This book will ask researchers to undertake two things they are not used to doing - to think of themselves as members of an evolving research community within an institution or network of institutions and to describe that community and its context (Who are we? What do we do? In what context do we do it?); and to identify the major thrust of their research as a group and a major lesson about the learning and teaching of algebra that has come out of it. One person in each group will be asked to be the respondent for the group and will be given a choice of either composing their chapter or providing the information and editing the chapter written by the volume editor. The names of all contributors will be acknowledged in each chapter. At this point twelve countries have been identified as places where there has been considerable algebra research over the past decades and where there is still a vibrant research community. Within these countries, one institution, geographical location, or network of researchers will be invited to participate as a ""research centre"". Examples of questions about the research centre could be the following: How long has your centre been involved in research in the learning and teaching of algebra? Who have been the main contributors over this time? (Names and brief profile with research interests, different collaborative teams). What has been student involvement (graduate and post graduate) in the research? What have been the (funded or not) research projects in the area of algebra? Describe colloquia and other events organized by the centre in this area. What are the other research interests of the centre? What is the school context in which the centre works? Describe school system briefly and the place of algebra within it. Each research centre will be asked to select one major lesson it has learned about the learning and teaching of algebra and this will constitute the main part of the chapter. The lesson should be general enough to encompass a large part of the research results of the centre. For example, in Montreal, the UQAM/Concordia research network might offer this lesson: The passage from arithmetic to algebra is fraught with obstacles. This would allow us to present the doctoral research of Kieran and Lee; the work of Bednarz & Janvier; Lee & Wheeler; Kieran, Boileau & Garancon; the historical work of Charbonneau & Lefebvre etc. Another example of a major lesson might be chosen by the Early Algebra Research Network in the USA: Young children can and do engage in algebraic thinking and activities and even seem to enjoy it. Another centre might have a lesson about the use of technology in the algebra classroom and another group about the passage from secondary to tertiary algebra.
Introduction.; Lesson 1: Algebra can successfully precede arithmetic in primary school (Russia E-D curriculum).; Lesson 2: Primary school children can do algebra and even seem to enjoy it (Early Algebra Group, Boston-Dartmouth, Mass.).; Lesson 3: The passage from arithmetic to algebra in middle school is fraught with difficulties (UQAM & Concordia, Montreal, Quebec).; Lesson 5: Middle and High School students can become competent problem solvers through a process approach to algebra (University of Hawai'i).; Lesson 6: Through specific and varied activities in middle school, the need for symbolic algebra can be created (U. of Bristol, UK).; Lesson 7: The use of technology in the introduction of algebra radically improves the classroom environment (CINVESTAV, Mexico).; Lesson 8: Viewing the classroom through the lens of "embodied cognition" provides valuable insights into the learning of elementary algebra (U. of Torino, Italy).; Lesson 9: The obstacles encountered in the passage to tertiary algebra provide valuable lessons for the teaching of early algebra (U. of Paris, DIDIREM, France).; Lesson 10: There are fundamental parallels in algebra learning experiences from middle school through university (Weizmann Institute, Israel). Conclusion: Algebra from a Global Perspective and the lessons for the future (Melbourne University, Australia).