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Abstract: We describe the algorithms used by the ALEKS computer learning system formanipulating combinatorial descriptions of human learners- states of knowledge,generating all states that are possible according to a description of alearning space in terms of a partial order, and using Bayesian statistics todetermine the most likely state of a student. As we describe, a representationof a knowledge space using learning sequences basic words of an antimatroidallows more general learning spaces to be implemented with similar algorithmiccomplexity. We show how to define a learning space from a set of learningsequences, find a set of learning sequences that concisely represents a givenlearning space, generate all states of a learning space represented in thisway, and integrate this state generation procedure into a knowledge assessmentalgorithm. We also describe some related theoretical results concerningprojections of learning spaces, decomposition and dimension of learning spaces,and algebraic representation of learning spaces.

Author: David Eppstein

Source: https://arxiv.org/


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