On the papers that exhibited this error, I wrote comments such as

I followed up by addressing this error in class. I wanted to address the problem to everyone, since I believe that notational issues like this often actually reflect serious misunderstandings and not just sloppiness or laziness. I also just wanted to point out which version was correct, and which was incorrect for this particular question, since the entire class was about to retake the test and I had given credit for both versions.Careful! [imath]\sqrt{3+1} \neq \sqrt{3}+1[/imath]. They are different numbers.

One student tried very hard to take this warning to heart when she encountered a problem that was almost identical. On her retest, where the correct answer was [math]\frac{\sqrt{3}-1}{\sqrt{3}+1},[/math] she very carefully wrote [math]{\sqrt{3}-1} \neq {\sqrt{3}+1}.[/math]

*learning --- acquiring new knowledge, behaviors, skills, values or preferences. The knowledge need not be true, nor the behaviors useful, the skills efficient, the values internally consistent, nor the preferences socially accepted.