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close this bookImproving Student Achievement in Mathematics (IAE - IBE - UNESCO, 2000, 48 p.)
View the document(introduction...)
View the documentThe International Academy of Education
View the documentPreface
View the documentIntroduction
View the document1. Opportunity to learn
View the document2. Focus on meaning
View the document3. Learning new concepts and skills while solving problems
View the document4. Opportunities for both invention and practice
View the document5. Openness to student solution methods and student interaction
View the document6. Small-group learning
View the document7. Whole-class discussion
View the document8. Number sense
View the document9. Concrete materials
View the document10. Students’ use of calculators
View the documentConclusions
View the documentAdditional resources
View the documentReferences
View the documentThe International Bureau of Education-IBE


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 (2000 Clarendon Boulevard, Arlington, VA 22201-2908, United States of America; phone (1) 800-791-9308; fax (1) 800-791-9309; and website:

ERS is a not-for-profit research foundation serving the research and information needs of educational leaders and the public. Established in 1973, ERS is sponsored by seven organizations: the American Association of School Administrators; the American Association of School Personnel Administrators; the Association of School Business Officials; the Council of Chief State School Officers; the National Association of Elementary School Principals; the National Association of Secondary School Principals; and the National School Public Relations Association. 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.

The first author of the present pamphlet, Douglas A. Grouws, is Professor of Mathematics Education at the University of Iowa. He was the editor of the Handbook of research on 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 presentations in Australia, China, Hungary, Guam, India, Japan, Mexico, Thailand 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. from the University of Wisconsin.

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 as a research chemical engineer. She received her bachelor of science degree in mathematics and chemical engineering from the University of Notre Dame and her master’s degree from the University of Mississippi.

The principles described in this booklet are derived in large part from the United States and other English-speaking countries. Other research also has important implications for the teaching of mathematics. An example is Realistic Mathematics Education, initiated by H. Freudenthal and developed since the early 1970s at the University of Utrecht (Dordrecht, The Netherlands, Kluwer, 1991). Another example is research on problem-solving summarized in a recent book by L. Verschaffel, B. Greer, and E. De Corte-Making sense of word problems (Lisse, The Netherlands, Swets & Zeitlinger, 2000).

The officers of the International Academy of Education are aware that this booklet is based on research carried out primarily in economically advanced countries. The booklet, however, focuses on aspects of learning that appear to be universal in much formal schooling. The practices seem likely to be generally applicable throughout the world. Even so, the principles should be assessed with reference to local conditions, and adapted accordingly. In any educational setting, suggestions or guidelines for practice require sensitive and sensible application and continuing evaluation.

Editor, IAE Educational Practices Series
University of Illinois at Chicago