Even after a number of innovative programs and proposals have met selective criteria, the Educational Research Commission will have a difficult task in assigning priorities and spreading resources. This paper offers many suggestions for handling the problems in research and evaluation related to innovative mathematics projects, especially K-3. For example, it is proposed that innovative programs be generalizable to the public schools to avoid the dangers of elite staffing in innovative schools. The rationale and internal logic of a new curriculum should be evaluated by competent mathematicians, then the pedogogical soundness should be examined by educators and others qualified in a number of appropriate areas. Each innovative school should have computer services at its disposal. An in-depth study of the nature of mathematics and its role in the technological culture of the future should be made with implications for K-3, while Piagetian studies on mathematical learning should also be reviewed. It is also suggested that a common pool of evaluative resources be developed and pretested so that they could be drawn upon for a variety of research and evaluative purposes. Some innovative enterprises should be directed toward the education of minority groups. Work on reading instruction might merge with mathematics at times. Finally, since some of the innovative proposals cannot be evaluated in terms of criteria for a final product, these proposals must be judged by their spirit and design. (CK)