Education System Intervention Modeling Framework
indicator function defined in equation 5 . The first term in both equations captures the relationship between teacher1 and teacher2 , where w teacher2 is the weight for this term ,
is the relationship between teacher1 and teacher2 at time t , and
is the inquiry teaching level of teacher2 at time t . The second term is for PD given to the teacher where : wpd is the weight for this term , GT pd
( t ) is the PD level at time period t , and are more likely to form ties with other individuals who are similar to them in a variety of ways including demographics , hobbies , and interests . Structural balance assumes that individuals are more likely to form positive ties with friends of friends , negative ties with friends of enemies , and positive ties with enemies of enemies .
For the SLIDER intervention , we have explicitly modeled the change in relationships among the teacher , administration , and GT . In this case , the relationship between the school administration and GT is affected by the administration ’ s support for intervention . The following equation represents the change in relationship between the administration and GT : is the weighted average of the self-efficacy and support for intervention of teacher1 at time t . Again , w teacher2
+ w pd
= 1 . The above equation illustrates the overall structure of change equations where an agent ’ s attributes is affected by three things : its own attributes , its relationship with the other agents , and attributes of other agents . The only difference is the addition of GT pd
( t ), the resource flow , to the second term . This resource flow variable allows us to capture differences in PD quality and duration for different interventions .
Rules : Change in Relationships
In addition to attributes , relationships also change over the course of the intervention : relationships can become more positive , stay the same , or may sour . Two concepts from social network theory aid in modeling relationship changes : homophily and structural balance ( Davis , 1963 ; Heider , 1958 ). Homophily assumes that individuals
In this equation , p change _ rel _ admin _ GT
( t + 1 ) represents the internal change equation for the relationship between administration and GT at time t + 1 . I x
( t ) is the same indicator function defined in equation 5 , and x is the support for intervention attribute . Here ,
w admin is a weight and is equal to 1 because no other factors affect relationship quality in this case .
These equations , when extended to the other agents , attributes , and relationships , complete the model for the SLIDER intervention at the individual schools . Before moving forward into analysis , the model is validated using SMEs , including the SLIDER research team , public policy researchers , and one of the teachers involved in the intervention .
3.3 Model Analysis
In this phase of the framework , simulation results were generated and analyzed . Data collected during the
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