Different kinds of tests are given to determine student achievement. Standardized achievement tests are often used, but have many limitations. They may be useful in determining the content students should learn and its relevance for future learning and the curriculum. Criterion referenced tests eliminate a major weakness of standardized tests in that there are accompanying objectives teachers can use in teaching students. When a constructivist approach is taken to assessment, evaluation is based on contextual situations. The portfolio represents a constructivist approach that can really sample student achievement. Computer-based tests have many advantages, especially in the immediacy of feedback to students, but they also have limitations centering on the lack of opportunity for students to raise questions or have input into the curriculum. Many problems remain to be resolved with regard to assessing student attainment, but new ways to assess student achievement are definitely needed. (Contains nine references.) (SLD)