 87–91.
  31. Payne Carter, S.; Greenberg, K.; Walter, M. (2016), The Impact of Academic Usage in Academic Performance: Evidence from a Randomized Trial on the US Military Academy, Working Paper #2016.02, US Military Academy, Available online: https://seii.mit.edu/research/study /the-impact-of-computer-usage -on -academic-performance-evidence-from-a-randomized-trial-at-the-united-states-military-academy .
  32. Rifkin, J. (2011), The Third Industrial Revolution: How Lateral Power is Transforming Energy, the Economy and the World; Palgrave McMillan: London, UK.
  33. Rifkin, J. (2014), The Zero Marginal Cost Society: The Internet of Things, the Collaborative Commons and the Eclipse of Capitalism; St. Martin’s Press: New York, NY, USA.
  34. Salem, A.-B.M. (2010), Ontological engineering in e-learning. In Proceedings of 8th International Conference on Emerging E-Learning Technologies and Applications, Information and Communication Technologies in Learning, Stara Lesna, The High Tatras, Slovakia, 27–29 October.
  35. Salem, A.-B.M. (2011), Intellectual e-learning systems. In Proceedings of the Annual International Conference on Virtual and Augmented Reality in Education, Vidzeme University of Applied Sciences, Valmiera, Latvia, 18 March; pp. 16–23.
  36. Salem, A.B.M.; Parusheva, S. (2018), Exploiting the knowledge engineering paradigms for designing smart learning systems. East. -Eur. J. Enterp. Technol., 2, 38–44.
  37. Salem, A.B.M. (2019), Computational intelligence in smart education and learning. In Proceedings of the International Conference on Information and Communication Technology in Business and Education, University of Economics, Varna, Bullgaria, pp. 30–40.
  38.  Salem, A.B.M.; Nikitaeva, N. (2019), Knowledge engineering paradigms for smart education and smart learning systems. In Proceedings of the 42nd International Convention of the MIPRO Croatian Society, Opatija, Croatia, 20–24 May; pp. 1823–1826.
  39. Schwab, K. (2016), The Fourth Industrial Revolution; Crown Publishing Group: New York, NY, USA,.
  40. Smith, J.L.M.; Saez, L.; Doabler, C.T. (2016), Using explicit and systematic instruction to support working memory. Teach. Except. Child., 48, 275–281.
  41. Taber, K.S. (2011), Constructivism as educational theory: Contingency in learning, and optimally guided instruction. In Educational Theory; Hassaskhah, J., Ed.; Nova Science Publishers: Hauppauge, NY, USA; Chapter 2, pp. 39–61.
  42. Taipale, S.; Vincent, J.; Sapio, B.; Lugano, G.; Fortunati, L. (2015), Introduction: Situating the human in social robots. In Social Robots from a Human Perspective; Vincent, J., Taipale, S., Sapio, B., Lugano, G., Fortunati, L., Eds.; Springer: Dordrecht, The Netherlands; pp. 1–17.
  43. Tankelevcience, L.; Damasevicius, F. (2009) Characteristics for domain ontologies for web based learning and their applications for quality evaluation. Inform. Educ., 8, 131–152.
  44. Voskoglou, M.G. (2005), The application-oriented teaching of mathematics. In Proceedings of the International Conference on Mathematics Education, Svishtov, Bulgaria, 3–5 June; pp. 85–90.
  45. Voskoglou, M.G. (2008), Case-based reasoning: A recent theory for problem-solving and learning in computers and people. Commun. Comput. Inf. Sci., 19, 314–319, Springer: Berlin/Heidelberg, Germany.
  46. Voskoglou, M.G. (2010), Problem-solving as a component of the constructivist view of learning. J. Educ. Res., 4, 93–112.
  47. Voskoglou, M. G.; Buckley, S. (2012), Problem solving and computers in a learning environment. Egypt. Comput. Sci. J., 36, 28–46.
  48. Voskoglou, M.G. (2013), An application of the APOS/ACE approach in teaching the irrational numbers. J. Math. Sci. Math. Educ., 8, 30–47.
  49. Voskoglou, M.G.; Salem, A.B.M. (2014), Analogy based and case based reasoning: Two sides of the same coin. Int. J. Appl. Fuzzy Sets Artif. Intell., 4, 5–51.
  50. Voskoglou, M.G. (2016), Problem solving in the forthcoming era of the third industrial revolution, Int. J. Psychol. Res., 10, 361–380.
  51. Voskoglou, M.G. (2017), Finite Markov Chain and Fuzzy Logic Assessment Models: Emerging Research and Opportunities; Create Space Independent Publishing Platform, Amazon: Columbia, SC, USA.
  52. Voskoglou, M.G. (2019), Communities of practice for teaching and learning mathematics. Am. J. Educ. Res., 7, 186–191.
  53. Voskoglou, M.G. (2019), A Markov chain representation of the “5 E’s” instructional treatment. Phys. Math. Educ., 3, 7–11.
  54. Voskoglou, M.G. (2019), Comparing teaching methods of mathematics at university level. Educ. Sci. 2019, 9, 294.
  55. Voskoglou, M.G. (2019), Generalizations of fuzzy sets and relative theories. In An Essential Guide to Fuzzy Systems, Commentary; Voskoglou, M. (Ed.); Nova Science Publishers Inc.: Hauppauge, NY, USA; pp. 345–353.
  56.  Voskoglou, M.G. (2019), An application of the “5 E’s” Instructional treatment for teaching the concept of the fuzzy set. Sumer. J. Educ. Linguist. Lit., 2, 73–76.
  57. Wallace, B.; Ross, A.; Davies, J.B.; Anderson, T. (2007), The Mind, the Body and the World: Psychology after Cognitivism; Imprint Academic: Upton Pyne, UK.
  58. Yang, X. (2019), Accelerated move to AI in China. ECNU Rev. Educ., 2, 347–352.
  59. Zadeh, L.A. (1965), Fuzzy sets. Inf. Control, 8, 338–353.
Додано: 26.08.2020 | Переглядів: 62 | Рейтинг: 0.0/0
Статті з теми:
Всього коментарів: 0