Connected Mathematics is committed to developing mathematical skills, skills that include more than quickness with paper-and-pencil algorithms. Skills also encompass the ability to use mathematical tools, resources, procedures, knowledge, and ways of thinking to make sense of new situations. For example, students need to recognize when an exact answer is required and when an approximate answer is sufficient, and they need to have a variety of methods for finding an answer. If an approximate answer is called for, a paper-and-pencil algorithm may not be the most efficient method.
Students need to know how and when to use paper-and-pencil algorithms, mental computation, calculator procedures, and estimation strategies, and it is critical that students acquire these methods with understanding. For example, students should be able to add two simple fractions quickly by finding a common denominator, but they should also understand why this algorithm works. Understanding equivalent fractions is the foundation for developing algorithms for fractions.
In Connected Mathematics, students develop understanding of algorithms and strategies in a variety of ways. As they work on investigations, they use and refine their skills. They learn to recognize when an algorithm or strategy applies to a new context and when they can build on the skills and strategies they know to develop new strategies. In these processes, students practice skills as an ongoing activity throughout the curriculum.
Source: Connected Mathematics Web site