CME Project makes a conscious choice not to think of each course as a list of topics to cover, but rather as an opportunity to develop mathematical themes in different areas of mathematics. These themes provide students with insight about what it means to “think like a mathematician” and can be applied to many different (even non-mathematical) situations.
An example of one mathematical theme is invariance. Students gain experience in noticing invariants in diverse mathematical situations. They develop conjectures around their observations and then work to prove those conjectures. Eventually, whenever students encounter a new situation, they learn to look for invariants and think about possible causes for them. A document is available that discusses many more of the mathematical themes we develop and what it means to organize curriculum around these themes rather than around topics.
(download the PDF)
CME Project also uses some unique approaches to thorny content topics, from making sense of the arithmetic of signed numbers to understanding the relationship between an equation and its graph. These approaches have been developed, tested, and refined over years of classroom experience and help students come to a deeper and more robust understanding of difficult material. A document is available that outlines some of these approaches. (download the PDF)