Translation:Would you like to understand Chinese history?
First of all, 更了解 is good Chinese, most commonly used when you want to compare one person's knowledge about X with either another person's knowledge about X, or the same person's knowledge about Y:
你更了解中国的历史 = You know more about Chinese history (e.g. than I do / than Chinese literature)
I wanted to say 想更了解 is bad Chinese, but I should take that back. First, there are 371k results for it on Google, and some of them sound just fine to me:
我只是想更了解自己。 = I just want to learn more about myself.
想更了解對方就問他喜歡看什麼片！ = If you want to learn more about that person, just ask him what movies he likes to watch!
I frowned on the one below, which follows the same pattern as 想更了解中国的历史:
想更了解霍金的思想，可以阅读哪些书？ = If I want to learn more about [Stephen] Hawking's ideas, which books should I read?
But this is purely my intuition, and I'm not so sure about it now, especially after another native speaker told me that 想更了解中国的历史 sounds just fine to her.
Nevertheless, in all these sentences, you can replace 想更了解 with 想进一步了解, which is 100% good Chinese.
They are all acceptable to duolingo, which means they are spoken by a population of native speakers, or is idiomatic to them. However, there remains the question of whether or not it is accurate, standard Chinese.
All the examples given in this comment-thread are acceptable. Whether or not they are "accurate" and "standard" （标准） is harder to say for sure, since we are all not language teachers with the latest information from the Language Authority Boards or howsoever it is called, and even so would like only be expert on one such Board, e.g. from China or Taiwan, hence at the risk of perhaps delving too far in what is, after all, meant to be a language learning app and one for preparation of language exams, I'll reiterate that what is considered good can be either acceptable/idiomatic and accurate/"standard" or one of them. In duolingo, I'd say the difference doesn't matter so if you've read this far, thank you and apologies if I'm going too much into semantics and such.
P.S. You're most welcome @PeaceJoyPancakes.
I think it's implied in at least one of the senses of 了解, which is essentially "to find out (about)".
But perhaps it's not strictly necessary here.