Formation of the Skills to Prove the Statements of the Theory of Limits (By Means of Testing Technology)

Метою статті є актуалізація питання розвитку вмінь доводити твердження теорії границі, розробка тестових завдань для діагностики, контролю, навчання та надання методичних рекомендацій щодо їх застосування. Для досягнення поставленої мети використані теоретичний та емпіричний методи дослідження. Авторами запропонована система тестових завдань, які в різній комбінації можуть слугувати різним цілям. Акцент робиться на завданнях, які можуть бути використані з навчальною метою, а саме для формування вмінь доводити твердження. Перспективу вбачаємо в подальшому розширенні бази тестових завдань, створенні курсу дистанційного навчання та впровадженні тестів у систему онлайн-тестування.The modern system of education needs revision of teaching methods, forms and tools of training, the embedding of new technologies into the educational process. Testing is a reliable and efficient way of diagnosing and monitoring of the skills. As a rule, tests in mathematics are designed to test the level of formation of practical skills. It is not enough for university graduates. Ability to prove statements is important for the future teachers of mathematics. Some topics of calculus are fundamental and do not permit formalities. Properly formed conceptual apparatus of the theory of limits lays the basis for successful mastery of the course calculus in general. It is proved that some topics of mathematical analysis are fundamental and do not admit the formalities. The aim of the article is the mainstreaming of the development of skills to prove the statements of theory of limits, the development of tests for the diagnosis, monitoring, training and providing of guidelines for their application. To achieve this goal the theoretical and empirical research methods are used. The authors have proposed a system of tests, which can serve different purposes in different combinations. We have divided the module “Theory of limits” into three main parts. For monitoring each of which we have created three tests: “Limit of a numerical sequence”, “Limit of a function”, “Continuity function”. This article is focused on the second test “Limit of a function”. To create the test we have used a different kind of test tasks: the task of the closed form (with a choice of one correct answer, multiple choice, modified with a choice of one correct answer, the task to establish compliance, to establish the correct sequence of steps of the proof), and the task of the open form (task on supplement, and task with detailed answer). The article gives a set of examples of the tasks. The focus is on the tasks that can be used for educational purposes, namely for the formation of skills to prove the approval. Test items which should be used for this purpose are shown. The prospect of further research is seen in the base of test tasks, creating a distance learning course and implementation of tests in online testing