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For a major article in the history of mixed methods development:

Greene, J. C., Caracelli, V. J., & Graham, W. F. (1989). Toward a conceptual framework for mixed-method evaluation designs. Educational Evaluation and Policy Analysis, 11, 255-274. doi:10.3102/01623737011003255

Abstract: In recent years evaluators of educational and social programs have expanded their methodological repertoire with designs that include the use of both qualitative and quantitative methods. Such practice, however, needs to be grounded in a theory that can meaningfully guide the design and implementation of mixed-method evaluations. In this study, a mixed-method conceptual framework was developed from the theoretical literature and then refined through an analysis of 57 empirical mixed-method evaluations. Five purposes for mixed-method evaluations are identified in this conceptual framework: triangulation, complementarity, development, initiation, and expansion. For each of the five purposes, a recommended design is also presented in terms of seven relevant design characteristics. These design elements encompass issues about methods, the phenomena under investigation, paradigmatic framework, and criteria for implementation. In the empirical review, common misuse of the term triangulation was apparent in evaluations that stated such a purpose but did not employ an appropriate design. In addition, relatively few evaluations in this review integrated the different method types at the level of data analysis. Strategies for integrated data analysis are among the issues identified as priorities for further mixed-method work.

For information on the dialectical pluralism worldview in mixed methods:

Johnson, R. B. (2017). Dialectical pluralism: A metaparadigm whose time has come. Journal of Mixed Methods Research, 11(2), 156-173. doi:10.1177/1558689815607692

Abstract: There has been much debate about the role of paradigms in mixed methods research. In the face of past calls for each researcher to operate within a single paradigm, it turns out that some researchers/practitioners find many positive features in more than one paradigm. This “multiparadigmatic perspective” used in mixed methods research needs a systematic framework for the practice of engaging in difference. Also, individuals committed to a single paradigm need a philosophical/theoretical framework for working in multiparadigmatic teams. This article provides such a framework. It is a metaparadigm, and it is labeled dialectical pluralism 2.0 or more simply dialectical pluralism. The word “pluralism” refers to the acceptance and expectancy of difference in virtually every realm of inquiry, including reality, and the age-old word “dialectical” refers to the operative process which is both dialectical and dialogical. Dialectical pluralism provides a way for researchers, practitioners, clients, policy makers, and other stakeholders to work together and produce new workable “wholes” while, concurrently, thriving on differences and intellectual tensions.