Three case studies are offered that illustrate the use of schemata for teaching and learning.

In the Mayonnaise Problem, naive cooks are asked to identify what mayonnaise is made of. Because they have no direct knowledge of mayonnaise, they are forced to rely on the closest schema available, that of creamy white sauces. Typical guesses of ingredients include whipped cream, marshmallows, perhaps some mustard. These guesses are "intelligent;" that is, they are based on existing schemata that might be relevant to solving the problem. Lacking specific information, the learner backs up to a more general schema and reasons by analogy, with successive modification toward the goal.

Schematic conflicts are illustrated in the White Sauce Problem. Tutorial interactions were studied in the cooking of French white sauces. The tutor happily lectures for 20 minutes on white sauces, concluding with "I think that's all there is to say." The student has been following, nodding and affirming appropriately. But at the end, she asks a question that betrays her fundamental misunderstanding, confusing American and French white sauces. Only then does the tutor realize the problem, back-tracking in order to correct the misconception and continuing the lesson another 45 minutes. "When an [expert] tutors a beginner, there is a tendecy to lecture at first... Then, when the overview description has been completed, the beginner's lack of understanding often surfaces, causing a fumbling, exploratory interaction in which each tries to understand what the other is thinking" (p. 188).

The Jump Problem comes from a student learning the "jump" command in a simple programming language. The tutor presents a series of increasingly complex code fragments, each time asking the student to predict the computer's behavior and observe the actual outcome. We observe a successive pattern of hypothesis formation based upon [on] current understanding, followed by revisions in schemata based on actual outcomes. The case illustrates the way schemata are tested and revised during instruction. Instruction that facilitates such testing and revision of schemata is likely to be more effective than the kind of initial lecture found in the White Sauce Problem above.

Taken together, the three cases offer concrete and memorable metaphors for the functioning of schemata in instruction. In each case, student schemata provide the basis for hypothesis generation and testing, with instruction providing a basis for testing and revision of schemata as students move toward improved understanding of the subject matter.