Nardi Amongst Mathematicians

Teaching and Learning Mathematics at University Level
2008
ISBN: 978-0-387-37143-6
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 3, 341 Seiten

Reihe: Mathematics Teacher Education

This book offers a unique perspective on ways in which mathematicians: perceive their students' learning; teach; reflect on their teaching practice. Elena Nardi achieves this by employing two fictional, yet entirely data-grounded, characters to create a conversation on these important issues. The construction of these characters is based on large bodies of data including intense focused group interviews with mathematicians and extensive analyses of students' written work, collected and analyzed over a substantial period.

About the author: Elena Nardi was born in 1968. She studied mathematics (BSc) in Thessaloniki, Greece and mathematics education at Cambridge (MPhil) and Oxford (DPhil) in the UK. Her research is in various areas of mathematics education, with a particular emphasis on the psychology of mathematical learning and the teaching and learning of mathematics at the undergraduate level. She is Senior Lecturer in Mathematics Education at the University of East Anglia in Norwich, UK. She is involved with graduate supervision and with teaching mathematics education and research methods, she co-ordinates UEA's group of researchers in mathematics education and she is Joint Editor in Chief (2008-2010) of Research in Mathematics Education the new international journal of the British Society for Research into the Learning of Mathematics. Her book Amongst Mathematicians: Teaching and Learning Mathematics at University Level is due in the spring/summer of 2007 by Springer. For more information on Elena's work: http://www.uea.ac.uk/-m011/

Autoren/Hrsg.

Nardi, Elena

Inhaltsverzeichnis

1;ACKNOWLEDGEMENTS;7
2;TABLE OF CONTENTS;8
3;PROLOGUE;13
4;CHAPTER 1 BACKGROUND AND CONTEXT;14
4.1;SUMMARY;14
4.2;1. TALUM: A GENERAL INTRODUCTION;15
4.3;2. A CERTAIN TYPE OF TALUM RESEARCH;17
4.4;3. THE TALUM STUDIES THE BOOK DRAWS ON;20
5;CHAPTER 2 METHOD, PROCESS AND PRESENTATION;26
5.1;SUMMARY;26
5.2;1. DATA SAMPLES AND M;27
5.3;2. THE DIALOGIC FORMAT;29
5.4;3. STYLE, FORMAT AND THEMATIC BREAKDOWN OF CHAPTERS 3 – 8;40
5.5;NOTE TO READER: RECOMMENDATIONS ON HOW TO READ CHAPTERS 3 – 8;49
6;CHAPTER 3 THE ENCOUNTER WITH FORMAL MATHEMATICAL REASONING: CONCEPTUALISING ITS SIGNIFICANCE AND ENACTING ITS TECHNIQUES;50
6.1;EPISODE 3.1 THE TENSION BETWEEN THE FAMILIAR (NUMERICAL, CONCRETE) AND THE UNFAMILIAR (RIGOROUS, ABSTRACT): RESORTING TO THE FAMILIARITY OF NUMBER;51
6.2;EPISODE 3.2 THE TENSION BETWEEN THE GENERAL AND THE PARTICULAR: CONSTRUCTING EXAMPLES AND APPLYING THEORETICAL KNOWLEDGE IN CONCRETE CONTEXTS;57
6.3;EPISODE 3.3 USING DEFINITIONS TOWARDS THE CONSTRUCTION OF MATHEMATICAL ARGUMENTS;66
6.4;EPISODE 3.4 LOGIC AS A BUILDING BLOCK OF MATHEMATICAL ARGUMENTS: RECONCILING WITH INCONCLUSIVENESS;73
6.5;EPISODE 3.5 PROOF BY CONTRADICTION: SPOTTING CONTRADICTION AND SYNDROME OF THE OBVIOUS;79
6.6;EPISODE 3.6 PROOF BY MATHEMATICAL INDUCTION: FROM N TO N+1;92
6.7;EPISODE 3.7 PROOF BY COUNTEREXAMPLE: THE VARIABLE EFFECT OF DIFFERENT TYPES OF COUNTEREXAMPLE;98
6.8;SPECIAL EPISODE SE3.1: ‘SCHOOL MATHEMATICS, UK;102
6.9;SPECIAL EPISODE SE3.2: ‘INEQUALITIES’;111
6.10;SPECIAL EPISODE SE3.3: MATHEMATICAL REASONING IN THE CONTEXT OF GROUP THEORY;112
6.11;SPECIAL EPISODE SE3.4: ‘ALGEBRA / GEOMETRY’;115
7;CHAPTER 4 MEDIATING MATHEMATICAL MEANING THROUGH SYMBOLISATION, VERBALISATION AND VISUALISATION;120
7.1;EPISODE 4.0 TO APPEAR AND TO BE: CONQUERING THE ‘GENRE’ SPEECH OF UNIVERSITY MATHEMATICS;121
7.2;EPISODE 4.1 STRINGS OF SYMBOLS AND ‘GIBBERISH’ SYMBOLISATION AND EFFICIENCY;129
7.3;EPISODE 4.2 PREMATURE COMPRESSION;143
7.4;EPISODE 4.3 VISUALISATION AND THE ROLE OF DIAGRAMS;148
7.5;EPISODE 4.4: UNDERVALUED OR ABSENT VERBALISATION AND THE INTEGRATION OF WORDS, SYMBOLS AND DIAGRAMS;160
7.6;SPECIAL EPISODE 4.1: THE GROUP TABLE;161
7.7;OUT-TAKE 4.1: TYPED UP;168
8;CHAPTER 5 THE ENCOUNTER WITH THE CONCEPT OF FUNCTION;170
8.1;EPISODE E5.1 CONCEPT IMAGES AND CONCEPT DEFINITION;171
8.2;EPISODE E5.2 RELATIONSHIP WITH GRAPHS: ATTRACTION, REPULSION, UNEASE AND UNCERTAINTY;177
8.3;EPISODE E5.3 THE TROUBLING / POWERFUL DUALITY AT THE HEART OF A CONCEPT: FUNCTION AS A PROCESS, FUNCTION AS AN OBJECT;181
8.4;SPECIAL EPISODE SE5.1 THE TREMENDOUS FUNCTION-LOOKALIKE THAT IS TANX;185
8.5;SPECIAL EPISODE SE5.2 POLYNOMIALS AND THE DECEPTIVE FAMILIARITY OF ESSENTIALLY UNKNOWN OBJECTS;186
8.6;OUT-TAKE OT5.1 HISTORY RELIVED;188
8.7;OUT-TAKE OT5.2 EVOCATIVE TERMS FOR 1-1 AND ONTO;189
8.8;OUT-TAKE OT5.3 RR: A GROTESQUE AND VULGAR SYMBOL?;189
9;CHAPTER 6 THE ENCOUNTER WITH THE CONCEPT OF LIMIT;190
9.1;EPISODE 6.1 BEGINNING TO UNDERSTAND THE NECESSITY FOR THE FORMAL DEFINITION OF CONVERGENCE;191
9.2;EPISODE 6.2 BEYOND THE ‘FORMALISTIC NONSENSE’: UNDERSTANDING THE DEFINITION OF CONVERGENCE THROUGH ITS VERBALISATION AND VISUALISATION – SYMBOLISATION AS A SAFER ROUTE?;194
9.3;EPISODE 6.3 THE MECHANICS OF IDENTIFYING AND PROVING A LIMIT;202
9.4;SPECIAL EPISODE SE6.1: IGNORING THE ‘HEAD’ OF A SEQUENCE;204
9.5;OUT-TAKE OT6.1= OR > N?;208
9.6;OUT-TAKE OT6.2 SERIES;209
9.7;OUT-TAKE OT6.3 CONTINUITY AND DIFFERENTIABILITY;209
10;CHAPTER 7 UNDERGRADUATE MATHEMATICS PEDAGOGY;214
10.1;EPISODE 7.1: INTERACTION / PARTICIPATION;215
10.2;EPISODE 7.2: INTRODUCING, CONTEXTUALISING THE IMPORTANCE OF NEW IDEAS;224
10.3;EPISODE 7.3: CONCEPT IMAGE CONSTRUCTION;226
10.4;EPISODE 7.4 ABSTRACTION AND RIGOUR VERSUS CONCRETISATION, INTUITION AND EXEMPLIFICATION;229
10.5;SPECIAL EPISODE SE7.1: TEACHING WITHOUT EXAMPLES;259
10.6;SPECIAL EPISODE SE7.2: DO NOT TEACH INDEFINITE INTEGRATION;260
10.7;SPECIAL EPISODE SE7.3: TEACHING OF FUNCTIONS, PROCESS – OBJECT, POLYNOMIALS;262
10.8;SPECIAL EPISODE SE7.4: RULES OF ATTRACTION;263
10.9;SPECIAL EPISODE SE7.5: CONTENT COVERAGE;264
10.10;OUT-TAKE OT7.1 DOES LEARNING HAPPEN ANYWAY?;264
11;CHAPTER 8 FRAGILE, YET CRUCIAL: THE RELATIONSHIP BETWEEN MATHEMATICIANS AND RESEARCHERS IN MATHEMATICS EDUCATION;266
11.1;EPISODE 8.1 BENEFITS;267
11.2;EPISODE 8.2 REFLECTION AND CRITIQUE OF THE PRACTICES OF RME;273
11.3;SPECIAL EPISODE 8.1: THE REVIEWS;294
12;EPILOGUE;302
13;POST-SCRIPT AMONGST MATHEMATICIANS: MAKING OF, COMING TO BE;305
14;BIBLIOGRAPHY;319
15;THEMATIC INDEX: MATHEMATICS;341
16;THEMATIC INDEX: LEARNING AND TEACHING;343
17;AUTHOR INDEX;345
18;MATHEMATICS TEACHER EDUCATION;349