Abstract
As implemented in the system discussed here, the assessment of knowledge in a learning
space for a scholarly topic, such as beginning algebra, is comprehensive by design,
in that the types of problems that can be asked in any assessment come from a large
collection encompassing the full curriculum for the topic. The product of an assessment
is a knowledge state gathering all the types of problems that the student is capable of
solving. Typically, the number of feasible knowledge states is large, on the order of 107.
The duration of an assessment is nevertheless tolerable, ranging around 30−35 problems.
We summarize the basic concepts underlying learning spaces and report the results of
a large scale study (210,102 assessments) investigating whether such an assessment is
predictive of the subject’s responses to problems that are not part of the assessment. In
each assessment, an additional question was asked, the response to which is predictable
from the assessed state. The mean correlation between predicted and observed responses
(correct or false) was around .67, and the mean log odds ratio 2.75. This type of analysis
resembles the standard item-test correlations computed for the evaluation of psychometric
instruments. The essential technical and philosophical differences between the two
approaches are discussed.
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