Pronunciation involves far more than individual sounds. Word stress, sentence stress, intonation, and word linking all influence the sound of spoken English, not to mention the way we often slur words and phrases together in casual speech. 'What are you going to do?' becomes 'Whaddaya gonna do?' English pronunciation involves too many complexities for learners to strive for a complete elimination of accent, but improving pronunciation will boost self esteem, facilitate communication, and possibly lead to a better job or a least more respect in the workplace. Effective communication is of greatest importance, so choose first to work on problems that significantly hinder communication and let the rest go. Remember that your students also need to learn strategies for dealing with misunderstandings, since native pronunciation is for most an unrealistic goal.
A student's first language often interferes with English pronunciation. For example, /p/ is aspirated in English but not in Spanish, so when a Spanish speaker pronounces 'pig' without a puff of air on the /p/, an American may hear 'big' instead. Sometimes the students will be able to identify specific problem sounds and sometimes they won't. You can ask them for suggestions, but you will also need to observe them over time and make note of problem sounds. Another challenge resulting from differences in the first language is the inability to hear certain English sounds that the native language does not contain. Often these are vowels, as in 'ship' and 'sheep,' which many learners cannot distinguish. The Japanese are known for confusing /r/ and /l/, as their language contains neither of these but instead has one sound somewhere between the two. For problems such as these, listening is crucial because students can't produce a sound they can't hear. Descriptions of the sound and mouth position can help students increase their awareness of subtle sound differences.
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