THE VARIATIV MODEL FOR RESEARCH TRAINING FOR MATH STUDENTS USING COMPUTER-ORIENTED METHODICAL SYSTEM

Keywords: teaching mathematics, research objectives, computer experiment, computer systems, mathematics, computer-oriented methodical systems for research training, mathematical modeling; model, formalization, similarity, analogy, the properties of the model

Abstract

The author examines methodological principles of simulation relating to the theory of knowledge. Special attention is paid to the concept of analogy as well as to its importance for simulation, synthesis and abstraction, isomorphism and homomorphism. The article considers some peculiarities of modeling and highlights the versatility of simulation as a research method. The article also outlines the need for experimental research as well as for the research method for teaching mathematics to school students. Research objectives are considered as a kind of learning tasks for problem situations solving, requiring the experimentation with dynamic models of mathematical objects. The author examines the use of special mathematical software and mathematical methods for teaching mathematics as well as for the experiments in mathematics, including computer modeling application. The classification of educational software for the development of students’ creative potential is proposed. The paper considers method system of research training in mathematics as a computer-oriented training system. The author focuses on the possibilities of using systematic research techniques and teaching methods, variative didactic constructs for teaching mathematics. The level model of research training and the classification of research objectives are studied. We offer the possibility of adjustment to the user of the computer-oriented system of education. The relationship between the model, on the one hand, and material and non-material types of the prototype, on the other hand, is analysed. The features of new information and communication technologies application are discussed. The author clarifies the definition of the model. Attention is also paid to the model stages which facilitate the content of the simulation algorithm reveal. The article considers the possibility of using computer mathematics systems in computer studies while teaching mathematics in the classroom and in extracurricular time. In the study we formulate the objectives on the generalization of properties, types, tasks, and functions as a universal method of knowledge (parametricity, consistency, information, imagery, abstraction, simplification). The paper clarifies the definition of a model and specifies the properties of the model as an epistemological tool.

Author Biography

Olena O. Hrybiuk , Institute of Information Technologies and Learning Tools of the NAES of Ukraine

PhD of Pedagogical Sciences, Leading Researcher

References

В.П. Беспалько, “Образование и обучение с участием компьютеров (педагогика третьего тысячелетия)”, Москва, Изд-во Моск. психол.-социал. ин-та, Воронеж: МОДЭК, 2002.

В.Ю. Биков, “Моделі організаційних систем відкритої освіти: Монографія”, Київ, Атіка, 2008.

В.М. Глушков, “Основы безбумажной информатики”, Москва, Наука, 552 с., 1987.

А.П. Ершов, “Компьютеризация школы и математическое образование”, Информатика и образование, 5-6, С. 3-12, 1992.

M.I. Zhaldak, “Mathematics with a Computer”, Kyiv, National Dragomanov Pedagogical University, 2016.

М.П. Лапчик, “Информатика и информационные технологии в системе общего и педагогического образования. Монография”, Омск, изд-во ОмГПУ, 1999.

Е.И. Машбиц, “Психологические основы управления учебной деятельностью”, Киев, Высшая школа, 1987.

Н.Н. Моисеев, “Время определять национальные цели”, Москва, Изд-во МНЭПУ, С.172-173, 1997.

И.А. Новик, “Современные тенденции в проведении исследований по теории и методике обучения естественным наукам (математике, физике, информатике): пособие”, Минск, БГПУ, 2005.

S. Papert, “Mindstorms. Children, Computers and Powerful Ideas”, Second Edition,. NY, «BasicBooks», 1993.

Е.С. Полат, “Современные педагогические и информационные технологии в системе образования: учебное пособие для вузов”, Москва, Академия, 2007.

И.В. Роберт, “Современные информационные технологии в образовании: дидактические проблемы; перспективы использования”, Москвa, Школа-Пресс, 1994.

Tim S. Roberts, “Online Collaborative Learning: Theory and Practice Central Queensland University”, Australia Release Date, July, 2003.

В.П. Беспалько, “Образование и обучение с участием компьютеров (педагогика третьего тысячелетия)”, Москва, Изд-во МПСИ, Воронеж, МОДЭК, 2002.

М.І. Жалдак, “Використання комп’ютера в навчальному процесі має бути педагогічно виваженим”, Інформатика та інформаційні технології в навчальних закладах, 1, С.10-18, 2013.

К.К. Колин, “Социальная информатика: Учебное пособие для вузов”, Москва, 2003.

Е.И. Машбиц, “Психологические основы управления учебной деятельностью”, Киев, Высшая школа, 1987.

И.В. Роберт, “Развитие информатизации образования на основе цифровых технологий: интеллектуализация процесса обучения, возможные негативные последствия”, Наука о человеке: гуманитарные исследования,. № 4 (30), С.65-71, 2017.

В.А. Сластенин, Л.С. Подымова, “Педагогика: инновационная деятельность”, Москва, Магистр, 1997.

М.Л. Смульсон, “Психологія розвитку інтелекту”, Київ, Нора-друк, 2003.

Н.Ф. Талызина, “Педагогическая психология: учеб. пособие”, Москва, Академия, 288 с., 1998.

W. Blum, “ICMI Study 14: Applications and modelling in mathematics education-Discussion document”. Educational Studies in Mathematics, 51(1-2), 49-171, 2002.

M. Niss, W. Blum, “Galbraith, Introduction”. In W. Blum, P. L. Galbraith, H.-W. Henn, M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study, New York: Springer, pp. 3–32, 2007.

G. Kaiser, B. Schwarz, N. Buchholtz, “Authentic modelling problems in mathematics education”. In G. Kaiser, W. Blum, R. Borromeo Ferri, G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling, Dordrecht, Springer, pp. 591–601, 2011.

A. Bhattacherjee, “Social Science Research: Principles, Methods, and Practices”, 2012.

P. Frejd, “Mathematical modelling as a professional activity: Lessons for the classroom”. In G.A. Stillman, W. Blum, & G. Kaiser (Eds.), Mathematical modelling and applications, Cham: Springer, pp. 371–388, 2017.

Н. Г. Чикуров, “Моделирование систем и процессов: Учебное пособие”, ИЦ РИОР, НИЦ Инфра, М, 398 с., 2013.

А. А. Самарский, А. П. Михайлов, “Математическое моделирование: Идеи. Методы. Примеры”, 2-е изд., испр., Москва, Физматлит, 320 с., 2001.

Е. С. Кубрякова, “Краткий словарь когнитивных терминов”, Москва, Филол. ф-т МГУ им. М.В. Ломоносова, С. 14-145, 1997.

А.П. Ершов, “Компьютеризация школы и математическое образование. Избранные труды”, Новосибирск, Наука, С. 18, 1994.

В.И. Арнольд, “Математика и математическое образование в современном мире”, Математическое образование, Вып.2, С.109-112, 1997.

O. Hrybiuk, “Problems of Expert Evaluation in Terms of the use of Variative Models of a Computer-oriented Learning Environment of Mathematical and Natural Science Disciplines in Schools”, Zeszyty Naukowe Politechniki Poznańskiej. Seria: Organizacja i Zarządzanie, Zeszyt Nr 79, Poznań, Wydawnictwo Politechniki Poznańskiej WPP, s. 101-119, 2019.

О.О. Гриб’юк, “Математичне моделювання при навчанні дисциплін математичного та хіміко-біологічного циклів: навчально-методичний посібник для учителів ”, Рівне, 207 с., 2010.

О.О. Гриб’юк, “Дослідницьке навчання учнів предметів природничо-математичного циклу з використанням комп’ютерно орієнтованих методичних систем. Монографія”, Київ, НПУ імені М.П. Драгоманова, 848 с., 2019.

O. Hrybiuk, “Improvement of the Educational Process by the Creation of Centers for Intellectual Development and Scientific and Technical Creativity”, Advances in Manufacturing II. MANUFACTURING 2019. Lecture Notes in Mechanical Engineering. Springer, Cham Online, 2019,

О.О. Гриб’юк, “Перспективи впровадження варіативних моделей комп’ютерно орієнтованого середовища навчання предметів природничо-математичного циклу у загальноосвітніх навчальних закладах України”, Збірник наукових праць Кам’янець-Подільського національного університету імені Івана Огієнка. Серія педагогічна, Випуск 22: Дидактичні механізми дієвого формування компетентнісних якостей майбутніх фахівців фізико-технологічних спеціальностей, Кам’янець-Подільський, Кам’янець-Подільський національний університет імені Івана Огієнка, С. 184-190, 2016.


REFERENCES (TRANSLATED AND TRANSLITERATED)

V.P. Bespalko, Education and Learning Involving Computers (Pedagogy of the Third Millennium), Moscow, Moscow Publishing House of Psycho-Social Institute, Voronezh: MODEK, 2002 (in Russian).

V.Yu. Bykov, Models of the Open Education Organizational Systems: Monograph, Kyiv, Atika, 2008 (in Ukrainian).

V.M. Glushkov, Basics of Paperless Computer Science, Moscow, Nauka, 552 p., 1987 (in Russian).

A.P. Ershov, “Computerization of School and Mathematical Education”, Informatics and Education, 5-6, pp. 3-12, 1992 (in Russian).

M.I. Zhaldak, Mathematics with a Computer, Kyiv, National Dragomanov Pedagogical University, 2016 (in English).

M.P. Lapchik, Informatics and Information Technologies in the System of General and Pedagogical Education. Monograph, Omsk, Omsk State Pedagogical University Publishing House, 1999 (in Russian).

E.I. Mashbits, Psychological Foundations of Learning Activity Management, Kyiv, Higher School, 1987 (in Russian).

N.N. Moiseev, Time to Define National Goals, Moscow, Publishing House of the International Independent University of Environmental and Political Sciences, pp. 172-173, 1997 (in Russian).

I.A. Novik, Modern Tendencies in Conducting Research in the Theory and Methods of Teaching Natural Sciences (Mathematics, Physics, IT): A Manual, Minsk, Belarus State Pedagogical University, 2005 (in Russian).

S. Papert, Mindstorms. Children, Computers and Powerful Ideas, Second Edition, NY, BasicBooks, 1993 (in English).

E.S. Polat, Modern Pedagogical and Information Technologies in the Education System: A Textbook for Students of Higher Educational Institutions, Moscow, Academy, 2007 (in Russian).

I.V. Robert, Modern Information Technologies in Education: Didactic Problems; Perspectives of Usage, Moscow, Shkola-Press, 1994 (in Russian).

T. S. Roberts, Online Collaborative Learning: Theory and Practice Central Queensland University, Australia Release Date, July, 2003 (in English).

V.P. Bespalko, Pedagogy and advanced learning technologies, Moscow: PRESS, 1995 (in Russian).

M.I. Zhaldak, “The use of computers in the educational process should be pedagogically balanced”, Informatics and Information Technologies at Schools, 1, pp.10-18, 2013 (in Ukrainian).

K.K. Kolin, Social Informatics: A Manual for Students, Moscow, 2003 (in Russian).

E.I. Mashbits, Psychology and pedagogical problems of a computerization of training, Moscow, Pedagogy, 1988 (in Russian).

I.V. Robert, “Development of Informatization of Education on the basis of Digital Technologies: intellectualization of the learning process, possible negative consequences”, Human Science: Humanities, № 4 (30), pp.65-71, 2017 (in Russian).

V.A. Slastenin, and L.S. Podymova, “Pedagogy: Innovative Activity”, Moscow, Master, 1997 (in Russian).

M.L. Smulson, Psychology of Intellect Development, Kyiv, Nora-Druk, 2003 (in Ukrainian).

N.F. Talyzina, Pedagogical Psychology: A Manual, Moscow, Academy, 288 p., 1998 (in Russian).

W. Blum, “ICMI Study 14: Applications and Modelling in Mathematics Education-Discussion document”. Educational Studies in Mathematics, 51(1-2), pp. 49-171, 2002 (in English).

M. Niss, and W. Blum, “Galbraith, Introduction”. In W. Blum, P. L. Galbraith, H.-W. Henn, M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study, New York: Springer, pp. 3–32, 2007 (in English).

G. Kaiser, B. Schwarz, and N. Buchholtz, “Authentic Modelling Problems in Mathematics Education”. In G. Kaiser, W. Blum, R. Borromeo Ferri, G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling, Dordrecht, Springer, pp. 591–601, 2011 (in English).

A. Bhattacherjee, Social Science Research: Principles, Methods, and Practices, 2012 (in English).

P. Frejd, “Mathematical Modelling as a Professional Activity: Lessons for the classroom”. In G.A. Stillman, W. Blum, & G. Kaiser (Eds.), Mathematical modelling and applications, Cham: Springer, pp. 371–388, 2017 (in English).

N.G. Chikurov, Modeling of Systems and Processes: A Manual, IC RIOR, SIC Infra, M, 398 p., 2013 (in Russian).

A.A. Samarsky, and A.P. Mikhailov, Mathematical Modeling: Ideas. Methods. Examples, 2nd ed., Edited, Moscow, Fizmatlit, 320 p., 2001 (in Russian).

E.S. Kubryakova, Short Dictionary of Cognitive Terms, Moscow, Philological Faculty of Lomonosov Moscow State University, P. 14-145, 1997 (in Russian).

A.P. Ershov, Computerization of School and Mathematical Education. Selected works, Novosibirsk, Nauka, p. 18, 1994 (in Russian).

V.I. Arnold, Mathematics and Mathematical Education in the Modern World, Mathematical Education, Issue 2, pp.109-112, 1997 (in Russian).

O. Hrybiuk, “Problems of Expert Evaluation in Terms of the use of Variative Models of a Computer-oriented Learning Environment of Mathematical and Natural Science Disciplines in Schools”, Zeszyty Naukowe Politechniki Poznańskiej. Seria: Organizacja i Zarządzanie, Zeszyt Nr 79, Poznań, Wydawnictwo Politechniki Poznańskiej WPP, s. 101-119, 2019 (in English).

O.O. Hrybiuk, Mathematical Modeling in the Teaching of the Disciplines of Mathematical and Chemical-Biological Cycles: A Manual for Teachers, Rivne: RSGU, 207 p., 2010 (in Ukrainian).

O.O. Hrybiuk, Research Studying of Students of the Subjects of the Natural and Mathematical Cycle Using Computer-Oriented Methodological Systems. Monograph, Kyiv: Drahomanov NPU, 848 p., 2019 (in Ukrainian).

O. Hrybiuk, “Improvement of the Educational Process by the Creation of Centers for Intellectual Development and Scientific and Technical Creativity”, Advances in Manufacturing II. MANUFACTURING 2019. Lecture Notes in Mechanical Engineering, Springer, Cham Online, 2019 (in English).

O.O. Hrybiuk, “Prospects of Introduction of Variational Models of Computer-Oriented Environment for Teaching Subjects of the Natural and Mathematical Cycle in Secondary Schools of Ukraine”, The Collection of scientific works of Kamyanets-Podilskyi Ivan Ogienko National University. Pedagogical Series, Issue 22: Didactic mechanisms of effective formation of competence qualities of future specialists of physical and technological specialties, Kamyanets-Podilskyi, Kamyanets-Podilskyi Ivan Ogienko National University, pp. 184-190, 2016 (in Ukrainian).

Published
2020-06-19
Section
ICT and learning tools in secondary education