Four papers follow and document the progress of the Center for Research on Evaluation, Standards, and Student Testing in understanding questions related to alternative assessment based on case studies in three elementary schools. The research questions include consideration of the logistical constraints that must be respected in developing alternative assessments and the features that can be feasibly integrated with instruction. Also considered are changes in teachers' knowledge and beliefs about assessment and instruction resulting from the project and the effect of new assessments on learning. The four papers are: (1) "Dilemmas and Issues for Teachers Developing Performance Assessments in Mathematics" (Roberta A. Flexer and Eileen A. Gerstner); (2) "Dilemmas and Issues in Implementing Classroom-Based Assessments for Literacy" (Elfrieda H. Hiebert and Kathryn Davinroy); (3) "Teachers' Ideas and Practices about Assessment and Instruction" (Hilda Borko, Maurene Flory, and Kate Cumbo); and (4) "Parent Opinions about Standardized Tests, Teacher's Information and Performance Assessments" (Lorrie A. Shepard and Carribeth L. Bliem). (Contains 57 references.) (SLD)