In creating the worksheets over the summer, we kept in mind that since most of the students in the class are juniors, the ACT and SAT are looming large in the near future for them. In the past we have given the students weekly review sheets containing exercises that, at least in part, served the purpose of reviewing some of the material they had in all likelihood forgotten. However, this year we have put at least one review exercise on each of the worksheets. And, as in the past, it always seems to be the geometry problems that cause the most difficulty. For instance, this week we spent at least an hour of class time on one problem...yes, one problem...that we still haven't resolved as a class. It made for great discussion, though, really forcing the kids to justify their assumptions about the picture that was given in the problem and about the relationships that result from those assumptions. Honestly, it's the kind of discussion I wish we could have about lots of the exercises and concepts. To get there, though, means writing the correct kinds of questions that will lead to those discussions. As such, the worksheets are already being revised, and will probably be in a constant state of revision.
One final thought for this week: it occurred to me this week that despite the fact that we haven't done a lot of basic mechanics practice ("drill and kill"), the kids have gained a remarkable fluency with the basic mechanics of the material. Factoring, solving exponential and logarithmic equations, and the like, have not been specific "stand alone" questions, but rather have been necessary to solve some of the exercises on the worksheets, and in the process the kids have remembered (or in some cases, finally really learned) and practiced the mechanics. It truly put my mind at ease on Thursday when the kids were using and explaining the laws of logarithms...all without me saying a word. The worksheets and discussions are not sacrificing the basics for the "advanced", which makes me all the more convinced that this really is the best way for kids to honestly learn and not just memorize the material.