**Christopher J. MacLellan**
HCI Institute

Carnegie Mellon University

cmaclell@cs.cmu.edu

In this project I simulate students learning in the following fractions tutor:

In general, I download different publicly available datasets from DataShop then I use the Apprentice Learner Architecture to create different models of student learning. I create a simulated agent for each human in the dataset. Next, I compare the behavior of the simulated and human agents.

For example, I downloaded student data from one Fraction Arithmetic dataset and simulated all of the students; i.e., I gave each simulated student exactly the same tutor and order of problems as the human students received. Here is a graph comparing the human and the simulated agents:

I then downloaded data from a second Fraction Arithmetic dataset that was broken up into two conditions: blocked and interleaved. In the blocked condition, students received all the fraction addition problems with same denominators, then all the fraction arithmetic problems with different denominators, then the fraction multiplication problems. In contrast, in the interleaved condition, students received all the problems in a randomized order.

Here are the graphs generated from two types of simulated agents for these two conditions. The full-memory agent has a perfect memory of all training examples and the one-back-memory agent only recalls the last and current example when training.

In general, the simulated agents are able to predict the main differences between conditions. They are also able to predict the effect of tutor condition on posttest score (I give the simulated agents the posttest). Below are the aggregate graphs, showing these predictions.

© Christopher J. MacLellan