I once taught middle- and high-school teachers who wanted to get certified to teach math. I was a TA for a class in geometry (basically 8th or 9th grade Euclidean geometry.) I had an incredibly hard time explaining to them that “draw a circle with center point A” means that A goes in the middle of the circle, instead of on the boundary. As I recall, it took more than a week of daily problem sessions before they got that.
Of course, I may have been a bad teacher. But I was trying.
I find that very surprising; I thought of using “circle” to refer to just the boundary and not the interior as being primarily a mathematical usage… though I suppose not to the same extent as it is with “sphere”.
I once taught middle- and high-school teachers who wanted to get certified to teach math. I was a TA for a class in geometry (basically 8th or 9th grade Euclidean geometry.) I had an incredibly hard time explaining to them that “draw a circle with center point A” means that A goes in the middle of the circle, instead of on the boundary. As I recall, it took more than a week of daily problem sessions before they got that.
Of course, I may have been a bad teacher. But I was trying.
I find that very surprising; I thought of using “circle” to refer to just the boundary and not the interior as being primarily a mathematical usage… though I suppose not to the same extent as it is with “sphere”.