Article 21316

Title of the article

AVAILABILITY OF BASIC INDEXES OF MATHEMATICS LEARNABILITY AS THE BASIS OF MATHEMATICS LEARNABILITY DIAGNOSTICS OF STUDENTS

Authors

Farkov Alexander Viktorovich, Candidate of pedagogical sciences, associate professor, sub-department of mathematics, Northern (Arctic) Federal University named after М. V. Lomonosov (building 2, 17 Severnoy Dviny embankment, Arkhangelsk, Russia), a.farkov@mail.ru

Index UDK

51: 371

DOI

10.21685/2072-3024-2016-3-21

Abstract

Background. The modern state of development of the school system is characterized by the contradiction between the need to take into account the learnability during differentiated teaching of mathematics and the undeveloped issues in the theory and methodology of mathematics teaching, associated with the essence, structure, indicators of mathematics learnability, as well as mechanisms for diagnostics of both the availability levels of basic indexes of learnability and the levels of mathematics learnability, especially a high level of learnability. The aim of the work is to scientifically substantiate and develop methods of mathematics learnability diagnostics for students of secondary educational institutions.
Materials and methods. The research tasks were implemented on the basis of the study and analysis of psychological, pedagogical and methodological literature, results of dissertation works on the subject matter; the analysis of programms, text-books, tutorials for secondary schools; the analysis of published texts, tests, texts of mathematical contests; the survey and interviewing of math teachers and pupils; the observation of math classes at schools; the pedagogical experiment; the statistical processing and analysis of results of the experiment carried out.
Results. The author has developed a conception of mathematics learnability diagnostics based on the system of basic indexes of mathematics learnability: a de-gree of student’s mathematical knowledge, student’s pace of learning new mathe-matical material, independence in mastering new mathematical material, perceptiveness to teacher’s assitance, availability of intellectual functioning, skills to solve nonstandard mathematical problems. On the basis of the present conception there have been developed the following methodologies: a) the method of construction and usage of multilevel tests in geometry in order to determine a level of the students’ knowledge; b) the method of construction and application of tests to determine levels of knowledge and learnability of students in mathematics; c) the method of composition and usage of subtests in mathematics as a means of diagnostics of such intellectual functioning elements as analogy, classification, abstracting and generalization; d) the method of application of reasonably selected exercise systems for diagnostics of total learnability of students as well as some indexes thereof. The author has also developed practical recommendations to the content of monitoring materials for conducting the uniform state examinations in mathematics in order to achieve a more objective selection of the most teachable students to universities of Russia. The article defines the notion of a mathematical contest problem and suggests a typology of mathematical contest problems. The author has also developed recommendations to texts of school and municipal mathematical contests, offered changes to the methodology of conducting mathematical contests at schools with small amount of students, developed a new type of contests – multilevel contests.
Conclusions. The conception of mathematics learnability diagnostics, presented in the articles, is implementable and requires further development.

Key words

learnability, mathematics learnability diagnostics, main indexes of mathematics learability, level of knowledge.

Download PDF
References

1. Farkov A. V. Diagnostika osnovnykh pokazateley obuchaemosti uchashchikhsya matematike: praktiko-orientirovannaya monogr. [Diagnostics of main indexes of mathe-matical learnability: practice-oriented manaograph]. Saarbrücken, Germany: LAP LAMBERT Academic Publishing GmbH & Co., 2012, 301 p.
2. Farkov A. V. Sibirskiy pedagogicheskiy zhurnal [Siberia pedagogical journal]. 2010, no. 3, pp. 210–217.
3. Bespal'ko V. P. Obrazovanie i obuchenie s uchastiem komp'yuterov (pedagogika tret'ego tysyacheletiya) [Education and learning involving computers (pedagogy of the third millenium)]. Moscow: MISI; Voronezh: MODEK, 2002, 352 p.
4. Kalmykova Z. I. Produktivnoe myshlenie kak osnova obuchaemosti [Productive thinking as a basis of learnability]. Moscow: Pedagogika, 1981, 200 p.
5. Kolyagin Yu. M. Zadachi v obuchenii matematike. Ch. I. Matematicheskie zadachi kak sredstvo obucheniya i razvitiya uchashchikhsya [Problems in mathematical teaching. Part 1. Mathematical problems as a means of teaching and development of students]. Moscow: Prosveshchenie, 1977, 110 p.
6. Kolyagin Yu. M. Zadachi v obuchenii matematike. Ch. II. Obuchenie matematike che-rez zadachi i obuchenie resheniyu zadach [Problems in mathematical teaching. Part II. Teaching mathematics through problems and problem-solving teaching]. Moscow: Prosveshchenie, 1977, 142 p.
7. Krutetskiy V. A. Psikhologiya matematicheskikh sposobnostey shkol'nikov [Psychology of mathematical skills in students]. Moscow: Prosveshchenie, 1968, 432 p.
8. Perevoshchikova E. N. Teoretiko-metodicheskie osnovy podgotovki budushchego uchitelya matematiki k diagnosticheskoy deyatel'nosti: dis. d-ra ped. nauk [Theoretical and methodological bases of future mathematical teacher training for diagnostic acticity: dissertation to apply for the degree of the doctor of pedagogical sciences]. Nizhniy Novgorod, 2000, 344 p.
9. Sarantsev G. I. Uprazhneniya v obuchenii matematike [Exercises in teaching mathema-tics]. Moscow: Prosveshchenie, 1995, 240 p.
10. Simonov V. P. Diagnostika stepeni obuchennosti uchashchikhsya: ucheb.-sprav. posobie [Student learnability diagnostics: study and reference book]. Moscow, 1999, 48 p.
11. Kholodnaya M. A. Psikhologiya intellekta. Paradoksy issledovaniya [Intellectual psy-chology. Research paradoxes]. 2nd ed., rev. and expanded. Saint-Petersburg: Piter, 2002, 272 p.
12. Tret'yakov P. I., Sennovskiy I. B. Tekhnologiya modul'nogo obucheniya v shkole: praktiko-orientirovannaya monogr. [Modular education technology at school: practice-ori¬ented monograph]. Moscow: Novaya shkola, 2001, 352 p.
13. Farkov A. V. Matematika v shkole [Mathematics at school]. 2011, no. 1, pp. 27–33.
14. Farkov A. V. Matematika v shkole [Mathematics at school]. 2011, no. 10, pp. 24–32.
15. Farkov A. V. Shkol'nye tekhnologii [School technologies]. 2010, no. 1, pp. 175–182.
16. Farkov A. V. Shkol'nye tekhnologii [School technologies]. 2003, no. 2, pp. 86–88.

 

Дата создания: 27.01.2017 11:11
Дата обновления: 30.01.2017 10:47