摘要：evaluation is not an easy task when assessing student attainment even if we are evaluating such a well-measured subject as knowledge of mathematics. This subject is discussed in a number of papers. Their authors are of the same opinion that even when the evaluation criteria is matching in detail, different teachers evaluate the same work differently. Subjectivity in knowledge assessment is researched in this paper. Not only teachers’’ individual characteristics in assessing student attainment are analyzed, but also problems of designing objective evaluation criteria of evaluated object, for example, solved problem. Authors analyze their own works and researches of other scientists in this field. The paper describes the authors’ original experiments and the results of their statistical analysis. As the solution of the evaluation subjectivity problem authors propose a methodology which allows dividing students to groups according to their attainment level. This methodology could be applied not only for evaluation of mathematical knowledge, but also for attainment evaluation in other disciplines.The experiment, when 15 accidentally selected student’s works in higher mathematics were independently verified by 6 teachers, is described in the paper. The analysis of the total test result and the results of individual tasks was performed with nonparametric statistical methods. To check the compatibility of teachers assessment Kendall’s coefficient of concordance W was calculated, nonparametric Friedman’s test was applied. The conclusion of the investigation was that all 6 teachers’ estimates were rather similar when evaluating students’ attainment except the estimation of the fifth task. Page’s L test was applied to the total test result to determine trend and consequently norm-referenced estimate of tested students. Least significant differences between sums of neighbouring ranks were calculated to establish 5 groups in which students received the same marks, so the criterion-referenced evaluation of student attainment was performed. The first task is not suitable for testing of this group of testees, because it is too easy for them. Tasks that are too easy or, conversely, too hard, are not suitable, because the results of such assignments are well predicted and do not distinguish between students.The fifth task should be recognized as inappropriate, because it does not affect the total assessment score and the criterion-referenced evaluation of the total test score is performed based on only the first four tasks.The applied nonparametric statistical methods were described in the paper in detail. The results were summarised in inferences and recommendations. The recommendations to escape or reduce the influence of subjectivity in attainment evaluation were formulated:• to assign more points to the task, where teachers disagree in their assessment of students knowledge,• to use standard tests for attainment evaluation,• to formulate more strict evaluation criteria and agreement on the most often occurring mistakes of evaluation.The proposed methods could be applied not only for attainment in mathematical assessment, but also in other natural sciences.
