The purpose of this article is to examine the components required to assess student problem solving in technology environments. The article begins with a brief discussion of the purposes of testing, theft provides an example demonstrating the difference between retention and transfer, defines and analyzes problem solving, and explores techniques and standards for measuring the quality of student understanding. Families of cognitive demands (e.g. problem solving) are identified that can serve as the frameworks for the design of learning, teaching, and testing applications. These models are intended to be implemented in various subject matters. Next, a set of key validity and fairness standards are presented to be considered in assessing the quality of assessments. Further, the criteria for validity are discussed that are particularly relevant to computer-based assessment of problem solving. These criteria include cognitive complexity, sensitivity to instruction, meaningfulness, reliability, fairness, and linguistic appropriateness. It is argued that these purposes of assessment with appropriate cognitive demand frameworks and with key standards can be integrated into a coherent, technology-based system of assessment for use in both public and classroom discourse. (C) 1999 Elsevier Science Ltd. All rights reserved.