Good teaching requires the use of several models together in order to represent the math facts. This is useful because it simply presents several, complimentary ways of learning the facts and organizing them. Children retain facts and become more adept in using them at upper levels if the facts are presented with complimentary tools and in a sequential manner. This type of presentation is one of the primary jobs of the math teacher and in order to accomplish this, we must teach our kids how to translate between mathematical models. We achieve connectivity between the models by teaching our students how to translate properly.
Connectivity makes for better retention of the facts.
Repetition and speed drills are the other means we must incorporate into our instruction at the grammar level to insure that our children will have a firm foundation in math. The curriculum we choose will either hamper or enhance our efforts to properly instruct our children. Since this combination provides for the necessary connectivity of facts, repetition and speed drills, I have found success as an instructor. Most importantly, my children have been able to efficiently and effectively learn the foundational math facts. In The Seven Laws of Teaching , John Milton Gregory lists the seven laws, along with rules for the teacher, and the common mistakes and violations of each law.