To provide information to the Congress in its continuing debates over improving science and mathematics (S/M) education as well as to education policymakers, the General Accounting Office (GAO) synthesized past evaluation and research studies and used other methodologies to examine four issues: (1) the nature of the problem and its remedies; (2) prospects for upgrading existing S/M teachers; (3) prospects for reducing the S/M teacher shortage by retraining teachers from other subject areas; and (4) the current ability to evaluate the quantity and quality of S/M teaching. Observations on the implications of this work for S/M education legislation are included. GAO does not find evidence that training programs to upgrade existing S/M teachers will improve teaching effectiveness. Such programs are a prominent part of proposed federal legislation. Teacher shortage problems, which are also addressed in the proposed legislation, may be easier to solve. Programs to retrain teachers of other subjects to teach science and mathematics classes seem to be one viable solution to technical teacher shortages. In addition, gaps in information available to policymakers are so severe that GAO could not determine if there are net nationwide shortages of S/M teachers and if the quality of technical teaching has declined in recent years. (JN)