The Learning Principle

The Learning Principle, from the Principles and Standards for School Mathematics, and the NCTM (National Council for Teachers of Mathematics) discusses the importance of conceptual knowledge in a student's ability to understand any subject and any content, i.e. mathematics. It states that, "When students understand mathematics, they are able to use their knowledge flexibly." They can then combine their factual knowledge with their conceptual understanding to fully harness their ability to comprehend and grow in mathematics.
The section then moves on to discuss that while learning the basics is important, as these lay the groundwork for a students further growth and knowledge apprehension, in many cases the students who simply memorize the facts without actually understanding the reason behind these facts (essentially the why behind the what) often struggle when trying to apply the mathematical concepts behind these facts in other settings. More simply put, these students can solve the problems that they have memorized but cannot use the math skills required to solve these problems to solve those that they have not encountered yet. On the other hand, the students that have conceptual knowledge of mathematics can often time apply the skills they have learned in solving these problems to help them solve those problems of which they are unframiliar with.
This section later discusses the importance of becoming autonomous learners. This is important because it allows students to take control of their own learning, instead of simply being told what and when to do things, they can apply the knowledge that they have been taught to their own problems and solve them on their own, further allowing them to grow in their understanding and conceptual knowledge of mathematics.
The section closes by stating the simple principle that the school setting should not inhibt students ability to grow in their knowledge of mathematics by limiting them to the memorization of basic facts, but should provide them the framework to flourish.