CUMULATE parametrized asymptotic knowledge assessment: Difference between revisions
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[[CUMULATE parametrized asymptotic knowledge assessment|Parameterized asymptotic knowledge assessment]] algorithm is an attempt to overcome shortcomings of its [[CUMULATE asymptotic knowledge assessment|non-paramterized]] version. | |||
=Computation= | =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 [[CUMULATE asymptotic knowledge assessment|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 | |||
[[Image: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'' | |||
* 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 | |||
* ''pV'' - speed of knowledge growth parameter | |||
* ''OPP'' - over-practicing parameter, controlling the penalty for repetitively solving one problem (correctly) | |||
=Examples= | =Examples= | ||
Revision as of 20:34, 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
, 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