As the study progressed, we came to see change in a different light. We found that none of these satisfactorily captured the nature of the diverse changes we observed. The changes we observed were not always the same as those the teachers saw in themselves and their work. Teaching a different mathematics differently did not necessarily feel the way it looked to an observer. Real change, in a curriculum or in a teacher, operates at too many levels to be captured in neat formulations.
Real change is messy and problematic.
We attempted to capture some of the manifold facets of the changes we and the teachers saw by offering contrasting poles of some dimensions along which change appeared. The curriculum of the CPTA textbook was constantly evolving due to the teachers' desires to stay on the cutting edge of new technology and new problem situations. Structure vs. Function CPTA represents a shift away from mathematical structures that rest on a foundation of axioms and are used to build definitions and theorems. The focus of the Contemporary Precalculus course was on the function of mathematics in making sense of the world. The CPTA curriculum emphasized mathematical modeling and using mathematical concepts to solve realistic problems.