Children with a solid understanding of number principles have an easier time when they are asked to memorize addition and multiplication facts. It is much easier for a student to memorize facts when she understands how the numbers fit together on a number line and how they are related to each other. Students who do not have this number sense end up trying to memorize strings of seemingly abstract numbers instead of understanding how they are related.
Ironically, competence with number principles reduces the need for rote memorization. When students understand how numbers fit together and are related to each other they do not need to rely on memorization as much. Students with a strong understanding of number principles are able to reason their way to an answer rather than relying on memorization. While some math concepts are best memorized, students with a good understanding of number principles are more able to compute their way to answers.
Children who understand number principles and how numbers are related to each other are more successful and accurate when it comes to counting or placing numbers on a number line. These are important number skills in kindergarten and early parts of first grade. Students who have trouble counting accurately or understanding how numbers are related to each other often struggle as math concepts become more difficult and complex.
According to Nancy Jordan, author of "Early Math Matters," weak understanding of number principles in kindergarten has been linked to lower math achievement at the end of first grade. Children who come to kindergarten with strong number principles, and those who develop strong number principles during kindergarten, generally showed higher math achievement at the end of first grade than students who came to kindergarten with weaker number principles and did not progress.