To our English speaking friends

From everyday thought to mathematics

Publisher : Ellipses, 32 rue Bargue, 75740 Paris cedex 15 (ISBN vol. 1 [2006] : 978-2-7298-3028-1 ; vol. 2 [2008] : 978-2-7298-3905-5)

Nicolas Rouche, Ginette Cuisinier, Lucie De Laet, Christine Docq, Jean-Yves Gantois, Chritiane Hauchart, Manoëlle Tancré et Rosane Tossut

Under this title, we wrote a two volume book :

Volume 1 : Numbers, Magnitudes, Proportions

The birth of natural numbers. Addition and subtraction. Multiplication and division. The birth of magnitudes. From measured magnitudes to decimal numbers. From divided magnitudes to fractions. Proportionality. Numbers with a sign. Multiples and divisors. \vspace9cm

Volume 2 : Geometry

Vertical and horizontal. Plane representations of solids. Superposability, motions, symmetries. Starting from the square. Starting from the rectangle. Starting from the equilateral triangle and the circle. Tilings and angles of polygons. Areas and perimeters of plane surfaces. Volumes and areas of solids. Constructions. Shadows and projections. Pythagoras and other classical theorems.

Foreword, critical appendices, commented bibliography, index.

A book for whom ?

This book will be of interest to

 teachers and future teachers from K-level to junior high school

 authors of curricula and textbooks

 teachers of future teachers

 parents trying to help their children

 teenagers looking for some forgotten notion

 at last, and maybe principally, anyone in search of elementary mathematics meaning, of the questions they cope with, how they evolve out of everyday thought, which they complete and support.

Why another book ?

Why another book on elementary mathematics ? Besides our appreciation for existing books - including some teacher’s manuals - we wanted to show

 how to avoid an overestimation of absolute rigor, a source of damage in elementary school, how to find, in every context, an appropriate level of rigor and generality

 how to get away with the idea that learning proceeds from general to particular

 how to proceed the opposite way, i. e. from the very particular to the moderately general, focussing on intriguing phenomena more than on contemplation of concepts ; definitions are tools to understand phenomena and elaborate proofs, more than revelations of the true nature of things. Only an already known thing can be defined.

The authors

This book was written by a group of teachers of mathematics from junior high school to university. All members of the Groupe d’Enseignement Mathématique (the GEM, Group for Mathematical Teaching) of Louvain-la-Neuve in Belgium, they decided to reconstruct their most elementary notions. It lasted more than five years. Their draughts were criticized by elementary school teachers, but also by some people having lost all acquaintance with mathematics. The text was clarified, due to the observations of these highly critical people.