Difference between revisions of "CUMULATE parametrized asymptotic knowledge assessment"

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([http://chart.apis.google.com/chart?cht=lxy&chs=300x240&chd=t:0,10,20,30,40,50,60,70,80,90,100%7C0,50,75,87,93,97,98,99,100,100,100%7C-1%7C0,47,71,83,90,94,97,98,98,99,100%7C-1%7C0,42,64,77,85,89,93,95,96,97,98%7C-1%7C0,35,54,66,73,79,83,86,88,90,92%7C-1%7C0,30,45,55,62,67,70,74,76,78,80%7C-1%7C0,25,38,45,51,55,58,61,63,65,66&chco=24588E,4C9B46,F3A030,CF1E2B,78387B,7C807F&chxt=x,y&chxl=1:%7C0%7C.2%7C.4%7C.6%7C.8%7C1%7C0:%7C0%7C1%7C2%7C3%7C4%7C5%7C6%7C7%7C8%7C9%7C10&chm=o,24588E,0,-1,10%7Co,4C9B46,1,-1,10%7Co,F3A030,2,-1,10%7Co,CF1E2B,3,-1,10%7Co,78387B,4,-1,10%7Co,7C807F,5,-1,10&chg=10,20&chdl=OPP=.01%7COPP=.10%7COPP=.25%7COPP=.50%7COPP=.75%7COPP=1.0&chdlp=b&chtt=Knowledge+level+growth+for+different+penalty%7Cparameters+vs.+number+of+successful+attempts alternatively] via [http://code.google.com/apis/chart/ Google Chart API])]]
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==Example 3==
 
==Example 3==

Latest revision as of 21:50, 20 January 2010

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

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
  • 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 two graphs above

CUMULATE parameterized asymptotic knowledge assessment - knowledge growth and penalty.png
(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.

CUMULATE parameterized asymptotic knowledge assessment - knowledge growth for diff OPP.png
(alternatively via Google Chart API)

Example 3

Graph below shows differences the growth of knowledge while speed of learning varies. No penalty is given.

CUMULATE parameterized asymptotic knowledge assessment - knowledge growth for diff pV.png
(alternatively via Google Chart API)

Studies

Contacts

Michael V. Yudelson

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