Ретроспективний аналіз вивчення початків аналізу в старшій школі
Вантажиться...
Дата
2013
Автори
Назва журналу
Номер ISSN
Назва тому
Видавець
Анотація
У статті висвітлено основні етапи розвитку методики викладання початків аналізу в школі (з ХVII ст. до сьогоднішнього часу), ураховуючи розвиток цих понять безпосередньо в математичній науці. Порівняно підходи щодо введення поняття функції, границі, похідної функції. Проаналізовано навчальні програми різних часів та основні підручники. Встановлено, що зміст навчання початків аналізу в старшій школі значно розширився, він має більш прикладне спрямовування, а час на його вивчення зменшився. Таким чином, на сьогодні маємо проблему невідповідності змісту навчання початків аналізу в школі часу, що відведено на його вивчення.
The article elucidates the key stages in the development of teaching methods of the first analysis at school (from the seventeenth century up to now), compares the approaches to the introduction of the concept of function, limit, derivative function. The curriculum of various stages and basic textbooks are analyzed. It is established that the content of training in the analysis beginnings in high school has considerably extended, it has more applied focus, and time for its studying decreased, thus today there is a problem of discrepancy of the content of training in the analysis beginnings at school of time which is taken away on its studying. For many years the concept of functions and other concepts of mathematical analysis has improved along with them and changed their attitude to teaching at school. The course content analysis starts from the time has changed. Exploring the concept of function and other elements of mathematical analysis in school has become even more important because thanks to them you can build a variety of mathematical models for the study and processes events in different areas of life, economics, engineering, manufacturing and others. In order to choose today the most successful methods and forms of study concepts in high school, it is necessary to track the evolution of both the science, with terms of methodology of teaching. It is necessary to remember that identify the mathematical analysis in high school is propaedeutics study them in higher education. The author of this paper examines eight periods of formation and development of study of mathematical analysis in the national school represented by A. Savin and gives them a detailed description. Transition to multilevel (the level of standard, academic level, profile and level of in-depth study of mathematics) has reduced the number of hours of the level of the standard (4 hours) and the study of integral – 2 hours, which is not much more than at academic level. Therefore, we solve the problem of lack of quality time by introducing innovative, intensive methods and learning of mathematics, the use of innovative learning tools. A highly skilled teacher who has the ability, knowledge, experience and desire to implement innovations in the learning process play an important role in this process. We believe that this issue is sufficiently multifaceted and must be addressed at all levels of the educational process. At the present stage of the development of new methods, tools learning mathematics that promote a required set of students’ competencies, as well as a set of guidelines for school teachers to help them implement these methods and forms in the learning process is a necessary condition.
The article elucidates the key stages in the development of teaching methods of the first analysis at school (from the seventeenth century up to now), compares the approaches to the introduction of the concept of function, limit, derivative function. The curriculum of various stages and basic textbooks are analyzed. It is established that the content of training in the analysis beginnings in high school has considerably extended, it has more applied focus, and time for its studying decreased, thus today there is a problem of discrepancy of the content of training in the analysis beginnings at school of time which is taken away on its studying. For many years the concept of functions and other concepts of mathematical analysis has improved along with them and changed their attitude to teaching at school. The course content analysis starts from the time has changed. Exploring the concept of function and other elements of mathematical analysis in school has become even more important because thanks to them you can build a variety of mathematical models for the study and processes events in different areas of life, economics, engineering, manufacturing and others. In order to choose today the most successful methods and forms of study concepts in high school, it is necessary to track the evolution of both the science, with terms of methodology of teaching. It is necessary to remember that identify the mathematical analysis in high school is propaedeutics study them in higher education. The author of this paper examines eight periods of formation and development of study of mathematical analysis in the national school represented by A. Savin and gives them a detailed description. Transition to multilevel (the level of standard, academic level, profile and level of in-depth study of mathematics) has reduced the number of hours of the level of the standard (4 hours) and the study of integral – 2 hours, which is not much more than at academic level. Therefore, we solve the problem of lack of quality time by introducing innovative, intensive methods and learning of mathematics, the use of innovative learning tools. A highly skilled teacher who has the ability, knowledge, experience and desire to implement innovations in the learning process play an important role in this process. We believe that this issue is sufficiently multifaceted and must be addressed at all levels of the educational process. At the present stage of the development of new methods, tools learning mathematics that promote a required set of students’ competencies, as well as a set of guidelines for school teachers to help them implement these methods and forms in the learning process is a necessary condition.
Опис
Ключові слова
функція, похідна, границя, викладання, реформування, навчальна програма, підручник, зміст навчання, методика, function, derivative, limit, teaching, reforming, curriculum, textbook, content of training, technique
Бібліографічний опис
Кухарєва, О. С. Ретроспективний аналіз вивчення початків аналізу в старшій школі [Текст] / О. С. Кухарєва // Педагогічні науки: теорія, історія, інноваційні технології : науковий журнал / Міністерство освіти і науки України, Сумський державний університет імені А. С. Макаренка ; редкол.: А. А. Сбруєва, Дж. Бішоп, О. В. Єременко та ін. – Суми : СумДПУ імені А. С. Макаренка, 2013. – №8 (34). – С. 100–110.