This review brings diverse research to bear on the contention that current achievement tests may underestimate students' subject-matter knowledge and problem-solving ability because of the mismatch between the symbolic form that typical achievement tests use and the specificity of students' symbolic encoding that arises from instruction and individual differences. More specifically, the possibility that alternative representations of science problems affect achievement estimates is examined for students varying in socioeconomic and ethnic/racial backgrounds. Theory and research are examined for the effects of symbolic encoding on information processing and the effects of translation among symbol systems on problem solving. Testing with alternative symbolic representations is placed in the context of the literature on minority group testing. Research on minority group testing has rarely focused on the possibility of alternative symbolic forms of tests or test items. There has been little attempt to determine the strengths of particular cultural and language groups and to develop tests that capitalize on them. Instead, research on minority group testing has concentrated on: (1) the validity of group differences in test scores (test bias); (2) the testing of linguistic minorities; and (3) the development of culture-fair tests. A 70-item list of references is included. An appendix describes the development of a taxonomy used in science textbooks to present concepts of heat and temperature. (SLD)