The method of ensuring the proper preparation of senior pupils for undergoing of external independent assessment is an extremely topical pedagogical problem. For the time being, the Math test of EIA contains four forms of items: with alternatives, with a short answer, setting matches and open form with full explanation. At the same time, the tasks of the last form were absent for a long time in the external testing of mathematics, and therefore there was a need for the development of methodological recommendations concerning the particularities of solving these test tasks. The purpose of the article is to highlight the peculiarities of the structure of items with full explanations, which are part of the standardized tests, the formulation of general recommendations for preparation for their solution, as well as demonstration of concrete examples of their solutions. When they are included in standardized tests, tasks with full explanation try to construct in such way, that they are mostly solved in the same way, using explicit and indirect guidance for this purpose. Such structure of the items of this form limits the mathematical creativity of the test participants to some extent, but is justified, because it provides the opportunity for most pupils to evaluate the correctness of the solutions given by them based on common positions. During solving the item with full explanation, pupils should take into account the above-mentioned tips and identify the stages of the decision that will be assessed during the review. At the same time, it is important at each particular stage to understand what particular facts need to be thoroughly proved, and which to be only to formulated, since excessive detail when making a decision only complicates the work of a specialist during the inspection. In order to ensure the proper quality of preparation for solving tasks with full explanation, coordinated work is required both by the testing participant and by the specialists who prepare him for external testing. If the first one, for the most part, requires the execution of large number of training test items, then the latter requires understanding of what the structure should be these training tasks, how to break their decision on the stages and how to arrange the solution so that it was mathematically literate and concise at the same time.
In 2015 Ukraine has attempted introduction of two-level system of external assessment of quality of knowledge in mathematics. The naturalness and usefulness of such system of testing in math was based in our series of publications in scientific pedagogical literature. In these works we proposed two-level system of standardized national assessment of educational progress in mathematics for Ukrainian pupils. Implemented by the Ukrainian Center for Educational Quality Assessment in 2015 two-level test in mathematics is different from our project, although some of our suggestions were taken into account. We believe that the option of two-level testing in math, consisting of test advanced level, which includes as part basic level is not perfect and has some shortcomings that should be removed in the future. We are aware that the introduction of a two-level math test raises a number of methodological issues for professionals who prepare pupils for this type of assessment. It was very difficult for Mathematics teacher to provide adequate quality of math testing in 2015, since the decision to impose of two-level math test was made quite suddenly. The second reason for the complexity of training of Ukrainian pupils for two-level math test 2015 is tedious for most of them the 210-minute marathon, you need to write in-depth test. In our view, not all pupils are capable to thinking in the situation of stress for so long. As a result, it is not clear what actually checks realized test: physical endurance of the test participant or his knowledge, skills (competencies)? We hope that the above mentioned disadvantages of introducing two-level math testing will continue to be taken into account. It is also noted that, despite the rejection of the two-level model of testing in 2016, methodological publications on the specifics of preparation have not lost relevance because, in our opinion, returning to such model is only a matter of time and valuable experience. In this paper we consider the features of two-level independent external assessment of quality of knowledge in math compared with traditional one-tier system of national standardized test and put methodological recommendations for preparing pupils for this type of testing related to topics «Plane geometry» and «Space geometry».
Today the national standardized tests in mathematics become familiar to all members of educational process in Ukraine,but the problem of adequate methodological support of standardized tests in math and prepare for them remains relevant. In terms of constant change format of standardized assessments and lack of proper methodological support to them, many teachers have a desire to create their own methodological support, but, unfortunately, many of these teachers received special education when test technology checks the quality of pupils achievements wasn’t included in curriculum for mathematics teachers. Our experience in teaching courses for teachers of mathematics shows that the creation of quality tests in mathematics is not an easy task even for teachers with significant teaching experience. This article is devoted to detailed analysis of the essence of the concept of “quality test task” and development on the basis of this analysis and on author's experience guidelines for the establishment of quality tests in mathematics different forms. We define the concept of “quality” according to production approach: a quality facility considered if it meets certain quality standards set by society. For math items their quality are defined by purpose for which these tasks are applied. In other words, math item is considered qualitative if its application in the classroom is really allows you to check the knowledge, skills (competencies), that are planned to test by this item. For math tests that are part of the standardized tests we improve the notion “specification” as the characteristic of test item which it must meet to become a component of standardized test. However, even if math test item meets all specifications, it’s too early to consider it qualitative, since it’s unknown whether the use of this task will achieve the objective pursued by the authors, including this task in the test. It is best to check compliance test item to its purpose is done by calculating psychometric characteristics of the item after testing on significant sample. But testing of test items can be carried out not always, in this case quality evaluation of test item performed by expert estimates. Our circuit quality evaluation of math test item includes the following stages: 1) analysis of correctness conditions; 2) analysis of compliance to form of expression; 3) check for the possibility of guessing the answer; 4) checking for compliance to goal. In this article we illustrate the implementation of the scheme mentioned above by examples of specific test items of different forms. In recent years we have been actively working to create methodological support for preparing of pupils to standardized assessments in mathematics and accumulated in this area some experience. Proposed methods for creating and analyzing of test item quality after proper implementation should contribute to ensuring adequate assessment of educational achievements of pupils who participate in standardized testing.
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