Open AccessON THE TRAINING METHODOLOGY FOR COMPILING SOME TYPE OF ARITHMETIC PROBLEMS
Author(s) -
Gennady G. Khamov,
Larisa N. Timofeeva
Publication year - 2020
Publication title -
âroslavskij pedagogičeskij vestnik
Language(s) - English
Resource type - Journals
eISSN - 1813-1476
pISSN - 1813-145X
DOI - 10.20323/1813-145x-2020-6-117-64-69
Subject(s) - relation (database) , task (project management) , context (archaeology) , computer science , process (computing) , development (topology) , mathematical problem , mathematics education , mathematics , programming language , paleontology , mathematical analysis , management , database , economics , biology
The article is devoted to a current topic related to the development of methods for composing problems in teaching students of pedagogical universities of mathematical faculties. This problem becomes especially important in the context of the need to involve students in independent creative activities to acquire and apply knowledge. The material is presented in relation to the section of the discipline «Algebra and number theory», dedicated to solving Diophantine equations, the main objectives of which are not only mastering the theory and algorithms for solving basic problems, but also obtaining the necessary knowledge and skills for further professional activity. Solving a problem, the student must not only solve it correctly and quickly enough, but also show the creative component of the activity, using it as much as possible for their mathematical development. In this regard, the process of composing problems by students is undoubtedly useful, which reflects the systematic application of the material and elements of mathematical actions based on the laws and methods of mathematics. In addition, the ability to compose problems will be required in future activities related to teaching mathematics. The processes of solving and composing tasks are interconnected and this allows you to increase the efficiency and effectiveness of composing and solving tasks. Therefore, the teacher can give a task to the student with the requirement to compose (fully or partially) and solve the problem. In this paper, examples of tasks for the compilation of indefinite equations solvable in integers are considered, for the solution of which the methods of number theory are used: the study of possible residuals from dividing an algebraic integer expression by a specific integer; finding integer solutions to a linear equation with two variables. The stages of composing Diophantine equations are described in detail, the ways of obtaining equations solvable on a given set of integers or natural numbers are analyzed, and the application of various theoretical propositions used for their solution is shown.