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This is an introduction to a Didactique, research program that has been going on in France since the ´70s and whose importance is now widely recognized, but whose content is still not easy access to anglophones. The work of Dr. Guy Brousseau has remained largely, in his native France, untranslated and largely unknown. This book will unlock the secrets of Didactique and provide an opportunity for researchers, teacher educators, and students to learn of this important methodology.

The field of Didactique is rich, deep and extensive. To a large extent, it owes its shape and even its existence to the energy and inspiration poured in by Guy Brousseau starting in the 1960´s. Many others have since added their ideas and energies to produce a unique, vibrant, multi-faceted research program. Invitation to Didactique provides an easily accessible general introduction to the field, hitting the high spots and focusing largely on the contributions of Brousseau himself. Teaching Fractions through Situations: a Fundamental Experiment takes one fundamental aspect and examines it in a great deal more depth from several perspectives. It gives a detailed description of a particularly interesting way of teaching fractions and decimals which should be interesting to any reader who enjoys seeing children learn mathematics. It then examines two other aspects of the lesson sequence, first describing the exciting and challenging role of the teachers handling a highly unfamiliar approach and then placing the whole experience in its context in the very earliest phases of the development of this very important field of research.

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1. Basic elements of Didactique.- 2. Two illustrative examples.- 3. A fundamental situation for statistics.- 4. Gael and the didactical contract.- 5. Glossary.- Index.- Bibliography.

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Virginia Warfield received her doctorate from Brown University in 1971 under the direction of Wendell Fleming and continued to contribute to the field of stochastic analysis for several years. At the same time she became increasingly absorbed by problems of mathematics education through her work with Project SEED, a highly regarded mathematics program whose goal was to promote sense-making mathematical activities for fourth through sixth grade students. She was instrumental in creating Washington Teachers of Teachers of Mathematics (WAToToM), at which members of departments of mathematics and mathematics education from around the State get together for a week-end of conversation and idea-sharing. During the past ten years she has played a leading role in three major NSF-funded teacher enhancement projects: Creating a Community of Mathematics Learners, Extending the Community of Mathematics Learners, and Graduate Teaching Fellows in K-12 Education (GK-12), all of which partner University of Washington faculty and graduate students with in-service teachers of mathematics. Warfield is described as a master in integrating various levels of math learners-creating relationships between grade school teachers and mathematicians-and as having special concern for students from economically disadvantaged backgrounds and underrepresented groups. Among her many professional activities, Warfield has been a member of the National Faculty (by election), of Sigma Xi, of the Association pour Recherche en Didactiques des Mathématiques, and of the Mathematical Association of America´s committees on Professional Development and Mathematical Education of Teachers. For the Association for Women in Mathematics she has served in several capacities: Chair of the Education Committee, Member of the Association Review Group for the revision of the NCTM Standards, Member-at-large of the Executive Committee, and Education Column Editor for the AWM Newsletter.

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