Imagine if math was presented as the poetic beautiful thing it is in our “schools”. Here is a great article by Patrick Honner on how that would look.

The formula is as useful as it is likely to appear in the dictionary under “math anxiety,” and a quick look shows you why:

$$\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$

As intimidating as this looks, hiding inside is a simple secret that makes solving every quadratic equation easy: symmetry. Let’s look at how symmetry makes the quadratic formula work and how a lack of symmetry makes solving cubic equations (of the form $a{x}^3+b{x}^2+cx+d=0$) much, much harder. So much harder, in fact, that a few mathematicians in the 1500s spent their lives embroiled in bitter public feuds competing to do for cubics what was so easily done for quadratics.

Symmetry! Make it a part of your homeschool quadrivium. Read that whole thing – an elegant pleasure even for the “verbal” minded.