Difference between revisions of "CUMULATE asymptotic knowledge assessment"
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[[CUMULATE asymptotic knowledge assessment|Asymptotic knowledge assessment]] is [[CUMULATE]]'s legacy user modeling algorithm for computing user knowledge with respect to problem-solving. | [[CUMULATE asymptotic knowledge assessment|Asymptotic knowledge assessment]] is [[CUMULATE]]'s legacy user modeling algorithm for computing user knowledge with respect to problem-solving. | ||
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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 | ||
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* ''<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. | 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]] | [[Image:CUMULATE asymptotic knowledge assessment - knowledge growth.png]] | ||
<br/>([http://chart.apis.google.com/chart?cht=lxy&chs=300x215&chd=t:0,10,20,30,40,50,60,70,80,90,100|0,42,56,72,79,83,85,87,88,90,92&chco=24588E&chxt=x,y&chxl=1:|0|.2|.4|.6|.8|1|0:|0|1|2|3|4|5|6|7|8|9|10&chm=o,24588E,0,-1,10&chg=10,20&chtt=Growth+of+knowledge+level+vs.|number+of+successful+attempts alternatively] via [http://code.google.com/apis/chart/ Google Chart API]) | <br/>([http://chart.apis.google.com/chart?cht=lxy&chs=300x215&chd=t:0,10,20,30,40,50,60,70,80,90,100|0,42,56,72,79,83,85,87,88,90,92&chco=24588E&chxt=x,y&chxl=1:|0|.2|.4|.6|.8|1|0:|0|1|2|3|4|5|6|7|8|9|10&chm=o,24588E,0,-1,10&chg=10,20&chtt=Growth+of+knowledge+level+vs.|number+of+successful+attempts alternatively] via [http://code.google.com/apis/chart/ Google Chart API]) | ||
Revision as of 20:17, 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.
