I'm wondering if ASL is learned in something of the same way that students of non-phonetic languages learn. For instance, English, Spanish, Italian, other European languages, are all phonetic languages. Once you learn the phonetic rules, you can sound out most words (although English complicates things with having so many spellings for the same sound).
Chinese is not phonetic. Small children spend hours practicing and memorizing the characters that make up the language. There is no way to know how a word is pronounced just by looking at the characters.
Is ASL something like that? Each word has its sign, but you have to memorize the signs, since there is no way to figure out what a sign means by its shape alone?
Chinese ideograms are not the Chinese language. In fact there is no Chinese language, which is why the ideograms exist. China, like Europe, is made up of many differing peoples, each with their own language, customs, etc. The two main ones are Mandarin and Cantonese. I think I read that there are 300 different languages.
The idea of the ideograms was to develop a system of writing that could be read and understood by the speakers of all the languages. A very interesting and useful idea.
To address something you are not asking directly, but may be alluding too.
There are connections in ASL that are absorbed internally and seldom if ever understood overtly, just as in English.
For instance in English you have the "i" sound. High, light, bright, rise, sky -- Which all refer to those things that are upward, bright, and bountiful. Easy to see and easy to understand.
Then you have that set of sounds that tend to represent all things low, dark, and mysterious. Down, Dark, under, below -- Ah, Ow, Un, and the minute you hear words with those sounds in them you tend to think in terms of lower, less, dark, and mysterious.
Edgar Allan Poe was a master of such sound usage:
"Once upon a midnight dreary
While I pondered weak and weary"
The same is true with the horizon in ASL.
All things above the horizon line or rising above it are bountiful, bright, clear, understandable. All things below or falling are dark, suspicious, mysterious, unknown.
The sign for analysis is literally "digging in the dirt."
Watch some of Clayton Valli's ASL poetry.