There are some good instruments (questionnaires/rating scales) available to assess quantitatively, but I am interested in qualitative assessment of learning environment of a classroom.
The 'World is your oyster'. You could choose any qualitative methodology for a topic such as this. The 'correct' methodology is more related to what your research question is, what you want to achieve and how you want to collect data.
Could you define what you mean by quality and from whose perspective: student, teacher, school administration, governing body/government, society?
In terms of students' perceptions of the learning environment there have been a number of doctoral studies that have used mixed methods (both rating and qualitative data). So some of these may be of interest.
In terms of quality. One of my doctoral colleagues is researching Quality from the perspective of the Soka education philosophy (Buddhist) in early childhood settings. She used a combination of individual and focus group interviews with teachers, parents and principals. She also did classroom observations and participated in guided tours of the various schools.
Thanks for your clarification. Yes, from quality, I mean students' engagement in and assessment of learning AND teachers' work/activities from an observer/researcher perspective. And thanks for the guidance and information on studies.