Modeling mathematics tests

The test on mathematics developed by an original technique is used for an assessment of level and structure of knowledge of university students. The author's computer program generates individual versions of a test for each student. The teacher can offer test tasks with open or closed forms. In the course of testing one group was performing a test with tasks of the open form, and two other groups - with tasks of the closed form with a list of five response selection. Based on the analysis of test results of three groups of examinees the statistical characteristics of the test are studied. Test scores of students have normal distribution, the test has a high differentiating ability, it can be used as a standard-based test, that makes it possible to separate students with different levels of knowledge. The reasons of differences in test results with open or closed form of test tasks are investigated. The relative simplicity of closed tasks in comparison with open tasks is connected with both possibilities of guessing the answer, and self-detection of error in the task when the response received does not match any answer in the list of options. The testing results enabled to construct the scales of task complexity for each group of examinees. The hypothesis of maintaining order in the scale of task complexity for the tests in the open and closed forms and for students with different levels of knowledge was checked and confirmed. The patterns of student knowledge constructed due to the test results are studied. In the case of a dichotomous assessment of assignments (0 - the task is solved incorrectly, 1 - the task is solved correctly) the pattern is a set of ones and zeros, that student receives for performed test tasks. Investigation of patterns makes it possible to estimate the degree of ordering of students’ knowledge and helps to identify the students, who has studied the material fragmentary or violated the test rules (tips, cheating, etc.). Each pattern is associated with regularity - a number which characterizes the degree of correctness of the pattern. It was found that in all groups the pattern of students’ regularities takes values ranging from 0 to 0,4, that indicates the correct structure of the knowledge of the examinees. The regularity of distribution and its statistical characteristics are studied.

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