("Arithmetic is numbers you squeeze from your head to your hand to your pencil to your paper till you get the right answer", poet Carl Sandburg.)

 The teaching of ARITHMETIC in elementary school fails in many ways:

1. The rich relationship of arithmetical concepts, operations, algorithms should easily control the subject (as my GENRATICS program shows), endowing users with many diverse ways of solving a problem. This allows each student to understand and use arithmetic in his/her individual way. But this relationship is not taught. So, teachers, children, citizens all (incorrectly!) believe "there's just one way to solve an arithmetic problem'. And performance suffers throughout America!
2. Arithmetic is taught by "top-down" quasi-axiomatic methods (which fragment "The Three R's"!), as if the subject were brought by the stork, or handed down like the "Ten Commandments" from Mount Sinai. This ignores a "bottom-up" method going back to the ancient Pythagoreans. For generatics-based arithmetic unifies "The Three R's", since language-learning and arithmetic-learning mutually support each other. ("Word-bone connected to the Number-bone!") In essence, it projects the "connectivity" spoken of in the previous item, providing many ways of solving an arithmetic problem. And it would be of advantage to many girls -- often are superior to boys in the language arts. But generatic arithmetic isn't taught! Teachers, students, citizens alike are ignorant of its long-time existence and great value.

3. ARITHMETIC is not taught in its HISTORICAL CONTEXT, showing how it matured from tallying and writing in Roman numerals as such. A dose of what I call "ALFANUM ROOTS", and given here, is correctively "more nourishing".

4. Arithmetic is not taught so that ideas for numerical algebra, analytic geometry, trigonometry, the differential and integral calculus, etc. are planted (as my genratics program does) for later development, resulting in fragmented mathematical education. Hence, the first component of our mathematical "DNA" is not effectively available for "nourishing" our students, providing useful workers for our economy.

5. Mathematicians have a name for "higher arithmetic". It is called "Number Theory". Its history is replete with challenging problems that involve fascinating number patterns. This could motivate the ARITHMETIC part of a Laboratory for teaching STRATEGY and TACTICS. But this is another neglected aspect of arithmetic teaching.

6. Here is a neglected resource of ARITHMETIC. In an associated file, I teach PRESCHOOL KIDS to build a PLAIN PECKING ORDER WITH THREE PEEWEES. For ELEMENTARY SCHOOL KIDS, this BECOMES A LATTICE OF THE FACTORS OF THE NUMBER 30.

   The second "Mathematical DNA" component is TOPOLOGY.