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A New Method for Assessing Student Knowledge

We often say that one person knows more than another about a given topic - whether the character of an acquaintance, the news headlines, or academic subjects like math, literature, chemistry, or history. These claims, though largely true, are imprecise because 1) they may lack clear evidence, 2) certain concepts are not at hand, or 3) the attempts to measure the evidence, if available, are not made. In this paper, we address these issues. The central idea is of a concept of set of traits in one’,s mind. Different traits distinguish different concepts. Interpreted as what two people know, the two concepts comprise the different amounts of knowledge of the one person (the student) and the other (the expert), or the same person at different times. With various levels of attention, we observe the concept traits of others and ourselves. Formally and informally, we see what others say or not say, write or not write, reveal or not reveal. To promote this method, we define several metrics, such as concept differences, concept distance, knowledge ratio, and ignorance ratio. Examples are drawn from math, statistics, computing, movies, song lyrics, among other subjects. The method complements other methods of assessment.Keywords: concept traits, concept differences, concept distances, knowledge, knowledge ratio, measurement, assessment

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