Changes in educational assessment are currently being called for, both within the fields of measurement and evaluation as well as in disciplines such as statistics. Traditional forms of assessment of statistical knowledge provide a method for assigning numerical scores to determine letter grades but rarely 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 to achieve more relevant goals, such as being able to explore data and to think critically using statistical reasoning. This paper summarizes current trends in educational assessment and relates these to the assessment of student outcomes in a statistics course. A framework is presented for categorizing and developing appropriate assessment instruments and procedures.