All-Attainment Teaching in Secondary Mathematics: Philosophy, Practice and Social Justice

214 Pages·2022·4.541 MB·English

by  Colin Jackson

Colin Jackson
All-Attainment
Teaching in
Secondary
Mathematics
Philosophy, Practice and Social Justice
All-Attainment Teaching in Secondary
Mathematics
Colin Jackson
All-Attainment Teaching
in Secondary Mathematics
Philosophy, Practice and Social Justice
Colin Jackson
Formerly of Sheffield Hallam University
Sheffield, UK
ISBN 978-3-030-92360-0 ISBN 978-3-030-92361-7 (eBook)
https://doi.org/10.1007/978-3-030-92361-7
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to Hilary and Hannah
Preface
This research is focussed on the grouping of students in English secondary school
mathematics classes by a conception of their “ability”. Focussing particularly on
mathematics education I argue that this practice is unjust, as previous research
shows, and that a socially just education system should treat all of its students,
including working-class students, equitably.
This research focusses on a small group of teachers who do not accept this
“common- sense” “ability” thinking but who instead believe that all students should
have access to all of the curriculum and that all are capable of learning without
limits. During 2016, I carried out in-depth interviews with these teachers in Brierley
Grove, an inner London comprehensive with a largely working-class intake,
Shortvalley, a comprehensive on the south coast and Duckworth Community School
(DCS), a rural comprehensive in Cambridgeshire.
This research is the only current in-depth study of mathematics teachers who are
committed to all-attainment teaching. My research identified three major themes:
• What sustains the teachers.
• How they introduce, develop and maintain all-attainment.
• How they make all-attainment work in the classroom.
Drawing together the findings, I present two interrelated models of the knowl-
edge and understandings the research has generated. The first attempts to explain
how the teachers are situated with regard to their teaching. The second, encom-
passed within the first, illustrates how the teachers through all-attainment mathe-
matics are attempting to enable the students not only to develop and succeed
mathematically but to become agentic so that they are not restricted in the life
choices they have.
I discuss the implications of the study for those connected in a variety of ways to
the teaching and learning of secondary school mathematics in all-attainment groups
and make recommendations for further research.
Sheffield, UK Colin Jackson
vii
Acknowledgements
I wish to thank my father, Harry Jackson, a lifelong trade unionist and socialist, who
was responsible for awakening the idea of social justice within me. My father, along
with my mother, Eileen, believed in the power of education and wanted all of their
children to have the education opportunities they never had. They never stopped
believing in me or my siblings despite the setbacks we invariably underwent from
time to time. They inspired me to want the same opportunities for all children.
I wish to thank all of the teachers who took part in my research including those
teachers whose interviews I didn’t use in my study. They all welcomed me into their
schools and their classrooms and were extremely generous with their time. Thank
you—Pete, Philippa, Akhila, Fred, Chandra, Jean, Sarah, Bob, Samira, Mick,
and Adara.
ix
Contents
1 Backstory: Growing Up Working-Class in Northern
Ireland: Schooling Not Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Northern Ireland: A Sectarian State . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Experiences of Schooling: Parents, Relatives, My Primary School
and the 11 Plus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Pedagogy and the Grammar School . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Problematising My Schooling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
After School . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Being an Educator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Why My Backstory Is Important in This Book? . . . . . . . . . . . . . . . . . . . 17
The Context in Which the Research Took Place . . . . . . . . . . . . . . . . . . . 18
Social Justice and Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
What I Set Out to Achieve Through the Research . . . . . . . . . . . . . . . . . 19
The Book Chapters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3 Class, Schooling and the Legitimation of Inequality . . . . . . . . . . . . . 23
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Education for … Society or the Individual? Post-war Mass
Schooling: Educating the Workers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Post 1976: The Era of Neoliberalism . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4 Class, “ability” Groups and Mathematics in English Secondary
Schools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Current Patterns of Attainment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
“Ability” Grouping as a Social Justice Issue . . . . . . . . . . . . . . . . . . . . . 38
Some “ability” Grouping Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
xi
xii Contents
Class and “ability” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Student Attainment, “intelligence” and the Idea of “ability” . . . . . . . . . 43
“Ability” Grouping and Levels of Attainment . . . . . . . . . . . . . . . . . . . . 45
Allocation of Children to “ability” Groups . . . . . . . . . . . . . . . . . . . . . . . 47
“Ability”: Beliefs and Practices of Teachers . . . . . . . . . . . . . . . . . . . . . . 49
“Ability” Grouping: Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . 51
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5 Methodological and Method Considerations . . . . . . . . . . . . . . . . . . . 59
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
My Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Philosophical Approaches Underpinning My Methodology . . . . . . . . . . 60
Critical Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Issues of Rigour, Reliability and Validity in Critical
Theory Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Gadamer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Gramsci . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Research Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Choosing Interviews . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Designing the Interviews . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Finding the Participants: The Sample . . . . . . . . . . . . . . . . . . . . . . . . . 70
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6 Data Collection, Processing and Analysis . . . . . . . . . . . . . . . . . . . . . . 75
Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Refining My Research Question . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Approach to Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Storytelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
A Second Analytical Strand: Using Thematic Analysis . . . . . . . . . . . . . 80
Thematic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
7 Introducing the Teachers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
The Teachers’ Stories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Pete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Philippa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Bob . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Final Word from Bob . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Sarah . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Adara . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
Akhila . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Ethical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
8 The Teachers: What Sustains Them . . . . . . . . . . . . . . . . . . . . . . . . . . 127
The Teachers and Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
An Interest in Research and/or Curriculum Development . . . . . . . . . . . 129
Contents xiii
Experiences Prior to Qualifying as Teachers . . . . . . . . . . . . . . . . . . . . . 131
The Teachers: Relationship to “ability” Thinking . . . . . . . . . . . . . . . . . 132
Expectations About Achievement and Implications for Curriculum
Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
Student Attainment and Enjoyment of Mathematics . . . . . . . . . . . . . . . 135
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
9 Introducing, Developing and Maintaining All-Attainment
While Convincing Others . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
The Need for Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
Support from Above . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
Support from Colleagues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Convincing Others . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Collaborative Approach to Curriculum Planning and Creating
Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
10 How the Teachers Make All-Attainment Work
in the Classroom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
The Role, Influence and Nature of Assessment . . . . . . . . . . . . . . . . . . . 155
Approach to Teaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
Understanding Rather than Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
Critical Thinking Beyond Mathematics . . . . . . . . . . . . . . . . . . . . . . . 158
Collaboration and Creative Planning . . . . . . . . . . . . . . . . . . . . . . . . . 159
Teacher Methods: How the Students Work . . . . . . . . . . . . . . . . . . . . . . . 160
Type of Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
Learning How to Learn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
Critical Thinking, Independence and Responsibility
in Mathematics Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
Exploration and Inquiry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
Talk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
Groupwork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
11 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
The Purpose of My Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
Key Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
Transformative Pedagogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
The Teachers’ Situation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
The Teachers, Their Intentions and What They Do . . . . . . . . . . . . . . 179
Cornerstone One: Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Cornerstone Two: Community . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
Cornerstone Three: Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
The Apex Cornerstone: Critical Thinking . . . . . . . . . . . . . . . . . . . . . . 182