Assessment of knowledge through assessment of ignorance: Semantic approach in information theory, information value (importance), assessment of knowledge through tests of the multiple choice type.

Introduction. Tests (multiple-choice tests), consisting of dichotomous items (a question with one correct and one or more incorrect answers (distractors)) are widely used in modern education, in particular in engineering, to assess students' knowledge. Test developers face the problem of converting the number of correct answers into a numerical grade for the knowledge of the assessed. Usually, the number of correct answers is converted into a grade based on the evaluators' inner sense of fair evaluation. Objective: In the present work, a model for knowledge evaluation through dichotomous tests is proposed, based on the so-called semantic branch of Information Theory. Results: A critical opinion is given for the Classical Test Theory and the more modern Item Response Theory as tools for knowledge assessment. Some concepts in these theories leave the feeling that it could be desired more in respect of assessing knowledge through them. A new, entirely different approach to knowledge assessment by tests is proposed in the paper. In the proposed information model for knowledge assessment, the process of knowledge assessment is considered as an information process with information transfer. The information is generated by a source (the assessed), which has a goal - to get as close as possible to the error-free solution of the test. The information in the form of an information signal (the answers to the test that the assessed gives) is directed to the recipient - the assessor. The assessor evaluates the value (importance) of this information signal, which is a measure of the knowledge of the assessed. The value of the information signal is measured by the progress of the examinee towards reaching the goal. Formulas are obtained, linking the value of the information signal with a numerical grade of knowledge of the assessed. In particular, evaluation formulas are derived for the six-score scale (used in Bulgaria) for tests of the most used types - with items with 3, 4, and 5 answers. [ABSTRACT FROM AUTHOR]