Theorems in School

From History, Epistemology and Cognition to Classroom Practice


Volume Editor:
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.

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Origin of mathematical proof
History and Epistemology
Pages: 25–42
The proof in the 20th century
From Hilbert to Automatic Theorem Proving Introduction
Pages: 43–63
Construction problems in primary school
A Case From the Geometry of Circle
Pages: 219–247
Approaching theorems in grade VIII
Some Mental Processes Underlying Producing and Proving Conjectures, and Conditions Suitable to Enhance Them
Pages: 249–264
Geometrical proof
The Mediation of a Microworld
Pages: 285–304
Further Reading
Pages: 325–327
Educational Researchers and their students
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