Yes, and in the hands of a brilliant artist, mud and coffee stains can make a lovely painting. That does not mean art teachers should use mud and coffee as the only tool for teaching one how to paint.<p>Unfortunately, most high school math teachers are undertrained, underpaid, overworked, and pressured to focus on exams. The two-column proof is a crutch. It&#x27;s not the only awful part of high school math education, nor is it the sole bane of a student&#x27;s math education (I never said it was). But it is the most egregious example of bad math education.