Utilitarian value of English:

Career: It might be that they don’t believe they can get a job where knowing some English can be useful. Prove them wrong. Try to find someone from their community.

Connecting & Communicating: Your task is easier if at least one of your students has a computer , preferably with a good internet connection, especially as IT has become the natural habitat for English.

Fun: Well, almost everybody likes music, films, TV and games.

BUT

If there is no technology available (no internet, no computers, no mobiles), English music and films are seen as a no-no by the elders, and if there is not a slightest chance of having a job where English might come in handy, don’t’ forget that classes can have intrinsic feel-good effect & offer escapism:

If they like your classes, if they feel happy, they will become motivated to learn. Praise them for their effort, not necessarily always just related to your English classes. Engage them, let them choose an activity or topic.

If their everyday life is dreary, you can offer them a way out, to keep (day)dreaming – this is what all children do. I know that some parts of the coursebooks  can make them feel down, such as units related to travel and holidays, as they are not likely to get away to the seaside in their lifetime.

I also teach some underprivileged children from rural parts, some of whom spend four hours commuting  every day plus they have to help their parents on their farms; some of these students come hungry to school (I always make sure to pass around some chocolate buiscuits before tests, so that they could concentrate), and many of them believe they have rather bleak prospects of ever finding a job other than toiling on the farm. But I think I have managed to build up their self esteem, and it is an excellent starting point.

Build good rapport with your students. Get to know them, what makes them tick; then interweave their personality and secret aspirations into your classes, even/especially when focusing on grammar points.

Get community support – get their parents interested in English. If you have the energy and time, why not get involved in a community project that would indirectly demonstrate the benefit of knowing English.

If the problem is overwhelming lethargy, well….

And never give up.

Cheers,

A

For primary aged kids, I'd recommend greatly increasing the amount of storytelling in class.

Find a great fairytale that they're unlikely to be familiar with and use it as the basis for a series of classes - one chapter per class.

Full stories might appear (or even really be) too difficult for them at first, but if you use a lot of pictures, gestures, sound effects, and perhaps some very occasional translation, they can be helped to understand the story well enough to become really interested in it.

You will also need to interrupt the stories at key points to involve the students by asking them their personal opinions (eg. Is the princess mean or nice?  Do you think princesses are usually like her?  What do other people think about her?) and predictions (eg. Will the dragon eat her, or will it turn into a knight and marry her, or something else...?) as well as inviting them to join in with gestures and sound effects (eg. "Then along came a wolf... What sound does a wolf make?... [kids: aarroooohhh]... Yes... Along came the wolk, arrooohhh." etc).

Once the students get hooked on the first chapter, they'll be dying to hear to the next chapter in the next class. 

Just don't overdo the 'teaching'.  Treat it as a storytelling class rather than an English class, and let the students' subconscious ability to learn do the work.

You can explain that if they want to change their situation they should learn english which can then help them to communicate with the wider world and that gives them an influence over their future.