Abstract
An easy and common way of assessing a student’s knowledge consists of a written examination. A list of questions is presented, the student’s answers are collected, and finally the examiner returns an appreciation, which usually boils down to a single number or percentage. Table 1.1 presents an excerpt of such a test in elementary arithmetics and will be used for exemplary purpose. We first argue that the information provided by the testing procedure is poorly reflected by a single number. Knowing that a student provided correct answers only to questions, say, α, c, and e, entails more than a numerical appreciation (60% correct) of his or her work. It shows mastery in performing multiplications, and deficiency in division operations. Weaknesses and strengthes of the student’s preparation have thus been revealed. Hence advices for further study can be inferred.
Our work in this area is supported by NSF grant IRI 8919068 to Jean-Claude Falmagne at the University of California, Irvine. We thank the editor and three anonymous referees for their careful reading of a preliminary version of the manuscript, and for their useful remarks.
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Doignon, JP. (1994). Probabilistic assessment of knowledge. In: Albert, D. (eds) Knowledge Structures. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-52064-8_1
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