The International Academy of Education (IAE) is a not-for-profit scientific association that promotes educational research,its dissemination , and the implementation of its implications. Founded in 1986, the Academy is dedicated to strengthening the contributions of research, solving critical educational problems throughout the world, and providing better communication among policy makers, researchers and practitioners. The seat of the Academy is at the Royal Academy of Science, Literature and Arts in Brussels, Belgium, and its coordinating centre is at The general aim of the IAE is to foster scholarly excellence in all fields of education. Towards this end, the Academy provides timely syntheses of research-based evidence of international importance. The Academy also provides critiques of research, its evidentiary basis, and its application to policy. The current members of the Board of Directors of the Academy are: 3 Preface This booklet has been adapted for inclusion in the Educational Practices Series developed by the International Academy of Education (IAE) and distributed by the International Bureau of Education (IBE) and the Academy. As part of its mission, the Academy provides timely syntheses of research on educational topics of international importance. This booklet is the fourth in the series on educational practices that generally improve learning. The material was originally prepared for the Handbook of research on improving student achievement, edited by Gordon Cawelti and published in a second edition in 1999 by the Educational Research Service (ERS). The Handbook, which also includes chapters on subjects such as generic practices and science , is available from ERS (and website:www.ers.org). ERS is a not-for-profit research foundation serving the research and information needs of educational leaders and the public. As Vice-President of the Academy and editor of the present series, I thank ERS officials for allowing the IAE and the IBE to make available the material adapted from the Handbook to educators around the world. mathematics teaching and learning (Macmillan,1992) and has a large number of other publications on research in mathematics education to his credit. He has made invited research pre-and the United Kingdom. He has directed several research projects for the National Science Foundation (NSF) and other agencies in the areas of mathematical problem-solving and classroom teaching practices. His current NSF work involves mathematics and technology. He received his Ph.D. The second author, Kristin J. Cebulla, is a mathematics education doctoral student at the University of Iowa.She previously taught middle-school mathematics. Before teaching, she worked
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