One of the most well known approaches to adult education comes from the Brazilian teacher Paulo Freire. The Freirean approach to adult literacy education bases the content of ABE or ESOL language lessons on learners' cultural and personal experiences, encouraging a participatory model and rejecting a "banking" model.
If you're interested in learning more, read his classic work Pedagogy of the Oppressed and then the overview of "The Freirean Approach to Adult Literacy Education" for some perspective on how the ideas apply to the BPL's work with adults and English learners, and adult literacy more generally.