CUMULATE asymptotic knowledge assessment

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Asymptotic knowledge assessment is CUMULATE's legacy user modeling algorithm for computing user knowledge with respect to problem-solving.

Computation

The formula below is used to update the knowledge levels of concepts (c) addressed in a problem (p) CUMULATE asymptotic knowledge assessment.png, where

  • Ko - is the starting level of knowledge (here we always start from 0)
  • res - result of user action (0 -error, 1 - correct); we only update knowledge levels upon correct user actions and do not penalize errors
  • Wc,p is a weight of concept c in problem p
  • &SigmaWc,p is the sum of weights of all concepts in problem p
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