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E-grāmata: Pragmatics of Mathematics Education: Vagueness and Mathematical Discourse [Taylor & Francis e-book]

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In this examination of the crossroads between linguistics and mathematics, Rowland (mathematics education, Homerton College, U. of Cambridge) argues that vagueness in mathematical discourse (particularly for those of us just learning something) can be viewed as a "subtle and versatile device which speakers can and do deploy to make mathematical assertions with as much precision, accuracy, or as much confidence as they judge is warranted by both the content and the circumstances of their utterances." The foundation of this theory came from mathematical conversations Rowland held with students (ages 5-25) in which he examined the circumstances when vagueness arose in mathematical talk. Annotation c. Book News, Inc., Portland, OR (booknews.com)
List of Figures and Tables
viii
Series Editor's Preface ix
Preface xi
Acknowledgments xiii
Preview and Methodology
1(19)
Two Principles
2(2)
Aims and Themes
4(1)
A Context in Language Research
5(1)
Mathematical Conversations
6(5)
Contrary Trends: Framing and Sample Size
11(1)
Ethnography and Interpretation
12(4)
Interpretation and Participant Observation
16(2)
Summary
18(2)
Generalization
20(30)
Generalization and Inductive Reasoning
21(3)
What is Inductive Reasoning?
24(2)
Induction and the Mind
26(6)
Mathematical Heuristic
32(2)
Truth and Conviction: the Theory of Numbers
34(4)
Explanation and Proof: Generic Examples
38(3)
Generic Examples and `Real' Undergraduate Mathematics
41(6)
Recollection
47(1)
Summary
48(2)
Perspectives on Vagueness
50(21)
Viewpoint: Mathematics and Mathematics Education
52(4)
Interface: Mathematics and Language
56(5)
Viewpoint: Philosophy of Language
61(3)
Modality
64(2)
Pragmatics and Vagueness
66(2)
Summary
68(3)
Discourse and Interpretation
71(25)
Reference
72(1)
Pronouns and Reference: Power and Solidarity
73(5)
Some Approaches to Discourse
78(15)
Overview: Approaches to Discourse
93(1)
Summary
94(2)
Pointing with Pronouns
96(19)
The Informants
96(1)
The Exclusive `We'
97(2)
`It'
99(10)
On `You' and Generalization
109(4)
Summary
113(2)
Hedges
115(30)
Method
118(2)
`Make Ten': Frances and Ishka
120(3)
Hedge Types in Mathematics Talk
123(15)
Hedges: the Taxonomy Revisited
138(2)
Hedges and Politeness
140(1)
The Zone of Conjectural Neutrality
141(1)
Summary
142(3)
Estimation and Uncertainty
145(26)
Estimation
145(3)
Counting
148(1)
Enquiry Focus
149(1)
Method
150(3)
Data
153(3)
Observations
156(1)
Interpretive Framework
157(3)
Interpretation of the Data
160(7)
Gender Differences
167(1)
Modal Auxiliaries
168(1)
Prosody
168(1)
Summary
169(2)
Pragmatics, Teaching and Learning
171(36)
The Informal Research Group
171(1)
Hazel
172(6)
Ann
178(3)
Judith
181(5)
Rachel
186(4)
Sue
190(4)
The Public Lecture
194(1)
Open University Video
195(3)
Jonathan
198(7)
Summary
205(2)
Summary and Review
207(11)
Pronouns
208(1)
Modality, Hedges and Indirect Speech Acts
209(2)
The Zone of Conjectural Neutrality
211(1)
Validation and Classroom Application
212(3)
Interpretation of Transcripts of Mathematics Talk
215(1)
Conclusion
216(2)
Appendix 1 Transcript Conventions 218(1)
Appendix 2 Index of Transcripts 219(2)
References 221(14)
Author Index 235(3)
Subject Index 238
Tim Rowland