Abstract:

Practice improves the human performance. The progress of this improvement is represented by a learning curve, which shows measures of the performance in learning, e.g. the time required for one trial and error rate, as the number of trials is increased. It is known that the learning curves follow the power law in many cases (Newell and Rosenbloom, 1981), However, there are learning curves that do not follow the power law (Suzuki, 2008). This raises the question: when does the learning curve follow the power law?.

The authors pay attention to the fact that, the averaged curve of many learning curves is smoother than each individual one (Ritter and Schooler, 2001) since an individual learning curve made with some specific problems and students may have different the averaged curve. Therefore, we can find when the learning curves follow the power law, creating many learning curves with different problems and students.

That is, the goal of this paper is to examine differences between learning curves made by students with some characteristics and to find factors that make the learning curve follow power law. To clarify the shape of the learning curve helps to formulate a guidance curriculum tailored to the learner’s understanding level. Also, to clarify the factors for shaping the learning curve helps to think about guidance for students who grow slower than predicted learning curve.

To this end, we made a pseudo learner by computer simulation, based on SimStudent (Matsuda, 2009), which is a computational model of human learning to explore science of learning by simulating of students and to make students learn by teaching the SimStudent. To prepare various learners, we made pseudo learners learning the set theory of mathematics by extending the SimStudent. Thereby, for example, the learner can combine some solution rules.

Among given problems, the original SimStudent tries to search, with some prior knowledge, some rules common to positive and negative problems, and obtain how to solve problems as a rule. So the prior knowledge is the only parameter for a pseudo learner. However, the more knowledge a learner has, the more intelligent it is. Therefore, we introduce some mechanisms to deal with meta-rules which be assumed as a concept, such as a chunking mechanism, which combines frequent rules into a new rule, and will clarify how these mechanisms affect on learning curves.

With different pseudo learners, we conducted simulation experiments and compared learning curves made by them. As a result, in many cases, the learning curves showed a form close to the power law, but we found the factors that bring the learning curve especially closer to the power law, like how to form a meta-rule and situations.

References:
[1] Newell, A. and Rosenbloom, P. S., Mechanisms of skill acquisition and the law of practice, in Anderson, J. R. ed., Cognitive Skills and Their Acquisition, 1981
[2] Suzuki, H., Ohnishi, H., Takeba, C., A Case Study Approach to the Sources of Slumps in Skill Learning, Transactions of the Japanese Society for Artificial Intelligence Vol. 23 No. 6 SP-A, pp. 86-95, 2008
[3] F.E. Ritter, L.J. Schooler, The learning curve, International encyclopedia of the social & behavioral sciences, pp. 8602–8605, 2001
[4] N. Matsuda, A. Lee, W. W. Cohen, K. R. Koedinger, A Computational Model of How Learner Errors Arise from Weak Prior Knowledge, Proc. of the Actual Conf of the Cognitive Science Society, 2009

Keywords:

Computational model of learning, learning curve, simulation of learning.