When students delve deeply into mathematics, they gain not only conceptual understanding of mathematical principles but also knowledge of, and experience with, pure reasoning. One of the most important goals of mathematics is to teach students logical reasoning. The logical reasoning inherent in the study of mathematics allows for applications to a broad range of situations in which answers to practical problems can be found with accuracy.  

As students progress in the study of mathematics, they learn to distinguish between inductive and deductive reasoning; understand the meaning of logical implication; test general assertions; realize that one counterexample is enough to show that a general assertion is false; understand conceptually that although a general assertion is true in a few cases, it may not be true in all cases; distinguish between something being proven and a mere plausibility argument; and identify logical errors in chains of reasoning.  Mathematical reasoning and conceptual understanding are not separate from content; they are intrinsic

California Department of Education: Mathematics Framework for California Public Schools 2008