In assessing the quality of science teaching for an effort such as the National Assessment of Educational Progress (NAEP), it is important to understand what is meant by scientific thinking--the search for explanations. Instruction should involve higher-order cognitive skill development, but it is difficult to measure reasoning and understanding with traditional multiple choice tests. Additionally, time spent on improving students' multiple-choice test performance reduces the time available for strengthening more complex skills. Increased use of tests in other formats would encourage the teaching of these skills. Cognitive theorists have recognized that thinking and learning rely heavily on the construction of explanations. In the many examples of learning activities presented in this paper, cognitive learning is shown to be driven by the search for explanations. Current developments in cognitive research justify that effort be dedicated to the assessment of explanatory skills. Testing alternatives include multiple choice tests designed with less emphasis on factual memory, essays, free response tests, interviews, thinking aloud protocols, and performance tests. Empirical studies of explanation are recent. They include literature on the development of explanatory skills and on the social role of explanations. Tests of divergent productions are the result of psychometric studies of explanation. The development and use of tests that sample students' ability to offer scientific explanations could add an important dimension to NAEP. (GDC)