Difference between revisions of "CUMULATE parametrized asymptotic knowledge assessment"
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==Example 3== | ==Example 3== | ||
Graph below shows differences the growth of knowledge while speed of learning varies. No penalty is given. | Graph below shows differences the growth of knowledge while speed of learning varies. No penalty is given. | ||
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[[Image:CUMULATE parameterized asymptotic knowledge assessment - knowledge growth for diff pV.png]] | [[Image:CUMULATE parameterized asymptotic knowledge assessment - knowledge growth for diff pV.png]] | ||
<br/>([http://chart.apis.google.com/chart?cht=lxy&chs=300x240&chd=t:0,10,20,30,40,50,60,70,80,90,100|0,1,2,3,4,5,6,7,8,9,10|-1|0,10,19,27,34,41,47,52,57,61,65|-1|0,25,44,58,68,76,82,87,90,92,94|-1|0,50,75,88,94,97,98,99,100,100,100|-1|0,75,94,98,100,100,100,100,100,100,100|-1|0,100,100,100,100,100,100,100,100,100,100&chco=24588E,4C9B46,F3A030,CF1E2B,78387B,7C807F&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|o,4C9B46,1,-1,10|o,F3A030,2,-1,10|o,CF1E2B,3,-1,10|o,78387B,4,-1,10|o,7C807F,5,-1,10&chg=10,20&chdl=pV=.01|pV=.10|pV=.25|pV=.50|pV=.75|pV=1.0&chdlp=b&chtt=Knowledge+growth+for+different+problem+learnig|speeds+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=300x240&chd=t:0,10,20,30,40,50,60,70,80,90,100|0,1,2,3,4,5,6,7,8,9,10|-1|0,10,19,27,34,41,47,52,57,61,65|-1|0,25,44,58,68,76,82,87,90,92,94|-1|0,50,75,88,94,97,98,99,100,100,100|-1|0,75,94,98,100,100,100,100,100,100,100|-1|0,100,100,100,100,100,100,100,100,100,100&chco=24588E,4C9B46,F3A030,CF1E2B,78387B,7C807F&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|o,4C9B46,1,-1,10|o,F3A030,2,-1,10|o,CF1E2B,3,-1,10|o,78387B,4,-1,10|o,7C807F,5,-1,10&chg=10,20&chdl=pV=.01|pV=.10|pV=.25|pV=.50|pV=.75|pV=1.0&chdlp=b&chtt=Knowledge+growth+for+different+problem+learnig|speeds+vs.+number+of+successful+attempts alternatively] via [http://code.google.com/apis/chart/ Google Chart API]) | ||
Revision as of 02:18, 9 April 2009
CUMULATE's parameterized asymptotic knowledge assessment algorithm is an attempt to overcome shortcomings of its non-paramterized version. Namely, one-fits-all nature, prohibiting parameter tuning for individual users' abilities and problem complexities.
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
, 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, pV ∈ [0, 1]
- OPP - over-practicing parameter, controlling the penalty for repetitively solving one problem (correctly), OPP ∈ [0, 1]
Examples
Example 1
Below is a graph of concept's knowledge level growth and the penalty coefficient vs. number of successful attempts to apply it in a problem. The lines denote:
- the blue line denotes a successful use of a concept in a new problem (pV = .5)
- the green line denotes a penalty coefficient -- 1/(succattp+2)OPP -- as if it was the same problem (OPP = .25)
- the red line merges the prior two graphs
(alternatively via Google Chart API)
Example 2
Below the speed of problem learning is held constant (pV = .5) while the penalty for practicing the same problem changes.
(alternatively via Google Chart API)
Example 3
Graph below shows differences the growth of knowledge while speed of learning varies. No penalty is given.
(alternatively via Google Chart API)
Studies
Coming soon
