SimEd models.

overview.

Our SimEd models are centered around three mutually interacting levels: classroom, schoolhouse and school district. At each level, we define agents with different roles: students, teachers and administrators. We model interactions amongst agents within a level and between agents across levels. Interactions are motivated by one or more goals and are constrained by the structure of the system and by the requirements of interactions across adjacent layers.

classroom model.

We use as the basis for interaction modeling a game theoretic approach inspired by the Iterated Prisoner's Dilemma (IPD) [Axelrod,1984]. This dialogic framework, developed in previous work by Sklar and collaborators as the Meta-Game of Learning (MGL) [Pollack and Blair, 1998; Sklar, 1998], is essentially a restatement of the IPD within the context of education and is used to describe a student-teacher relationship and, broadly speaking, the types of interactions that can take place between these two types of agents. In the MGL, one agent, the teacher, provides either easy or hard questions to another agent, the student; and the student responds with either right or wrong answers. The goal is student learning, which theoretically only occurs when the teacher asks hard questions and the student provides the right answers, i.e., in IPD terms, when both agents "cooperate".

    student
    right answer
"cooperate"
wrong answer
"defect"
teacher hard question
"cooperate"
learning frustration
easy question
"defect"
verification boredom

The Meta-Game of Learning (MGL).

We apply the MGL to the SimEd classroom model and modify it in order to construct a more robust model that captures some of the complexities of human interaction, especially in a learning environment. We examine the question of what makes a teacher agent decide to ask an easy or a hard question and what makes a student agent answer the question correctly or not. We examine what factors lead to student learning and posit that the notion of continual cooperation on the part of both agents is not realistic in this setting, and the true path to student learning is a delicately evolved sequence of easy and hard questions on the part of the teacher. We propose that the "best" sequence can be personalized to the type of student involved in the learning process.

Further, we delve into the design of a student agent, considering factors of ability, emotional state and motiviation in determining whether a student provides a right or wrong answer to a question.

school district model.

The school district model is an attempt to study problems in resource allocation and examine the various factors that contribute to student learning from the point of view of parents and school district administrators. Factors we consider are economic and demographic, modelling the performance of individual students, aggregated to provide a performance value for a school. Following the "No Child Left Behind" policy, we demonstrate what happens when school districts give students the opportunity to change schools based on a school's overall performance value. Parents decide whether their children should move to another school. Economic factors determine whether a student's family can support the student moving as well as an overall "happiness" quotient on the part of the student and her/his parents.