I do sometimes tend to go on and on about common errors students make, such as dividing by zero or assuming what they are trying to prove. The Most Common Errors In Undergraduate Mathematics1 is a long-standing page written by Eric Schechter. It probably contains every error that I’ve ever seen (and more) so should be required reading by all maths students.
A few errors taken at random from the page, hopefully they will encourage you to read it in more detail
Everything is additive
Everything is commutative
I do like this one, since it gives the right answer via multiple errors
Oh and he has a go at teachers:
- Some teachers are hostile to questions. That is an error made by teachers. Teachers, you will be more comfortable in your job if you try to do it well, and don’t think of your students as the enemy. This means listening to your students and encouraging their questions.
Surely there aren’t many of these type of teachers about are there ?
1. Undergraduate here is an American term so the page is also highly relevant to A-Level maths students in the UK