As indicated earlier in Figure 5.3, the main strategy adopted by the current study is multilevel. This quantitative strategy was employed in connection with the measurement of pupil attainment and pupil progress as well as the identification of the predictors of pupil attainment (age 6) and pupil progress at the pupil, the classroom and the school level. This ties-in with the first research question: what are the predictors of pupil attainment/pupil progress for mathematics after adjusting for factors at the pupil, classroom and school level? Identifying the predictors of pupil achievement in conjunction with the classification of ―effective‖, ―average‖ and ―ineffective‖ schools allows the evaluation of similarities and differences with regards to the pupil, classroom and school level predictors of pupil progress across differentially effective schools.
This ties-in with the second research question: how do the pupil, classroom and school level predictors of pupil progress differ across (and possibly within) differentially effective schools? Quantification alone does not yield sufficient detail about the quality of head teacher and Year 2 teacher strategies in differentially effective schools.
Detailed records about the routines and strategies of head teachers and Year 2 teachers, which were used to elaborate case studies of practice, were maintained in the school and the classroom profiles. The case study approach was adopted to avoid the pitfalls of adopting an overly narrow and empirical definition of effectiveness (Elliot, 1996;
Campbell et al., 2004; Goe, Bell & Little, 2008; Thrupp, 2001) and to focus on head teachers and teachers in broader ways. This ties-in with the third research question:
how does the practice of head teachers and Year 2 teachers differ across and within differentially effective schools?
5.2.2.1 The Models for Attainment (Age 6) and Progress (Quantitative - Multilevel)
Various similar steps were involved in the construction of two multilevel models for the examination of pupil attainment (age 6) and pupil progress between the age of 5 (Year 1) and 6 (Year 2). The analysis of pupils‘ age 5 scores was limited to the pupil level.
No explanatory variables for the classroom level were collected as part of The Numeracy Survey (Mifusd et al., 2005). Therefore, it was not possible to identify the predictors of pupil attainment at age 5 on a like-with-like basis with the predictors of
pupil attainment at age 6. With regards to the construction of the models for pupil attainment (age 6) and pupil progress, a null model was first constructed through use of the software MLwiN. Then the age-standardised age 5 or age 6 scores of pupils were set as the independent variable in each model. After this, a pupil/parent model was constructed by including pupil level variables already listed in Table 5.2. The addition of prior attainment transformed the pupil/parent model from one for the examination of attainment (age 6) to one for the examination of progress. A teacher/classroom model was then constructed. Variables in this model refer to teacher attributes and broader teaching conditions in classrooms (Table 5.3). After this, a teacher beliefs model was constructed by including the relevant variables to the teacher/classroom model.
Variables in this model refer to responses given by Year 2 teachers to statements about beliefs regarding the teaching (and learning) of mathematics (Table 5.3). This was followed by the construction of a teacher behavior model. Variables in the teacher behaviour model refer to the frequency of effective behaviours observed of Year 2 teachers during lessons of mathematics (Table 5.3). Finally, a head teacher/school model was constructed by including variables to the teacher behaviour model. These variables refer to broader conditions at school and head teacher attributes (Table 5.4).
This step was the same in the models for attainment (age 6) and progress.
5.2.2.2 The School and Classroom Profiles (Qualitative – Case Study)
Elliot and Lukeš (2008) argue that the purpose of case studies is to complement the study of samples rather than to supplant their study. In the current study, the study of the samples (and of the characteristics) of pupils and their parents, Year 2 teachers in classrooms and primary school head teachers in schools refers to data that is hierarchical in structure. However, the levels of data also house within them layers of data that concern the practice of head teachers and the practice of teachers within the systemic organisation of education in schools and in classrooms. Therefore, a case study approach was adopted by the current study to provide a richer picture about the activity and practice characterising head teachers and teachers following the classification of differentially effective schools (and classrooms). Elliot and Lukeš (2008:88) also consider that case studies refer to: ―a form of inquiry into a particular instance of a general class of things that can be given sufficiently detailed attention to
illuminate its educationally significant feature‖. This implies the more open character of case studies. Therefore, the current study sought to provide a more structured framework for the textual data yielded by the field notes and MECORS (A) about conditions in schools and classrooms and about the practice of head teachers and teachers were employed to maintain 89 classroom profiles and 37 school profiles. Data held within the school and classroom profiles then contributed towards the elaboration of case studies of head teacher and teacher practice. Profiles were compiled according to critieria in Table 5.9.
Table 5.9 – Criteria for the School and the Classroom Profiles
School level criteria Research instrument
Type of school Field notes
Size of school Field notes
Predominant socio-economic composition of pupils in school
Parents‘/guardians questionnaire and field notes
Sex of head teacher Head teacher questionnaire and field notes
Age range of head teacher Head teacher questionnaire and field notes
Head teacher experience of teaching at primary
Head teacher questionnaire and field notes
Leadership
Monitoring of teachers by the head teacher
Field notes Involvement of head teacher with
teachers
Field notes Selection of teachers by the head teacher Field notes Replacement of teachers by the head
teacher
Field notes Vision
Availability of school development plan Field notes Implementation of school curriculum Field notes
Climate and order Field notes
Time scheduled for mathematics Field notes Relationships
Forming of relationships with teachers Field notes
Parental involvement Field notes
Practice
Head teacher involvement of teachers Field notes Head teacher monitoring of staff Field notes Head teacher discusses instructional
quality with staff
Field notes Head teacher discusses curricular issues
with staff
Field notes
Table 5.9 – Criteria for the School and the Classroom Profiles (continued) Classroom level criteria Research instrument
Size of classroom Field notes
ABACUS topics covered Field notes
ABACUS topics not covered Field notes Socio-economic composition of
classroom
Parent/guardian questionnaire and MECORS (A)/field notes
Sex of teacher Teacher questionnaire and MECORS
(A)/field notes
Age range of teacher Teacher questionnaire and MECORS (A)/field notes
Teaching qualifications Teacher questionnaire and MECORS (A)/field notes
Lessons Research instrument
Duration in minutes MECORS (A)
Disruptions to lessons in minutes MECORS (A) Duration of mental warm-up MECORS (A) Number of explanatory activities MECORS (A) Duration of each explanatory activity MECORS (A)
Duration of plenary MECORS (A)
Number of times per week mathematics homework is assigned
MECORS (A) Nature of mathematics homework MECORS (A)
Instructional practice