Numbers and math - learning to think in another language
This is a general enough question that it applies across languages, although it is French in particular that I am stumbling over. But the same applies for me in Spanish.
When listening to another language I work really hard to avoid translating, instead simply trying to think in the language and understand in that language.
However, I simply do not seem to be able to do that for numbers except for the most basic (~ under 10). Essentially, I always convert them to English in my head, particularly to manipulate them in any way. That in turn causes a little bit of a break in my comprehension, I will often lose the thread of a passage right there. I can't even find a way to try to improve this.
Any ideas or experience out there?
I don't know if this is true, but apparently counting and calculating are among the things people do in their native languages the longest. Even fluent speakers tend to unconsciously switch languages for it. My own experience matches this; while I don't find counting hard, I am almost incapable of doing even the easiest algebra in languages other than German or English. I get around it by not converting to a different language but into numbers, that is to say I imagine the written numbers. It doesn't cause any confusion between languages and is also a little faster. Hope that helps.
I use English, which is a foreign language for me, pretty much everywhere and the whole day, every day. My job (in English) even includes quite a bit of numbers, but I still find it hard to use English when counting or especially calculating something, I always switch to my native language for that. I don't know how to stop doing that but since it's usually not a big problem, I'm not really trying to fix it. It really only becomes a problem if I have to explain a calculation in English. When I'm just thinking about it, in a way I don't think about numbers in any language, I think about them as numbers. For example, if I'm thinking about number 125, I think of it as 125, not as hundred twenty five or sto dvadeset pet or hundert fünf und zwanzig. As you can see, I don't even know how to write them properly.
Like the others have said I think numbers pose a special difficulty. I don't necessarily have to translate phone numbers and the like into English to understand them, but I often have to repeat them to myself in the language I've just heard them in (which means I often don't remember for a phone number said rapidly) so as to process them and get the numeric values they correspond to "show up" in my head so as to write them down, or whatever else.
I find german numbers particularly tricky as you have to rearrange them to understand them, as you do some of the French ones of course. And as for Danish... Anything other than single word numbers put a stumbling block into fluid listening or reading as a break is needed to translate, especially at first. Oddly quantity words like those for some or every cause similiar pauses in my fluidity of understanding. I think it may be about the degree of precision they require. You only need a sense of what an adjective means but a number or quantity you need to pin down more firmly to keep track of what is going on. And of course there are an infinite number of possibilities. You learn them in a different way than other words, as a formula to be assembled rather than a chunk to be remembered. A bit like verbs but with far more variants. No wonder the processing is different. I will try making sure to visualise digits instead of english words when I translate, that might well speed it up.
I am going to experiment with doing an elementary school level math course for Francophones, but I suspect it will be very hard to get out of the translation rut. The first step may just be having the translation become nearly instantaneous for numbers below say 1000.
It is really an interesting point that shows how differently the brain processes different activities. By vivid contrast, my real breakthrough in Spanish came playing football as the only English speaker. I simply did not realize I was using and understanding Spanish until a teammate complimented me on how much I had improved in a month. The difference must be math requires a very high level of abstraction, sport almost none.