Modelado a través de sistemas de inferencia borrosa

Partly due to the availability of the required data, the first phase of this research project was to establish a simple statistical representation of the student composition of Free Schools in England. Further to this, and in an attempt to make the research more robust, the intakes of schools close to the Free School were observed in order to make comparisons on a yearly basis. Whilst giving us a clear overview of the school compositions, basing findings purely on percentages of students with different characteristics had problems too. First, many of the Free Schools opened with very small numbers of students. To calculate percentages using these, and to then compare them with schools that had fully established intakes provided, in some cases, skewed and unreliable results. Second, it was understood that the data being used were for the Free Schools’ initial years. It is quite possible that the compositions of the schools when they first opened would alter as the school became more established. Despite these concerns, it was still thought that calculating such figures could give some useful insight into the proportions of disadvantaged pupils at the schools, their local competitor schools and in their LAs. It was also necessary, however, to focus on the distribution of children across a certain set of schools and to gain a clearer picture of whether individual schools were taking their ‘fair share’ of disadvantaged pupils. For this, the segregation ratios were used.

The data, chosen measures and analytical methods that are used in this part of the project are discussed in the sections below. Attention has been given to ensuring that the analysis of the data is straightforward and replicable, and that it can be continued in future years in order to track trends that may begin to emerge from the Free Schools programme.

5.4.2.1 Data and indicators

The analyses here are based on data from the Annual Schools Census (ASC) which is administered annually by the Department for Education. All state-funded schools in England are required to submit details about their student body on a range of indicators including sex, age, ethnicity, FSM take-up and eligibility, first language and Special Educational Needs

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(SEN) status. It also includes the number of full and part-time students attending each school, and details of students’ attainment. The ASC is an invaluable resource for researchers and policymakers aiming to gain an overview of schools across the country. Whilst it is acknowledged that there will inevitably be some missing or inaccurate data, the benefits of having such a detailed and accessible dataset far outweigh such limitations.

A major advantage of the ASC data is that it can be used longitudinally. For this project that meant that it was possible to track the compositions of the Free Schools year on year. In addition, it meant that it is possible to identify any changes in student intakes in local non- Free Schools following their introduction. Data on the schools before the Free School opened was examined and compared with the same data following the introduction of the new school in order to establish whether there had been any change in numbers on roll or composition.

While the ASC records numbers of students with certain characteristics in each school, it is important to highlight the fact that the definition of these indicators sometimes alters slightly over time (Gorard et al., 2003). Furthermore, sometimes new indicators are included to take into account for new government policies or to enable additional analysis. Examples of this include the addition of data relating to Pupil Premium eligibility and more detailed SEN measures.

5.4.2.2 Indicators

One of the objectives of the first phase of this study was to establish the extent to which Free Schools are allocating places to socioeconomically disadvantaged students. The Department for Education currently define ‘disadvantage’ as those eligible for Free School meals and Looked After children (DfE, 2014c). The measurement of FSM using the ASC will be considered below. Due to it sensitivity, it was not possible to attain data on Looked After children and so this will not form part of the current study.

5.4.2.3 Free School Meals

Socioeconomic disadvantage has been the indicator most focused on when analysing the intakes of academies and Free Schools to date (Gooch, 2011; Gorard, 2005). This tends to be measured using the binary FSM variable which highlights whether a child’s family is in

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receipt of certain state benefits (such as Jobseekers Allowance, Income Support or Child Tax Credits), and is therefore deemed to be living in poverty. The 2014-2015 ASC showed that 15.2% of pupils in state-funded schools in England were eligible for FSM, down from 16.3% the previous year (DfE, 2015c). Data are collected on both the numbers of students eligible for FSM and the numbers who take-up the FSM. It is important to be aware of this distinction, and to be aware that each year, some children do not take the FSM that they are eligible for. This might be for dietary, cultural or other reasons. In recent years the difference between the two measures has continued to decrease, however, for the purposes of this study eligibility is used as the sole indicator of poverty.

There are still some further methodological issues with the FSM measure that deserve consideration in order to more fully understand the limitations of the analyses included in this study. First, FSM eligibility can be subject to change when new government guidelines alter the rules for who can or cannot apply. Since 2003/4, for example, additional benefits have been added to those which designate a pupils’ eligibility for FSM (Hobbs and Vignoles, 2008). Secondly, claiming FSM, and therefore, the reporting of FSM eligibility by schools relies on parents applying for them. It is thought that the introduction of the Pupil Premium (increased per-pupil school funding for children who are Looked After or eligible for FSM) has encouraged some schools to ensure that they know who is able to claim FSM (Carpenter

et al., 2013). Despite this, there are still considerable numbers of pupils with missing FSM

data. Researchers have highlighted the problems with this, particularly with the assumptions that are made about the students without FSM data, creating an element of bias when using the measure. Gorard (2012), for example, argues that the FSM-missing pupils should be considered as a separate group of potentially ‘super-deprived’ students, rather than being assumed to be like non-FSM children as is often the case (Gorard, 2012).

It should be noted that the focus of the FSM measure is on poverty not class. Whilst it is acknowledged above that measuring socioeconomic disadvantage is relatively straightforward using the dichotomous FSM indicator, an attempt to measure social class via the ASC would be impossible. No data on this area is requested from schools in this country. Even if it were, it would be difficult to know what indicators the DfE would use to measure it due to the ongoing complexities associated with defining social class (see for example, Savage et al.,

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2015). Some other smaller-scale studies of school choice have attempted to use parental occupation/level of education as an indicator for categorising families or students based on class (Benson et al., 2015; Gewirtz et al., 1995). However, as these data were not available nationally (as is the case in Sweden, for example), and as these indicators still have substantial problems when equated with a definition of social class, no such measure was included within this phase of the research.

5.4.2.4 Segregation ratios

In addition to analysing the proportions of FSM children in each Free School, in nearby schools and within the LA, the idea of segregation relative to student compositions is considered. Croxford and Paterson (2006) define ‘evenness’ between schools as ‘whether a group is over-represented in some schools, and under-represented in others’ (Croxford and Paterson, 2006; p. 384). Segregation ratios are able to indicate these levels of evenness, providing useful comparisons between Free Schools and their nearby competitors.

The SR specifies the level of social stratification in an individual school; where the SR is equal to one for all of the schools in a defined area, there would be no segregation that year. But if a school has an SR of 0.5 it is taking half of its ‘fair share’ of disadvantaged children. As a result of this other schools will be taking proportionally more FSM eligible students. This could be calculated in relation to all schools nationally or for the relevant LA but for the purpose of this analysis the SRs for the nearest six schools to the Free School are presented in order to make comparisons on a more local basis (Gorard et al. 2003). The SR is calculated as follows:

SR = (Ai/A) / (Ci/C)

where: Ai,the number of disadvantaged children in school i; Ci,the number of children in

school i; A, the total number of disadvantaged children in a subarea; C, the total number of children in a subarea. For further detail on calculating segregation, see Gorard et al. (2003). Exley (2009) has reiterated the benefits of using the SR, arguing that rather than giving an overall figure of unevenness within a particular area, it is able to indicate exactly from which schools children would have to move in order to establish more balance across the defined locality. This is particularly useful when exploring whether there are differences between individual schools or school types.

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5.4.3.1 Gathering the data

The first research question focused on the ways which Free Schools were prioritising and allocating places for children. As a result, it was necessary to analyse the admissions policies, and particularly the oversubscription criteria being used. All secondary Free Schools that opened between 2011-2014 were included within this study. According to the Admissions Code (DfE, 2014a) schools “must publish a copy of the determined arrangements on their website” (DfE, 2014a, p. 19). This meant that, where Free Schools had complied with this requirement, gathering the necessary data was straightforward. All schools must have separate oversubscription criteria for each relevant age group (DfE, 2014a) and therefore in the analysis of ‘all-through schools’ only the criteria applicable to secondary age children would be used.

The most up-to-date admissions policies available were used; the majority of these were for the 2015-2016 academic year although a small number stated that they were for the 2013 or 2014 academic years or had no year mentioned on them. Unless specified, only approved, final copies of admissions arrangements were used for analysis as opposed to copies that were in draft or consultation stages. As a comparator, the oversubscription criteria for Local Authority maintained schools in the area where each Free School was situated was also collated. In a small number of authorities included in the study, there are no longer any secondary LA-maintained schools and so this comparison was not possible.

5.4.3.2 Analysing the data

The analysis of the oversubscription criteria followed similar methods to those used in a study by White et al. (2001) on the school allocation procedures employed by Local Authorities. As such the oversubscription criteria for each school were collated, grouped into categories and then tabulated in order to establish the ranking of each criterion. This allowed for comparisons of which criteria had and had not been used by each school, as well as the significance attributed to the criteria based on where it featured within the allocation procedure.

Frequency and percentage tables were produced, showing which criteria were used by different schools and the priority that the schools gave to each criterion. These were analysed

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alongside the LA admissions criteria in order to establish the extent to which the Free Schools were utilising their freedoms in relation to allocation procedures.