dear seberle i agree that the alternative meaning of spiraling the one you removed is a misuse of the term but so was the point of the text removed by you that in contrast with sm many us curricula which characterize themselves as spiral are not e g everyday math is considered spiral as far as i understand the idea is that different groups of students in the same class pick different aspects of the topic and progress with different pace upon revisiting it this spiraling is not the same as in sm where each topic is taught to mastery in the first visit and is revisited only at the next level to emphasize the distinction i restored the sentence and provided a reference hopefully illustrating this point borisovich talk