European Research in Mathematics Education I - Fakultät für ...

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European Research in Mathematics Education I 8 Mathematical proof .............................128 Argumentation in mathematics .......................129 Reference corpus ..............................130 Tools of analysis and comparison of argumentation and proof .......130 Analysis and comparison of argumentation and proof as products .......131 About the reference corpus .........................131 How to dispel doubts about a statement and the form of reasoning. ....133 The processes of argumentation and construction of proof ...........135 Some educational implications ..........................137 References ....................................139 DISCRETE MATHEMATICS IN RELATION TO LEARNING AND TEACHING PROOF AND MODELLING ..........................140 Denise Grenier, Charles Payan What are discrete mathematics? .........................140 Didactical transposition of discrete mathematics in France ...........141 Global research questions ............................144 Proof and modelization in discrete mathematics. ................145 An example of proof method: induction ..................145 Two examples of modelization .......................147 A particular tool: the pigeonholes principle .................149 Conclusion ....................................151 References ....................................151 STUDENT'S PERFORMANCE IN PROVING: COMPETENCE OR CURRICULUM? .................................153 Lulu Healy, Celia Hoyles Aims .......................................153 Method ......................................154 Results ......................................154 Some contrasting views of proof .........................157 Discussion ....................................165 References ....................................166 http://www.fmd.uni-osnabrueck.de/ebooks/erme/cerme1-proceedings/cerme1-proceedings.html
European Research in Mathematics Education I 9 INTERACTION IN THE MATHEMATICS CLASSROOM: SOME EPISTEMOLOGICAL ASPECTS ....................168 Andreas Ikonomou, Maria Kaldrimidou, Charalambos Sakonidis, Marianna Tzekaki Introduction ....................................168 Theoretical framework ..............................169 Methodology ...................................170 Presentation of data and discussion. .......................171 Elements of mathematical content. .....................172 Elements of mathematical activity .....................176 Conclusions ....................................179 References ....................................181 GROUP 2: TOOLS AND TECHNOLOGIES TOOLS AND TECHNOLOGIES ........................183 Angel Gutiérrez, Colette Laborde, Richard Noss, Sergei Rakov Tools and technologies in the didactics of mathematics .............183 Tools and knowledge ...............................184 Interactions between tool and learner ......................186 Tools and technologies in the curriculum ....................187 The papers ....................................187 CONSTRUCTING MEANING FOR FORMAL NOTATION IN ACTIVE GRAPHING ...................................189 Janet Ainley, Elena Nardi, Dave Pratt Background ....................................189 Method ......................................190 Analysis. .....................................192 http://www.fmd.uni-osnabrueck.de/ebooks/erme/cerme1-proceedings/cerme1-proceedings.html 182
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