The question of standard English is a thorny one for those of us who work with adult learners, and you will hear many opinions about how we should teach students who come from communities who use non-standard English.
Standard English is the language spoken by people who have been educated in the mainstream system. That means it is the language invented by people who have power, who are wealthy and who are white. It is by definition not the language invented by our students.
Standard English is not “correct” in itself, and in fact is constantly changing. For example, it is now considered correct to sometimes split an infinitive, and in Canada most people manage to get through days, weeks, and even months, without using “whom.”