Translation

[Yell0w]

I'd say that word doesn't belong there. I would have said deeper understanding instead.

I think "deeper theories" would make more sense than understanding; i.e. expert teachers have different ideas about how to teach than lesser teachers

In the context of the whole study TheHumanDydra's explanation makes the most sense.

No, I think it's intentional, but as I said, used as jargon, technical terminology. The sentence "experts do differ in how they organize and use this content knowledge" implies to me "representations" is intended to mean "mental structures by which knowledge is organized." By "deeper" they mean those structures are more sophisticated.

There simply is no valid one-sentence translation into German, at least that I can see.

[TheHumanHydra]

There simply is no valid one-sentence translation into German, at least that I can see.

Even with all the words German can mash into one? Sorry, I don't know any German, so I can't really be of any more help. Good luck!

[flugauto]

I think in the given context "representations" stands for understanding.

"A major attribute of experts is their deep understanding of teaching and learning."

[Yell0w]

I think in the given context "representations" stands for understanding.

"A major attribute of experts is their deep understanding of teaching and learning."

Yes, but understanding can mean a lot of things and this is a scientific text. German has this stupid scientific language that I believe most Germans can't understand.
I personally can sometimes understand scientific texts better in English than in German.
"representation" in this context just didn't make any sense to me. In any way if I translated it like you suggested which is pretty easy I would still have to explain what understanding exactly means.

If I translate what I made out of it to English again:
"Expert teachers can utilize their knowledge - within the teaching and learning context - better."

I'd phrase it a little different if I had to translate the German sentence to English, this is pretty much a word to word translation.
I pretty much took the explanation
"A major attribute of experts is their deep representations about teaching and learning. Experts and
experienced teachers do not differ in the amount of knowledge they have about curriculum matters
or knowledge about teaching strategies. But experts do differ in how they organize and use this
content knowledge. Experts possess knowledge that is more integrated, in that they combine new
subject matter content knowledge with prior knowledge; can relate current lesson content to other
subjects in the curriculum; and make lessons uniquely their own by changing, combining, and
adding to them according to their students’ needs and their own goals."
and tried to turn in into a sentence. Thats what I usually fall back to if there is no appropriate translation: Take the sense and meaning and turn it into a new sentence.

Again, thanks for all the help, especially TheHumanHydra


EDIT:
I attached the whole text should someone wish to read it. It's a meta study proofing what your common sense tells you anyways: teachers are an important factor in the education of an individual.

[Bigger]

That reminds me of a philosophy class I took in College. I had a native-born German professor (with a pretty thick German accent), and he was reading a passage of Heidegger to us (20th century German philosopher). He read a few sentences to us (in English) - very dense stuff with several words that Heidegger made up to express a meaning there was no previous word for (German philosophers have a tendency to make new words). Then he giggled out loud and said "this doesn't make any more sense in the original German."