English is an international language which people from all over the world learn in order to communicate with each other. Accuracy and Fluency are two factors which can determine the success of English language students in the future.
Essentially accuracy is the ability to produce correct sentences using correct grammar and vocabulary. On the other hand, fluency is the ability to produce language easily and smoothly.
Accuracy is relative. A very young child isn't capable of the same level of accuracy as an adult. The child will make mistakes and misuse vocabulary.
Teachers who concentrate on accuracy help their students to produce grammatically correct written and spoken English, ideally aiming towards the accuracy of a native speaker of similar age and background.
The emphasis in the classroom will be on grammar presentations and exercises, reading comprehension and suchlike.
A fluent speaker, on the other hand, may well make grammatical errors but will speak or write efficiently (without pauses). They will be able to converse freely and talk with native-speakers about many different subjects.
Fluency generally increases as learners progress and become more comfortable using the language.
Language teachers who concentrate on fluency help their students to express themselves in English. They pay more attention to meaning and context and are less concerned with grammatical errors.
Typical fluency activities are role playing and more communicative activities where English is used as a medium of communication rather than an end in itself.
Taken as a given that students' needs should always dictate what you teach them, the question of whether it is more important to work on accuracy or fluency in the language classroom remains.
Many teachers believe that fluency is a goal worth striving towards only with students who are at a fairly advanced level. Other teachers, strong in the belief that the learning of a language is about communication, feel that fluency should be the main goal in their teaching and that it should be practiced right from the start.
More traditional teachers tend to give accuracy greater importance; more liberal teachers tend towards fluency.
Often a rigid educational system where tests and exams are the focus, will have students (and their traditional teachers) believe that language accuracy is what matters most, and giving the "correct" answers often becomes an obsession. Students who have been taught this way can complete any grammar gap-fill you care to give them, but will struggle to order a coffee in a real English speaking situation.
On the other hand, a more communicative approach will produce students who can converse at length on almost any subject but could well make horrendous spelling and grammatical mistakes in their writing.
In the end, however, it really boils down to the the needs of the student.
As far as teaching methodologies are concerned, very broadly speaking the communicative approach is the one that favours fluency the most, while the audio-lingual and grammar-translation approaches favour accuracy.
Typically, at beginner level when the students don't have enough language to worry about fluency, teachers tend to focus on accuracy.
This carries on through to pre-intermediate when fluency activities like discussions and debates are introduced.
Later, when the students are reasonably independent language users, a mix of accuracy and fluency is used, with the focus shifting to fluency as students advance.
One important point to bear in mind, however, is that too much bias one way or another is not good. Accuracy without fluency is not useful in the same way that fluency without accuracy is also not useful. A good mixture - biased towards the needs of the student - is the ideal way to go.
Excelling in tests represents but a small part of language competence and a lot of students' needs relate to performing in situations that are non-exam focused. However, English competence exams do drive a lot of the ELT industry and contribute to perpetuating the supremacy of accuracy over fluency (for example, tests like IELTS and TOEFL are very much focused on accuracy).
Benchmark testing on the other hand is a great example of tests that are not accuracy based (though a higher degree of accuracy obviously accompanies a higher level of fluency).