Theorems in school : : from history, epistemology and cognition to classroom practice / / editor, Paolo Boero.

• Superior document: New Directions in Mathematics and Science Education ; 2
• TeilnehmendeR: Boero, Paolo,
• Place / Publishing House: Rotterdam, Netherlands ;, Taipei : : Sense Publishers,, [2007]; 2007
• Year of Publication: 2007
• Language: English
• Series: New Directions in Mathematics and Science Education ; 2.
• Physical Description: 1 online resource (vi, 327 ); ill.
• Notes: "NDMS 2"--P. [4] of cover.; "Edited volume"--Cover.

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.

Table of Contents

Preliminary Material / Paolo Boero -- The ongoing value of proof / Gila Hanna -- Theorems in school: An introduction / Paolo Boero -- Origin of mathematical proof / Gilbert Arsac -- The proof in the 20th century / Ferdinando Arzarello -- Students' proof schemes revisited / Guershon Harel -- Curriculum change and geometrical reasoning / Celia Hoyles and Lulu Healy -- The tradition and role of proof in mathematics education in Hungary / Julianna Szendrei-Radnai and Judit Török -- Cognitive functioning and the understanding of mathematical processes of proof / Raymond Duval -- Some remarks about argumentation and proof / Nadia Douek -- Making possible the discussion of "impossible in mathematics" / Greisy Winicki-Landman -- The development of proof making by students / Carolyn A. Maher , Ethel M. Muter and Regina D. Kiczek -- Approaching and developing the culture of geometry theorems in school / Marolina Bartolini Bussi , Paolo Boero , Franca Ferri , Rossella Garuti and Maria Alessandra Mariotti -- Construction problems in primary school / Maria G. Bartolini Bussi , Mara Boni and Franca Ferri -- Approaching theorems in grade VIII / Paolo Boero , Rossella Garuti and Enrica Lemut -- From dynamic exploration to "theory" and "theorems" (from 6th to 8th grades) / Laura Parenti , Maria Teresa Barberis , Massima Pastorino and Paola Viglienzone -- Geometrical proof / Maria Alessandra Mariotti -- The transition to formal proof in geometry / Ferdinando Arzarello , Federica Olivero , Domingo Paola and Ornella Robutti -- Further Reading / Paolo Boero.