Let's start with a word problem:
Sally is on a road trip with her parents. She is making a list of all the different state license plates that she sees. So far she has seen 27 different state plates. How many more of the 50 states does she need to complete her list?
My student knew to subtract, but since the 27 came before the 50, she tried to do 27-50. Then, finding that she couldn't subtract 2-5, she borrowed from the ones column. Her final answer was 76, and she at least saw that it didn't make sense. Still, she maintained that she had done the work correctly.
I laughed and laughed at her unique math (she laughed too). This is the same student who insisted that 130 divided by 8 was 1 with a remainder of 780.
In fact, for a while all her long division was done on the "find an easy number to use and accept a huge remainder" method. Which means that she did 39 divided by 7 and got 2 remainder 25. While this is technically true, it's very bad math.
Another student was introduced to the concept of right angles. It confused her because she then wanted all other angles to be wrong angles. When I explained that there are also acute and obtuse angles, she was really lost. Besides this, if she was looking for right angles and picked one that wasn't a right angle, her answer was wrong. The angle, on the other hand, was not known as a wrong angle.
I don't know why I try to teach them math.