Patterns in Mathematics Classroom Interaction: A Conversation Analytic Approach

163 Pages·2021·10.892 MB·English

by  Jenni Ingram

Patterns in Mathematics
Classroom Interaction

Patterns in Mathematics
Classroom Interaction
A Conversation Analytic approach
JENNI INGRAM
1
1
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First Edition published in 2021
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Library of Congress Control Number: 2020952680
ISBN 978–0–19–886931–3
DOI: 10.1093/oso/9780198869313.001.0001
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Acknowledgements
This book reflects many of the conversations that have occurred at different
times and places, in different classrooms, at research conferences, and with
colleagues. I am indebted to all the teachers who opened up their classrooms
and allowed me to video them teaching, or who offered up videos of their
teaching. I am also grateful for the financial support from the John Fell Fund,
which partly funded the collection of videos for one of the projects that the
data and the analysis arose from. Many colleagues have made me stop and
think; in particular, I would like to thank Nick Andrews, who helped me tease
out what it was I wanted to say in my writing but has also done more to make
me think about my practice as both a teacher educator and a researcher than
anyone else. I would also like to thank Ann Childs, Katharine Burn, and Velda
Elliott, who commented on drafts of my writing, prompted some of the
insights I share in this book, and have continued to support me.
I would also like to thank my family, who gave me the space and time to
write, and who inspired me to think more about mathematics teaching and
learning. Through conversations with my husband, Jon, about mathematics
and the teaching of mathematics, and the disagreements about how to teach
quadratic equations to our son James during the pandemic, in which most of
this book was written, I was able to see my data from different perspectives.
Thanks also need to go to my children James, Daniel, and Lissie, who each
gave me time to think and write, but also kept me grounded in the everyday.
James, I am particularly glad that you were learning how to bake whilst I
wrote this book.

List of Extracts
1- 1 Jefferson transcript of classroom interaction. 5
1-2 Verbatim transcript of interaction from Extract 1- 1. 5
2- 1 Identifying teachers and students in interaction. 21
2-2 An example of self- repair. 30
2- 3 Another student performs a repair. 30
3-1 Teacher controls turn- taking. 35
3- 2 Example of a student self- selecting to ask a question. 36
3-3 Students self- select to repair an earlier response. 37
3- 4 Several students self- select to take the next turn. 38
3-5 Students self- select with contrasting answers. 39
3- 6 Students self- select to address each other. 40
3-7 Sanctioning for speaking out of turn. 41
3- 8 Students sanctioning each other for speaking out of turn. 42
3-9 Ignoring what a student has said when self- selecting. 42
3- 10 An example of an IRE sequence. 43
3-11 Revoicing where student affirms the revoicing. 48
3- 12 Sequence of questions that make knowledge public. 50
3-13 The difference between an expression and an equation. 52
3- 14 Students can pause at the beginning of their turns. 54
3-15 Tyler responds to pauses as being an indication of a problem. 55
3- 16 Todd responds to pauses as being an indication of a problem. 55
3-17 Teacher repeats question before nominating a student. 56
4- 1 Teacher initiates but does not perform a repair. 60
4-2 Teacher initiated peer- repair. 61
4- 3 A student initiates and performs the repair. 61
4-4 Teacher initiates and performs repair. 62
4- 5 Teacher reformulates the question after a student hesitation. 63
4-6 Many pauses during the asking of a question. 63
4- 7 Breaking down a question into its parts. 64
4-8 Teacher invites students to talk to each other first. 66
x List of Extracts
4- 9 Working to avoid giving a negative evalu ation. 68
4-10 Withholding an evalu ation. 69
4- 11 Correcting students’ language. 70
4-12 Deliberately initiating a repair. 71
4-13 Students mitigating their responses with accounts. 72
4-14 Point of contention does not arise. 73
4- 15 Disagreeing with another student. 74
4-16 Adding an explanation when speaking out of turn. 75
5- 1 Tristin in a K+ pos ition. 78
5-2 Tanya in a K− pos ition. 79
5- 3 Epistemic rights of the teacher. 80
5-4 Tyler introduces the objective as being about understanding. 82
5- 5 Trish introduces the focus as being about understanding. 82
5-6 Tanya explains the aim of the task is to understand it. 83
5- 7 Theresa introduces new task with a focus on understanding. 83
5-8 Todd asks students to check their understanding. 83
5- 9 Thelma states that you understand if you can explain it. 83
5-10 Understanding check in Tyler’s lesson. 84
5- 11 Understanding check in Toby’s lesson. 84
5-12 An understanding check with no opportunity for a response. 85
5- 13 Does an understanding check require a response? 85
5-14 Understanding the meaning of isosceles. 86
5- 15 Understanding the meaning of a pro ced ure. 87
5-16 Explain so that we understand. 88
5- 17 The point of doing this is to get you to understand. 89
5-18 I don’t understand your ex plan ation. 89
5- 19 Student unsolicited claim of understanding. 90
5-20 Student demonstration of understanding. 91
5- 21 A student claim of not understanding. 92
5-22 Response to a demonstration of not understanding. 93
5- 23 Trish pursuing an answer following ‘I don’t know’. 94
5-24 Tyler pursues an ex plan ation. 95
5- 25 Tom pursues an answer by re- explaining. 96
5-26 Trish responds to a student claim of not remembering. 96
5- 27 Thea redirects the question following ‘I can’t remember’. 97
List of Extracts xi
5-28 Reframing ‘I don’t know’ as ‘I don’t remember’. 97
5- 29 Tim orienting to the role of expert. 98
5-30 Tyler models a problem-solving process. 99
5- 31 Tim connecting problem to an image. 100
5-32 Todd models what it means to be convinced in math em at ics. 101
5- 33 Todd asks students what they understand by the word proof. 102
5-34 Tim revoices Steven’s answers. 103
6- 1 Teresa prompting the use of mul tiples. 111
6-2 Teresa prompting further use of the word ‘multiple’. 113
6- 3 Teresa encourages students to use mathematical words. 114
6-4 Tanya asks students to think about the problem differently. 117
6- 5 Tyler asks students to think about the question as a problem. 118
6-6 Tara contrasts between two types of problem. 118
6- 7 Solving a linear programming problem. 119
6-8 Tyler solving the problem with his class. 120
6- 9 Tyler introducing the task. 122
6-10 Tyler continues by focusing on the second part of the task. 122
6- 11 Tyler asking if the sequence stops. 123
6-12 Tim introducing a frequency table task. 124
6- 13 Continuation of the introduction to the frequency table task. 125
6-14 Interpreting the values in a frequency table. 126
6- 15 Is a parallelogram a tra pez ium? 127