The Pragmatics of Mathematics Education: Vagueness in Mathematical Discourse

Tim Rowland

Psychology Press, 2000 - Education - 242 pages

Drawing on philosophy of language and recent linguistic theory, Rowland surveys several approaches to classroom communication in mathematics. Are students intimidated by the nature of mathematics teaching? Many students appear fearful of voicing their understanding - is fear of error part of the linguistics of mathematics? The approaches explored here provide a rationale and a method for exploring and understanding speakers' motives in classroom mathematics talk. Teacher-student interactions in mathematics are analysed, and this provides a toolkit that teachers can use to respond to the intellectual vulnerability of their students.

Contents

• Preview and Methodology: 1
• Two Principles: 2
• Aims and Themes: 4
• A Context in Language Research: 5
• Mathematical Conversations: 6
• Framing and Sample Size: 11
• Ethnography and Interpretation: 12
• Interpretation and Participant Observation: 16
• Summary: 18
• Generalization: 20
• Generalization and Inductive Reasoning: 21
• What is Inductive Reasoning?: 24
• Induction and the Mind: 26
• Mathematical Heuristic: 32
• the Theory of Numbers: 34
• Generic Examples: 38
• Generic Examples and Real Undergraduate Mathematics: 41
• Recollection: 47
• Summary: 48
• Perspectives on Vagueness: 50
• Mathematics and Mathematics Education: 52
• Mathematics and Language: 56
• Philosophy of Language: 61
• Modality: 64
• Pragmatics and Vagueness: 66
• Summary: 68
• Discourse and Interpretation: 71
• Reference: 72
• Power and Solidarity: 73
• Some Approaches to Discourse: 78
• Approaches to Discourse: 93
• Summary: 94
• Pointing with Pronouns: 96
• The Exclusive We: 97
• It: 99
• On You and Generalization: 109
• Summary: 113
• Hedges: 115
• Method: 118
• Frances and Ishka: 120
• Hedge Types in Mathematics Talk: 123
• the Taxonomy Revisited: 138
• Hedges and Politeness: 140
• The Zone of Conjectural Neutrality: 141
• Summary: 142
• Estimation and Uncertainty: 145
• Counting: 148
• Enquiry Focus: 149
• Method: 150
• Data: 153
• Observations: 156
• Interpretive Framework: 157
• Interpretation of the Data: 160
• Gender Differences: 167
• Modal Auxiliaries: 168
• Summary: 169
• Pragmatics Teaching and Learning: 171
• Hazel: 172
• Ann: 178
• Judith: 181
• Rachel: 186
• Sue: 190
• The Public Lecture: 194
• Open University Video: 195
• Jonathan: 198
• Summary: 205
• Summary and Review: 207
• Pronouns: 208
• Modality Hedges and Indirect Speech Acts: 209
• The Zone of Conjectural Neutrality: 211
• Validation and Classroom Application: 212
• Interpretation of Transcripts of Mathematics Talk: 215
• Conclusion: 216
• Transcript Conventions: 218
• Index of Transcripts: 219
• References: 221
• Author Index: 235
• Subject Index: 238

Bibliographic information

• Title: The Pragmatics of Mathematics Education: Vagueness in Mathematical Discourse; Volume 14 of Studies in mathematics education series; The Pragmatics of Mathematics Education: Vagueness in Mathematical Discourse, Tim Rowland
• Author: Tim Rowland
• Edition: illustrated
• Publisher: Psychology Press, 2000
• ISBN: 0750710128, 9780750710121
• Length: 242 pages
• Subjects: Education / General; Education / Schools / Levels / Secondary; Education / Teaching / General; Education / Teaching / Subjects / Mathematics; Mathematics / Study & Teaching