Dialogue and Learning in Mathematics Education: Intention, Reflection, CritiqueDialogue and Learning in Mathematics Education is concerned with communication in mathematics class-rooms. In a series of empirical studies of project work, we follow students' inquiry cooperation as well as students' obstructions to inquiry cooperation. Both are considered important for a theory of learning mathematics. Special attention is paid to the notions of `dialogue' and `critique'. A central idea is that `dialogue' supports `critical learning of mathematics'. The link between dialogue and critique is developed further by including the notions of `intention' and `reflection'. Thus a theory of learning mathematics is developed which is resonant with critical mathematics education. |
Contents
COMMUNICATION IN THE MATHEMATICS CLASSROOM | 21 |
MISTAKES AND CORRECTIONS | 23 |
BUREAUCRATIC ABSOLUTISM | 26 |
PERSPECTIVE | 28 |
HOW MUCH DOES A NEWSPAPER FILL? | 30 |
LEARNING AS ACTION | 41 |
INQUIRY COOPERATION | 45 |
FROM EXERCISES TO LANDSCAPES OF INVESTIGATION | 46 |
TRAVEL AGENCY | 138 |
INTENTION | 154 |
Intentionsinlearning | 156 |
Underground intentions | 158 |
Resources of intentions | 160 |
REFLECTION AND LEARNING | 165 |
CARAMEL BOXES | 166 |
REFLECTION | 184 |
ENTERING A LANDSCAPE OF INVESTIGATION | 51 |
WHAT DOES THE DANISH FLAG LOOK LIKE? | 54 |
INQUIRY COOPERATION MODEL | 62 |
OBSTRUCTIONS TO INQUIRY COOPERATION LEAVING A LANDSCAPE OF INVESTIGATION | 65 |
FURTHER DEVELOPMENT OF THE INQUIRY COOPERATION MODEL | 69 |
THE ICMODEL RECONSIDERED | 100 |
Getting in contact | 101 |
Identifying | 103 |
Advocating | 105 |
Thinking aloud | 107 |
Reformulating | 108 |
Challenging | 109 |
DIALOGUE AND LEARNING | 113 |
THE SOCRATIC DIALOGUE | 114 |
DIALOGIC QUALITIES | 115 |
Making an inquiry | 118 |
Running a risk | 122 |
Maintaining equality | 124 |
HOW TO DO THINGS WITH DIALOGUE | 126 |
DIALOGIC ACTS THE ICMODEL RECONSIDERED | 128 |
DIALOGIC TEACHING AND LEARNING AND ITS FRAGILITY | 130 |
DIALOGIC TEACHING AND LEARNING AND ITS SIGNIFICANCE | 132 |
INTENTION AND LEARNING | 137 |
Subject of reflections | 188 |
Context of reflections | 191 |
REFLECTION AND INTENTION EXPLOSIVE CONCEPTS | 193 |
CRITIQUE AND LEARNING | 195 |
THE CHALLENGE OF CRITIQUE | 196 |
TERRIBLE SMALL NUMBERS | 199 |
RELIABILITY | 202 |
RESPONSIBILITY | 217 |
CRITIQUE | 230 |
Intention and critique | 231 |
Reflection and critique | 233 |
Dialogue and critique | 235 |
THE CHALLENGE OF CRITIQUE TOO DIFFICULT? | 238 |
CRITICAL EPISTEMOLOGY AND THE LEARNING OF MATHEMATICS | 243 |
DIALOGICAL EPISTEMOLOGY | 247 |
NONCRITICAL EPISTEMOLOGY | 251 |
CRITICAL EPISTEMOLOGY | 255 |
LEARNING MATHEMATICS CRITICALLY | 259 |
| 263 | |
| 277 | |
| 281 | |
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Dialogue and Learning in Mathematics Education: Intention, Reflection, Critique Helle Alrĝ,Ole Skovsmose No preview available - 2003 |
Common terms and phrases
activities advocating Aktuelt Alice Anna becomes Brian calculations Caramel boxes Chapter characterised clarify concept consider context critical learning Danish Kroner Dewey dialogic acts dialogue discussion eggs elements emphasised ethnomathematics exercise paradigm formulation Freire getting in contact going Gran Canaria IC-Model identified inquiry co-operation inquiry process instance intentions interpretation ISBN landscape of investigation Law of Large learning mathematics learning of mathematics learning process Linda Lisa locating Malene Martin Mary and Adam mathemacy mathematics classroom means newspaper fill notion observe Oscar paper participants particular patterns of communication perspectives Peter philosophy of mathematics Piaget possible presented problem process of inquiry qualities of communication qualities of learning questions radical constructivism refer reformulating resistance group risk salmonella Sara school mathematics tradition scope of reflections Simon situation Skovsmose suggestion tag questions task Terrible small numbers thinking aloud traditional mathematics Vygotsky zooming-in zooming-out