Identifying the Distinct Types of Tasks

In the course of exploring the datasets with a view to addressing the research questions on tasks on p.7, 15 distinct task types were identified. These 15 distinct task types are presented in Table 4-12 below and what follows is the descriptions and rationales for identifying these task types.

Tasks Types and Associated Abbreviations

Abbreviations Task Types Abbrev. Task Types

1 ST Starter 9 MOD Modelling

2 SA Skill audit 10 CO Consolidation

3 D Definition 11 MIX Mixed ability

4 IN Interactive 12 EM Emergent

5 DS Diagnostics 13 FA Formative

6 D/V Differentiations/

Variations

14 PS Peer/self-assessment

96

7 EX Extension 15 PL Plenary

8 MR Multiple

representation

Table 4-12. Task types and associated abbreviations

Here, I will explain the processes of task identification, states what makes them distinct and point out where this overlaps.

These rationales and principles guided my identification and classification of the tasks.

o The teacher-specific labelling of the tasks on the board, in the lesson worksheet, and collected in the interview/post-lesson conversations. For instance, starter tasks, formative assessment tasks, definitions, differentiation/variation, modelling etc. were indicated as such by the teachers themselves.

o Tasks identified in textbooks, the schemes of work and online resources used by the teachers. For example, extension tasks, multiple representation tasks and modelling belong to this classification.

o Tasks I have identified through the analysis of the datasets. Within the groups of tasks, I tagged these as skill audit tasks; these are tasks like multiplication tables, quizzes, and addition and subtraction activities. The goal of these tasks, as the teachers indicated, was to enable the student to become confident in recall and use of basic number operations. Also, in this category are the

‘emergent’ and mixed-ability task types.

o Finally, I only included such tasks that were observed in the lessons and teachers reported they had used. Where there are overlaps in the task types, I have provided further explanations in the case study reports. (There are instances were starter tasks for one teacher are plenary tasks or formative assessment tasks for another.)

Table 4-12 above shows the 15 task types and I have also included related abbreviations for ease of in-text referencing. These tasks are listed from the SCAN observation notes, screen capture data, mathematics-specific documents and interview transcripts. A more detailed description of each type of task is given, and the teacher-stated purpose of each task type is presented in the case study report in the subsequent Chapters 6-8. Here, my focus is on presenting the datasets on tasks, the

97 emergence of these tasks, and my considerations in the process of classifying these tasks.

I also present Table 4-13, which indicates the task type by teachers across the three schools.

Table 4-13 Task types by individual teachers

Table 4-13 above shows the task types as used by teachers in their lessons. My initial thought was to look to the three-part lesson plan for explanation, but on a closer examination, the teachers were using different approaches to their lesson structures.

Since all the teachers included starter tasks, and two teachers included plenary as elements in the sequence of their lesson activity. Starter and plenary are constructs drawn from the three-part lesson plan discussed in the literature review.

However, I realised the teachers were not consistent in all their lessons with this form of lesson structuring. Upon further analysis of the official and mathematics-related documents like the scheme of work, it emerged from the documents that there are several underlying influences (shown in Table 4-14 below) that were impacting on

98 the way the teachers structured their lessons and consequently the types of tasks they pose in the sequence of lesson activity.

At the core of the varied influences mentioned in the opening paragraph of this subsection and shared across the three schools is the ‘mastery teaching phenomenon’.

Recent research has argued that the mastery approach to teaching mathematics is central to current policy in mathematics education in England, influenced by East Asian success in transnational assessments (Boylan et al., 2018).

In Table 4-14 below, I present a recommended lesson structure drawn from the central resources used by each of the three schools. While none of the teachers was observed using any of these lesson plan structures in full, some elements were present in their lesson structure.

Table 4-14 Mastery teaching approaches, influences and associated lesson structure.

23 http://www.mathshubs.org.uk/what-maths-hubs-are-doing/teaching-for-mastery/

24 https://www.pearsonschoolsandfecolleges.co.uk/secondary/Mathematics/11-16/GreatMathsTeaching/maths-5-year-curriculum-11-16.aspx

25 Available on school website and screen shot used in the case description.

Mastery Teaching Approaches

99 For example, in school C, Richelle uses only the terms ‘starter’ and ‘extension’

explicitly in her worksheet. In school B, while tasks under lesson structure provided by the Pearson curriculum designer were used, Gray’s and Gavin’s lessons were structured differently. In my opinion, teachers in the three schools were using the official resources as one of the many resources they can draw tasks and inspiration from.

Teachers in school A adopt various maths-hub-recommended key elements of the Chinese variant of the mastery-teaching approach for secondary schools in England.

This was considered alongside the uptake of the new curriculum. Here, I outline some of these elements:

o Lesson designed to have a high level of teacher-student and student-student interactions

o Teachers should keep the whole class learning together

o The use of differentiation, variation and multiple representations o Recommendation of intelligent practice and regular use of formative

assessments

o Number facts using multiplication tables and formulae to avoid cognitive overload²⁶

The lesson structure in school A column is what is to be promoted in the class and in the training of other teachers through the maths hub led by school A.

In school B, the Pearson ActiveTeach and ActiveLearn digital learning and teaching platform is the central resources for mathematics teachers’ activities. (This is discussed in the case study report for school B in Chapter 7.) The Pearson website stated this with regards to mastery approach: “Mastering mathematics involves all students achieving a true depth of understanding of mathematical concepts. Our UK-built approach to teaching for mastery underpins our 11-16 schemes, KS3 Maths

26

https://www.ncetm.org.uk/public/files/19990433/Developing_mastery_in_mathematics_october_201 4.pdf

100 Progress and Edexcel GCSE (9-1) Mathematics²⁷”. The Pearson resources designers seem to argue for a “UK-built approach to teaching for mastery” and in the second columns for school B in Table 4-14, the e-textbook and related scheme of work recommend the above five-part lesson structure and strategy for implementing the Pearson variant of mastery teaching.

School C subscribed to Collins Connect, an educational publishing company which provides resources for school C. They claim that “based on the successful maths programme delivered in Shanghai, these comprehensive resources provide authentic mastery practice adapted for the English curriculum and we help your class to achieve mastery in maths with The Shanghai Maths Project”²⁸. As such they make available to mathematics teachers in school C a so-called ‘GCSE mastery scheme of work’ and in the third column under school C is how Richelle adapted and implemented this in her lesson structure.

In spite of the renewed wave of interest in the mastery teaching approach and associated lesson design, there is still a high level of uncertainty among researchers as to whether this will be a ‘seasonal vogue’ or lead to lasting changes in practices and, if changes are effected, whether they will improve learners’ outcomes (Boylan et al., 2018). From the vantage point of my research observation and datasets, the three schools and the seven teachers in this study seem to be ‘enthusiastic’ about the prospect of their particular version of the mastery teaching approach.

The mastery teaching approach subscribed to by each school varies considerably from school to school. From the data, each teacher seems to have interpreted, adapted and implemented their personal idea of mastery and what they deemed fit for their teaching purposes. Also, the teachers, I argue, relying on the evidence from my data,

27 https://www.pearsonschoolsandfecolleges.co.uk/secondary/Mathematics/11-16/GreatMathsTeaching/maths-5-year-curriculum-11-16.aspx

28 https://collins.co.uk/pages/secondary-maths-the-shanghai-maths-project

101 have structured and presented their tasks in a sort of ‘mix and match’ from previous knowledge of the three-part lesson structure and the emerging mastery teaching strategy. All seven teachers retained the use of elements that reflect the three-part lesson plan (starter, plenary, extension) and merging these with elements associated with the mastery approach (such as differentiation and variation). This extended background provides the context and the subtle influences through which I identified the 15 distinct tasks and their classifications.