My Honors Students Start to Panic

I'm teaching the honors section of the gen-ed class. I'm pretty much following the standard syllabus for the course, but I'm going faster and covering more. And I'm assuming that my students know how to add fractions.* Most of the students in this class have succeeded in math classes because hard work has given them the ability to mimic calculations. Others are genuinely very good at algebra.

The regular version of the course has a tightly scripted unit on logic, culminating in the proof that there are more real numbers than there are natural numbers (it takes well over a week to build to this result). Today in the honors version I got to watch heads explode as I proved Cantor's Theorem for arbitrary sets. Their previous math classes have not been proof-based and have hidden any of the annoying details that lurk in foundational mathematics, and they were clearly uncomfortable with having to think deeply about what was going on.

Today they were clearly restless. We'll see how things go on Wednesday: I've told them that we're devoting the entire class to review in preparation for Friday's test. Their fear should calm down next week. We'll return to the familiar by proving the Pythagorean Theorem.


*Got an email from someone teaching two sections of the regular version. He put an adding fractions question on his midterm. Over 50% of the students in his classes could not add fractions with unlike denominator. Not rational expressions: rational numbers.