Q methodology as an integrative approach: bridging quantitative and qualitative insights in a mixed methods study on mathematics teachers' beliefs.

Abstract

This study explores the beliefs of pre-service mathematics teachers regarding the teaching and learning of mathematics. We employed a mixed methods approach, combining quantitative Likert-scale surveys and Q methodology, an integrative quantitative and qualitative approach. A sample of 33 pre-service teachers participated in the study. Initially, Likert-scale surveys were used to ascertain general trends in belief orientations. Subsequently, the same participants engaged in a Q sort exercise, which allowed for a nuanced exploration of individual belief systems by prioritizing the same survey statements within a forced-choice grid. Qualitative interviews further enriched these findings. Q methodology analysis identified distinct belief profiles, characterized by their prioritization of specific educational practices and the contextual and subjective interpretations that underpin these preferences. The qualitative interviews provided deeper insight into the reasoning behind participants' choices in the Q sort, illustrating the complex, sometimes contradictory nature of personally held beliefs that traditional Likert-scale approaches may obscure. Our results underscore the utility of combining Q methodology with conventional teacher belief survey techniques to achieve a more holistic understanding of pre-service teachers' beliefs. This approach reveals the complexity within individual belief systems and highlights the potential for mixed methods research to refine the measurement and interpretation of psychological constructs in educational settings.