A framework for designing intelligent assistance in a discovery learning environment is proposed in this paper. The process of discovery learning is analyzed and the required functions for intelligent assistance are discussed. A flexible simulator that fits any type of discovery learning is necessary. The problem solvers that perform fundamental tasks of discovery are also needed: hypothesis generator and experiment designer. In particular, the paper focuses on another important function: evaluator of the effectiveness of counterexamples. Counterexamples have many clues for learning, but a learner often feels difficulty in utilizing them. This paper proposes the method of evaluating counterexamples from two educational viewpoints that ask the following: "Does it suggest the occurrence of error clearly?" (visibility), and "Does it suggest the cause of error?" (suggestiveness). Some case studies are presented to illustrate these functions, followed by a description of the framework. (Contains 12 references, 5 figures, and 4 tables.) (Author/AEF)