This paper describes the global feedback in ActiveMath, a Web-based adaptive learning environment for mathematics and beyond. It addresses some of the cognitive foundations and the architecture of the suggestion mechanism with its components. This architecture separates components for diagnosis from components for suggestions and different types of information: the observable facts about the student, implied non-observable diagnoses about the student's actions, suggestions implied from the observable and non-observable diagnoses, and the actual rendering of the suggestions. This mechanism is highly adaptive. (Contains 4 figures.)