The Acceptable Zone

Underlying these adaptive processes is the understanding that the experiences and perceptions that stakeholders favour will guide the exploration and ultimate choice of all possible strategic options. In addition, there is a limit to the levels of deprivation these stakeholders are willing to accept before they search for alternative paths. Accordingly, for the SIP to be “successful”, agents’ responses/adaptations to changes in the systems should actively improve the state of system, or at least remain within the ‘Acceptable Zone’. While this might vary across stakeholders, for this research the acceptable zone will simply encapsulate a set of states in which the implementation of the SIP will yield quality teachers, headteachers, School communities and schools. In this case, the acceptable zone has been defined after close consultation and interviews with key informants and centres on the conditions under which each of these agents have specified as their minimum requirements to participate in the SIP intervention. A common set of conditions emerged from

these perspectives; the first was the necessity of having basic needs covered (salaries paid in a timely fashion) and the second was the sustainability of the supplementary support they each require to implement the programme. Whilst in the space of acceptability, a change can start or continue to occur. Recall that it is the premise of ESSPIN that the SIP intervention should shift the current trend in the education system into the acceptable zone (as defined here) and it is the focus of the SIPM to investigate if the intervention does this, as well as if the system in which it operates enables or inhibits this process.

With reference to the work done by Mital, Moore and Llewellyn (2014) and Blumenfeld et al., (2000), the acceptable zone is conceptually modelled on three gaps affecting the implementation of the intervention: policy management gaps, capability79 gaps, and cultural gaps. These gaps are

composed of a set of attributes at the macro level of the system. They represent the difference between the ideal state and the actual state of the attributes (each of which are summarised in Figure 6.3 below).

Figure 6.4 3D representation of the acceptable zone and gaps Source: Mital (2015)

Each of the three gaps presented in the figure above are made up of certain attributes (at the micro level of the system) which are manifested at the macro level of the system. A gap is calculated as

79 _{In this research, capability is technical term that describes the abilities of individuals. It captures personal} characteristics, and is affected by external factors such the availability and conversion of resources into real opportunities and achievement. This conception of capability is also consistent with Sen (1992) which is concerned with freedom of choice, and the feasibility for a person to achieve.

the average difference between ideal and actual states of the attributes that compose of the gap (each of which are further defined in the next chapter). Therefore, the SIPM is designed to illustrate transitions from the initial to end states of the system (with the implementation of the intervention), while showing agents that fall within and outside the acceptable zone. In some cases, the acceptable zone is realised, while in others it is not. A useful way of capturing these changes is by utilising a fitness function for the overall system. It encapsulates a space where an intervention can be successful, even as the system is operating short of the ideal state. To stay in this state, all three gaps must be within an acceptable tolerance level. However, the probability of sustainability is always subject to change over time (ideally, the value should improve). This probability is calculated based on the three gaps and a modified logit probability model developed by Mital (2014). In summary, the function allows that the probability of sustainability decreases as the gap increases (and vice versa), changes in gaps are averaged over time periods, and larger gaps are penalised more (especially when outside the acceptable zone gap tolerance). This procedure has the added benefit of producing binary responses from continuous variable i.e. success (sustainability) or failure (unsustainability) of the intervention. These features are incorporated to develop a probability of sustainability P(S) (Equation 1) with reference to the three gaps outlined

Equation 1. Calculation for sustainability probability

where wpm + wca + wcu represent the weights corresponding to the three gaps, and sum up to 1. This

is a fine balance and so if a particular gap is large in magnitude, the corresponding probability function will be low. Therefore, for the SIP to be successful, all the gaps have to be sufficiently low. It is therefore useful to study the effects of adjusting the size of the gaps:

• _{if only one gap is large, the sustainability probability of the intervention will typically be} low

• however, when the gaps are weighted equally, even with one large gap, probability of sustainability can still be achieved.

To further test the effect of weightings in this probability calculation, a series of treatments using a combination of weighting schemes (harmonic and dynamic weight assignments) were applied to study the differentiation in gaps (see Mital, 2015 for detailed calculations). Based on a comparison of the performance of the different functions, the P(S) equation above best fulfilled one important

criteria: the difference between gaps was not masked when one gap was particularly high and the other low. In addition, this calculation produces intuitive probability values and is easy to compare across different systems.

On another level, public policy analysts might find these probability measures useful for quantifying risks when implementing interventions in the education system. A high probability for sustainability would imply a low risk environment for the intervention and vice versa. Of course, most reform programmes would be targeted at improving the performance of schools in high risk environments with the goal of moving them into a low risk environment and into the acceptable zone. If the reverse were to occur, it would also be a useful indication of unsuccessful reform policies and/or strategies. As pertains to the SIPM, the procedures outlined above will be applied to define the acceptable zones. The gaps for all attributes will be held constant when calculating any one gap. The acceptable tolerance for each attribute will be taken as the difference between the two highest levels. This calculation provides an estimation of how much agents deviate from the acceptable zone, and based on this, the overall fitness and probability of sustaining the intervention can be calculated. The next two chapters respectively explain and model this process in more detail.

This chapter was concerned with making a strong connection between the research data and modelling stages identified in the methodological approach (presented in Chapter 3, highlighted in Figure 3.3). The literature reviewed (Dey, 1993; Yang and Gilbert, 2008; Daly et al., 2015) and utilised (Bharwani, 2004; Mital, 2015) to develop the conceptual framework in this section all demonstrate that it is unrealistic to expect any model to simulate all psychological and social processes, or even to model them to great levels of detail. As such, the SIPM attempts to extract the most compelling features of the education system and the effects of ESSPIN on that system. After an extensive study of the local education context and the available analytical frameworks for modelling the system (Chapters 2 to 5), this chapter delves into the frameworks as applied to data collected from the fieldwork portion of this research. The mixed methods approach of this thesis is illustrated here by the combination of frameworks used to formalise the data, build the model, and analyse the results. Bennett’s framework facilitates in capturing the nuances of stakeholder experiences and thus, understanding and qualitatively defining the factors that would influence change in the system. ESIM (as developed by Mital, 2015) provides the necessary abstraction (it is

beyond the scope of this research to model each individual in the system) and practical techniques to quantitatively define the state of the system and measure those transitions. The next chapter sets the ground work of the model. It goes through the design, calibration, and validation phases using the earliest implementation period of ESSPIN as a test case. Here, the exact parameters for the SIPM are refined and adjusted before the SIP can be run and analysed from start to finish.