As dissatisfaction with the current status of school mathematics grows worldwide, educators and professionals alike are calling for reforms and instructional changes. Yet, significant changes can only be achieved if each educator of school mathematics personally rethinks various aspects of mathematics instruction, and identifies concrete ways in which their current practice could be modified. Before such visions can be meaningfully implemented in classrooms, it is important that mathematics teachers and educators examine critically both the assumptions and implications of the vision for school mathematics that the reports propose. This book is intended to support educators in such a challenging enterprise by focusing attention on "errors" and their use in mathematics instruction. Throughout the book, an approach to errors as opportunities for learning and inquiry will be developed and employed both as a means to create the kinds of instructional experiences advocated for school mathematics reform, and as a heuristic to invite reflections about school mathematics as well as mathematics as a discipline. REVIEWS: "...Raffaella Borasi's newest book offers important contributions to the current debate on school mathematics reform." - Journal for Research in Mathematics Education "There are some great bits of philosophy in this book..." - Mathematics Teaching
Author(s): Raffaella Borasi
Publisher: Ablex Publishing
Year: 1996
Language: English
Pages: 333
Contents ......Page 6
Acknowledements ......Page 8
Motivation and scope of the book ......Page 12
A new metaphor for error making ......Page 15
A first illustration of using errors as springboards for inquiry-Error case study A ......Page 18
Content and organization of the book ......Page 21
2 Reconceiving mathematics education within an inquiry framework ......Page 26
Current mathematics teaching practices: An exemplification of the transmission paradigm ......Page 27
Major critiques of a transmission pedagogy ......Page 28
Key elements of an inquiry framework ......Page 34
Contributions to a view of errors as springboards for Inquiry ......Page 38
A critical view of existing uses of errors in Mathematics education ......Page 42
Some historical error case studies ......Page 56
A first analysis of using errors as springboards for inquiry in mathematics ......Page 74
Error case studies generated by my own exploration of specific errors ......Page 80
First thoughts about using errors as springboards for inquiry as an instructional strategy ......Page 119
6 Capitalizing on errors in mathematics instruction:A first analysis ......Page 130
Error case studies reporting on error activities experienced by secondary students within a teaching experiment ......Page 131
Important variations within the instructional strategy of capitalizing on errors ......Page 142
Potential benefits of capitalizing on errors in mathematics instruction ......Page 150
7 Capitalizing on errors in mathematics 149 ......Page 0
Instruction: A teaching experiment ......Page 160
Overview of the teaching experiment ......Page 161
Brief description and analysis of all the error activities developed in the teaching experiment ......Page 162
Evaluation of what the students gained from the experience and from the uses of errors made in it ......Page 175
Error case studies reporting on error activities developed in secondary and college mathematics classes ......Page 180
Further considerations on capitalizing on errors in regular classrooms ......Page 213
Error case studies experienced by teachers ......Page 220
Potential benefits of engaging mathematics teachers in a use of errors as springboards for inquiry ......Page 264
10 Creating a learning environment supportive of inquiry ......Page 270
The assumptions informing a use of errors as springboards for inquiry revisited ......Page 271
Major implications of adopting an inquiry approach to school mathematics ......Page 278
Supporting teachers in the implementation of an inquiry approach in their classrooms ......Page 283
Using errors as springboards for inquiry in mathematics instruction: A summary ......Page 288
Looking ahead ......Page 293
Appendix A: Summary of categories, codes, and abbreviations employed in the book ......Page 296
Appendix B: Title and abstract of error case studies ......Page 302
References ......Page 312
Author Index ......Page 320
Subject Index ......Page 324
