The Concept of Theoretical-Empirical Dualism in Teaching Math
Among the problems of mathematical education, the article highlights: (1) insufficient attention paid to the fundamental, structure-forming role of mathematics; (2) speculative learning, its isolation from practice. The concept of theoretical-empirical dualism in teaching is formulated as the unity...
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| Format: | Article |
| Language: | English |
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Moscow Polytechnic University
2020-05-01
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| Series: | Высшее образование в России |
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| Online Access: | https://vovr.elpub.ru/jour/article/view/2200 |
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| author | G. D. Gefan |
| author_facet | G. D. Gefan |
| author_sort | G. D. Gefan |
| collection | DOAJ |
| description | Among the problems of mathematical education, the article highlights: (1) insufficient attention paid to the fundamental, structure-forming role of mathematics; (2) speculative learning, its isolation from practice. The concept of theoretical-empirical dualism in teaching is formulated as the unity of the abstract-theoretical and experimental-empirical cognitive activity of students. According to the author, a priori and a posteriori mathematical knowledge should be distinguished. A priori knowledge either seems to an individual to be completely obvious, indisputable, or he assimilates it uncritically, “on faith”. A posteriori mathematical knowledge subjectively arises in the process of student’s intense theoretical and practical activity, and is being actively and comprehensively verified experimentally – either using mathematical applications, or through mathematical experiments. The empirical component of teaching mathematics implies a variety of forms and methods of active (including computer) and professionally oriented learning, giving experience in independent formulation of problems, joint search for ways to solve them, interaction and teamwork. Particular attention is paid to the use of mathematical experiments in those frequent cases when it is necessary to replace or supplement complex evidence, illustrate new knowledge, and give research skills. Monte Carlo mathematical experiments are demonstrated, which serve, in particular, as a bright, figurative, and convincing form of reinforcing theoretical knowledge in the field of stochastic branches of mathematics. The research work of students is considered as the highest stage of the students’ theoretical-empirical activity. The article proposes subjects of research activities of students in the process or upon completion of the study of probabilistic and statistical disciplines. |
| format | Article |
| id | doaj-art-98d8e6c99f634aa29e7968c06d52b3b5 |
| institution | Kabale University |
| issn | 0869-3617 2072-0459 |
| language | English |
| publishDate | 2020-05-01 |
| publisher | Moscow Polytechnic University |
| record_format | Article |
| series | Высшее образование в России |
| spelling | doaj-art-98d8e6c99f634aa29e7968c06d52b3b52025-02-01T13:14:27ZengMoscow Polytechnic UniversityВысшее образование в России0869-36172072-04592020-05-01294859510.31992/0869-3617-2020-29-4-85-951603The Concept of Theoretical-Empirical Dualism in Teaching MathG. D. Gefan0Irkutsk State Railway UniversityAmong the problems of mathematical education, the article highlights: (1) insufficient attention paid to the fundamental, structure-forming role of mathematics; (2) speculative learning, its isolation from practice. The concept of theoretical-empirical dualism in teaching is formulated as the unity of the abstract-theoretical and experimental-empirical cognitive activity of students. According to the author, a priori and a posteriori mathematical knowledge should be distinguished. A priori knowledge either seems to an individual to be completely obvious, indisputable, or he assimilates it uncritically, “on faith”. A posteriori mathematical knowledge subjectively arises in the process of student’s intense theoretical and practical activity, and is being actively and comprehensively verified experimentally – either using mathematical applications, or through mathematical experiments. The empirical component of teaching mathematics implies a variety of forms and methods of active (including computer) and professionally oriented learning, giving experience in independent formulation of problems, joint search for ways to solve them, interaction and teamwork. Particular attention is paid to the use of mathematical experiments in those frequent cases when it is necessary to replace or supplement complex evidence, illustrate new knowledge, and give research skills. Monte Carlo mathematical experiments are demonstrated, which serve, in particular, as a bright, figurative, and convincing form of reinforcing theoretical knowledge in the field of stochastic branches of mathematics. The research work of students is considered as the highest stage of the students’ theoretical-empirical activity. The article proposes subjects of research activities of students in the process or upon completion of the study of probabilistic and statistical disciplines.https://vovr.elpub.ru/jour/article/view/2200mathematicsa priori knowledgea posteriori knowledgeactive teaching methodsmathematical experimentsstochasticsstudent research |
| spellingShingle | G. D. Gefan The Concept of Theoretical-Empirical Dualism in Teaching Math Высшее образование в России mathematics a priori knowledge a posteriori knowledge active teaching methods mathematical experiments stochastics student research |
| title | The Concept of Theoretical-Empirical Dualism in Teaching Math |
| title_full | The Concept of Theoretical-Empirical Dualism in Teaching Math |
| title_fullStr | The Concept of Theoretical-Empirical Dualism in Teaching Math |
| title_full_unstemmed | The Concept of Theoretical-Empirical Dualism in Teaching Math |
| title_short | The Concept of Theoretical-Empirical Dualism in Teaching Math |
| title_sort | concept of theoretical empirical dualism in teaching math |
| topic | mathematics a priori knowledge a posteriori knowledge active teaching methods mathematical experiments stochastics student research |
| url | https://vovr.elpub.ru/jour/article/view/2200 |
| work_keys_str_mv | AT gdgefan theconceptoftheoreticalempiricaldualisminteachingmath AT gdgefan conceptoftheoreticalempiricaldualisminteachingmath |