Going Beyond the Numbers: An Explanatory Sequential Mixed Methods Study in Postsecondary Mathematics

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

Abstract

Mixed methods research is a relatively new research paradigm that focuses on combining quantitative and qualitative methods in ways that balance the weaknesses of the individual paradigm, yet utilize the strengths of both (Creswell & Plano Clark, 2018; Greene et al., 1989; Johnson et al., 2007; Onwuegbuzie & Combs, 2011). In addition, mixed methods research can provide a deeper and richer understanding of complex phenomena, such as teaching mathematics in the postsecondary classroom. The study reported in this session will discuss an explanatory sequential mixed methods design, which is quantitatively dominant, to illuminate teaching methods and practices in the introductory postsecondary mathematics classroom (Bergin, 2018; Creswell & Plano Clark, 2018; Onwuegbuzie & Combs, 2011).
Participants were mathematics faculty who teach introductory mathematics courses in the U.S. and were recruited by random geographic selection. Data were collected in two phases and guided by an overall mixed-methods research question (RQ) and five sub-questions. The overall (RQ) was: How do college introductory mathematics faculty classify their own teaching methods and practices, and are they related to and/or informed by effective teaching practices established by the Mathematical Association of America (MAA) or the National Council of Teachers of Mathematics (NCTM)? Of the sub-questions, two were quantitative and three were qualitative in nature.
The first phase captured quantitative data through a national survey that included two inventories and demographic information from 113 participants from 37 states. One inventory measured general teaching practices, and the second measured general teaching methods (Trigwell et al., 2005; Wieman & Gilbert, 2014). Teaching methods were defined by Kilbane and Milman (2014) and the NCTM (2014) practices. The results of this phase addressed the two quantitative sub-questions, revealed several statistically significant relationships, and provided two regression models. The second phase was designed using an embedded multiple-case study to qualitatively follow up on statistically significant trends with four purposefully selected participants from the first phase (Creswell & Plano Clark, 2018; Yin, 2018). Qualitative analysis provided evidence for the three qualitative sub-questions, as well as preferences for teaching methods and practices. Overall, four themes were found to describe preferences for specific teaching methods and practices.
After the quantitative and qualitative analysis, the author “mixed” the data by quantizing qualitative codes and themes and quantitatively analyzing them. Joint tables and regression prediction equations were utilized to guide the data integration. By “mixing” the data, the author gained a richer and deeper understanding of why specific teaching methods and practices were preferred by faculty in introductory college mathematics courses. The author also found that inventory measures were consistent with initial findings in the first phase. This design method allowed the author to go beyond the statistically significant trends in the quantitative phase and themes in the qualitative phase through data integration and triangulation. The mixed data provided insights into the reasons behind the reported teaching methods and practices as well as the faculty’s preferences, which have implications for faculty professional development opportunities and support in the classroom (Elrod & Strayer, 2018; Olitsky, 2015).

Author

• Molly Christine Bowen, Baylor University