Student-Centered, Problem-Based Active Learning

The CPM courses emphasize reasoning, critical analysis, mathematical modeling, and justifying; students are active participants in their learning. The problem-based nature of each lesson provides guided, purposeful investigations that support deep conceptual understanding of the mathematical objective. The problem set structures students’ work so that they see how an idea develops, how it is related to other ideas, and why a particular algorithm works. Procedures are based upon an understanding of the process rather than memorized algorithms. A strength of the curriculum is coherence: big mathematical ideas flow throughout each course so that individual lessons do not become a series of disconnected topics.

CPM textbooks contain fewer problems than a typical mathematics textbook, allowing students to concentrate on the mathematics and persevere in solving any given problem. The problems are non-routine (encouraging application and extension), team-worthy (requiring reasoning and collaboration), and engaging (leading to a more positive disposition toward mathematics), and they ask for a variety of outcomes (reports, diagrams, models, presentations). Justification of thinking and communication of mathematical arguments are constantly expected.

In a CPM course, students make sense of mathematics through frequent work in study teams. When solving complex problems, students benefit by working interdependently in these teams: sharing information, insights, and expertise; providing clarification to each other; analyzing; building on the ideas of others; and productively critiquing other students’ work. By working in teams, students can access higher-level, more sophisticated problems. Furthermore, many tasks are simply more interesting when done within a team, leading to perseverance and therefore more success.

The regular interaction with the students in a problem-based setting allows teachers to monitor the individual progress of each student and the class as a whole by circulating among the student study teams as each lesson progresses. In this way, the teacher can intervene to help overcome a moment of confusion and correct errors. When necessary, the teachers can pull the class together and address a challenging concept, correct a misconception, or provide additional information with a brief discussion.