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), firstname.lastname@example.org
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.
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