Collaborative Learning: Students learn ideas more deeply when they discuss ideas with classmates.
Problem-Based Learning: Students learn ideas more usefully for other areas when they learn by attacking problems– ideally from the real world.
Mixed Space Practice: Students learn ideas more permanently when they are required to engage and re-engage with the ideas for weeks or even months.
*These pillars are reflected in current NCTM standards and research in mathematics education; what we know about their benefits for mathematics learning continues to deepen and expand but not shift.
CPM Educational Program, a California non-profit corporation, has provided problem-based instructional materials and professional development for teachers since its inception in 1989. CPM teaching strategies focus on how students best learn and retain mathematics. The research-based principles that guide the course are the following:
Students should engage in problem-based lessons structured around a core idea.
Guided by a knowledgeable teacher, students should interact in groups to foster mathematical discourse.
Practice with concepts and procedures should be spaced over time; that is, mastery comes over time.