THIS REPORT OF AN INTERNATIONAL RESEARCH ALLIANCE OF TWELVE COUNTRIES EXPLAINS THE ESTABLISHMENT OF PROCEDURES OF RESEARCH AND QUANTITATIVE ASSESSMENT FOR THE COMPARATIVE STUDY OF EDUCATION THROUGHOUT THE WORLD. RESEARCH INSTITUTES FROM TWELVE COUNTRIES ORGANIZED THE COUNCIL OF THE INTERNATIONAL PROJECT FOR THE EVALUATION OF EDUCATIONAL ACHIEVEMENT (IEA). THOSE PARTICIPATING WERE (1) AUSTRALIA, (2) BELGIUM, (3) ENGLAND, (4) FEDERAL REPUBLIC OF GERMANY, (5) FINLAND, (6) FRANCE, (7) ISRAEL, (8) JAPAN, (9) NETHERLANDS, (10) SCOTLAND, (11) SWEDEN, AND (12) UNITED STATES. THE UNITED STATES OFFICE OF EDUCATION PROVIDED FUNDS TO SUPPORT THE STUDY. THE STUDY WAS DESIGNED TO TEST A NUMBER OF FUNDAMENTAL HYPOTHESES RELATED TO A VARIETY OF EDUCATIONAL SYSTEMS IN DIFFERENT CULTURAL, ECONOMIC, AND SOCIAL CONTEXTS. AMONG THE MOST IMPORTANT OF THE COMPLEX PROBLEMS WAS THE CONSTRUCTION OF VALID MEASURING INSTRUMENTS WITHIN BOTH THE COGNITIVE AND NONCOGNITIVE DOMAIN. BECAUSE OF THE APPARENT UNIVERSALITY OF IMPORTANCE GIVEN TO MATHEMATICS, IT WAS DECIDED THAT THE STUDIES SHOULD START WITH THE FIELD OF MATHEMATICS. VOLUME I EXPLAINS (1) THE INTENTIONS AND BACKGROUND OF THE PROJECT, (2) ITS ADMINISTRATION, (3) FORMULATION OF HYPOTHESES, (4) EXAMINATION OF SUBJECT AREAS TO BE TESTED, (5) MECHANICS OF TEXT CONSTRUCTION, (6) ADMINISTRATION AND PROCESSING OF THE TESTING PROGRAM, (7) COMPARATIVE STATISTICS OF EDUCATIONAL SYSTEMS, AND (8) CULTURAL ENTITIES. APPENDIXES CONTAIN A SUMMARY OF TOPICS IN THE MATHEMATICS I AND II TESTS AND A TABULATION OF VARIABLES IN THE IEA STUDY. A LIST OF REFERENCES AND A SUBJECT INDEX ARE GIVEN. RESULTS AND ANALYSIS OF THE TESTING PROGRAM ARE REPORTED IN A SECOND PUBLICATION, INTERNATIONAL STUDY OF ACHIEVEMENT IN MATHEMATICS-A COMPARISON OF TWELVE COUNTRIES, VOLUME II. THIS DOCUMENT IS AVAILABLE FROM JOHN WILEY AND SONS, 605 THIRD AVENUE, NEW YORK, NEW YORK 10016. (DH)