This digest discusses how well authentic mathematics assessment tests can be expected to meet the needs of mathematics instruction that focuses on conceptual insights and analytical skills. In the new mathematics curriculum, situational lessons or real-life problems attempt to include dimensions of thinking and reasoning, individual or small-group settings, use of mathematical tools, and student attitudes and dispositions. New assessments require students to formulate problems, devise solutions, and interpret results. Several state assessment programs are engaged in developing new modes of assessment to reflect the emerging consensus on mathematics instruction. In California, for example, educators are developing the following types of assessment items: (1) open-ended questions; (2) short investigations (60- to 90-minute tasks); (3) multiple-choice questions emphasizing understanding of important mathematical ideas and generally involving integrating more than one mathematical concept; and (4) portfolios. The California Mathematics Program has been using open-ended questions for the last 3 years at the 12th-grade level. Currently, only a small sample of student responses are scored, but these exercises provide opportunities for districts to become involved in the state assessment, to administer the essays, and to train teachers to score them. (SLD)