Comment by ndriscoll
Given that most math teachers haven't studied algebra/likely haven't seen the definition of any of these things, and the distinction is not relevant when discussing rounding, I highly doubt that the teacher was making that distinction, or even aware it exists. More likely, the teacher was making a distinction that does not exist, which only confuses students.
In any context that a child is working in, 6/2 and 3.0 are a whole numbers. If the teacher says otherwise, they are wrong. Just because the teacher wants to teach a lesson doesn't mean that lesson is actually correct. The teacher is just confused.
If they weren't confused, it would be highly inappropriate to go into that level of detail with anyone other than a curious gifted kid that's asking questions that are years ahead of a normal curriculum. So much so that it's beyond the level of knowledge expected of a schoolteacher.
You also wouldn't mark it wrong because the entire point is to define things in a way that makes the distinction go away. Even after that distinction has been presented and is front-of-mind, you still generally write down whatever representative is convenient.
It's either literally wrong, philosophically/pedagogically wrong, or both.
> most math teachers haven't studied algebra
Pretty sure all teachers I had even in elementary school studied at least high school level algebra. In middle school and above they all had masters or better in mathematics.
> the distinction is not relevant
> I highly doubt that the teacher was making that distinction, or even aware it exists
> the teacher was making a distinction that does not exist
The distinction both exists and does not exist. Incredible.
> it would be highly inappropriate to go into that level of detail
The detail of a thing that does not exist, right?
> it's beyond the level of knowledge expected of a schoolteacher.
Right, the teacher is wrong because you wouldn't expect the schoolteacher to be smart enough to be right about it.