Teachers College Press has just published a book from the QUASAR Project, intended to help people implement staff development. I've been reading it this week, and it's just about the most useful resource I can imagine in planning on-going staff development to help teachers implement mathematics programs designed around the NCTM standards. (At the high school level, this includes curricula like Core Plus and the Interactive Mathematics Project (IMP). At the Middle school level, this includes programs like Connected Mathematics. At the elementary school level, this includes programs like Investigations in Number, Data, and Space. Many of these curricula have been selected as "exemplary" by the Department of Education.)

The book is called "Implementing Standards-Based Mathematics Instruction: A Casebook for Professional Development". As the title indicates, it contains a number of "cases" for teachers to study and discuss, as they learn to implement high-level mathematics tasks successfully. The strength of the book is that it is organized around QUASAR's "Mathematical Tasks Framework". This framework trains teachers to analyze mathematics tasks as being at any of a number of levels: Doing Mathematics; Procedures With Connections; Procedures Without Connections; Unsystematic Exploration; Nonmathematical Activity.

QUASAR has found that tasks tend to degrade, i.e., they can be designed at a high level ("doing mathematics" or "procedures with connections") but migrate to a "lower" level either when the teacher initially sets up the lesson, or as the lesson procedes (the "implementation" phase). Their data (which I've seen in other studies, not this case-book) demonstrates that student achievement is enhanced when the task is designed, set up, and IMPLEMENTED at a high level. The case-book describes factors that cause a high-level task either to be implemented at a high level, or to degrade. Then, it provides cases (i.e., classroom teaching episodes described in great detail)in which one or the other happens, and helps teachers analyze why. Not only are the cases themselves very useful for learning: the process of analyzing the cases gives teachers the skills they need to analyze their OWN lessons.