Policy and Complex Systems
Rules : Change in Attributes The internal change probability ,
p internal
( t ), for a particular agent is a function of three inputs : the current attributes of the agent , the agent ’ s relationships with other agents , and the attributes of the agents with whom the agent has relationships . As an example , for the SLIDER case study , the internal probability of change equations for ‘“ support for intervention ”’ of a teacher is the following :
using sensitivity analysis . In the above equations and the equations presented next , the function p (.) can take either positive or negative values . If p (.) is positive , then it represents the probability of the attribute to improve ( p improve
), and 1-p (.) represents the probability of the attribute to stay the same ( pstay ). If p (.) is negative , then the absolute value | p (.)| represents the probability of the attribute to worsen ( p worsen
), and 1- | p (.)| represents the probability of the attribute to stay the same ( p stay
). The above equations are representative of change equations for modeled attributes .
Rules : Effect of Resource Flows
In the above equations , p ( t + 1 ) and p transient _ ( t + 1 ) represent the support steady _ support transient and steady steady-state change components for teacher ’ s support for intervention in period t + 1 . I x
( t ) is a modified indicator function with x being a given normalized attribute value ; this term is used only in the steady steady-state equations and is used to capture attribute changes . The first term in both transient and steady steady-state equations reflects the teacher ’ s own attributes , and w teacher is the weight for this term . All attribute values are initialized using survey or SME data collected on a Likert scale and then normalized . The second term captures the relationship of the teacher with the administration , where :
w admin is the weight for this term , and
`One resource flow from GT to the school agents is in the form of Professional Development ( PD ), which affects teachers ’ pedagogical skills with respect to inquirybased learning and content knowledge . A teacher ’ s inquiry-based teaching skill is a multi-faceted attribute capturing specific pedagogical practices , including studentcentered structuring of lessons where the teacher serves as a facilitator rather than a lecturer ( Llewellyn , 2014 ). A teacher ’ s inquiry skill is also assumed to be affected by relationships with other teachers in the school receiving PD . In the example below , there are two teachers at a single school who are receiving PD from Georgia TechGT , and the equations model the change in inquiry teaching skill of teacher1 . and
represent the relationship strength between the teacher and administration and the administrative support for intervention at time t , respectively . Again , w teacher
+ w admin
= 1 and the effects of the weights are tested
In the above equations , p transient _ inq ( t + 1 ) and p steady _ inq
( t + 1 ) represent the transient and steady steady-state change equation components for teacher1 inquiry teaching in period t + 1 . I x
( t ) is the same
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