The College Preparatory Mathematics (CPM) curriculum is about problem solving within a team environment. A team can be two to four people. The problems are student-centered. That means that the students work together to make sense of the problem and the teacher facilitates and supports the problem solving. This is different than a direct teaching method where the teacher demonstrates, or models, how to solve a problem and then the students practice the same process. In our class, the direct teaching method is used when needed rather than being the primary method of teaching.
Central to the CPM experience is reading comprehension. As the students read the problems they must cooperate and collaborate to understand and solve the problems. This means that communication and being able to positively communicate within your group is very important. These four C's of CPM - Comprehension, Cooperation, Collaboration, and Communication - correspond to the California State Standards on Mathematical Practices (MP) 1 and 3. MP 1: make sense of problems and persevere in solving them. MP 3: construct viable arguments and critique the reasoning of others.
Mastery over time is fundamental to the CPM curriculum. This means that topics are not learned and then assessed in discrete segments. Rather, topics are explored and examined in class, and then practiced in homework assignments, and eventually assessed in a future test. In addition, to maintain understanding and continue the process towards mastery, prior topics are assessed in current tests. As this type of testing is formative, the results are examined to adjust the classroom experience to the needs of the students.
Homework is for practice and preparation. The concepts that are practiced in the homework will prepare the students for the upcoming test.
Mastery over time and homework practice are acknowledgments that students learn at different rates. Approaching this from a growth mindset it is important to encourage deep thinking rather than rapid progress. Moreover, a student's grade reflects their current state of progress and accomplishment towards mastery.