Numbers are hard in Chinese because you don't understand them in English
Numbers are always a stopping point when learning foreign languages.
The first reason for this is that they fall into a category of things that is very hard to memorise: sets. Any type of set is hard to learn compared to discrete units of other information.
There is another reason numbers are hard to learn though, which is that you don't even understand them in your native language.
This isn't me saying that you're stupid. The issue here is that we don't actually understand numbers in the way we think we do. We think that we're capable of mentally handling concepts like “forty-two”, “one hundred” or “six-hundred-and-seventy-four”, when really we just deal with rules and abstractions.
To illustrate this, how many dots are in the square below?
If you said ten thousand, well done. But even if you did spot that, did you do just see and understand ten thousand, or did you do it by assessing the sides of the square, and then calculating 100 * 100?
Very few people, if any, can see a number like that. Most of us can immediately recognise one, two, three, perhaps four and five objects.
Beyond that, even if we won't admit it, recognising quantities is a case of breaking them into smaller groups and remembering how the groups add together. Seeing seven is a case of seeing three and four for most people.
Numbers are a poem
Even if we like to think that we can mentally hold the concept of, say, “eleven”, integers are actually no more than a convenient mnemonic for counting things in sequence.
Knowing the sequence 1,2,3,4,5… and how it continues indefinitely doesn't mean that you can actually see or feel all those numbers. It just means you've memorised a poem that makes it easier to count things and to place quantities in a sequence.
Once we know the sequence, we learn all sorts of other operations and rules for working with items in the sequence. I know that ten million is ten times one million, but I don't have any real grasp of those quantities.
To be clear, I'm not talking about maths here. I'm talking about how we often mistake mathematical understanding and ability for an intuitive understanding of numbers.
More accurately, we don't distinguish numerals and numbers. That is, we often don't distinguish numbers in language from numbers in mathematics.
This whole point is best illustrated by the fact that some languages do not have numerals. Numbers are fundamental mathematically, but they are not fundamental in human cognition. They are an abstraction that we have created to understand the world (an abstraction that has led to incredible development and insight).
Some languages do not have numerals because the speakers of those languages don't need them. They might treat the objects they encounter as unique and recognise them individually, rather than keeping track by counting.
What has this got to do with learning Chinese?
Coming back to my original point, this can be quite a revelation when you're struggling with interpreting numbers in a foreign language, or with expressing them.
Hearing and understanding “一千万” is hard at first because you're trying to convert it into “ten million”. You're trying to convert it into “ten million” because you think you need “ten million” in order to _understand _the number.
If the above is true, though, you never understood “ten million” in the first place. It's just a placeholder in a giant sequence that helps you keep track of numbers.
By this logic, 一千万 makes just as much sense to your brain as “ten million” does. There's no point converting; just remember 一千万.
When you're listening to Chinese and a speaker says some large number, there's no point trying to figure out what the number “is" in English. You'll have no more concept of the underlying number in English than in Chinese.
A better goal is to build up the same numerical operations knowledge you have in English in Chinese.
The big problem is that most courses, textbooks and so on test your comprehension of numbers by getting you to translate them into your native language. Unfortunately, translating numbers from Chinese into English can often require a fair bit of mental arithmetic due to things like 万 and 亿.
I'd say you're better off just working with Chinese numbers in Chinese and keeping mental arithmetic clearly separate as a skill. It's a nice skill but it shouldn't be part of any assessment of your Chinese.
Similarly, expressing numbers in Chinese is often hard because you need to do maths if you haven't already memorised the number.
Again, I think it's better to just memorise important large numbers in Chinese and stop pretending that you can convert easily between English and Chinese just because you know the number.
What do you think? Is this totally obvious? Or is it total rubbish?