Abstract
In this paper, the authors have proposed the small-step test having high validity for grasping a state of learner's understanding. In order to ensure the high validity of small-step test, both test-analysis (analysis of a series of questions) and response-analysis are adopted. The test-analysis is to analyze contents of small-step test, and the response-analysis is to analyze responses of learners for a small-step test. Both analyses are alternately repeated so far as to ensure the high validity. As the result of this study, the structure of understood scientific concepts, the structure of those knowledges (items) and also the structure of questions given as a small-step test to see those concepts constructed in learners are made clear by the analyses. These three structures have been represented as the hierarchical structure which is usually adopted in the informatics. The hierarchy shows a sort of the projection of the perception of learners or an instructor for a particular scientific concept.
