Schoenfeld (36,37) reported results from a year-long study of detailed observations, analysis of videotaped instruction, and follow-up questionnaire data from two tenth-grade geometry classes. These classes were in select high schools and the classes were highly successful as determined by student performance on the New York State Regent's examination. Students reported beliefs that mathematics helps them to think clearly and they can be creative in mathematics, yet, they also claimed that mathematics is learned best by memorization. Similar contrasts have been reported for the National Assessment (5). Indeed our conversations with teachers and our observations portray an overwhelming predisposition of secondary school mathematics students to view problem solving as answer getting, view mathematics as a set of rules, and be highly oriented to doing well on tests. Schoenfeld (37) was able to tell us much more about the classes in his study. He makes the following points.