Journal on Policy and Complex Systems
L . Here , the measure of student performance is mapped to a set of discrete classes . This can be an automated process or even be the result of policy given to a school administrator . Although in real applications there are multiple factors that go into class assignment , in this stylized model we propose a simple partitioning of GPA performance to make that decision . For this model , we will assume that the decisions form a cover of uniform intervals over the performance domain ,
In this case , the GPA domain is split into intervals of width , ∆ , which determines the number of class partitions . For this scenario , ∆ = 1 . This function is surjective in that multiple GPA values map to class assignments . Class assignment is performed for each student by randomly assigning over the set of qualifying classes of the identified level ,
Complex System Model ( Application ). The classroom performance model roughly has the form
where the number of disruptors , n d
, is dependent on the number of students in the school ( N ), the proportion of students that are off by 1 class level , φ 1
, and the proportion of students that are off by 2 class levels , φ 2 and the initial proportion of disruptors in the classroom , θ . The model form is a simple ABM of student placement using NetLogo , a multi-agent modeling environment ( Wilensky , 1999 ). Whereas the training data does not explicitly encode the student arrangements and compounding effects resulting from decisions , these
can be simulated . In an ABM , we can account for the local interactions of students ( agents ) over a physical space . In this case , we use a regular lattice ( or grid ) to create simple peer networks . In other words , students may be influenced to become disruptors by other students in their “ network ”. The localized interactions that occur through these simple network structures are critical to generating the dynamic processes behind the social system . Figure 2 shows the modeling interface .
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