Difference between revisions of "CUMULATE parametrized asymptotic knowledge assessment"

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(Computation)
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* knowledge is updated only upon correct user answers, there is no penalty for errors
 
* knowledge is updated only upon correct user answers, there is no penalty for errors
 
* solving a problem correctly multiple times will result in diminishing update (growth) of the knowledge level of the concepts as the number of successes grows
 
* solving a problem correctly multiple times will result in diminishing update (growth) of the knowledge level of the concepts as the number of successes grows
 +
in addition:
 +
* the initial level of knowledge, speed of knowledge growth, and penalty for repetitive (correct) solutions to the problem - are now adjustable parameters
 
[[Image:CUMULATE parameterized asymptotic knowledge assessment.png]], where
 
[[Image:CUMULATE parameterized asymptotic knowledge assessment.png]], where
 
* ''Ko'' - is the starting level of knowledge, Ko ∈ [0, 1]
 
* ''Ko'' - is the starting level of knowledge, Ko ∈ [0, 1]
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* ''Wc,p'' - is a weight of concept ''c'' in problem ''p''
 
* ''Wc,p'' - is a weight of concept ''c'' in problem ''p''
 
* Σ''Wc,p'' - is the sum of weights of all concepts in problem ''p''
 
* Σ''Wc,p'' - is the sum of weights of all concepts in problem ''p''
* ''<sub>succ</sub>att<sub>p</sub>'' - is a number of successful solutions to problem p prior to current attempt
+
* ''<sub>succ</sub>att<sub>p</sub>'' - is a number of successful solutions to problem ''p'' prior to current attempt
 
* ''pV'' - speed of knowledge growth parameter
 
* ''pV'' - speed of knowledge growth parameter
 
* ''OPP'' - over-practicing parameter, controlling the penalty for repetitively solving one problem (correctly)
 
* ''OPP'' - over-practicing parameter, controlling the penalty for repetitively solving one problem (correctly)
 
  
 
=Examples=
 
=Examples=

Revision as of 20:36, 8 April 2009

Parameterized asymptotic knowledge assessment algorithm is an attempt to overcome shortcomings of its non-paramterized version.

Computation

The formula below is used to update the knowledge levels of concepts (c) addressed in a problem (p). This formula reflects the following principles (identical to the predecessor algorithm).

  • there are several domain concepts (knowledge items, rules, productions) involved in solving a problem; the knowledge of each of them is updated proportionally to the others
  • knowledge is updated only upon correct user answers, there is no penalty for errors
  • solving a problem correctly multiple times will result in diminishing update (growth) of the knowledge level of the concepts as the number of successes grows

in addition:

  • the initial level of knowledge, speed of knowledge growth, and penalty for repetitive (correct) solutions to the problem - are now adjustable parameters

CUMULATE parameterized asymptotic knowledge assessment.png, where

  • Ko - is the starting level of knowledge, Ko ∈ [0, 1]
  • res - result of user action (0 -error, 1 - correct);
  • Wc,p - is a weight of concept c in problem p
  • ΣWc,p - is the sum of weights of all concepts in problem p
  • succattp - is a number of successful solutions to problem p prior to current attempt
  • pV - speed of knowledge growth parameter
  • OPP - over-practicing parameter, controlling the penalty for repetitively solving one problem (correctly)

Examples

soon

Studies

Contacts

Michael V. Yudelson