A Case of Crossover Mixed Analyses in Mathematics Education Research

• In Event: Innovative Mixed Methods Research Practices in Mathematics Education Contexts

Abstract

Johnson & Onwuegbuzie, 2004; Tashakkori et al., 2021). This perspective reflects what Goldkuhl (2012) calls “methodological” pragmatism; different combinations of methods (qualitative and mixed) are used to further the research goals.
The case being reported has a qualitative-dominant mixed methods design (Leech & Onwuegbuzie, 2009), with qualitative and mixed analysis happening sequentially. The source of data comprised the methods and results for two mixed methods studies reporting on the work of a larger project (Donovan et al., 2024; Johnson et al., 2024). The studies drew 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. There are two research questions (RQs): (1) How did this case integrate CMA and what purposes did those analyses serve, and (2) How could the use of an additional type of CMA complement and expand existing findings? To answer RQ1, two types of qualitative analysis were used: Data displays (Miles & Huberman, 1994), and the Description-Analysis-Interpretation triad (Wolcott, 1994). To answer RQ2, mixed analysis was used, to qualitize quantitative data reported by Author et al. (Year1b). The qualitizing drew on two goals put forward by Greene et al. (1989), complementarity and expansion of existing data.
Results of RQ1 revealed four empirically-grounded purposes for CMA in MER: (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. Results of RQ2 offered a fifth purpose: (5) to narrate significant associations between elements of different constructs. The findings illustrate how different types of CMA (i.e., quantitizing and qualitizing) can be used in sequence to advance MER goals.
A defining characteristic of CMA is the use of one tradition (qualitative, quantitative, mixed) to transform data from another tradition (Onwuegbuzie & Johnson, 2021). This transformation also can include a “re-transformation” of data that already has been quantitized or qualitized. This case study re-transformed quantitized data via qualitizing. The use of qualitizing brought voice to results emerging from quantitizing in ways that went beyond the original sources of qualitative data (i.e., narrations of associations between students’ forms of graph reasoning and the accuracy of their graph selections). Future studies using CMA can examine different orderings and purposes for the re-transformation.

Authors

• Heather Lynn Johnson, University of Colorado - Denver

• Courtney Donovan, University of Colorado - Denver

• Evan McClintock, University of Colorado - Denver