This challenging study, which took 3 years to complete, demonstrates the feasibility and benefits of synthesizing qualitative and quantitative data in an exploratory, classificatory tradition of inquiry. Also, in the spirit of Becker’s advice “to think about your research while you’re doing it," this case provokes discussion of how measurement innovations and forms of data analysis that are seldom used in one’s own field can yield new discoveries. We argue that a measurement innovation (within-person calibration of relative priorities in questionnaire responses) and some computationally intensive tools for pattern detection and data visualization (dissimilarity measures, cluster analysis, and multidimensional scaling [MDS]) enabled us to detect and make sense of some important but initially hidden subtleties in the literacy-learning philosophies of the participants in our study. Also, we celebrate the benefits gained by returning to interviewees with an opinions-gathering, opinions-juxtaposing questionnaire compiled in part from all interviewees’ previous statements. The education of children born in Taiwan to an immigrant mother and a Taiwanese father—5% of newborns in 1998 and five times that 10 years later—had been surrounded by controversy and public attention. Despite headlines and presumptions of educational deficiency, surprisingly little was known about the educational thinking, activity, and resources of adults in such families. The first author, under the supervision of the co-author, planned this PhD research project in 2009 to help fill this gap in knowledge and thereby improve mutual understanding. Specifically, she sought to gain a better understanding of the literacy-learning philosophies of three adult groups: immigrant mothers, their husbands, and their children’s teachers. After comparing two plausible methodological alternatives (interpretivist, Verstehen-seeking qualitative methodologies and survey research), we concluded that a mixed-methods research approach that combined the two was best suited to achieve the research goal.