The following are probably not exhaustive, but at least will constitute a start in language-learning and study abroad research using Q methodology:

Bang, Hyeyoung, & Diane Montgomery (2013, July/August). Understanding international graduate students’ acculturation using Q methodology. Journal of College Student Development, 54(4), 343-360.
Collins, L., & Angelova, M. (2015). What helps TESOL methods students learn: Using Q methodology to investigate students’ views of a graduate TESOL methods class. International Journal of Teaching and Learning in Higher Education, 27, 247-260.
Pereira Silva, L.L. (2012). Cognições de professores e formadores sobre pesquisas relacionadas ao processo de ensino e aprendizagem de LE—um estudo Q [Cognitions of teachers and teacher trainers
about research on the process of teaching and learning a foreign language
A Q-methodology study
]. Master’s thesis (Linguistics), Universidade Federal de Uberlândia, Brazil.

Sartori, A. (2013,). Perceptions of EFL students and teachers on vocabulary acquisition: A Q study. Doctoral dissertation, Department of Applied Linguistics, Language Studies Institute (IEL), University of Campinas (UNICAMP), São Paulo, Brazil.
Sell, D.K. (1980). Attitude change as a result of living and learning in another culture: The Kent State in Mexico program. Master’s thesis (Political Science), Kent State University.

Sell, D.K., & Brown, S.R. (1984). Q methodology as a bridge between qualitative and quantitative research: Application to the analysis of attitude change in foreign study program participants. In J.L. Vacca & H.A. Johnson (Eds.), Qualitative research in education (Graduate School of Education Monograph Series) (pp. 79‑87). Kent, OH: Bureau of Educational Research and Service, Kent State University.

Sell, D.K., & Craig, R.B. (1983). The use of Q methodology to investigate attitude change in American students who participate in foreign study programs: A review of the literature. Operant Subjectivity, 7, 14-29.
Stollery, R.L. (2013). A Q methodological study of the support valued by students with English as an additional language. Doctoral thesis (Educational and Child Psychology), University of Sheffield, UK.
Taba, H. (1953). Cultural attitudes and international understanding.. New York: Institute of International Education Research Program.
Wanjau Mutai, F.W. (2007). Perceptions of current and prospective Kenyan international students of the Kenyan international student lifestyle in the United States. Doctoral dissertation (Education), Kent State University.
Yuan, W. (2010). Investigating international student perceptions of adjustment through Q methodology. Intercultural Communication Studies, 19, 235-252.

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