Judy Roitman says: >Spiraling is the one thing about Saxon that everyone seems to like. What >other series spiral? I think UCSMP does, but never having used it don't >know for sure.
Does Saxon spiral or circle? Usually spiraling has the connotation of revisiting a topic at increasing levels of sophistication over a period of time. Saxon does revisit topics, but at basically the same level. I would characterize this as circling or reinforcing rather than spiraling.
Regarding other series that "spiral". The Algebra Learning Project developed here at the University of Hawaii uses "development over time", meaning that students encounter problems on a given topic over the course of 7 or so lessons, in contrast to the one-day/one-topic approach. This provides students with multiple interactions with a topic, but this to my mind is not really spiraling either.
The Geometry Learning Project (of which I am the director) takes a similar approach to development over time, and also revisits topics at different times during the year at different levels of abstraction (cf. Van Hiele levels). While it has aspects of spiraling, that is more an outcome than an a priori intent.
There was a famous project during the New Math era that truly spiraled. I haven't seen it for years, but I liked it a lot when I studied from it in junior high. Of course, its name slips my mind. I wonder how I would react to it now.
The main point of all this seems to be... one-shot learning is a myth. Students need multiple encounters with an idea in order to construct knowledge (for all you constructivists out there) or to develop skills (for all the DanH's out there :) or to achieve whatever goals you may have.
Hope this helps... Gary
============================================================ W. Gary Martin 1776 University Ave. University of Hawaii Honolulu, HI 96822 Curriculum R & D Group (808)956-9956; FAX (808)956-4984