An Illustration of the Use of Markov Decision Processes to Represent Student Growth (Learning)

Author(s):

Almond, Russell G.

Publication Year:

2007

Report Number:

RR-07-40

Source:

ETS Research Report

Document Type:

Report

Page Count:

61

Subject/Key Words:

Markov Process, Growth Models, Prerequisites, Zone of Proximal Development, Stochastic Approximation, Particle Filter

Abstract

The general action model (also called the bowtie model) separately models the factors contributing to the success or effectiveness of an action, proficiency growth when the action is successful, and proficiency growth when the action is unsuccessful. This class of models requires parameterization, and this paper presents two: a simple linear process model (suitable for continuous proficiencies) and a birth-and-death process model (for proficiency scales expressed as ordered categorical variables). Both models show how to take prerequisites and zones of proximal development into account. The filtering process is illustrated using a simple artificial example.

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• http://dx.doi.org/10.1002/j.2333-8504.2007.tb02082.x