A case of crossover mixed analyses in mathematics education research

Crossover mixed analysis, which integrates qualitative and quantitative traditions, is fruitful for advancing mixed methods research. Employing a pragmatic theoretical perspective, we report a case study investigating the use of crossover mixed analyses in mathematics education research. Our source of data comprises the methods and results for two mixed methods studies reporting on the work of a larger project. The studies draw on the same data set, undergraduate student responses (N = 673) to a fully online, six-item measure of graph selection and reasoning for dynamic situations. The case we report has a qualitative-dominant mixed methods design, with qualitative and mixed analysis happening sequentially. There are two research questions: (1) How did this case integrate crossover mixed analysis and what purposes did those analyses serve, and (2) How could the use of an additional type of crossover mixed analysis complement and expand existing findings? Our analysis revealed four empirically-grounded purposes for crossover mixed analyses in mathematics education research: (1) to validate a researcher-developed measure, (2) to corroborate a theoretical framework of students’ mathematical activity, (3) to test a theoretically grounded model relating different constructs, and (4) to form associations between elements of different constructs. To complement and expand methods and results reported in the two studies, we qualitized quantitative data, to offer a fifth purpose: (5) to narrate significant associations between elements of different constructs. Our findings illustrate how different types of crossover mixed analyses (i.e., quantitizing and qualitizing) can be used in sequence to advance mathematics education research goals.