The Context of School A

School A is located in the West Yorkshire. The school is a Church of England trust for students aged 11 to 19 years with over 1676 students. The school is reported to have an excellent reputation and the school’s vision is to be ‘outstanding within outstanding’. The OfSTED report of 2013³³ judged the academy outstanding in the four areas of inspection: achievement of pupils, quality of teaching, behaviour and safety of pupils, and leadership and management. OfSTED also reports how students’

achievement is high, with students enjoying great success in crucial areas such as

33 https://reports.ofsted.gov.uk/inspection-reports/find-inspection-report/provider/ELS/136094

118 mathematics and literacy. In 2015, the most recent results available, 72 percent of pupils at school A gained at least 5 A* to C grade GCSEs including English and Mathematics. In 2017, the Progress 8³⁴score stood at +0.65, which puts school A in the top 3 percent of schools nationally and means that students, on average, achieve over half a grade better in eight subjects than their peers in other schools. The Progress 8 score is a new rating for English secondary schools which was introduced in the 2016/2017 academic school year. It is an average score for all students at a school, showing how well they have progressed academically from the end of primary school to when they finish in secondary education. Students’ results at a school are compared to those from children at other schools who had attained similar academic results at the end of their primary education. The principal³⁵ describes School A:

As one of the country’s leading academies we are in the vanguard of school improvement. We are the flagship academy in the Multi Academy Trust, a national sponsor (which means we support other schools), a designated teaching school (Teaching School Alliance) and a Maths Hub of excellence.

We have received two outstanding judgments since opening.

School A is designated as a National Support School due to its work in improving other schools as well as a lead in the teaching school alliance across many authorities.

It hosts one of the White Rose Maths Hubs³⁶ (a collection of national networks of school initiatives) where the use of digital resources and the Shanghai teacher exchange programme are encouraged and supported. The school hosts many visitors in the course of the data collection year including mathematics teachers from China as part of the UK-Shanghai exchange programme. The students are taught in mathematics mixed-ability groupings.

School A was rebuilt in 2000 as part of the UK government’s £45-billion ‘Building Schools for the Future’ (BSF) investment programme. It was aimed at refurbishing or

34 https://www.gov.uk/government/publications/progress-8-accountability-measure-schools-responses

35 On school website page

36 http://www.mathshubs.org.uk/find-your-hub/white-rose-maths-hub/

119 rebuilding all 3500 secondary schools in England by 2020. The purpose was to remedy the decline in the overall state of school buildings and making them fit for purpose in meeting the educational demands of teaching and learning in the twenty-first century (Mahony & Hextall, 2013). A UK study argues that capital investment in school buildings has a strong influence on students’ performance, on teacher motivation and effective learning time (CABE, 2006). However, another study contended that no such link exist, arguing instead that further research is needed to illuminate the connections between school building and institutional effectiveness (Mahony & Hextall, 2017).

The architecture of the school took into cognisance the nexus between pedagogy, technology and the design of the learning space for the school of the twenty-first century. There are plenty of open spaces and corridors lined with desktop computers and study desks. School A has dedicated a mathematics department, a common working room for all mathematics teachers with a library of textbooks, a computer suite for students and teachers and mathematics-related texts, and a trolley of handheld resources. The mathematics staffroom is equipped with desktop computers for every teacher. This context encourages and supports collective work. The departmental ethos expects and facilitates a continuous atmosphere of discussion, asking and sharing, and whatever resources the majority deems useful are always added to the shared departmental bank of resources.

6.1.1 Content and Approach

The central ongoing innovation in mathematics in school A is the move towards the Singapore/Shanghai mastery-type approaches to teaching mathematics including the use of digital resources. UK mathematics education reform³⁷is currently focused on how the UK’s mathematics performance compares to the highest-attaining mathematics education systems internationally. There is a government-backed

37 https://www.gov.uk/government/collections/national-curriculum

120 mandate to explore, adapt and embed the Singapore/Shanghai model of mastery teaching and assessment for learning approaches across England and Wales (You &

Morris, 2016). “Mastery learning can be described as a set of group-based, individualized, teaching and learning strategies based on the premise that virtually all students can and will, in time, learn what the school has to teach” (Anderson, 1975, p. 4). This has been the major influence on the mathematics teachers in School A in adopting the key elements of feedback, mathematical fluency and enrichment as tools towards enabling higher levels of achievement, deep understanding and confidence among students. The use of a ‘concrete, pictorial and abstract’ approach of mathematics teaching for mastery, and assessment (Guskey, 2010) for learning has become the regular means of teaching for understanding. It is reported in The Guardian that 30 Shanghai mathematics teachers were flown in by the Department for Education in the hope they can raise flagging standards in schools across England (Weale, 2015). However, a study raised some doubt on the current enthusiasm in the West, especially in England, for copying East Asian mathematics teaching methods.

The finding shows that second-generation immigrants of East Asian descent outperform their native Australian peers in mathematics by more than 100 PISA test points – roughly the equivalent of two and a half years of schooling. In England also, children of Chinese origin have the highest GCSE scores of any ethnic group – in 2014, 78 percent gained at least five A*-C GCSEs, compared with the UK national average of 60 percent. Jerrim (2015) argued that the decisive factor is culture not curriculum, suggesting that widespread cultural factors beyond school also play a part in their success.

This adoption of the mastery approach has had a major influence on the appropriation of resources by mathematics teachers for lesson preparation and classroom practices.

In the course of my data collection, two invited Chinese mathematics teachers were there to train the resident mathematics teachers and helped them adapt to the mastery approach of teaching. Kitty reported in an interview on the role of the Chinese teachers in relation with CPD:

We do have professional development sessions. Last year for example when we were doing a lot of work on the Singapore bar modelling, we had a CPD

121 session every week where we were talking about teaching and learning how to deal with it using the bar modelling methods, yes, we did last year. This year it is not as frequent; however, we have mentioned as a department that we are learning a lot from the Chinese teachers every minute who are helping us, and they actually meet every day after the lessons. We were thinking maybe we should have more meetings like that where you are maybe observed and filmed, and you looked back. All you are looking at is the pedagogy behind that lesson to improve that particular thing you are questioning and students' learning that comes from that. (1intK:15#).

The teachers in School A have regular formal and informal CPDs on pedagogy, the new curriculum, on available resources and on how to assess, select and adapt resources for use in teaching specific mathematical concepts. There are rich varieties of sources of resources for the teachers. This is shown in the subsequent subsection of the case study reports.

6.1.2 Grouping and Assessment for Learning

In all the classes observed in school A, students are taught in mixed-ability groups.

Students’ progress is closely monitored on a regular basis, with the use of a variety of digital resources – Plickers, QR code, Socrative (explained in more detail in section 6.2.3, p. 138) – that provides instant marking and indication of areas of difficulty or identifies students who are struggling and need further support. An interesting emergent focus lies at the intersection of teachers’ resource systems for mastery teaching and their appropriation of digital tools for formative assessment (FA). FA is also referred to in the literature as assessment for learning (AfL) where student seat-work is instantly analysed during lessons which allows the teacher to enact changes in the tasks. Heritage (2018, p. 52) considers that

Assessment for learning (AfL) is integral to teaching and learning and has as its central foci (i) pedagogical intervention in the immediacy of student learning, and (ii) the students’ agency in the learning and assessment process.

The role that students adopt in AfL is consistent with the idea of self-regulated learning, which involves students as metacognitively, motivationally, and behaviourally active agents in their own learning.

Self-regulated learning through self- and peer-assessment by learners is a regular aspect of formative assessment in the mathematics classrooms observed. The use of 'traffic lights', pasted in bold typeface into the backs of learners’ notebooks, serve as

122 a simple means for students to communicate judgements about their understanding of an ongoing task. Learners raise up a coloured square to indicate to call teacher’s attention to where they are. Figure 5.1 below is a sample of the traffic light colour device.

Figure 6-1. Traffic light colour coded device

Figure 6-1 shows the system for assessing students’ progress and understanding based on a ‘traffic light colour code’ approach, denoting the level of complexity – green, amber and red – whereby children are encouraged to self-assess their work. Black and Harrison (2001, p. 46) state that “one advantage of the traffic lighting device is that the teacher can identify at a glance the main learning difficulties that have arisen, without lengthy interrogation of each student individually. It also facilitates communication between students”. This device allows the teacher to quickly identify situations that require intervention.

6.1.3 School Ethos

School A has a very well-established, rich Christian ethos built around four core values: empathy, honesty, respect and responsibility. Its admissions policy welcomes all students irrespective of their religious backgrounds or affiliations. This Christian character and vision are intended ‘to ensure that young people in our care fulfil their

123 potential’. SIAMS³⁸, the body responsible for inspecting provision in church-based schools, has also judged the impact of the Christian ethos in creating an atmosphere of purposeful learning and aspiration throughout the academy as outstanding³⁹. The curriculum review policy stipulated

Monitoring of standards, systems and teaching and learning across the Academy is the responsibility of the Senior Leadership Group (SLG).

Monitoring of the quality of lessons on a daily basis is the responsibility of the Curriculum Leadership Team. Each subject has ongoing Quality Assurance throughout the year via learning walks, lesson observations, work scrutiny, student voice and weekly SLG link meetings⁴⁰.

The curriculum is targeted at a model of the mastery teaching approaches in the hope that this will impact positively on students’ learning and progress, working towards developing students as well-rounded global citizens of the twenty-first century both academically and socially.

Having described the context of school A, I now turn to consider the individual case study report for the four participating teachers in this school.

The case study report is presented in the following sections for each of the four teachers. The profile of the teachers, their roles in the department, their tasks deployed in their lessons observed, their resources and the collectives the four teachers participate in are explored and presented.

38 National Society Statutory Inspection of Anglican and Methodist Schools 39 School website

40 School A curriculum policy document

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