I didn't read everything here but I may have a story that relates. Recently my dd10 took a unit pre- test on angles and lines. They gave it back to her with the exact same post test to compare to two and to see how much she learned. She came home a bit confused. The pre test asked her to draw a 90 degree angle. My DD drew a Right angle using Line Segments. Made the three points, labeled them A, B, and C and made the little right angle box inside the angle. She got the problem wrong because she didn't use arrows on her lines to represent lines.
She said to me "but an angle is an angle even if it is made with line segments, right?" I emailed the teacher to let her know that DD was confused and the response was that since my DD showed profinciency on the post test she is not concerned about any misunderstanding.
Now this woman is only a Math teacher. I have never had Math after highschools and am not "gifted" but I really don't believe our educators are educated. Either that or they simply don't care. Or maybe they don't have time to care. I don't know.
