My suggestion, find her obsession, whatever it is, all of those with aspergers have "extreme absorption" of a certain subject. Meaning they will learn it with ease and amazing speed, luckily math and "LITERAL" language was mine, I could talk like a full grown adult at the age of 2, selectively mute until around the age of 8, I taught myself how to add, subtract, multiply and divide before I was in the first grade.
Also you should know that we will also eventually learn everything we need to. I was tested a while back and had a 98% chance of being Aspergers, got tested recently and now its 94%
My doctor said I was text-book Aspergers fitting every symptom to the T and I didn't really have any major problems.
To be honest we would all need quite a bit more information on the child in question in order to answer questions, such as what tendencies does she have? Does she have tendencies of both AS and autism? Also there is a good chance that either you or the other parent can, since aspergers usually runs in families, communicate well with the child. Also if shes anything like me then you should try to get the child reading books, books of any kind. At around 8 I was reading around 150 page mystery books, at around 10-15 I was reading the harry potter/wheel of time/redwall/keys to the kingdom/seventh tower series.
If she seems to be staring off into space a lot then she's probably completely lost in deep thoughts, it used to happen to me quite often, getting lost in my own little world of thoughts. The problem with this is that it may take quite a bit of coaxing in order to get us to come back to reality, the books basically allow me to enter my own little world without being completely lost in thought, as such its easier for me to break away and talk to people and then enter straight back into it without losing pace. Think of it as a catalyst or a bridge to bring us back to reality more quickly.
Just remember all AS and autistic children are different and what works for one, or what works for many may not work for your child.
Think of it like this, the army generalizes (like normal people) so that every soldier can perform at basic level on everything and the marines are highly specialized in whatever field they are in (AS/Au)
An AS obsessed with rifles could probably hit a dime at 1000 yards and then when they try to hit a pumpkin with a handgun they'll miss at 15 yards.
One last thing, we will also learn differently, I'll use another gun example (you can tell I went to the shooting range today can't you?) If 10 normal people shoot 10 guns, chances are all of them will be better at one particular gun than all the others while still being able to use the others.
If 10 Aspies shoot 10 different guns chances are whichever gun the AS person likes the most, they are going to shoot very well with it even if its their first time shooting, on the other hand, if they show little to no interest in the other guns, well..... let's just say the broad side of a barn is just barely big enough. If you can find what works with her then you can run with it finding out exactly how she learns is what will take time.
Just keep it simple, step by step, broken down explanations are what work for me.
and for heavens sake don't use sarcasm until you know she fully understands it and can recognize it because if you say "GOOOOOD JOB" with sarcasm then if she is classic AS then she WILL think she did a good job. Every AS in my family has had horrible trouble with sarcasm and they take things literally all the time so I believe thats fairly common.
Last thing for real this time, remember if anything we say doesn't fit with your childs problems feel free to ignore it, as with all others we do have similarities but we also have our differences. Also if you do an IQ test, don't take the score seriously, the test is based off of our weakness during 9/10 of it, communication. A test based off of your weakness won't show your strength.
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Never argue with an idiot because they will only bring you down to their level and beat you with experience.