Ask a class what $(a+b)^2$ is and some will answer $a^2 + b^2$. Ask what $\sqrt{9 + 16}$ is and someone will say $3 + 4 = 7$. These errors are so common, and so similar from one school to another, that they cannot be chance. They follow a rule. The rule that stretches too far In 1982 the American researcher Marilyn Matz studied the algebra errors of high-school students and proposed that many of them come from false rules (malrules) built out of true ones. The most productive of all is the distributive law: