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EN
This article presents the test evaluation technology of pupils’ competencies that are used in international studies program PISA and project TIMSS. The goal of two international studies is highlighted and forms of assessment of pupils’ competencies are also revealed. The aim of the research according to the PISA program is to identify whether 15-year-old pupils who received general compulsory education possess the knowledge and skills that they need to have for sterling living in society. The purpose of the study that is being carried out by the project TIMSS is a comparative assessment of general education of pupils in grades 4 and 8 as to mathematics and natural sciences in the countries with different educational systems and to identify the factors that affect the level of such training. The forms of assessment in these two studies are presented by tests and questionnaires. In tests there are open (with the option of correct answer) and closed tasks (with short or long answer) available.In a PISA research program the tests evaluate the three types of pupils’ competences (literacy): competence of reading, mathematical competence, naturalistic competence. The tests refer to the real situations in which the pupils’ knowledge is being evaluated as well as understanding of basic concepts and ability to apply their knowledge and skills in the similar, modified and new situations. In a TIMSS research project the tests are the tools for checking of academic achievement of pupils in mathematics and science. The tests evaluate the student’s knowledge and understanding of basic concepts as well as the laws and principles and ability to apply the knowledge in a standard and unfamiliar situation. So, in the tests of international research PISA program and TIMSS project the questions that evaluate the pupils’ understanding of basic concepts, possession of basic studying methods, the ability to apply their new knowledge and skills with a practical purpose, to explain the phenomena of daily life and conducting of the study or processing of the obtained data are used.Such tasks, according to the Ukrainian teachers’ opinions are the most difficult for pupils and therefore they should be widely used in secondary schools. The examples of tasks used in the research program PISA and the TIMSS project with their brief description will be helpful for the teachers while creating the authors’ tests by them to assess the competence of pupils.
EN
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.
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