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For English, this website has a range of songs and audio lessons, on numbers, comparisons, time, metric system, countries, alphabet, simple business questions, which you can download and practice. If you teach English, there are notes for teachers.
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For the following languages, you can start with numbers on LanguageGuide.org. They teach the numbers 0-102 or 0-21, depending on language.
For 30 other languages, start with numbers 1-9 on Book2.de. (Recommendations here are honest. I do not take commissions or fees from any program reviewed.)
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If you want a language not on Book2, check the List of Languages to find reviews of self-teaching courses in hundreds of languages. The List rates self-teaching courses from 1 to 5 stars; more stars are given for programs which teach beginners good pronunciation and a lot of material quickly and well. If you want to analyze the list, you can download it as a spreadsheet in the free format of Open Office (.ods).
Many courses start with social conversation, but the Foreign Service Institute reports that social conversation is the hardest topic, with many rules to memorize. Therefore this site suggests you start with numbers, which are an easier route to good pronunciation and broad understanding.
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Then choose any other topics which interest you from Language Guide or Book2, Both are free. Language Guide is very good since it is visual, so you learn new words from native speakers with no distractions from your own language. They show pictures of food, technology, office items, government, geography, parts of the body, clothing, etc. You mouse over the pictures to hear each word, as often as you need to. Book2 has more words in more languages.
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If you can afford $25-40, try Transparent (in 76 languages), or at least a month of Pronunciator (in 60 languages). These listen when you speak into a headset or microphone, so they can score your pronunciation. Transparent has the best graphs of your pronunciation and is especially helpful for tonal languages like Chinese. Pronunciator lets beginners learn from pictures, with no distractions in your own language, and they have more vocabulary, Pronunciator conjugates 100 verbs, and it lets you choose topics which interest you. Transparent has some grammar, and you can keep using it without a monthly subscription.
If you want to learn through headphones without a computer, borrow a computer to download MP3 files from any of the courses (such as Book2) with downloadable audio, shown with ► or > in the list of "Best Courses". Then copy the MP3 files to your player, and you can use them when you want.
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Many websites have free introductory examples. Use them to hear different voices and speeds, and see which give you the best help at each stage in your learning. Try all the free sites and the free samples available from paid sites.
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You can start quickly with the best of these courses. Expect to study 600-2200 hours before you reach full fluency. If you studied 4 years of language at school, you had 400-480 hours of language class, only a start. Or in an hour per day for a month before a trip, you will spend 30 hours, enough to learn some friendly words for various situations before switching to English. You will still have a noticeable accent, but after 30 hours you can be understandable.
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The reviews here cover sites which teach numerous languages. See "All Languages" for links to other sites which teach only one or a few languages. Separate articles discuss common omissions from the courses, and the optimum time needed to learn different languages.
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Scoring Your Pronunciation
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Several sites have computer analysis to score your pronunciation. This is a very valuable tool to improve your accent, giving feedback more patiently than any human.
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Talk to Native Speakers
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Several sites help you find people who want to learn your language, and are native speakers of the language you want to learn. Talk to them regularly in each language, so you both practice.
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MP3 Learning away from a Computer
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If you want to learn away from a computer (while driving, walking, etc.), this site's List of Language Courses shows which sites have downloadable MP3 or audio CDs in the language you want. Most cars since 2005 have plugs to connect an MP3 player or thumb drive to the car's stereo, or you can get adapters to connect to older cars. (A computer person can also convert MP3 files to an audio CD, and play it in a CD player.)
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Most audio files have pauses for you to repeat the words. Language Guide, Book2 and some others (shown in the List) lack pauses. Arguelles says it is better to use these recordings without pauses. He recommends speaking along with the native speaker, at about the same volume, so you can compare your voice to the native speaker (shadowing). People learn songs this way, so try it for languages. He says to walk with good posture while speaking so your voice is clear. At first you can only speak sporadically, until you hear phrases enough to say them with the native speaker.
Some lessons use a "backward build-up" as described by the US State Department: "learn the longer sentence by repeating small parts of the sentence, starting from the end and working toward the beginning."
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Intermediate Learners
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While this site is focused on beginners, the List of Language Courses identifies which language programs may be helpful to intermediate learners. Some programs are good for both beginners and intermediate: starting at the beginning and covering a lot of ground. Others are primarily for beginners, not covering enough to help intermediate learners. Some are too hard for beginners, but good once you learn the basics elsewhere.
This site has songs in English, and YouTube has videos of the words and music of many songs in Arabic, Chinese, English, French, Indonesian, Russian, Spanish, etc.
Next: Omissions