Changes in educational assessment are currently being called for, both within the field of measurement and evaluation as well as in particular disciplines such as statistics. Tradional assessment of statistical knowledge typically look like textbook problems that either rely heavily on numerical calculations or on the ability to recall isolated pieces of information. Although this type of assessment seems to succed in providing instructors with a method for assigning numerical scores for determining letter grades ranking students within a course, these types of assessment rarly reveal information about how students actually understand and can reason with statistical ideas or apply their knowledge to solving statistical problems. As statistics instruction at the college level begins to change in response to calls for reform (e.g., Cobb, 1992) there is an even greater need for appropriate assessment methods and materials to measure students' understanding of probability and statistics and their ability achieve more relevant goals such as being able to explore data and to think critically using statistical reasoning. This paper attempts to summarize current trends in educational assessment and relate these to the assessment of student outcomes in a statistics course.