One of the most difficult barriers in Russian study is the disconnect between the words and pronunciations you learn in a book and those you hear in daily speech.
In English, we write "I am going to..." but we say "I'm gonna". We write "what do you think?", but we say "Whaddya think?" This same phenomenon happens all over the world in other languages, and it will confuse you if you try to learn from books and in classes.
In my super-fast year of Russian study, I took in a lot of vocabulary and had a lot of work to just learn the basics and reach a point where I could understand what I was hearing. This worked out well for me since most of my Russian friends here are former-Soviets, so they speak in a very educated and proper way. But on my trip to Tashkent, I found out that modern, young Russian-speakers use a lot of slang.
Fortunately, there is a fun resource that allows you to keep up with some of the slang people use when they speak, and do it in a fun way: Russian LOLCats. Just like the English phenomenon with which you are probably already familiar, it's a bunch of pictures of cute cats, made funnier by adding witty captions. The captions are supposed to be in the voice of the cat, so you get a good dose of slang.
One of the first words you learn in Russian is что (shto), which means "what". A lot of your subsequent study will be built upon this word. But when you find yourself among young Russian-speaking people, you won't ever hear that word. Instead, they say чë (cho).
In other regions (the Russian-speaking world is big!), instead of чë (cho), people say шо (sho) or що (scho).
And an interesting usage note, чë (or шо/що, etc) isn't only "what". It can also be used as "why"? As in the phrase чë так, which is literally a meaningless "what thus", but when you hear it, it usually means something like "why not?"
Another slang shorthand I picked up on was the shortening of тебе (tebyeh) into something more like те (tyeh), and тебя (tebya) into тя (tya).
You can also notice shortening of сейчас (seychass), meaning "now", into the shorter form щас (schas), or even ща (scha).
These Russian LOLCats can be an endless source of fun, of course. But they are also a great way to stay up to date on the way Russian is actually being spoken, rather than the stiff, scholarly way it is taught in books. And you can add the RSS feed to your Google Reader to get regular updates and practice your Russian.
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