There are actually several modeling tools which a good math instructor will use in order to teach math. Each one of these models may be used to represent grammar material during the grammar stage. As representations, these models are language tools. Languages can be memorized and translated. These are grammar level skills, and thus, all the models are appropriate conveyors of grammar material.
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.