WI A major problem with most traditional mathematics classes is that students can memorize how to solve problems in one chapter, take the test and then forget all about the concepts. The unit is over and students won't see that material again until they start cramming for the final. As with any skill, mathematics skills which are not used are forgotten. The CPM teacher-authors addressed this problem when they designed their books.
Every major topic is seen over and over again.
New ideas are first foreshadowed, then introduced, developed and practiced. These new concepts are re-introduced either in a familiar form or in a new form, at first every day, then frequently as part of the homework, and then as subproblems in applications for the rest of the year or, with core concepts, such as ratios, functions, and graphs, into the next course. For example, ratios, a central topic in mathematics and science, is the subject of four different chapters in algebra and geometry. As a result of this careful spiraling and integration of ideas, students do not have a chance to forget the big ideas and can call upon them whenever they are needed. It is also joyous to hear students buzzing when they are confident enough about math to converse with their classmates while working to solve problems.