Difference between revisions of "CUMULATE asymptotic knowledge assessment"
From PAWS Lab
(→Computation) |
|||
| Line 2: | Line 2: | ||
==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. | + | 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 | * 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 | * 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 | ||
[[Image:CUMULATE asymptotic knowledge assessment.png]], where | [[Image:CUMULATE asymptotic knowledge assessment.png]], where | ||
| − | * Ko - is the starting level of knowledge (here we always start from 0) | + | * ''Ko'' - is the starting level of knowledge (here we always start from 0) |
| − | * 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'' |
| − | * ΣWc,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 |
Revision as of 19:35, 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
