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Writing Mathematically: The Discourse of 'Investigation' [Kõva köide]

(University College London, United Kingdom.)
  • Formaat: Hardback, 244 pages, kõrgus x laius: 234x156 mm, kaal: 690 g
  • Ilmumisaeg: 17-Jun-1998
  • Kirjastus: Routledge Falmer
  • ISBN-10: 0750708115
  • ISBN-13: 9780750708111
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  • Formaat: Hardback, 244 pages, kõrgus x laius: 234x156 mm, kaal: 690 g
  • Ilmumisaeg: 17-Jun-1998
  • Kirjastus: Routledge Falmer
  • ISBN-10: 0750708115
  • ISBN-13: 9780750708111
Applying linguistic theory in a critical analysis of the role of written language in assessing math ability, Morgan (mathematics education, U. of London) raises the intriguing question of whether some students are failing to adequately communicate their competence. This new perspective on math education including the concept of a register to discern what is special about language in mathematical settings presents implications for teacher pre-/in- service education re: improved assessment, more open-ended tasks (like those of real mathematicians), and other innovations in this curriculum area. Distributed in the US by Taylor & Francis. Annotation c. by Book News, Inc., Portland, Or.

School mathematics curricula internationally tend to emphasise problem-solving and have led to the development of opportunities for children to do maths in a more open, creative way. This has led to increased interest in 'performance-based' assessment, which involves children in substantial production of written language to serve as 'evidence' of their mathematical activity and achievement. However, this raises two important questions. Firstly, does this writing accurately present children's mathematical activity and ability? Secondly, do maths teachers have sufficient linguistic awareness to support their students in developing skills and knowledge necessary for writing effectively in their subject area? The author of this book takes a critical perspective on these questions and, through an investigation of teachers' readings and evaluations of coursework texts, identifies the crucial issues affecting the accurate assessment of school mathematics.
List of Figures and Table
vii
Acknowledgments viii
Preface by Series Editor ix
Introduction
1(7)
`The Language of Mathematics' --- Characteristics of Written Mathematical Texts
8(14)
The Mathematical Register in General
9(2)
Academic Mathematics Texts
11(7)
School Mathematics Texts
18(4)
Writing in the Mathematics Classroom
22(15)
Student Writing in the Traditional Mathematics Classroom
23(2)
`Writing-to-Learn'-to-Learn' Mathematics
25(5)
The Forms of Writing Used by Students
30(4)
From `Writing-to-Learn' to `Learning-to-Write'
34(3)
Learning to Write Mathematically
37(13)
Natural Development or Deliberate Teaching?
38(3)
Evidence of Development in Mathematical Writing
41(2)
`Audience' as an Influence on the Development of Effective Writing
43(7)
The Public Discourse of `Investigation'
50(26)
`Official' Discourse
53(7)
`Practical' Discourse
60(8)
`Professional' Discourse
68(4)
Coherence and Tensions within the Discourse of `Investigation'
72(4)
A Critical Linguistic Approach to Mathematical Text
76(24)
Linguistic Analysis of Mathematical Texts
79(9)
Non-verbal Features of Mathematical Texts
88(8)
Applying the Analytical Tools
96(4)
Reading Investigative Mathematical Texts
100(15)
The Tasks
100(5)
The Students' Texts
105(10)
The Assessment of Investigations and Teacher Assessment
115(16)
New Developments in Assessment
115(6)
Teacher Assessment
121(10)
Investigating Teachers Reading Coursework
131(19)
The Sample of Teachers
131(1)
Design of the Teacher Interviews
132(2)
The Teacher as Interviewee
134(3)
Analysing the Interviews
137(2)
Variation and Validity in Teacher Assessment
139(1)
A Comparison of Two Teachers Reading Richard's `Inner Triangles' Text
140(8)
Consequences of Differences in Reading Strategies
148(2)
Teachers' Responses to Student Writing
150(30)
A Generic Demand for `Writing'
150(2)
Tables --- A Sign of `System'
152(3)
Diagrams --- Not Too Much of a `Good Thing'
155(2)
Algebra --- With or Without Words
157(6)
Statement of the Problem --- Copying vs. `Own Words'
163(2)
Narrative --- Telling the Right Story
165(3)
Explanation --- For Some
168(2)
Use of a Conventional Mathematics Register
170(3)
Coherence: A Case Study
173(7)
Assessing Difference: `Creativity' and Error
180(17)
How Is `Difference' Identified?
180(1)
Difference Is Desirable but Difficult
181(9)
Dealing with Error --- Is `Practical' Different?
190(7)
Towards a Critically Aware Mathematical Writing Curriculum
197(15)
The Myth of `Transparency'
197(2)
Teachers' Lack of Language Awareness --- and Its Consequences
199(6)
How May Students Learn to Write Mathematically?
205(2)
Teaching Mathematical Writing
207(5)
References 212(16)
Index 228
Candia Morgan