Theorems in School: From History, Epistemology and Cognition to Classroom PracticePaolo Boero Sense Publishers, 2007 - 327 oldal During the last decade, a revaluation of proof and proving within mathematics curricula was recommended; great emphasis was put on the need of developing proof-related skills since the beginning of primary school. This book, addressing mathematics educators, teacher-trainers and teachers, is published as a contribution to the endeavour of renewing the teaching of proof (and theorems) on the basis of historical-epistemological, cognitive and didactical considerations. Authors come from eight countries and different research traditions: this fact offers a broad scientific and cultural perspective. In this book, the historical and epistemological dimensions are dealt with by authors who look at specific research results in the history and epistemology of mathematics with an eye to crucial issues related to educational choices. Two papers deal with the relationships between curriculum choices concerning proof (and the related implicit or explicit epistemological assumptions and historical traditions) in two different school systems, and the teaching and learning of proof there. The cognitive dimension is important in order to avoid that the didactical choices do not fit the needs and the potentialities of learners. Our choice was to firstly deal with the features of reasoning related to proof, mainly concerning the relationships between argumentation and proof. The second part of this book concentrates on some crucial cognitive and didactical aspects of the development of proof from the early approach in primary school, to high school and university. We will show how suitable didactical proposals within appropriate educational contexts can match the great (yet, underestimated ) young students' potentialities in approaching theorems and theories. |
Tartalomjegyzék
INTRODUCTION | 17 |
THE HISTORICAL ANDEPISTEMOLOGICAL DIMENSION | 25 |
CURRICULAR CHOICES HISTORICALTRADITIONS AND LEARNING OF PROOF TWONATIONAL CASE STUDIES | 79 |
ARGUMENTATION AND PROOF | 135 |
DIDACTICAL ASPECTS | 183 |
Further Reading | 325 |
Más kiadások - Összes megtekintése
Theorems in School: From History, Epistemology and Cognition to Classroom ... Korlátozott előnézet - 2007 |
Gyakori szavak és kifejezések
activity algebra analysis angles approach argument Arzarello axioms Balacheff Bartolini Bussi best mark Boero Cabri choices circle classroom cognitive cognitive unity concepts concerning conference of PME constructed proofs context curriculum deductive deductive reasoning didactic discussion dragging drawing Duval dynamic exploration epistemic value epistemological Euclid Euclidean Euclidean geometry example fact familiar conjecture field of experience Figure formal proof Garuti grade Harel hypothesis ideas impossible International Conference intuitive knowledge Lakatos language learning logical Mariotti mathematical proof mathematicians mathematics education meaning method objects oblique stick perspective philosophy of mathematics pizza plane PME vol possible problem produced proof scheme Proofs and refutations propositions proving pupils quadrilateral question radius reasoning rectangle reductio ad absurdum reference relationships representation role segments semiotic shows situation solution solving statement straight line Studies in Mathematics sun rays sun shadows teacher teaching experiment theory tion triangle valid wheels
Népszerű szakaszok
322. oldal - How does the dragging affect the learning of geometry? International Journal of Computers for Mathematical Learning, 1, 169-187.