When dh was in elementary school, his teacher one year did a lesson on light. She turned off the classroom lights and closed the blinds, but left the hallway door open. "Look, children," she said. "We can still see. Light is coming in through the door. But look! That light is coming into the hallway from windows that aren't in a straight line with our door. Therefore, light bends!" Somehow she had never come across the idea that light is reflected off of surfaces. Instead she thought light turned corners. I doubt that this is an totally unusual belief for elementary school teachers (and other non-science oriented people) to hold. A lot of people probably haven't really thought about it much. That doesn't tend to be a problem unless you're then passing on this "knowledge."
My real point in telling this story is that dh has a Ph.D. in physics now, and was strongly interested in science even back then. He clearly remembers this day. I believe he actually knew at the time that she was wrong, but I can't remember if he argued with her or not. It's hard to picture him not arguing about it, but I think that it's certainly true that kids who are very interested in science (or math, or any other content area) can probably benefit from learning when it's helpful to try to have a discussion about something with a teacher and when it's not. It can be so hard, because especially to kids, it can seem like, "Well, *I* find this fascinating. Doesn't everyone else?" It also depends a lot on the teacher. I think discussions at home about how to decide whether it seems better to drop something during a classroom discussion and then pick it up again at home could help. You could even share this cartoon
with her. I'm sure it's familiar to a lot of us.
And in terms of "She's wrong, so she needs to learn to cope with being told that," well, sure, if the OP's dd is really sensitive to being wrong, it would be great for her to find ways of coping with that. At the same time, though, even if she had been wrong beyond the shadow of a doubt (which is clearly not the case, considering the length of this thread
), it really wouldn't take a lot of insight for the teacher to realize where she's gotten this idea. I would expect that the teacher's been exposed to E=MC^2 at some point. Wouldn't it be more helpful to respond in a way that honors the child's attempt to make connections and figure things out? Isn't that the whole idea behind "show your work"?