MMR Rationale & Positioning

Methodological Positioning

Mathematics education research has historically been dominated by quantitative methodologies, particularly in studies examining educational technology and student outcomes (Truscott et al., 2010). While mixed methods research (MMR) has gained traction in mathematics education over the past two decades, systematic reviews reveal that the field still lags behind other educational domains in embracing methodological diversity (Ross & Onwuegbuzie, 2012). More critically, when MMR is employed in mathematics education research, it tends to focus on measuring student achievement outcomes while underutilizing approaches that could illuminate teachers' pedagogical decision-making processes, lived experiences, and the biographical roots of their instructional practice.

Research on educational technology in mathematics classrooms exemplifies this gap. Studies frequently employ explanatory or exploratory sequential designs that prioritize quantitative data on student performance, using qualitative data primarily to explain unexpected statistical findings. What remains notably absent are studies that center teacher positionality, critical reflection, and the iterative development of pedagogical practices as primary objects of inquiry. This methodological gap is particularly problematic when studying equity-oriented pedagogical innovations, as it limits our understanding of how teachers' own experiences, identities, and critical consciousness inform their instructional choices—especially when working with students whom traditional mathematics instruction has historically underserved.

Our neighbors in fields such as teacher education and educational leadership have begun to address similar gaps by employing autoethnographic methods within MMR designs (Chang et al., 2014; Moerer-Urdahl & Creswell, 2004). These studies demonstrate how combining systematic self-study with analytical frameworks from other methodological traditions can generate both personally meaningful narratives and theoretically grounded insights applicable beyond individual contexts. However, mathematics education has yet to fully embrace this methodological approach, despite calls for more research that examines how teachers' critical pedagogical frameworks shape their technology integration practices and instructional decision-making for historically marginalized student populations.

This study contributes to closing the methodological gap in mathematics education research by integrating autoethnographic inquiry with systematic quantitative analysis of reflective practice patterns. This design allows for both deep exploration of lived experience and empirical examination of relationships between biographical experiences and present pedagogical choices, bridging constructivist and postpositivist epistemologies in service of understanding equity-oriented mathematics teaching.

MMR Rationale

This study employs a complementarity rationale (Greene et al., 1989; Johnson & Onwuegbuzie, 2004) to investigate how my lived experiences as a mathematics educator shape my pedagogical approaches to equity and access in the classroom, particularly when working with students retaking Algebra 1. The study integrates autoethnographic methods with systematic quantitative analysis to obtain more complete conclusions by using these approaches to examine different but complementary facets of the phenomenon under investigation.

The research is operationalized through a web-based Dissertation Tracker that serves as both research tool and data source, capturing three interconnected strands: formative memories with technology, mathematics, and education spanning my career; detailed documentation of my pedagogical decision-making processes; and explicit connections between past experiences and present practice. This "reflection through making" approach positions systematic documentation as the research itself, generating data that is simultaneously narrative and quantifiable.

The quantitative strand involves systematic coding and pattern analysis across documented tracker entries, examining frequencies of themes, temporal patterns in reflective practice, and categorical relationships between past experiences and present pedagogical choices. This strand addresses questions about WHAT patterns emerge: Which themes recur across my teaching career? When do certain types of memories surface? What relationships exist between specific biographical experiences and particular instructional decisions? The quantitative analysis provides empirical grounding for claims about connections between teacher biography and pedagogical practice.

The qualitative autoethnographic strand provides the interpretive depth necessary to understand what these patterns mean, exploring the lived experience behind the data points through thick description and reflexive analysis. This strand addresses questions about WHY patterns emerge and what they signify: Why do certain memories surface when designing for student agency? How do formative experiences with mathematics shape my current pedagogical choices? What does it mean to teach against parts of my own educational biography? The qualitative analysis privileges insider knowledge, reflexivity, and the embodied nature of pedagogical development—aspects of teacher learning that cannot be adequately captured through external observation alone.

These two methodological approaches are complementary rather than redundant because they address different dimensions of the same phenomenon. The quantitative strand describes the terrain—mapping the landscape of connections between biography and practice. The qualitative strand interprets that terrain—understanding the meaning and significance of those connections. Together, they provide both empirical rigor and interpretive depth. The strands integrate throughout the research process: the act of logging tracker entries generates both types of data simultaneously, and analysis moves iteratively between identifying patterns and interpreting meaning.

This complementarity rationale aligns with my broader commitment to bridging epistemological perspectives. By integrating constructivist methods (autoethnography) with postpositivist analytical approaches (systematic quantitative coding), this study resists the false dichotomy between subjective and objective knowledge production, instead recognizing that understanding complex pedagogical phenomena requires multiple ways of knowing. The goal is not to generalize my experience to other educators, but to deeply understand how one teacher's biography shapes their present practice in ways that might illuminate broader questions about who gets to do mathematics and how we might better serve students whom traditional approaches have failed.