Difference between revisions of "CUMULATE asymptotic knowledge assessment"
From PAWS Lab
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* ''res'' - result of user action (0 -error, 1 - correct); | * ''res'' - result of user action (0 -error, 1 - correct); | ||
* ''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 | ||
| + | |||
| + | ==Examples== | ||
| + | Below is a graph of concept's knowledge level growth vs. number of successful attempts to apply it in a problem. Every time the concept is applied correctly in a new problem. | ||
| + | [[Image:CUMULATE asymptotic knowledge assessment - knowledge growth.png]] | ||
Revision as of 20:12, 8 April 2009
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). This formula reflects the following principles.
- 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 (here we always start from 0)
- 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
Examples
Below is a graph of concept's knowledge level growth vs. number of successful attempts to apply it in a problem. Every time the concept is applied correctly in a new problem.
