A radical proposal for computer algebra in education

Unlike ordinary numeric computation, computer algebra systems can perform nonnumeric mathematical operations such as factoring and expanding or symbolically integrating and differentiating. These operations can entail complicated expressions containing thousands of terms. Moreover, the arithmetic that compliments these nonnumeric operations includes exact rational arithmetic, automatically using as many digits as necessary to accomplish this. These systems can even perform analytical operations on non-scalars such as vectors, matrices and tensors having nonnumeric components.None of the commonly-taught programming languages is very relevant to the typical primary through university math curriculum, but computer algebra is relevant to most of that curriculum. Consequently, a vast opportunity for beneficial mutual reinforcement and cross-motivation between math and computer education is being squandered. This paper substantiates these claims, then proposes remedies.