- "CMP is problem-centered. This means that important mathematical ideas are embedded in engaging problems. Students develop understanding and skill as they explore a coherent set of problems, individually, in a group, or with the class. "Effective instruction models good thinking, provides hints, and prompts students who can not get it on their own." (2) Inquiry, reflection, meaningful problems in a variety of contexts, and sense making, are all elements of the CMP program.
- Students' perceptions about a discipline come from the tasks or problems in which they are asked to engage. For example, if students in a geometry course are asked to memorize definitions, they think geometry is about memorizing definitions. If students spend a majority of their mathematics time practicing paper-and-pencil computations, they come to believe that mathematics is about calculating answers to arithmetic problems as quickly as possible. They may become adept at quickly performing specific types of computations, but they may not be able to apply these skills to other situations or to recognize problems that call for these skills. If the purpose of studying mathematics is to be able to solve a variety of problems, then students need to spend significant time solving problems that require thinking, planning, reasoning, computing and evaluating.
- CMP places important mathematics in problems in context. Research evidence from the cognitive sciences supports the theory that students can make sense of mathematics if the concepts are embedded within a context or problem. If time is spent exploring interesting mathematical situations, reflecting on solution methods, comparing methods, and examining why methods work, then students are likely to build more robust understanding of mathematical concepts and procedures.
- A problem-centered curriculum not only helps students make sense of the mathematics, it appears to also help them process the mathematics in a retrievable way. Teachers of CMP report that students in succeeding grades remember and refer to a concept, technique, or strategy, by the name of the problem in which they encountered the idea.
- Results from the cognitive sciences also suggest that learning is enhanced if it is connected to prior knowledge, and is more likely to be retained and applied appropriately to future learning. CMP Units build on each other. Concepts developed in one unit are deliberately connected to prior investigations and skills; and problems in future units further develop or refine strategies."
"Mathematics is a special language consisting of words, tables, graphs and symbols to represent and communicate mathematical ideas. As with all language acquisition, students learn to communicate mathematics by talking, listening, reading, and writing. In CMP classes students build the skills that allow them to communicate their thinking with many others. They make conjectures, try these out, report on progress and refine their thinking."